Download Novel methods in SEMG-Force estimation Javad Hashemi

Novel methods in SEMG-Force estimation
by
Javad Hashemi
A thesis submitted to the
Department of Electrical and Computer Engineering
in conformity with the requirements for
the degree of Doctor of Philosophy
Queen’s University
Kingston, Ontario, Canada
August 2013
c Javad Hashemi, 2013
Copyright ⃝
Abstract
An accurate determination of muscle force is desired in many applications in different fields such as ergonomics, sports medicine, prosthetics, human-robot interaction
and medical rehabilitation. Since individual muscle forces cannot be directly measured, force estimation using recorded electromyographic (EMG) signals has been
extensively studied. This usually involves interpretation and analysis of the recorded
EMG to estimate the underlying neuromuscular activity which is related to the force
produced by the muscle. Although invasive needle electrode EMG recordings have
provided substantial information about neuromuscular activity at the motor unit
(MU) level, there is a risk of discomfort, injury and infection. Thus, non-invasive
methods are preferred and surface EMG (SEMG) recording is widely used. However,
physiological and non-physiological factors, including phase cancelation, tissue filtering, cross-talk from other muscles and non-optimal electrode placement, affect the
accuracy of SEMG-based force estimation. In addition, the relative movement of the
muscle bulk and the innervation zone (IZ) with respect to the electrode attached to
the skin are two major challenges to overcome in force estimation during dynamic
contractions.
The objective of this work is to improve the accuracy of SEMG-based force estimation under static conditions, and devise methods that can be applied to force
i
estimation under dynamic conditions. To achieve this objective, a novel calibration
technique is proposed, which corrects for variations in the SEMG with changing joint
angle. In addition, a modeling technique, namely parallel cascade identification (PCI)
that can deal with non-linearities and dynamics in the SEMG-force relationship is applied to the force estimation problem. Finally, a novel integrated sensor that senses
both SEMG and surface muscle pressure (SMP) is developed and the two signal
modalities are used as input to a force prediction model.
The experimental results show significant improvement in force prediction using data calibrated with the proposed calibration method, compared to using noncalibrated data. Joint angle dependency and the sensitivity to the location of the
sensor in the SEMG-force relationship is reduced with calibration. The SEMG-force
estimation error, averaged over all subjects, is reduced by 44% for PCI modeling
compared to another modeling technique (fast orthogonal search) applied to the same
dataset. Significantly improved force estimation results are also achieved for dynamic
contractions when joint angle based calibration and PCI are combined. Using SMP
in addition to SEMG leads to significantly better force estimation compared to using
only SEMG signals.
The proposed methods have the potential to be combined and used to obtain
better force estimation in more complicated dynamic contractions and for applications
such as improved control of remote robotic systems or powered prosthetic limbs.
ii
Co-Authorship
Chapter 4 of this thesis has been published as a journal paper in co-authorship with
my supervisors, Dr. Evelyn Morin, Dr. Keyvan Hashtrudi-Zaad and Dr. Parvin
Mousavi in the Journal of Electromyography and Kinesiology in 2012. The contents
of this chapter has been partially used in a conference paper published in Engineering
in Medicine and Biology Society (EMBC) in 2011 with the same co-authors.
Chapter 5 has also been published as a manuscript in the same journal in coauthorship with my supervisors, Dr. Evelyn Morin, Dr. Keyvan Hashtrudi-Zaad and
Dr. Parvin Mousavi and Ms. Katherine Mountjoy in the Journal of Electromyography
and Kinesiology in 2012. Some of the contents of this chapter have also been published
as a conference paper in IEEE Engineering in Medicine and Biology Society (EMBC)
in 2010 with the same co-authors. Chapter 6 has been submitted as a journal paper
to the IEEE Transactions on Neural Systems and Rehabiliation Engineering with the
same co-authors. Initial results from Chapter 7 have been published in Engineering
in Medicine and Biology Society (EMBC) in 2012 co-authorship with my supervisors,
Dr. Evelyn Morin, Dr. Keyvan Hashtrudi-Zaad and Dr. Parvin Mousavi.
iii
Acknowledgments
I would like to thank my supervisors Dr. Keyvan Hashtrudi-Zaad , Dr. Evelyn Morin
and Dr. Parvin Mousavi for their guidance through this project.
I would also like to thank my labmates Amir Haddadi, Behzad Khademian and
Kamran Razi for their friendship and support.
Thanks to Mum for all the love and support, to Dad who taught me to never give
up, to my lovely sisters Rezvan and Samineh and my amazing brother Ali who have
always been there for me. Words cannot express how much I love you all and how
grateful I am for your support. Without you five, I most certainly would not be the
person I am today. Thanks to my parents in law for welcoming me into your family
and offering your support.
Above all I would like to thank my wife Golsa for her love and support, for always
being there. Thank you for being my best friend. I love you.
I would also like to acknowledge financial support for this project from the Natural
Sciences and Engineering Research Council of Canada (NSERC), Ontario Centre of
Excellence (OCE), FedDev Ontario and Queen’s Advisory Research Committee.
Javad Hashemi
August, 2013
iv
Statement Of Originality
I, Javad Hashemi, state that the research work presented in this thesis is my own and
was conducted under the supervision of Dr. Evelyn Morin, Dr. Keyvan HashtrudiZaad and Dr. Parvin Mousavi. All references to the work of other researchers are
properly cited.
v
List of Abbreviations
α(θ)
Modifying coefficient that compensates for joint related factors in EMG
apmlitude.
β
Mathematical model governing the EMG-force relationship.
θ
Elbow joint angle. Defined as external elbow angle, where zero degrees
occurs at full extension.
ANOVA
Analysis of variance.
ANN
Artificial neural network.
a(t)
Muscle activation.
am
Weighing term for candidate functions.
Bi
Biceps brachii.
Brd
Brachioradialis.
Cθ
Modifying factor representing the shift in IZ by changing joint angle.
CE
Contractile Element.
CMR
Common Mode Rejection.
CNS
Central Nervous System.
vi
DOF
Degree-of-Freedom.
EMG
Electromyography.
EMD
Electro Mechanical Delay.
e(n)
Estimation error.
e(t)
Processed EMG signal.
FOS
Fast Orthogonal Search.
F0
Maximal isometric force.
F CE
Force generated by the contractile element.
Fmi
Force generated by muscle i.
fl
Force-length relationship.
fθ
Force-joint angle relationship.
FPE
Force generated by the parallel elastic element.
F SE
Force generated by the series elastic element.
fv
Force-velocity relationship.
Fw
Force measured at the wrist.
FIR
Finite impulse response.
IC
Integrated circuit.
IED
Inter electrode distance.
IZ
Innervation zone.
L0
Muscle length in which a muscle can develop maximal isometric force.
vii
LDD
Longitude double differential.
M
Number of functions in a FOS model.
Mmi
Moment arm for muscle i.
Mf
Forearm length.
Melbow
Net moment about the elbow.
MAE
Mean absolute error.
MAL
Muscle activation level.
MU
Motor unit.
MUAP
Motor unit action potential.
MVC
Maximal voluntary contraction.
n
Discrete time sample index.
N
Total number of FOS candidate functions.
Pm (n)
FOS basis functions.
PCA
Principle component analysis.
PCI
Parallel cascade identification.
PCSA
Physiological Cross-Sectional Area. Total muscle area normal to the
longitudinal axis of the muscle fibres.
PE
Parallel Elastic Element.
RMS
Root mean square.
%RMSE
Percent Relative Mean Square Error.
SE
Series Elastic Element.
viii
SEMG
Surface Electromyography.
SMP
Surface muscle pressure signal.
SSE
Sum squared error.
STD
Standard deviation of all %RMSE calculated for FOS models developed
with data from one session.
Tri
Triceps brachii.
u(t)
Neural activation signal
vce
Contraction velocity
VAF
Variance accounted for.
y(n)
Measured system output in a FOS model.
ix
Contents
Abstract
i
Co-Authorship
iii
Acknowledgments
iv
Statement Of Originality
v
List of Abbreviations
vi
Contents
x
List of Tables
xiv
List of Figures
xvii
1 Introduction
1.1 Motivation . . . . . . . . .
1.2 Previous Work . . . . . .
1.3 Thesis Objectives . . . . .
1.4 Contributions . . . . . . .
1.5 Organization of the Thesis
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2 Background
2.1 Physiological Aspects of SEMG and Force Generation . . . . . . . . .
2.2 Upper Arm Muscles . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 EMG Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Factors Affecting Accurate Force Estimation . . . . . . . . . . . . . .
2.4.1 Precision of SEMG Amplitude Estimation . . . . . . . . . . .
2.4.2 Selectivity and Representativeness of SEMG Amplitude Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 SEMG-force Modeling . . . . . . . . . . . . . . . . . . . . . . . . . .
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2.5.1
2.5.2
2.5.3
SEMG Amplitude and IZ Localization . . . . . . . . . . . . .
Modeling Techniques . . . . . . . . . . . . . . . . . . . . . . .
Using additional recording to SEMG . . . . . . . . . . . . . .
3 Hardware Design
3.1 Experimental Testbed . . . . . . . . . . . . . . .
3.2 EMG Sensors and Driver Board . . . . . . . . . .
3.2.1 EMG Sensors . . . . . . . . . . . . . . . .
3.2.2 Design of the Driver Board . . . . . . . . .
3.3 SMP Sensors Evaluation and Driver Board Design
3.4 Design of a Multiple Integrated Sensor Patch . . .
3.4.1 Attaching the sensors . . . . . . . . . . . .
3.4.2 Pressure sensor coupling . . . . . . . . . .
3.4.3 Choosing a platform material . . . . . . .
3.5 Pre-processing . . . . . . . . . . . . . . . . . . . .
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4 Joint Angle Based SEMG Calibration
4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 Fast Orthogonal Search (FOS) . . . . . . . . . . . . . . . . . .
4.2.4 Angle-based Calibration Algorithm . . . . . . . . . . . . . . .
4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Effects of FOS parameters . . . . . . . . . . . . . . . . . . . .
4.3.2 Effects of Calibration . . . . . . . . . . . . . . . . . . . . . . .
4.3.3 FOS Candidate Terms . . . . . . . . . . . . . . . . . . . . . .
4.3.4 Limited Number of Calibration Values . . . . . . . . . . . . .
4.3.5 Generalization of the Model and Calibration Values at the Same
Contraction Level . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.6 Generalization of the Model and Calibration Values at a Higher
Contraction Level . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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5 PCI Modeling
5.1 Overview . . . . . . . . . . . . . . . . . .
5.2 Methods . . . . . . . . . . . . . . . . . .
5.2.1 Data Collection . . . . . . . . . .
5.2.2 SEMG-force Mapping Using PCI
5.3 Results and Discussion . . . . . . . . . .
5.3.1 Removing the Outliers . . . . . .
70
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5.3.2
5.3.3
SEMG Decimation . . . . . . . . . . . . . . . . . . . . . . . .
Effects of PCI Model Parameters on SEMG-based Force Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.4 SEMG-force Mapping . . . . . . . . . . . . . . . . . . . . . . .
5.3.5 Inter-Session Performance Variability . . . . . . . . . . . . . .
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Dynamic Force Estimation
6.1 Overview . . . . . . . . . . . . . . . . . . . . . . .
6.2 Methods . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Data Collection . . . . . . . . . . . . . . .
6.2.2 Force Estimation in Dynamic Contractions
6.3 Results and Discussion . . . . . . . . . . . . . . .
6.3.1 Constant-force, constant-velocity trials . .
6.3.2 Varying-force, varying-velocity trials . . .
6.4 Summary . . . . . . . . . . . . . . . . . . . . . .
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7 Force Estimation Using Integrated SEMG SMP signal
7.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.1 Data Collection . . . . . . . . . . . . . . . . . . . . . . . .
7.2.2 Correlation analysis between Input and Output Modalities
7.2.3 Principal Component Analysis (PCA) . . . . . . . . . . . .
7.2.4 Force Estimation Using the Integrated Sensor . . . . . . .
7.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . .
7.3.1 SMP variations with the joint angle . . . . . . . . . . . . .
7.3.2 SMP variations with force . . . . . . . . . . . . . . . . . .
7.3.3 SEMG-force linearity analysis . . . . . . . . . . . . . . . .
7.3.4 Training FOS models with a subset of the inputs . . . . .
7.3.5 Using PCA to select a subset of the inputs . . . . . . . . .
7.3.6 Training with all inputs . . . . . . . . . . . . . . . . . . .
7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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8 Conclusions and Future Work
141
8.1 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 141
8.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Bibliography
147
Appendices
163
xii
A Data Sheets
164
A.1 Invenium AE100 datasheet . . . . . . . . . . . . . . . . . . . . . . . . 164
A.2 Flexiforce A201 Datasheet . . . . . . . . . . . . . . . . . . . . . . . . 166
B Fast Orthogonal Search (FOS)
167
C List of Candidate Functions
172
D Parallel Cascade Identification (PCI)
175
xiii
List of Tables
3.1 The sum of squared error (SSE) and root mean square error (RMSE)
for three FSR401 sensors. The compliant couplings are elastic and
damp the abrupt changes in the pressure and act as a lowpass filter. .
3.2 the sum of squared error (SSE) and root mean square error (RMSE)
for four Flexiforce sensors. The non-compliant couplings have high
stiffness and do not change the frequency contents of the SMP signals.
5.1 Effect of removing outliers on %RM SE for NCAT, C 10N, and C 20N
data. Ten data points from both extremes are discarded, resulting in
keeping 95% of the data points for each subject. Both mean and SD
are reduced after removing the data points. NCAT represents the non
categorized data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Effect of decimation by factor of 10 on %RMSE. Decimation was used
to decrease time resolution and to reduce the number of data points
to accelerate the training process for the PCI models. The %RMSE
results are not affected by decimation. . . . . . . . . . . . . . . . . .
5.3 Effect of different polynomial degrees on %RMSE. First to third degree polynomials were used to train and evaluate PCI models for all
subjects. Lowest%RMSE values were obtained for second degree polynomials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Effect of memory lag magnitude on %RMSE for models developed
using 2nd degree polynomials. Three different memory lags (2, 15,
and 25 points) were tested and the results were averaged over 2600
%RM SE values. Lowest %RM SE values were obtained for 2 memory
lags . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 The %RMSE results obtained using optimal values for the PCI model
parameters: decimation factor of 10, polynomial degree of 2, and memory lag magnitude of 2. The results from the FOS model are shown
for comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiv
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6.1 The mean and standard deviation of the 300 % RMSE values for both
concentric and eccentric contractions for different polynomial degrees
used in the PCI models for all subjects. The values are reported for
both non-calibrated and calibrated data. 20 memory lags were used to
train the PCI models. * indicates a significant difference wrt the value
in the row above. The significance level was adjusted by the number
of repeated measures (0.05/4). . . . . . . . . . . . . . . . . . . . . . . 103
6.2 The mean and standard deviation of the 300 % RMSE values for both
concentric and eccentric contractions for different numbers of memory
lags used in the PCI models for all subjects. Second degree polynomials
were used in the PCI models. * indicates a significant difference wrt
the value in the row above. The significance level was adjusted by the
number of repeated measures (0.05/5). . . . . . . . . . . . . . . . . . 103
6.3 The mean and standard deviation of the 100 % RMSE values for models
trained with different percentages of the varying force-varying velocity
data. * indicates a significant difference wrt the value in the row above.
The significance level was adjusted by the number of repeated measures
(0.05/8).On the right hand side of the table the mean (std) of velocity
and force are compared for training and test data. . . . . . . . . . . . 106
7.1 p-values from the Wilcoxon test comparing the data in each of the
boxplots shown in Figure 7.6. The significance level of the test was
adjusted based on the number of repeated measures(0.05/6). . . . . . 125
7.2 Mutual p-values for the distribution of maximum cross-correlation values between SMP and force signals for 8 joint angles as shown in Figure
7.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
7.3 p-values from the Wilcoxon test comparing the data in each of the
boxplots for 6 locations shown in Figure 7.8. The significance level of
the test was adjusted based on the number of repeated measures(0.05/6).128
7.4 p-values from the Wilcoxon test comparing the data in each of the
boxplots for 8 joint angles shown in Figure 7.9. The significance level of
the test was adjusted based on the number of repeated measures(0.05/8)129
7.5 Mean ± standard deviation of %RM SE values for all results obtained
from different input modalities. . . . . . . . . . . . . . . . . . . . . . 131
7.6 The mean and standard deviation of 6 %RM SE results for the three
FOS models trained and evaluated with SEMG and SMP ramp data
from locations 4, 5 and 6 on the biceps and triceps brachii, and joint
angle (13 inputs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
xv
7.7 The mean and standard deviation of 6 %RM SE results for the three
FOS models trained and evaluated with the ramp dataset having all
25 channels (6 SEMG, 6 SMP and the joint angle) as input. Last row
(on the left) shows the previous results where only locations L4, L5
and L6 were used. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
7.8 List of the functions selected more than 5 (20% of total possible) times
in descending order. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.9 The number of times that functions from each location (L1 to L6) were
selected based on their location and type. . . . . . . . . . . . . . . . . 139
C.1 List of the used FOS candidate functions for the case where SEMG
signals from biceps brachii (EBi ), triceps brachii (ET r ) and brachioradialis (ERa ) were used as inputs to the FOS model along with the joint
angle (θ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
xvi
List of Figures
2.1 (a) The contraction commands travel from the CNS and reach the
muscle fibers via motoneurons. Each motoneuron and the muscle fibers
it innervates is a MU. Three MUs with different size are shown. The
fibers of the neighboring MUs are intermingled. (b) The hypothetical
SEMG signal obtained by summation of active motor units is shown
[33]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Muscles of the upper arm [76]. . . . . . . . . . . . . . . . . . . . . . .
2.3 Example of the line of action and moment arm for the biceps brachii
(from [59]). Elbow joint angle θ is defined as the external elbow angle,
where zero degrees occurs when the arm is at full extension. . . . . .
2.4 (A) Three components of a Hill muscle model. (B) Isometric contractile
element force F CE and parallel elastic element force F P E as a function
of muscle length [76]. (C) Force velocity relation. . . . . . . . . . . .
3.1 QARM, the exoskeleton robotic apparatus used to apply force profiles
to the wrist and to measure the elbow joint angle while constraining
the arm movements to the horizontal plane. . . . . . . . . . . . . . .
3.2 AE100 active SEMG sensor. . . . . . . . . . . . . . . . . . . . . . . .
3.3 Schematic of the optical isolation board. . . . . . . . . . . . . . . . .
3.4 Frequency content of SEMG signal before and after optical isolation.
3.5 SEMG linear envelope frequency content before and after optical isolation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Final SEMG driver circuit board, showing SMEG input connections
(top), and connectors to the A/D converter board (bottom). . . . . .
3.7 FSR and Flexiforce sensors. . . . . . . . . . . . . . . . . . . . . . . .
3.8 Driver circuit for the FSR sensor measurements. . . . . . . . . . . . .
3.9 Driver circuit for the Flexiforce sensor measurements. . . . . . . . . .
3.10 Linear fitting for FSR sensors. . . . . . . . . . . . . . . . . . . . . . .
3.11 Linear fitting for Flexiforce sensors. . . . . . . . . . . . . . . . . . . .
3.12 Dynamic test for the FSR (top) and the Flexiforce (bottom) sensor. .
3.13 Driver circuit board for the Flexiforce sensors. . . . . . . . . . . . . .
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3.14 Collocating the SEMG and SMP sensors to make the Sensor patch. .
3.15 Sensor patch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 Sample trial dataset for one subject for (a) isometric constant SEMG
level experiment for the biceps brachii and (b) isometric constant force
level experiment. The first three rows show the SEMG amplitude estimate from biceps brachii and triceps brachii and brachioradialis for the
duration of the trial. The fourth row shows the joint-angles at which
the recordings were collected and the fifth row shows the measured
force at the wrist. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Flowchart of the data collection and force estimation procedure. . . .
4.3 Modeling the isometric SEMG-force relationship: (a) before calibration
and (b) after calibration. . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Distribution of the subject %RM SE results for different numbers of
functions allowed in the FOS models. Seven FOS functions proved
to give better results, although not significant, in terms of mean and
standard deviation compared to the other numbers of FOS functions.
4.5 Distribution of the calibration values (α(θ)) for biceps brachii (solid
black lines) and triceps brachii (dotted grey lines) muscles over all
subjects. The calibration coefficients show an increase with joint angle
for the triceps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Distribution of the %RM SE for different approaches in choosing calibration joint angles. The first box-plot (scheme 1) represents the
results for non-calibrated datasets. In scheme 2 all calibration values
at 7 joint angles were used to calibrate the datasets. Schemes 3 and 4
show the results for models where the datasets were calibrated using
calibration values at 4 joint angles. In scheme 5 calibration values at
only 3 joint angles were used to calibrate the datasets. . . . . . . . .
4.7 FOS functions are sorted in descending order by the number of the
times they were selected in the models. . . . . . . . . . . . . . . . . .
4.8 The first and the third plots depict the measured and estimated α(θ)
at seven joint angles using schemes 3 to 5 in the biceps and triceps
brachii muscles for one subject. The second and fourth plots show
the corresponding error (the difference between the measured and the
estimated wrist force values) for each of the estimation methods for
the biceps and triceps brachii muscles respectively. . . . . . . . . . . .
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4.9 (a) Generalization of α(θ) at the same contraction level: α(θ) calculated from the first recording session was used to calibrate datasets
collected in a subsequent session. (b) Generalization of the models at
the same contraction level: models were trained with calibrated data
from the first recording session and were evaluated by datasets from
the second recording session. (c) Generalization of α(θ) at a higher
contraction level: α(θ) calculated from the first recording session was
used to calibrate datasets collected in the third session recorded at a
higher contraction level. . . . . . . . . . . . . . . . . . . . . . . . . .
5.1 Data collection and processing flowchart. The operations in the dashed
section were repeated five times. . . . . . . . . . . . . . . . . . . . . .
5.2 Structure of a PCI model. PCI mapping involves generating a parallel
connection of a series of linear dynamic and nonlinear static blocks.
The linear dynamic blocks are constructed from randomly selected
functions from the pool of cross-correlation functions of different orders
between the input x(n) and the residue yi−1 (n). . . . . . . . . . . . .
5.3 Flow diagram of the training process of a PCI model with multiple
inputs. In this scheme adding new cascades continues until one of
the stopping criteria is met. For this study, stopping criteria included
reaching the desired estimation %RM SE error or the maximum allowed number of accepted or rejected cascades. . . . . . . . . . . . . .
5.4 Boxplots comparing RMSE error for different polynomial degrees used
in the PCI models for NCAT data from all subjects. . . . . . . . . . .
5.5 Boxplots comparing RMSE error for PCI models obtained for session
1 for individual subjects. In most subjects the results are positively
skewed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6 Boxplots comparing RMSE error for PCI models obtained for session 2
for individual subjects. Comparison between the two sessions for each
subject reveals a significant difference between results from the two
recording sessions. It was attempted to minimize intersession variability by using standard electrode placement and skin preparation protocols. The presence of significant intersession variability may indicate
that more precise electrode placement and skin preparation protocols
are needed, or that subject motivation varied between sessions. . . . .
6.1 The SEMG sensor patch used to collect SEMG and force data. Adapted
from [39] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Data collection flowchart. . . . . . . . . . . . . . . . . . . . . . . . .
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6.3 Sample trial dataset for one subject for (a) isometric constant SEMG
level experiment for the biceps brachii, (b) dynamic (concentric and eccentric) constant force-constant velocity experiment and (c) dynamic
(concentric) experiment with varying force and velocity. The first two
rows show the SEMG amplitude estimate from biceps brachii and triceps brachii for the duration of the trial. The third row shows the jointangles at which the recordings were collected, the fourth row shows the
velocity represented by the derivative of the joint angle, the fifth row
shows the measured force at the wrist, and the last row shows the command given to the motor in volts to generate the force at the wrist. A
positive motor command indicates a force which must be overcome by
flexion and a negative motor commands indicates a force which must
be overcome by extension i.e. the direction of the force is opposite to
the direction of forearm motion. . . . . . . . . . . . . . . . . . . . . .
6.4 Boxplots comparing %RMSE error for models trained and tested with
non-calibrated (NC) SEMG data and joint angle (NC+JA), SEMG
data calibrated with values obtained from third degree polynomial fitting and joint angle (CP OL +JA), SEMG data calibrated with values
estimated from piece-wise linear fitting and joint angle (CP W L +JA)
and SEMG data calibrated with values estimated from piece-wise linear fitting without joint angle (CP W L ). (a) concentric experiments and
(b) eccentric experiments. . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Distribution of measured calibration coefficients at the 7 joint angles
shown among subjects for biceps (upper left) and triceps brachii (upper
right), with PWL fitting and estimated calibration coefficients using
POL fitting for biceps (lower left) and triceps brachii (lower right). The
different patterns of the top and bottom plots indicate the estimation
error introduced due to interpolation. . . . . . . . . . . . . . . . . . .
6.6 Distribution of 100 %RMSE values for models trained with different
data segment lengths for both calibrated (solid) and non-calibrated
(dashed) data. The lowest error is observed for models trained using
50% of the data for when calibrated and 60% when not calibrated. . .
6.7 Boxplots comparing distribution of 100 %RMSE values for models
trained and evaluated with FOS and PCI. . . . . . . . . . . . . . . .
6.8 Distribution of % RMSE values for using: 1) multi-channel SEMG noncalibrated (MN) 2) multi-channel SEMG calibrated 3) averaged SEMG
non-calibrated (AN) 4) averaged SEMG calibrated (AC). . . . . . . .
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6.9 The number of the times the inputs to the PCI were selected in the
models for non-calibrated and calibrated data. b1-b6 are SEMG channels 1 to 6 obtained from biceps brachii muscle. t1-t5 are SEMG channels 1 to 6 obtained from triceps brachii muscle. ja and vel represent
joint angle and velocity. . . . . . . . . . . . . . . . . . . . . . . . . . 109
7.1 Data collection and processing flowchart. . . . . . . . . . . . . . . . .
7.2 A sample force profile. The profile comprises a flexion (positive) and
extension (negative) portion at the eight joint angles. Joint angle increases from 15◦ to 105◦ at 15◦ intervals, from left to right on the plot.
The peak forces are at 50% MVC for each joint angle. . . . . . . . . .
7.3 Distribution of the averaged normalized SMP data points from the
biceps brachii for isometric data at each of the eight joint angles. Labels
on the x-axis represents the joint angles from 15◦ (JA1) to 105◦ (JA8)
at 15◦ intervals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4 Distribution of the averaged normalized SMP data points from triceps
brachii for isometric data at each of the eight joint angles. Labels on
the x-axis represents the joint angles from 15◦ (JA1) to 105◦ (JA8) at
15◦ intervals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.5 Cross-correlation analysis between SMP and the measured force at
wrist for ramp data for biceps and triceps brachii for all subjects. . .
7.6 Distribution of maximum cross-correlation values between SMP and
force signals for each location (L1 to L6) over all joint angles, trials
and subjects for ramp data from biceps brachii. . . . . . . . . . . . .
7.7 Distribution of maximum cross-correlation values between SMP and
force signals for each joint angle over all locations, trials and subjects
for ramp data. Labels on the x-axis represents the joint angles from
15◦ (JA1) to 105◦ (JA8) at 15◦ intervals. . . . . . . . . . . . . . . . .
7.8 Distribution of maximum cross-correlation values between SEMG and
force signals for each location (L1 to L6) over all joint angles, trials
and subjects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.9 Distribution of maximum cross-correlation values between SEMG and
force signals for each joint angle over all locations, trials and subjects.
Labels on the x-axis represents the joint angles from 15◦ (JA1) to 105◦
(JA8) at 15◦ intervals. . . . . . . . . . . . . . . . . . . . . . . . . . .
7.10 Histogram of the coefficients of the channels constructing the first three
principal components for SEMG recordings from biceps (left) and triceps brachii (right) muscles. . . . . . . . . . . . . . . . . . . . . . . .
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7.11 Histogram of the coefficients of the channels constructing the first three
principal components for SMP recordings from biceps (left) and triceps
brachii (right) muscles. . . . . . . . . . . . . . . . . . . . . . . . . . .
7.12 Results of the analysis performed to determine the optimum number
of functions to include in the FOS model. SEMG and SMP ramp
data from locations 4, 5 and 6 on the biceps and triceps brachii, and
joint angle (13 inputs) were used to train and evaluate the models.
The points are connected with straight lines to visualize the trend of
decrease in the error. Each point represent an average of 6 %RM SE
evaluation values obtained from two subjects. . . . . . . . . . . . . .
7.13 Histogram of the functions selected in the FOS models for all subjects.
Each number on the x-axis represents an index of one of the FOS
functions in the pool. . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.14 Results of the analysis performed to determine the optimum number
of functions to include in the FOS model. SEMG and SMP ramp data
from all 6 locations (L1-L6) on the biceps and triceps brachii, and
joint angle (25 inputs) were used to train and evaluate the models.
The points are connected with straight lines to visualize the trend of
decrease in the error. Each point represent an average of 6 %RM SE
evaluation values obtained from two subjects. . . . . . . . . . . . . .
7.15 The number of times that each FOS function was selected in the models
generated for all subjects for the case where SEMG and SMP ramp data
from all 6 locations (L1-L6) on the biceps and triceps brachii, and joint
angle (25 inputs) were included in the model. . . . . . . . . . . . . .
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Chapter 1
Introduction
1.1
Motivation
Human body movements, from the small movements of the eyeballs and eyelids to
more gross movements such as lifting heavy objects or walking, are accomplished
through contraction of muscles. Measurement of the intensity of a muscle contraction
is of interest in many fields such as the study of muscle physiology [35], gait analysis
[111], rehabilitation [77], ergonomic design [103], and human-machine interaction [11].
Direct measurement of individual muscle forces requires invasive sensors. Instead,
researchers have used limb force or joint torque measured with external force sensors
to obtain muscle force estimates for the above applications. However, commercial
force or torque sensors are bulky, expensive or impractical due to complex installation
requirements.
Muscle force estimation using the surface electromyogram (SEMG) has been widely
researched [15, 43, 61, 95], where estimates are obtained by finding a relationship between muscle electrical activity generally represented by the SEMG amplitude and
1
CHAPTER 1. INTRODUCTION
2
the force generated by the muscle. SEMG sensors are inexpensive and relatively
small, and can be considered as a potential substitute for force sensors for muscle
force estimation. Any SEMG-based muscle force estimation is generally performed
in two steps: SEMG amplitude estimation and SEMG amplitude to force mapping.
Some methods have also made use of additional information such as estimates of the
biomechanical parameters of the muscle(s) and the joint(s) involved, to increase the
accuracy of the force estimate.
SEMG is affected by physiological and non-physiological factors which impact
the accuracy of SEMG amplitude estimation and -consequently- SEMG-based force
estimation [6, 29]. These complicating factors introduce both non-linearity and dynamics into the SEMG-force relationship even for isometric (constant joint angle)
contractions. Nonlinearity in the SEMG-force relationship is due in part to the physiological processes by which the central nervous system (CNS) controls muscle force
generation: motor unit (MU) recruitment, and MU firing rate where a MU is the
smallest functional unit in the muscle. The increase in force with MU recruitment is
believed to be nonlinear with ascending slope due to the size principle phenomenon
in which larger MUs are recruited at higher contraction levels [32]. On the other
hand, the increase in force with increasing firing rate is reported to be nonlinear with
descending slope [32]. The degree of nonlinearity in the SEMG-force relationship
also depends on the contraction type (isometric, isotonic and concentric or eccentric)
[13, 22, 48, 60, 63] and contraction history and level, which all affect the relative contribution of recruitment and firing rate [99, 107]. Other factors such as load sharing
with unequal contributions of the synergistic muscles at different contraction levels
[10] and variation in joint stiffness [92] are reported to contribute to the nonlinearity
CHAPTER 1. INTRODUCTION
3
of the SEMG force relationship. Dynamics in the SEMG-force relationship are introduced by the muscle shortening effect and the time delay between SEMG onset and
force onset called the electromechanical delay (EMD) [99].
Accurate force estimation is even more complicated in dynamic contractions,
where joint angle and/or force level vary over time, due to additional factors that
impact force generation such as muscle contraction velocity and varying MU activation patterns during the contraction [56, 85, 101]. SEMG signal properties change at
a faster rate as a result of rapid recruitment and de-recruitment of MUs and variations
in joint angle [28]. Changing joint angle influences the force estimation by altering
biomechanical parameters, including muscle length and muscle moment arm, as well
as the relative location of the innervation zone (IZ) with respect to the recording
electrode [30, 66, 84].
Estimates of biomechanical parameters have been combined with SEMG amplitude estimates to achieve valid force predictions especially under dynamic conditions
[99]. However, the error introduced by estimation of biomechanical parameters such
as muscle length and muscle moment arm also affects the accuracy of the force estimates. Additionally, during dynamic contractions, a muscle may be stretched beyond
its optimal length, at which point a passive force will be generated due to the elastic
properties of the muscle. The contribution of this passive force to the total force generated by the muscle is not reflected in the SEMG and therefore cannot be estimated
through SEMG recordings.
CHAPTER 1. INTRODUCTION
1.2
4
Previous Work
Given the factors affecting SEMG signals discussed in the previous section, significant
effort has been made to understand the effects of each of these on SEMG signals and
to obtain a more accurate estimate of the underlying neuromuscular activity from
SEMG. These efforts can be grouped into three general categories: i) studies designed
to obtain more accurate SEMG amplitude estimates through advanced recording
devices or post processing techniques, ii) studies which aim to achieve lower estimation
errors by using better modeling (identification) techniques. iii) studies designed to
improve SEMG-based force estimation by incorporating additional information in the
SEMG-force model such as biomechanical measurements.
High density multi-channel SEMG recording yields better estimates of muscle
force compared to single channel recordings by providing an adequate representation
of the heterogeneous activity of MUs within a muscle. HD EMG recordings can be
used to track the location of IZs and compensate for their effects. However, multichannel recordings may require time-consuming computations since processing of a
large number of SEMG channels (up to 130) is involved [97, 96]. This precludes their
use in mobile and real time applications. A post processing method with the ability
to compensate for the effects of IZ shift using a lower number of inputs is of great
interest.
Different modeling methods have been employed to obtain more accurate estimates
of muscle force from recorded SEMG. Models which better capture the complexities of
the SEMG-force relationship may not require post processing to achieve a reasonable
estimation accuracy, thereby moving one step closer to real-time force estimation.
CHAPTER 1. INTRODUCTION
5
Linear and nonlinear methods have been presented for identification of the SEMGforce relationship based on the muscle under study and factors such as the type and
level of contraction. Linear modeling techniques are used mainly for their simplicity in
implementation [17, 102] while nonlinear approaches better describe the physiological
nature of the SEMG [94, 110].
Ideally, a model of the SEMG-force system should be able to capture the dynamics of the system and also cope with the inherent nonlinearities. The use of a
dynamic linear FIR model [16] and static polynomial fitting [20] have been separately
investigated and showed promising results for accurately mapping SEMG to force.
The former method has the ability to capture SEMG-force dynamics while the latter
can account for nonlinearities. However, neither method satisfies both requirements
together. Other methods such as the use of artificial neural networks (ANNs) [72]
and the fast orthogonal search (FOS) algorithm [72] can capture the nonlinearities
but the models are not intrinsically dynamic.
Some approaches have made use of additional information to obtain more accurate
force estimates. Modeling techniques based on Hill’s muscle model [113, 75, 12, 43, 51]
use the muscle length and contraction speed along with the estimated muscle activation level (MAL) obtained from processed SEMG as input to estimate the generated
force [23]. However, they require knowledge of the muscle and joint dynamics and estimation of some physiological characteristics, such as muscle optimal length. Surface
muscle pressure (SMP) has been recently used to study muscle behavior [112] and as
a signature of muscle generated grip force [109]. Unlike SEMG, SMP signals are not
affected by physiological factors and therefore can be used along with SEMG signals
for force estimation. Simultaneous use of co-located SMP and SEMG recordings and
CHAPTER 1. INTRODUCTION
6
using SMP as an additional signal modality for force estimation purposes has not
been investigated.
1.3
Thesis Objectives
This research encompasses the development of enhanced methodologies for estimating
muscle force from recorded SEMG and knowledge of the limb kinematics including
joint angle and angular velocity. The objectives are to improve the accuracy of the
force estimate under static conditions, and to devise methods that can be applied
to force estimation under dynamic conditions, a challenging problem. To achieve
these goals, new methods for obtaining more accurate force estimates via improved
SEMG amplitude estimation, enhanced SEMG-force modeling procedures and use
of an additional input modality are proposed and these methods are experimentally
assessed.
SEMG Amplitude Estimation
It is desirable to develop a method to compensate for changes in the relationship
between SEMG amplitude and force due to joint angle variation. The effects of joint
angle on muscle moment arm [3, 58, 80, 78, 83] and the force-length relationship [36,
82, 113] have been widely studied. However, only a few recent studies in the literature
have considered the effects of IZ shift on SEMG recordings and these researchers have
not investigated the effect of IZ shift on force estimation [5, 66, 84, 89]. A calibration
method which compensates for the combined impact of IZ shift, change in muscle
moment arm and force-length effects at different joint angles for single channel bipolar
SEMG recordings is introduced.
CHAPTER 1. INTRODUCTION
7
SEMG-force Modeling
Parallel cascade identification (PCI) is a dynamic identification algorithm which utilizes both dynamic linear FIR and static nonlinear fitting to achieve more accurate
system identification [55]. The capacity of a PCI model to capture the nonlinear and
dynamic effects in the physiological behavior of the muscles through the SEMG-force
relationship, for isometric contractions at a series of joint angles, is investigated.
PCI modeling is then combined with angle-based SEMG calibration to compensate
for the effects of changing joint angle and to capture the dynamics and nonlinearity in
dynamic contractions, thereby achieving an improved SEMG-force model for flexionextension contractions of the elbow over a range of elbow joint angles.
Using an Additional Signal Modality
In order to have more accurate SEMG-force estimates which are less influenced by
factors such as phase cancellation and IZ shift, a new multi-channel SEMG recording
approach based on a grid of active bipolar electrodes with integrated contact pressure
sensors is presented. It is hypothesized that contact pressure signals will increase
as contraction level, and internal muscle tension, increases and that they are not
influenced by the physiological and non-physiological factors that affect the SEMG.
Thus, these signals can be used with the SEMG to provide an integrated signal which
is more representative of the force generated by the muscle, than the SEMG alone.
This hypothesis is investigated and the potential of using SMP signals as an additional
information source for force estimation is studied.
CHAPTER 1. INTRODUCTION
1.4
8
Contributions
The major contributions of this thesis are as follows:
• a new procedural joint angle based calibration protocol that compensates for
IZ shift and other joint angle related factors that introduce nonlinearity into
the SEMG-force relationship. The method was experimentally evaluated and
resulted in improved force estimation.
• modeling of the SEMG-force relationship using PCI, an approach that has the
ability to simultaneously capture the dynamics of the system and cope with the
inherent nonlinearities of the modeling problem.
• a demonstration of the superiority of the combined application of angle-based
calibration and PCI modeling to the dynamic force estimation problem.
• development of a novel integrated sensor for recording collocated SEMG and
SMP signals, and use of the additional signal modality (SMP) for force estimation. Initial experimental results indicate that the use of SEMG and SMP as
model inputs leads to enhanced force estimation.
1.5
Organization of the Thesis
Chapter 2: Background on the physiology of SEMG, muscle force generation, the
muscles of the upper arm SEMG electrodes and SEMG-force estimation methods are
presented.
CHAPTER 1. INTRODUCTION
9
Chapter 3: The details of the data acquisition system comprising the testbed,
sensors including SEMG electrodes and contact pressure sensors, and design of the
electric circuit for driving the sensors are explained. As well, the design of a multichannel integrated sensor patch is described.
Chapter 4: A new calibration method which compensates for the effects of joint
angle on the SEMG-force relationship is presented.
Chapter 5: The use of PCI in SEMG-force modeling is described where the PCI
model is capable of dealing with non-linearities and dynamics in the SEMG-force
relationship.
Chapter 6: The combination of SEMG calibration and PCI modeling is applied to
SEMG-based force estimation under dynamic conditions and the results are assessed.
Chapter 7: The use of integrated SEMG and SMP data to obtain enhanced force
estimation results under dynamic conditions is presented and experiments are designed to evaluate the effectiveness of these techniques.
Chapter 8: A summary of the contributions and results of the thesis and suggestions for future research are provided.
Chapter 2
Background
Contraction force produced by individual muscles in in vivo experiments cannot be
directly measured by force sensing devices. At the same time, the amount of force
measured at the end of a limb segment or about a joint is related to the amplitude
of the surface EMG signal, or equivalently, to the estimated muscle activation level
[23]. However, several muscles may contribute to the overall force or torque. The
force generated in muscles is a function of two processes: “activation dynamics” and
“muscle contraction dynamics” [71]. Activation dynamics include voluntary and nonvoluntary (reflex) excitation signals and MALs as set by the central nervous system
(CNS) [72]. Muscle contraction dynamics include the mechanical properties of muscle
tissues and tendons, which are expressed as force-length and force-velocity relations
[71]. In a static position, the generated force about a joint depends on the MALs
of the muscles acting on the joint, and joint angle [104]. In dynamic contractions,
joint force is also a function of joint angular velocity [23]. Therefore, joint force can
be predicted by estimating the MALs using SEMG signals and measuring joint angle
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CHAPTER 2. BACKGROUND
11
and joint angular velocity. However, SEMG is affected by physiological and nonphysiological factors which impact the accuracy of the MAL estimates. Studies in
the literature have presented different approaches for improving the accuracy of force
estimation using SEMG recordings through solutions and enhancements in signal post
processing, SEMG amplitude estimation and modeling.
2.1
Physiological Aspects of SEMG and Force Generation
The smallest functional unit of muscle that contributes to muscle contraction is the
motor unit [68]. The electrical activity of a MU, which can be recorded using needle
or wire electrodes inserted in the muscle, is called the MUAP. Each MU is comprised
of a motor nerve and a number of muscle fibers with which the motoneuron makes
contact via its terminal branches, through specialized structures called neuromuscular
junctions [87]. The terminal branches have different lengths and innervate the muscle
fibers within a fixed region of the muscle, but do not necessarily innervate neighboring
muscle fibers (Figure 2.1(a)).
CHAPTER 2. BACKGROUND
12
Figure 2.1: (a) The contraction commands travel from the CNS and reach the muscle
fibers via motoneurons. Each motoneuron and the muscle fibers it innervates is a MU. Three MUs with different size are shown. The fibers of the
neighboring MUs are intermingled. (b) The hypothetical SEMG signal
obtained by summation of active motor units is shown [33].
Thus, different MU’s are interspersed in a region of the muscle. Commands from
the motoneurons are transferred to the muscle fibers by release of a chemical neurotransmitter into the gap between the nerve endings and the muscle fibers [87]. This
transmitter alters the permeability of the muscle fiber membranes to N a+ ions causing the membrane under the synapse to depolarize and generate an action potential
[87]. Ionic current flow to the innermost components of a muscle fiber excites the contractile proteins, which results in physical shortening and the generation of tension
in the muscle fiber. The action potentials which are initiated at the neuromuscular
junction (Figure 2.1a), propagate in opposite directions along the muscle fibers until
they reach the tendons at both ends [87]. The bioelectric cycle of each muscle fiber is
terminated at the tendons (Figure 2.1a) where monophasic non-propagating standing
waves are generated [99].
The membrane depolarization and action potential propagation cause a timevarying electric field that induces potential changes in the extracellular tissue and can
CHAPTER 2. BACKGROUND
13
be measured either within the muscle using needle electrodes or from the surface of
the skin using surface electrodes (Figure 2.1b). The spatial and temporal summation
of muscle fiber tensions results in muscle contraction (force). Action potentials in the
individual fibres of an active MU sum to generate a MUAP. The spatial and temporal
summation of MUAPs from multiple active MUs can be recorded from the skin surface
as the SEMG signal. This can be done using monopolar or bipolar sensors. Monopolar
electrodes measure the electrical activity over the muscle of interest with respect to
a reference point on the body where there is no significant electrical activity. Bipolar
electrodes measure the difference in electrical activity at two adjacent points over the
muscle under study.
The force generated by muscle is predominantly determined by the number of
active MUs, their size and their firing rate [70]. Therefore, to obtain an accurate
estimate of muscle force both spatial (active MUs) and temporal (firing rate) information is required. Accurate estimation of the number and size of the active MUs
and MU firing rate from the SEMG signal is difficult because the SEMG is affected by
many physiological and non-physiological factors, causing both temporal and spatial
correlation in the data [29].
2.2
Upper Arm Muscles
The focus of this thesis is the muscles in the upper arm. The anatomy of the upper
arm and the various muscles are shown in Figure 2.2. Throughout this thesis, the
force at the wrist, due to generation of flexion and extension torque about the elbow,
was modeled using SEMG data recorded from two elbow flexors, the biceps brachii
and brachioradialis, and a single extensor, the triceps brachii. Since we considered a
CHAPTER 2. BACKGROUND
14
supinated forearm posture, the SEMG amplitude of the biceps was increased and the
SEMG amplitude of the brachioradialis was diminished [46]. Thus, brachioradialis
SEMG was not recorded in some of the experiments.
Figure 2.2: Muscles of the upper arm [76].
Other muscles are involved in elbow flexion (brachialis) and extension (anconeus).
With the forearm supinated, both the biceps and brachialis contribute to elbow flexion
[4]. However, the brachialis muscle is primarily situated underneath the biceps and its
activity cannot be measured using surface electrodes. The anconeus makes a relatively
small contribution to elbow extension (up to 15% of the total extension moment at
low torque levels and less as torque increases) compared to the triceps brachii [114].
Thus, we assumed that flexion and extension forces induced at the wrist, as a result
of elbow motion or torque with supinated forearm posture, are primarily due to
activity in the biceps brachii, brachioradialis and triceps brachii muscles. Changing
the forearm posture alters the mechanical advantage of the muscles; however, the
biceps and triceps will still be major contributors to the forces induced at the wrist.
Although the focus of this study was on the upper arm muscles, many of the
presented methods can be applied to the SEMG signals obtained from other muscles
CHAPTER 2. BACKGROUND
15
too since no limiting assumption was made on the type of muscle.
Physiological characteristics of a muscle such as muscle moment arm, fiber direction and cross-sectional area vary based on limb position and the tasks each muscle
performs. Muscle moment arm is defined as the minimum distance perpendicular to
the line-of-action of the muscle, and the center of the elbow joint [79] and is shown
in Figure 2.3. Physiological cross-sectional area (PCSA) is defined as the total crosssectional area normal to the longitudinal axis of the muscle fibers [47]
Muscle line of action
Muscle moment arm
θ
Figure 2.3: Example of the line of action and moment arm for the biceps brachii (from
[59]). Elbow joint angle θ is defined as the external elbow angle, where
zero degrees occurs when the arm is at full extension.
Depending on the conditions under which a contraction is performed the physiological characteristics of a muscle may change. Muscle contraction types can be
divided into four categories: isometric, isotonic, quasi-isotonic, and dynamic. In an
isometric contraction, the length of the muscle (and joint angle) does not change. In
an isotonic contraction, the contraction force does not change. In a quasi-isotonic
contraction, the force increases or decreases at a very slow rate. Dynamic contractions involve changing joint angle which can be accompanied by some time-varying
CHAPTER 2. BACKGROUND
16
component, e.g. force level, contraction velocity or both.
Long and intense muscle contraction causes muscle fatigue in which the ability
of the muscle to generate force is reduced [81]. During muscle fatigue the amplitude
and frequency contents of the SEMG signals dramatically change compared to under
non-fatigue conditions. Therefore, unless the study is focused on fatigue itself, the
experimental conditions are often defined in order to avoid fatigue, since it will impact
the EMG-force relationship.
2.3
EMG Electrodes
Electrodes transduce ionic potentials into ohmic potentials so that they can be processed similar to a typical electrical signal. The electrodes used for the EMG recording
can be grouped into three general categories: i) in-dwelling electrodes, including needle and wire electrodes; ii) surface electrodes including passive and active electrodes;
iii) HD-grid electrodes. Electrodes in each group can be either monopolar or bipolar. Based on the specific application, different types of electrodes are necessary to
extract information about the underlying neuromuscular activity from the recorded
EMG signal. For example, in order to study muscle activation at the MU level, needle
electrodes are used. The distance between the active muscle fibers and a needle electrode can be small; and individual MUAPs can be recorded selectively at moderate
contraction levels [25]. On the other hand, conventional SEMG techniques that use a
single bipolar electrode in general, cannot be used to extract single MU information.
This is a consequence of the tissue between the active muscle fibers and the electrodes which acts as a low-pass filter and reduces the bandwidth of the SEMG signal
with respect to the intra-muscular EMG. Also, there is spatial averaging of multiple
CHAPTER 2. BACKGROUND
17
active MUs under the recording electrodes. Using multi-channel SEMG recording
electrodes instead of a single electrode recording along with signal decomposition algorithms makes it possible to extract information from the SEMG at the MU level
and use the SEMG in MU studies [67, 100]. Multi–channel electrodes can be one dimensional (linear electrodes) or they can comprise a two dimensional array of closely
arranged selective pickup units (HD-Grid sensors).
2.4
Factors Affecting Accurate Force Estimation
For accurate SEMG-based force estimation, a determination of MAL is necessary.
The factors which control MAL (number and size of active MUs, and firing rate)
cannot be directly measured from SEMG signals. Instead, MAL is usually estimated
as the normalized SEMG amplitude which provides an inaccurate representation of
its underlying parameters [99]. Three criteria are used to evaluate the accuracy of
MAL estimation methods: precision, representativeness, and selectivity [99]. A high
precision estimate has high signal-to-noise ratio and low variance estimation error.
A highly representative estimate is based on the activity of the whole muscle rather
than a portion of it. A selective estimate only contains the activity of the muscle
under study and does not contain contributions (cross-talk) from other neighboring
muscles. Many factors can affect the quality of SEMG amplitude estimation in terms
of the above criteria. In the following subsections these factors are explained and
techniques used for improving SEMG amplitude estimation are briefly discussed. It
should be noted that when studying muscle force, there are factors, in addition to the
MAL, that affect the force generated by the muscle. Instantaneous muscle length,
rate of length change, contraction history and fatigue are some of these factors [99].
CHAPTER 2. BACKGROUND
2.4.1
18
Precision of SEMG Amplitude Estimation
The surface EMG signal is formed by summation of polyphasic MUAPs. These
MUAPs occur at random times during muscle contractions and the signal recorded
from the surface of the muscle is their temporal and spatial summation. MUAP
summation can be either destructive or constructive. In constructive summation,
two signals with the same phase occur at the same time and the amplitude of the
resultant signal is increased; in destructive summation two signals with opposite phase
occur at the same time so the amplitude of the resultant signal is decreased with
respect to each of the constituents. This means that an increase in neural drive from
the CNS does not necessarily lead to a proportional increase in the amplitude of the
SEMG. Constructive and destructive interferences also contributes to variability of the
SEMG amplitude. That is, even for a constant neural drive, the SEMG amplitude is
variable [49]. Therefore, the force estimated from SEMG amplitude is not an accurate
indication of the force produced by the muscle. This issue -underestimation of the
MAL- is the main source of the lack of precision in SEMG force estimation [29, 31]. It
should be noted that phase cancellation effects on the signal dominate as the number
of active MUs increases [29, 31].
Other sources of SEMG amplitude variability are variation in electrode placement,
alignment of bipolar electrodes with respect to the muscle fibers, and electrode-skin
impedance. Variation in electrode placement between different recording sessions
changes the distance between the electrode and the signal sources, and consequently
changes the SEMG amplitude since the contribution of the source in SEMG recording
decreases with distance. Furthermore, even during a single recording session the
variation in amplitude still exists due to misalignment between the electrode and the
CHAPTER 2. BACKGROUND
19
muscle fibers. It has been shown that for accurate measurement of the traveling wave
along the muscle fiber, bipolar electrodes should be placed such that the electrode
axis is parallel to the underlying muscle fibres [96]. Misaligned bipolar electrodes
decrease the quality of amplitude estimation and make it more sensitive to joint angle
variations. A linear array or grid of sensors can detect the location of innervation
zones and muscle fiber directions. For more complex muscles such as the triceps
brachii whose fibers are not parallel to the line of action (pinnate fibers) and where the
fiber direction varies spatially within the muscle and dynamically during contraction,
a more advanced recording system such as a high density (HD) grid of sensors may
be required.
For dynamic contractions, the issue of electrode placement is more complex. Electrodes are more likely to be displaced relative to the underlying muscle during the
contraction and the distances between the electrodes and the signal source will change
due to relative movement of the muscle with respect to the skin surface. Moreover,
variations in muscle fiber direction and therefore misalignment between the electrode
and muscle fibers are more probable than under static contractions.
Tissue filtering effects and the size principal are two other sources that contribute
to the lack of precision in SEMG amplitude estimation. The tissue between the signal
sources (MUAPs) and the recording sites (electrode contacts) acts as a temporal lowpass filter and weights the sources inversely proportional to their distance from the
recording site. This means that even MUs with exactly the same anatomic and
physiologic structure and the same number of muscle fibers but located at a different
distance from the recording site, would have different contributions to the SEMG
amplitude. The size principle refers to the strategy that the CNS uses in recruiting
CHAPTER 2. BACKGROUND
20
MUs of different sizes based on the force level. When producing low level forces, small
MUs, located deep inside the muscle, are preferentially recruited. As the force level
increases large superficial MUs are also recruited. Therefore, during higher force level
contractions the superficial MUs contribute more to the recorded SEMG signal than
to the resultant force, masking the effects of deeper MUs at the same time [38].
The tissue between the signal source and recording electrode both decreases the
signal amplitude, and acts as a low pass filter by more severely attenuating the high
frequency components of the traveling wave that might contain useful information.
Whitening and highpass filtering have been used by different researchers to restore the
original signal bandwidth [18, 16, 88]. On the other hand, the assumption of tissue
acting as a temporal lowpass filter does not always hold true since there have been
experiments where standing waves which mainly contain high frequency contents,
were not filtered by the tissue [99]. As a result, in conventional SEMG recording
methods, bipolar sensors are used to remove the standing waves. The standing waves
are present at both contacts of the bipolar electrode and the embedded differentiation
in bipolar electrodes eliminates them [99].
Another factor that influences the force estimation precision is electrode placement
and configuration. Even at a constant neural drive generated through electrical stimuli during an isometric experiment, the amplitude of the SEMG may change between
different recording sessions. Aside from the constructive/ destructive summation theory, this could be a result of variation in placement of the electrodes and probable
changes in skin-electrode impedance [21]. These variations between different sessions
of data collection occur since the electrode is removed and may not be replaced at
the exact same location and under the same conditions.
CHAPTER 2. BACKGROUND
21
Surface multi-channel recording using monopolar electrodes have been proposed
to minimize the effects of phase cancellation. With multi-channel recording muscle
innervation zones can be located and the contribution of all active MUs in the signal
can be determined [99]. Furthermore, some researchers have suggested recording
monophasic standing waves rather than polyphasic propagating waves. Standing
waves occur at the tendons and contain higher frequency content which is not affected
by tissue filtering [24]. Monopolar electrodes are the best option to record these
signals. Some authors have suggested aligning electrodes perpendicular to the fibers
and also using high-pass filters to emphasize the standing waves of the MUs [99].
These new ideas have not been yet examined experimentally but have the potential
to improve amplitude estimation. On the other hand, since standing waves are not
attenuated by the intervening tissue, activity from other nearby muscles might also
be recorded. This artifact known as cross-talk, is discussed in Section 2.4.2.
2.4.2
Selectivity and Representativeness of SEMG Amplitude Estimation
Ideally, we are only interested in collecting SEMG signal data from the desired muscle but in reality interference signals from other sources are also recorded. One of
the contaminating sources in SEMG recording is motion artifact. These signals are
limited to low frequencies (less than 20 Hz) which are not significant in the SEMG
signal during isometric non-fatiguing contractions and can be attenuated by high-pass
filtering [106, 21].
Another source of signal contamination is cross-talk recorded from nearby active
muscles. Spatial double differentiation is commonly used to reduce the cross-talk
CHAPTER 2. BACKGROUND
22
in bipolar [105], one dimensional multi-electrode [90] and two dimensional multielectrode recordings [91]. High-pass filtering has also been proposed [91] to remove
the low frequency components that are believed to be the frequencies at which distant
muscle fibers have a major contribution to the recorded signal. This is based on
the notion that the tissue between the signal source and recording electrode acts
like a low-pass filter. Therefore, MUAPs traveling from active muscles far from the
muscle of the interest are more prone to low-pass filtering and their energy will be
primarily in the low frequencies. However, standing waves which occur at the muscle
fibre terminations are not temporally filtered and can interfere with the recorded
SEMG [99]. Dimitrova et al. [24] claimed that depending on the electrode type, the
relative contribution of the standing waves and thus high frequency components of
the MUAP, increases with MU depth. Therefore, the major contribution of cross-talk
in SEMG signals lies in the high frequency range and methods such as mathematical
differentiation and high-pass filtering cannot considerably reduce the cross-talk effects
[24].
Another factor that influences selectivity is electrode pickup area. An electrode
with large pickup area will more likely detect cross-talk from neighboring muscles in
addition to the SEMG signal of interest. The pickup area of a bipolar electrode can
be changed (with the interelectrode distance (IED)) to have more control over the
muscle region from which the signal is detected. However, bipolar electrodes are often
made with a constant IED. Densely spaced electrode arrays, as in HD-SEMG grids,
can be used to achieve desired electrode configurations with very small pickup areas.
The selectivity of the SEMG signal can also be increased by applying higher order
CHAPTER 2. BACKGROUND
23
spatial derivatives of the signals obtained from array electrodes [8]. However, Staudenmann [96] and Olivier [81] have shown that although these techniques increase
the selectivity of the SEMG signal, they do not improve force estimation quality significantly suggesting that the limiting factor in force estimation is representativeness
rather than selectivity [99].
A representative SEMG-based force estimate contains equal contribution from all
active MUs in the muscle of interest even if they are located far from the electrode.
Tissue filtering is a primary factor affecting representativeness, as it diminishes the
contribution of deep MUs. High-pass filtering can balance the contribution of near and
far MUs in the SEMG signal by removing the relatively high amplitude low-frequency
content of the propagating signals of the superficial MUs [98, 95]. Representativeness can also be improved by using multiple recording sites, in order to increase the
recording area over the surface of the muscle of interest [97]. Staudenmann et al.
claimed that even fine variations of the force generated by the triceps surae during
isotonic contractions can be captured when the entire muscle group is covered with
electrodes [99]. In conclusion, to achieve a highly representative force estimate, a fair
balance between deep and near MUs and a thorough coverage of the muscle under
study using multiple electrodes is necessary.
2.5
SEMG-force Modeling
Different approaches have been presented in the literature to obtain an accurate estimate of muscle force using SEMG signals. These approaches include the use of
advanced instrumentation such as HD-SEMG grids and signal modification (normalization, high pass filtering and/or whitening) to achieve improved SEMG amplitude
CHAPTER 2. BACKGROUND
24
estimation. The use of advanced modeling techniques and sources of information, in
addition to SEMG, have been used to achieve improved force estimation.
2.5.1
SEMG Amplitude and IZ Localization
In the recent literature [8, 26, 28, 33, 44], valuable spatial information has been
extracted from SEMG by utilizing multi-channel recording devices especially HDSEMG grids.
The shift in the IZ with contraction and its effects on the recorded SEMG have
been studied using multi-site recording [66, 84, 30, 5, 93]. Martin et al. [66] quantified
the amount of IZ shift with change in joint angle in the biceps brachii muscle using
a 16-channel linear electrode array based on the location of the reversal in the signal
propagation direction. They showed that this shift can be up to 30 mm in a direction
distal to the shoulder with elbow extension and, therefore, might have considerable
effect on SEMG levels [66]. Piitulainen et al. reported a shift up to 24 mm in the location of the IZ [84, 86]. They observed site-dependent changes in SEMG which might
mask exercise-induced changes and suggested discarding the channels over the IZ to
reduce such effects. Farina et al. [30] investigated muscle movement under recording electrodes during contractions with varying joint angle for muscles active in gait.
They concluded that although proper electrode location may improve SEMG analysis, changes in joint angle cause changes in SEMG spectral and amplitude variables
which may mask the physiological information. Beck et al. [5] studied the effects of
both electrode placement and IZ shift on SEMG variables. They noted that electrode
placement has a major effect on the recorded SEMG amplitude and suggested that
normalization reduces the effect of IZ shift on SEMG amplitude. Sacco et al. [93]
CHAPTER 2. BACKGROUND
25
developed recommendations for positioning bipolar electrodes for lower limb SEMG
recordings during dynamic contractions to avoid having the electrodes over the IZ(s)
during any phase of the contraction.
Although linear and HD-SEMG grids are capable of approximating the locations
of IZs, and to some extent the locations of MUs, they require SEMG collection from
a number of channels, which can go up to 130. They also may need time-consuming
computations which limits their applicability in real time applications. Therefore,
there is a need for a method that can reduce the effects of IZ shift with fewer channels
and more computational efficiency.
2.5.2
Modeling Techniques
Non-parametric and parametric model-based approaches have been proposed for human joint force estimation using SEMG signals. Parametric approaches have used
Hill’s muscle model [12, 42, 51, 113], which takes MAL as input and outputs the generated force as a function of muscle length and contraction speed [23]. Nonparametric
methods propose the use of polynomial functions or artificial neural networks (ANNs)
and have the capability of accounting for nonlinearities in the SEMG-force relationship [72]. One significant advantage of non-parametric estimation of the SEMG-force
relationship is that no knowledge of the muscle and joint dynamics is needed.
Parametric Methods
A.V. Hill suggested a method to model the bio-mechanical properties of muscle in
which the muscle is represented by three elements arranged in series and in parallel
[41]. This model has been used in many studies to estimate the force generated by a
CHAPTER 2. BACKGROUND
26
muscle [12, 51, 113].
During a contraction each muscle generates a moment about the joint on which
it acts. This moment is the product of the force generated by the muscle and the
muscle moment arm [79]. The net moment is the sum of the moments produced by
all contributing muscles.
Mnet =
I
∑
Fmi · Mmi
(2.1)
i=1
where i stands for the muscle index, I is the number of contributing muscles, Fmi
is the force generated by muscle i, and Mmi is the moment arm of muscle i. The
net moment Mnet can be measured using a force sensor. The force generated in each
contributing muscle (Fmi ) can be estimated by Hill-based muscle models [76]. The
classic Hill model is composed of a contractile element CE, which models the tension
produced by the muscle fibers, and two elastic elements, (SE and PE), that represent
the elasticity in the muscle tissues, as shown in Figure 2.4A [76].
Figure 2.4: (A) Three components of a Hill muscle model. (B) Isometric contractile
element force F CE and parallel elastic element force F P E as a function of
muscle length [76]. (C) Force velocity relation.
The force generated by the CE (F CE ) is equal to the force in the SE (F SE ), and
the total force generated by the muscle is the sum of the two forces in parallel:
Fmi = F CE + F P E
(2.2)
CHAPTER 2. BACKGROUND
27
F CE depends on the muscle length and Figure 2.4B shows this dependency. As
can be seen the maximum amount of active tension that a muscle generates (F0 )
occurs at a specific muscle length called “muscle optimal length” (L0 ). The parallel
elastic element force F P E is generated by elasticity in the connective tissues around
the muscle fibers; the connective tissues generate tension only when the muscle is
stretched to more than its resting length [76]. The non-linear behavior of F P E is
often modeled as an exponential or second degree polynomial relationship [76]. In
general, the force generated by a muscle is a function of muscle length (the forcelength relation-ship, fl ), contraction speed (the force-velocity relationship, fv ), and
muscle activation, u(t). One of the suggested models to explain the force generated
by a muscle is:
F CE = F0 · fl · fv · u(t)
(2.3)
where u(t) is obtained from the SEMG amplitude estimation methods, and F0 is
a constant value that can be calculated for each muscle; therefore to calculate the
F CE , fl and fv must be approximated. Different mathematical functions have been
presented to model the force-length relationship (fl ) [76]; Figure 2.4C shows the force
velocity relation in dynamic contractions. However, in static contractions fv has no
contribution i.e. fv = 1.
For accurate force estimation precise measurement of physiological parameters
such as optimal muscle fiber length, muscle-tendon moment arms, contraction velocity and PCSA [76] are needed. The first two measurements are usually obtained
from cadaver studies [1, 2, 57, 79]. The contraction velocity can be measured by
differentiating the instantaneous joint angle. PCSA values for different muscles can
be calculated from values of muscle volume and length reported in the literature [76].
CHAPTER 2. BACKGROUND
28
Non-parametric Methods
Using non-linear learning methods such as fitting polynomial functions, linear regression, ANNs, and FOS, non-parametric models capable of estimating the SEMG-force
relationship without any knowledge of the muscle and joint dynamics can be developed [72]. Clancy et al. [19, 20] used a third-order polynomial to estimate the
force generated in the elbow joint under non-fatiguing, quasi-isotonic, isometric conditions. SEMG in the biceps brachii and triceps brachii (see Figure 2.2) for a series
of flexions and extensions about the elbow were measured and SEMG amplitude was
estimated for both single and multiple channel SEMG recordings, using unwhitened,
whitened and adaptively whitened signals. The results were reported as variance error in force estimation expressed as percentage of the total force range. Best results
were obtained using multi-channel recording and fitting a third-order polynomial to
the amplitude-force relationship, which led to an error of approximately 3% of the
combined flexion/ extension force range [19, 20]. Misener et al. [71] considered the
SEMG-force relationship for isometric and dynamic (constant velocity) flexion/ extension contractions about the elbow. For static contractions, in addition to SEMG
amplitude they used the force-length properties of individual muscles which were derived from static contractions of the muscles at different joint angles and loads. The
same third-order polynomial fitting method described in Clancy’s work [20] was used
to estimate the moment about the joints. Bida et al. [7] studied SEMG-force relationship of biceps/triceps muscles about the elbow during non-fatiguing constant-posture,
quasi-isotonic contraction and used linear regression methods to map the SEMG-force
relationship. The estimated amplitude was also decimated in order to avoid spurious
CHAPTER 2. BACKGROUND
29
peaks in the estimated force. The best model was a 15th-order FIR model which produced an average error of 8% MVC with a percent variance accounted for (%VAF) of
78%.
Comparing model performance with and without advanced SEMG amplitude estimation techniques, Clancy et al. [16] concluded that using a 15th order FIR model
with a four channel per muscle, whitened SEMG amplitude estimator give the least
error (7.3% MVC) compared to single-channel un-whitened SEMG amplitude estimator which gave the worst results (9.9% MVC). The SEMG was obtained from the
biceps brachii and triceps brachii and the electrodes were placed midway between the
elbow and the midpoint of the upper arm, centered on the muscle midline.
Luh et al. [62] considered the SEMG-force relationship in non-fatiguing dynamic
contractions. A 3-layer feed-forward ANN structure using an error back-propagation
learning algorithm with an adaptive learning rate was proposed. The ANN was
trained using rectified, smoothed SEMG, joint angle, and joint angular velocity as
inputs and measured force as the desired output. They obtained a mean root mean
square (RMS) error of 0.14 in force estimation, which is a promising result. They
also performed sensitivity analysis of the results to the changes in ANN parameters
such as the number of hidden nodes, initial weight range, and the learning mode and
concluded that the model is robust to changes to these parameters. Mobasser et al.
[72] employed the FOS method to estimate wrist force from the SEMG signal during
flexion/extension of the elbow in the horizontal plane including isotonic, isometric
and light weight contractions. FOS [52] is a nonlinear estimation technique which
minimizes the mean square error of the estimate compared to the target data. Unlike
methods like ANN which uses iterative minimization for back-propagation training,
CHAPTER 2. BACKGROUND
30
FOS determines each basis function and its corresponding coefficient in a single iteration. That is, in each iteration, from the set of candidate basis functions, the function
that produces the greatest reduction in the estimation error is chosen. This process
continues until the desired criteria are met. From the results, it was concluded that
FOS produced an accurate model with fewer terms compared to ANN [72]. Moreover,
FOS proved to have faster training than ANN in most cases [72].
Some of the above-mentioned modeling methods in both parametric and nonparametric categories (ANNs and Hill based FOS), have the capability to model
the non-linearity involved in the SEMG-force relationship. Other methods such as
the linear FIR model are able to cope with the dynamics involved in the SEMG-force
relationship. However, there is a need for a method that can satisfy both requirements
(nonlinearity and dynamics) together.
2.5.3
Using additional recording to SEMG
Imaging techniques such as ultrasound and MRI [64] or estimations through optimization procedures using musculoskeletal models [34, 50] have been previously used
to obtain more accurate force estimates. Recently, SMP has been used to study muscle behavior [112] and as a signature of the muscle generated grip force [109]. SMP
signals can provide useful information about the changes in the shape of the muscle
with changing contraction level and joint angle during isometric or dynamic contractions. However, simultaneous use of SMP and SEMG recordings for force estimation
has not been investigated. SMP recordings are not affected by parameters such as
phase cancelation and size principle and therefore can potentially have complementary information to SEMG for estimating muscle force and may be useful in dynamic
CHAPTER 2. BACKGROUND
31
contractions to monitor the shift in the bulk of the muscle with changing joint angle.
Chapter 3
Hardware Design
In this chapter the experimental test-bed used for data collection in all subsequent
studies is described. This includes, QARM, the exoskeleton robotic apparatus that
was used to apply force profiles to the wrist and to measure the elbow joint angle while
constraining the arm movements to the horizontal plane. Also, the specifications of
the SEMG sensors and the design of electrical circuits designed to drive the sensors
are presented. The development of a novel, collocated SMP-SEMG sensor, and the
construction of a multi-sensor patch are described. Different design challenges to
obtain a reliable prototype sensor patch are also explained.
3.1
Experimental Testbed
The SEMG-force experiments were conducted on a single degree-of-freedom (1-DOF)
exoskeleton testbed, shown in Figure 3.1. The apparatus holds the shoulder and
wrist in a fixed position, and constrains flexion and extension of the right arm to the
horizontal plane. The axis of rotation of the elbow is aligned with a pivoting aluminum
32
CHAPTER 3. HARDWARE DESIGN
33
bar attached to a Maxon DC motor, with an 8:1 cable driven power system. The elbow
angle is measured at a resolution of 1/800 of a degree. Elbow torque, expressed as
force at the wrist, was measured using an ATI 6-DOF Gamma force/torque sensor
with a high stiffness of 9.1 × 106 N/m.
Feedback
Screen
Pivoting Bar
Force Sensorr
Motor
and
Encoder
Figure 3.1: QARM, the exoskeleton robotic apparatus used to apply force profiles to
the wrist and to measure the elbow joint angle while constraining the arm
movements to the horizontal plane.
CHAPTER 3. HARDWARE DESIGN
34
All data were sampled at a rate of 1000 samples per second with 14-bit resolution
through a Quanser Q8 dedicated data acquisition board to a dedicated acquisition
computer. The raw signals were processed off-line using software developed in MATLAB.
3.2
3.2.1
EMG Sensors and Driver Board
EMG Sensors
SEMG data were recorded using AE100 active bipolar SEMG sensors from Invenium
Tech. Inc. for each muscle (IED=15 mm, electrode diameter of 4 mm, CMMR=
80 dB, input impedance= 1010 ohm, gain= 300 v/v). The EMG recordings were
filtered with a bandpass filter integrated inside the AE100 electrode (see Appendix
A). Figures 3.2 shows a picture of an AE100 SEMG electrode.
Figure 3.2: AE100 active SEMG sensor.
3.2.2
Design of the Driver Board
The AE100 sensor is an active sensor with signal conditioning hardware embedded in
the electrode unit, thus it needs a power source to operate. A remote 8-channel driver
board to provide a clean regulated voltage with low noise and fluctuation at the sensor
terminal and to electrically isolate the sensor from the AC power supply was designed
and constructed. The design features a three-port isolation structure where each port
CHAPTER 3. HARDWARE DESIGN
35
(input, output, and power) remains independent. It also provides additional system
protection should a fault occur in the power source. Figure 3.3 shows the design
scheme in which the power supply section is isolated using transformers and the
SEMG sensors are optically isolated. The detected SEMG signal is digitized, the
digital stream is optically isolated and the isolated signal is re-converted to an analog
signal. The board provides 2500 V rms (continuous) and ± 3500 V peak (continuous)
common-mode voltage isolation between any two ports. The low input capacitance
of 5 pF results in a 120 dB common mode rejection (CMR) at a gain of 100, and a
low leakage current (2 mA rms max at 240 V rms, 60 Hz).
+5
G
-5
G
+5
-5
isolator
Electrode 1
to DAQ
Opto-isolator 1
G
+15
isolator
Electrode 1
to DAQ
Electrode 1
Electrode 1
Power
Supply
Output1 to DAQ
G
G
+15
Electrode 1
Figure 3.3: Schematic of the optical isolation board.
The performance of the SEMG sensor driver and isolation board was tested to
insure that the amplitude and frequency characteristics of the SEMG signal were
not affected. Two candidate integrated circuits (ICs) were considered for the optical
isolation: AD210 from Analog Devices and ISO124 from Texas Instruments. The
~
CHAPTER 3. HARDWARE DESIGN
36
AD210 had better performance in preserving the signal characteristics both in the
amplitude and frequency domain. Therefore, it was selected for further testing. One
second of SEMG data from 3 subjects was recorded simultaneously before and after
isolation and the signal amplitudes and frequency content were compared. The SEMG
amplitudes are shown in Figure 3.4.
Subject#1
0.1
0
-0.1
-0.2
Amplitude (v)
Amplitude(v)
20
20.01
20.02
20.03
20.04
20.05 20.06
Subject#2
20.07
20.08
20.09
20.04 20.05 20.06
Subject#3
20.07
20.08
20.09
0.1
0
-0.1
20
20.01
20.02
20.03
20.1
0.1
0
-0.1
20
20.01
20.02
20.03
20.04
20.05
20.06
Time(sec)
20.07
20.08
20.09
20.1
Figure 3.4: Frequency content of SEMG signal before and after optical isolation.
The highest root mean square error in amplitude between signals recorded before
and after isolation was 0.05. Figure 3.5 shows that the frequency content of the
data was not altered by the optical isolation circuitry. After confirming that the
isolation circuitry preserved the SEMG signal characteristics a printed circuit board
was fabricated to accommodate 8 SEMG channels. The final circuit board is shown
in Figure 3.6.
CHAPTER 3. HARDWARE DESIGN
37
Burg Power Spectral Density Estimate for subject#1
0
Before
After
Power/frequency
(dB/Hz)
Power/frequency (dB/Hz)
-20
-40
-60
-80
-100
-120
-140
0
50
100
150
200
250
Frequency (Hz)
300
350
400
Frequency (Hz)
Figure 3.5: SEMG linear envelope frequency content before and after optical isolation.
Figure 3.6: Final SEMG driver circuit board, showing SMEG input connections (top),
and connectors to the A/D converter board (bottom).
CHAPTER 3. HARDWARE DESIGN
3.3
38
SMP Sensors Evaluation and Driver Board Design
Two types of passive contact pressure sensor were considered to incorporate in the
SMP-SEMG integrated sensor: the A201 Flexiforce from Tekscan and the FSR402
sensor from Interlink Electronics (shown in Figure 3.7). For testing and comparing the
performances of the two, each sensor was connected to the driver circuit recommended
by the manufacturer as shown in Figures 3.8 and 3.9.
Figure 3.7: FSR and Flexiforce sensors.
Figure 3.8: Driver circuit for the FSR sensor measurements.
CHAPTER 3. HARDWARE DESIGN
39
Figure 3.9: Driver circuit for the Flexiforce sensor measurements.
In order to have the force evenly distributed over the sensing surface of the contact
pressure sensors, coupling disks were mounted over the sensing area. Then, the sensors
were loaded with 8 precision weights from 1 to 8 N. The measured values from the
sensors were calibrated to represent the measured force in Newtons. Calibration of
four Flexiforce sensors and three FSR sensors was conducted using 8 data points. For
all tests a gain of 2.3 was applied in Simulink and all measured readings were scaled
to Newtons i.e., the readings were multiplied by the highest force and divided by the
highest reading. A first order linear model, y=a(x-b) was fitted to the data points
using the least squares method to find a and b, offset and scaling parameters of the
model, as shown in Figures 3.10 and 3.11.
CHAPTER 3. HARDWARE DESIGN
9
8
7
6
5
4
3
2
1
0
-1
40
Measured
force (N)
Force (N) measured
9
8
FSR 1
FSR 2
FSR 3
FSR 1
FSR 2
FSR 3
7
6
5
4
3
2
1
0
-1
0
2
1
3
4
5
Applied force (N)
2
1
3
4
6
5
7
6
Force (N) applied
8
7
8
Figure 3.10: Linear fitting for FSR sensors.
9
8
7
6
5
4
3
2
1
0
-1
9
Measured
force (N)
Force (N) measured
8
7
6
5
Flexiforce 1
Flexiforce 2
Flexiforce 3
Flexiforce 4
Flexiforce
Flexiforce
Flexiforce
Flexiforce
1
2
3
4
4
3
2
1
0
-1
0
1
1
2
2
3
4
3
4
Applied force (N)
Force (N) applied
5
5
6
6
7
7
8
8
Figure 3.11: Linear fitting for Flexiforce sensors.
Results showed that both sensors exhibit the same linear behavior. High part-topart repeatability for both sensors was also observed. However, the Flexiforce sensors
exhibit better results in terms of lower error and offset. Tables 3.1 and 3.2 show
the sum of squared error (SSE) and root mean square error (RMSE) for the three
FSR401 sensors and the four Flexiforce sensors. The mean (standard deviation), SSE
and RMSE for FSR401 sensors was 0.89(±0.2) and for Flexiforce was 0.22(±0.07).
The average offset (term b in Tables 3.1 and 3.2) for Flexiforce is 0.09 while for FSR
CHAPTER 3. HARDWARE DESIGN
41
is 0.5.
Table 3.1: The sum of squared error (SSE) and root mean square error (RMSE) for
three FSR401 sensors. The compliant couplings are elastic and damp the
abrupt changes in the pressure and act as a lowpass filter.
Model
SSE
RMSE (v)
a
b (N)
Coupling type
FSR1
1.06
0.42
1.02
0.62
compliant
FSR2
0.66
0.33
1.07
0.53
compliant
FSR3
0.96
0.4
1.06
0.37
compliant
Average 0.89
0.38
1.05
0.5
Stdev
0.04
0.02
0.12
0.2
Table 3.2: the sum of squared error (SSE) and root mean square error (RMSE) for
four Flexiforce sensors. The non-compliant couplings have high stiffness
and do not change the frequency contents of the SMP signals.
Model
SSE RMSE (v)
a
b (N)
Coupling type
Flexiforce1 0.18
0.17
1
0.13
compliant
Flexiforce2 0.15
0.15
1.01
0.02
compliant
Flexiforce3 0.32
0.23
0.98
0.13
non-compliant
Flexiforce4 0.24
0.20
0.97
0.09
non-compliant
Average
0.22
0.18
0.99
0.09
Stdev
0.07
0.03
0.01
0.05
In another experiment the same calibration coefficients obtained from static loadings were used to calibrate the output of the sensors, for a dynamic motor-generated
force with a random pattern ranging between 0-10 N applied to both sensors. The
error between the applied force and the measured force was calculated, as shown in
CHAPTER 3. HARDWARE DESIGN
42
Figure 3.12. The Flexiforce A201 sensor had a better performance in the dynamic
test. Therefore, it was selected for the integrated SMP-SMEG sensor. Appendix A
shows Flexiforce A201 sensor datasheet.
Figure 3.12: Dynamic test for the FSR (top) and the Flexiforce (bottom) sensor.
Using the suggested driver circuit for the Flexiforce sensors, two identical 8 channel
driver boards were fabricated on a printed circuit board (PCB) as shown in Figure
3.13. Since the contact pressure sensors are resistive passive sensors and do not have
direct contact with the subject’s body no optical isolation is needed.
CHAPTER 3. HARDWARE DESIGN
43
Figure 3.13: Driver circuit board for the Flexiforce sensors.
3.4
Design of a Multiple Integrated Sensor Patch
An integrated SMP-SEMG sensor was designed and multiple sensors were arranged
on a sensor patch. Different design challenges were met to obtain a reliable prototype
sensor patch.
3.4.1
Attaching the sensors
FlexiForce A201 contact pressure sensors were mounted on the top of the AE100
SEMG sensors as shown in Figure 3.15 and Figure 3.15.
6
Figure 3.14: Collocating the SEMG and SMP sensors to make the Sensor patch.
CHAPTER 3. HARDWARE DESIGN
44
Figure 3.15: Sensor patch.
3.4.2
Pressure sensor coupling
In order to have an equal distribution of force on the sensing area of the sensor we
investigated various coupling disks with different shapes and compliance. A cylindrical shape non-compliant disc with an elastic dome on the top gave the most linear
pressure measurements. We calibrated all the sensors with these discs and stored the
calibration coefficients for each sensor.
3.4.3
Choosing a platform material
Different mounting materials, such as Neoprene, Alpha-gel and silicon molding materials, were investigated for constructing a patch of 6 integrated SEMG-pressure
sensors. Five prototype patches were made. These prototypes were evaluated under
the following criteria: the relative position of the sensors do not change when the
patch is wrapped over a subject’s arm; the patch is flexible such that the sensors lay
over the curvature of the muscle; the patch is breathable to avoid sweating; and the
patch will not irritate or disturb the subject’s skin. Two six sensor patches made
with the sensors sewn onto a soft fabric backing, with openings for the coupling disks
CHAPTER 3. HARDWARE DESIGN
45
over the pressure sensors, met the aforementioned criteria. A final prototype sensor
patch is shown in Figure 3.15. Two patches can be placed over the biceps brachii
and triceps brachii muscles and attached together using velcro tapes at both sides. A
regular blood pressure cuff (with the elastic inflatable part removed) is wrapped over
the sensor patches to hold the patches in place and load the pressure sensors.
3.5
Pre-processing
Any DC bias was removed from the raw SEMG signals and the linear envelope (LE)
was computed to estimate the signal amplitude as described in the literature [19, 69,
30]. The LE was obtained by rectifying the SEMG and smoothing with a 400 point
moving average filter (400 ms, 0.6 Hz).
The contact pressure readings and the recorded force at the wrist were smoothed
with a 100 point moving average filter. The filter length and the resulting delay were
chosen to approximate the delay (150 ms) between the collected SEMG signal and
the force generated by the muscle.
Chapter 4
Joint Angle Based SEMG
Calibration
4.1
Overview
Several confounding factors can affect the accuracy of force estimation using SEMG.
For static SEMG data recorded at multiple joint angles, or dynamic data recorded
as the joint angle is changing, SEMG amplitude is impacted by the force-length
characteristics of the muscle, changing muscle moment arm, and shifts in the location
of the IZ with respect to the recording electrodes.
In this chapter, an SEMG calibration procedure is proposed that compensates
for the three factors associated with changes in joint angle. The method produces
calibration parameters for selected joint angles based on sub-maximal constant SEMG
contractions and is used in force-SEMG modeling of isometric contractions of the
biceps and triceps brachii at several elbow joint angles. FOS is used to find a mapping
between the system inputs - estimated SEMG amplitudes and joint angle - and the
46
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
47
system output - measured force, for both calibrated and non-calibrated SEMG data.
The effectiveness of the calibration procedure is studied under different conditions:
using calibration coefficients obtained from all seven operational joint angles, using
coefficients from a subset of operational joint angles, and using coefficients from angles
which did not coincide with operational joint angles. As well, generalization of the
coefficients and force-SEMG models from one recording session to a subsequent session
is investigated.
In Section 4.2 the data collection procedure and the proposed calibration method is
described. In Section 4.3 the experimental results are presented and the observations
are discussed. In Section 4.4 a summary of the contribution of the experiment is
provided.
4.2
4.2.1
Methods
Data Collection
Data were collected from 9 male subjects with mean age of 25 years and no known
neuromuscular deficit. All subjects provided informed consent and the study was
approved by the Health Sciences Research Ethics Board, Queen’s University. SEMG
data were recorded from the biceps brachii, triceps brachii and brachioradialis muscles
of the right arm of each subject using two Invenium Technology AE100 active bipolar
SEMG sensors for each muscle. Electrode locations were measured with respect
to anatomical landmarks as suggested in the SENIAM project by the Biomedical
Health and Research program of the European Union [40] for each subject. Subjects
completed two sets of isometric flexion and extension tests - isometric constant SEMG
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
48
level and isometric constant force.
Isometric constant SEMG level tests
Subjects completed an isometric constant SEMG trial of the biceps brachii for flexion
and the triceps brachii for extension. Visual feedback of the SEMG amplitude was
provided. A constant SEMG amplitude level was specified for each subject and each
muscle such that for all joint angles the force at the wrist remained in the range 10-50
% MVC. Subjects were asked to maintain the specified SEMG level for 5 seconds at
seven elbow joint angles from 15◦ to 105◦ at 15◦ intervals, taking full arm extension
as an angle of 0◦ . The data were examined for co-contraction, where the level of
co-contraction was expressed as the ratio of the SEMG amplitude of the antagonist
muscle to the SEMG amplitude of the agonist muscle, taken as a percentage. Trials
for which co-contraction was greater than 20% were discarded. A sample trial for a
constant SEMG level recording is shown in Figure 4.1(a).
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
0.1
0
0
50
Triceps (mV)
0.1
50
0.2
0.1
0
50
100
50
0
0
50
0
Force (N)
10
0
0
50
Time (s)
(a)
100
100
150
0
50
100
150
0
50
100
150
0
50
100
150
0
50
100
150
0.2
0.1
0
100
50
100
20
50
0.1
0
0
0
0.2
100
Joint-angle
0
0.1
100
Radialis (mV)
0
0.2
100
0.2
0
Isometric constant force experiments
Biceps (mV)
Isometric constant SEMG level experiments
0.2
49
20
0
−20
Time (s)
(b)
Figure 4.1: Sample trial dataset for one subject for (a) isometric constant SEMG
level experiment for the biceps brachii and (b) isometric constant force
level experiment. The first three rows show the SEMG amplitude estimate
from biceps brachii and triceps brachii and brachioradialis for the duration
of the trial. The fourth row shows the joint-angles at which the recordings
were collected and the fifth row shows the measured force at the wrist.
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
50
Isometric constant force tests
All subjects completed 5 trials of alternating flexion and extension contractions at
seven joint angles: 15◦ , 30◦ , 45◦ , 60◦ , 75◦ , 90◦ , and 105◦ at a constant force level of
20 N. A two minute rest between trials was enforced to avoid fatigue. Visual feedback
of the measured wrist force was displayed to the subjects in real-time. A low target
force (20 N or approximately 25 %M V C) was used to ensure that fatigue free data
were collected in all five trials. Care was also taken to minimize co-contraction by
monitoring the antagonist muscle activity. Figure 4.1(b) shows a sample constant
force recording.
In order to investigate whether the proposed method can be generalized across
recording sessions, a second isometric constant force dataset was obtained from four
subjects, from the original subject group, in a subsequent recording session (session
2 - six months later).
A third isometric constant force dataset (session 3) was collected 12 months after
session 1 with the same protocol but at a higher contraction level (40 N ∼ 40%M V C)
from five randomly selected subjects from the original subject group. These data were
analyzed to determine if the calibration procedure could be generalized across muscle
contraction levels.
4.2.2
Pre-processing
For all trials, SEMG amplitude for the two recording locations over each muscle
were calculated and averaged. Also, in each trial the rest portions of the data were
discarded. SEMG amplitude was calculated and used for training a force estimation
model. Figure 4.2 shows a flow chart of the data collection and how each dataset is
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
51
used.
Subject # x
(x=1 to 9)
Constant EMG trial for
biceps brachii
Constant EMG trial for
triceps brachii
Constant force trials
repetitions 1 to 5
Calibration values for
biceps brachii
Calibration values for
triceps brachii
Calibrated data
repetitions 1 to 5
5 trained FOS models
(Trials 1 to 5)
Evaluate each FOS model
by four remaining trials
Figure 4.2: Flowchart of the data collection and force estimation procedure.
4.2.3
Fast Orthogonal Search (FOS)
FOS is a nonlinear identification method that very quickly approximates a system
output as a weighted sum of M linear or nonlinear basis functions pm (n) and coefficient terms am and aims to minimize the mean square error (MSE) between the
estimate and the system output [53, 52]. The FOS model takes the form:
y(n) =
M
∑
am pm (n) + e(n)
(4.1)
m=1
where e(n) is the estimation error, y(n) is the measured system output and n is the
discrete time sample index. FOS searches through a large pool of N available candidate basis functions, where N >> M and iteratively selects those functions which
contribute the greatest reduction in MSE. This approach is based on the principle of
Gram-Schmidt orthogonal identification, whereby orthogonal basis functions would
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
52
be generated from the candidate basis functions and coefficients found to minimize
the MSE of the estimate.
The pool of FOS candidate functions was constructed using the input signals with
modifying mathematical terms. The modifying mathematical terms were: quadratic
functions, limited square functions and square root functions. The functions were
constructed with the modified version of the input signals and their cross-terms adjusted by an angle-dependent factor which was either cos(θ) or sin(θ) where θ is joint
angle. The total number of functions in the pool depends on the number of inputs
used. A list of the functions used are provided in Table C.1 in Appendix C.
FOS models were trained and evaluated with the collected data. %RM SE was
used for evaluation where %RM SE is:
∑n
%RM SE =
j=1 (FW j − F̂W j )
∑n
2
j=1 FW j
2
× 100
(4.2)
where FW j is the measured force at the wrist, F̂W j is the FOS model estimate of
wrist force and n is the discrete time sample index. Complete details about the FOS
method are provided in Appendix B.
4.2.4
Angle-based Calibration Algorithm
The Hill muscle model equations for the SEMG-force relationship are used to explain
the concept of the proposed calibration method for a single muscle, in this case, the
biceps brachii. The method is extended to include two muscles for which calibration
values can be obtained independently.
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
53
Wrist force for a single contributing muscle
The force induced at the wrist due to torque about the elbow generated by a single
muscle “i” (mi ) can be expressed as:
FWθ = Mnet /Mf = Fm · Mm (θ)/Mf
(4.3)
where Fm is the muscle force, Mm (θ) is the muscle moment arm and Mf is the moment
arm of the loadcell measuring force at the wrist. Although Mf is also a function of
elbow joint angle, Mf variation is small over the joint angle range in our experiment
and is assumed to remain constant. Since muscle length is a function joint angle θ,
Equation 2.3 can be written as:
F CE = F0 · fθ (θ) · fv (v) · u(t)
(4.4)
where fθ (θ) represents the force-length or equivalently force-joint angle relationship.
The output of F CE peaks at the optimal joint angle (θ0 ) and decreases for values of
θ less than or greater than θ0 . In our experiment, F P E for the biceps and triceps
brachii is assumed to be negligibly small for the limited range of motion. As a result,
Fm ≈ F CE .
For an individual muscle, the amount of activation needed to generate a specific
level of force varies with joint angle, where, minimal effort is required at the optimal
joint angle, θ0 . Thus, for a constant muscle force the SEMG amplitude will vary with
joint angle. Part of this variation is described by the change in contraction dynamics
of the muscle, i.e. fθ (θ) in the Hill model and by variation of the muscle moment
arm, Mm (θ). SEMG amplitude is also affected by the movement of the muscle bulk
as joint angle changes, resulting in a shift in the relative position of the IZ and the
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
54
recording electrode [66, 86], which is not related to muscle mechanics.
Proposing an angle-based calibration for a single contributing muscle
Consider an isometric contraction of the biceps brachii, resulting in a flexion torque
about the elbow. Let the muscle activation, u(t), be truly represented by the SEMG
amplitude (EM G1 ) recorded at a single electrode site at a reference joint angle,
θ1 = θRef , that is u(t)θ1 = EM G1 . A change in joint angle introduces a modifying
factor, cθi , in the SEMG such that u(t)θi = cθi · EM Gi , i = 2, · · · , n represents the
true activation level of the muscle, where EM Gi is the amplitude of the recorded
SEMG. By definition, the factor, cθi , is due to the shift in the relative position of the
recording electrode and IZ. At the reference angle cθ1 = 1. Thus, the force induced
at the wrist at a joint angle θi due to the flexion torque is:
FWθi = F0 · fθ (θi ) · (cθi · EM Gi ) · Mm (θi )/Mf
(4.5)
As shown in Figure 4.3(a), a modeling procedure, such as FOS, attempts to find
a mapping (β) between the recorded SEMG and the recorded FWθi to derive:
β(θi ) = FWθi /EM Gi = F0 · fθ (θi ) · cθi · Mm (θi )/Mf
EMGi
Modeling
qi
a (qi ).EMGi
i
b (qi ) = ?
(a)
Modeling
qi
FWq
(4.6)
FWq
i
b (qi ) = ?
(b)
Figure 4.3: Modeling the isometric SEMG-force relationship: (a) before calibration
and (b) after calibration.
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
55
Although numerical or analytical models for fθ (θ) and Mm (θ) are available [2,
12, 14, 57, 65], no model for cθ is available as cθ is not directly observed from the
recorded SEMG. However, information on cθ at various joint angles can be observed
in the measured forces FWθ . Thus, in our proposed method, the calibration values
are derived from force measurements for a series of isometric constant SEMG trials
at different joint angles.
As it was previously described, during the isometric constant SEMG test the
subject was asked to contract the biceps brachii to a constant SEMG level at angles
θ1 , · · · , θn where θ1 is the reference angle i.e. θRef = θ1 . Then the induced wrist
forces will be:



FWθ1 = F0 · fθ (θ1 ) · EM G · Mm (θ1 )/Mf





 FW
= F0 · fθ (θ2 ) · (cθ2 · EM G) · Mm (θ2 )/Mf
θ2
..


.





 F
Wθn = F0 · fθ (θn ) · (cθn · EM G) · Mm (θn )/Mf
(4.7)
where EM G is the constant SEMG amplitude. The unknown factors, cθi , i = 2, · · · , n,
are reflected in the ratio of the measured forces, which we call the calibration coefficient α(θi ):
α(θi ) =
FWθi
F Wθ 1
=
fθ (θi ) · cθi · Mm (θi )
fθ (θ1 ) · Mm (θ1 )
(4.8)
The combined effects of variation in the force length relationship and change in muscle
moment arm and IZ shift are reflected in α(θi ).
The obtained coefficients, α(θi ), are used to calibrate the SEMG data recorded
from a limited number of joint angles (θi , i = 1, · · · , n) during isometric constant force
tests. Using the measured wrist force (FWθi ) the SEMG-force model tries to find the
mapping β̃ such that (α(θi ) · EM Gi ) · β̃ → FWθi (Figure 4.3(b)). By substituting for
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
56
FWθi from (4.5), one obtains:
α(θi ) · EM Gi · β̃ = F0 · fθ (θi ) · cθi · EM Gi · Mm (θi )/Mf
(4.9)
or after substituting for α(θi ) from (4.8):
β̃ =
F0 · fθ (θ1 ) · Mm (θ1 )
Mf
(4.10)
The new mapping β̃ can be ideally considered as constant across all angles, θi . The
signal α(θi ) · EM Gi is the calibrated version of the measured EM Gi which compensates for the force-length and moment arm effects, and the shift in IZ location. As a
result, the new SEMG-force model mapping, β̃, is simpler and may permit the use of
simpler modeling structures, thereby reducing training time.
Calibration for two muscles
The calibration method can be extended to a pair of agonist-antagonist muscles if
each muscle contributes primarily to concentric force generation with no significant
co-contraction. Thus, the calibration coefficients were obtained for biceps and triceps
brachii and were used to calibrate the SEMG for subsequent isometric, constant force
experiments for the corresponding muscles.
SEMG-force modeling
FOS models were generated for each of the five isometric constant force datasets
for each subject. Each model was evaluated four times using the data from the
four remaining trials, resulting in four validation %RMSE values for each model,
which were averaged to obtain a Model evaluation %RMSE (%RM SEmodel ). The
lowest value out of five %RM SEmodel terms was then chosen as the Subject evaluation
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
57
%RMSE value (%RM SESubject ). The %RM SESubject values were used as the primary
values to evaluate the success of the FOS model in predicting wrist force, FW . It
should be noted that the proposed SEMG calibration procedure is model independent
and can be used with any SEMG-force modeling technique.
Statistical analysis was done using the statistical toolbox from MATLAB (MATLAB 7.1, The MathWorks Inc). Wilcoxon signed-rank test was used to determine the
statistical significance of the proposed calibration method compared to estimation
results from non-calibrated data. The independent variable was the %RM SE and
the significance level was set at 5%.
4.3
Results and Discussion
4.3.1
Effects of FOS parameters
In order to find the number of FOS candidate terms which gives the model that best
represents the SEMG-force relationship, models were trained with 4 to 9 candidate
terms for all subjects, using non-calibrated SEMG data, and the results were compared as shown in Figure 4.4. There is no statistically significant difference between
the best and the worst results (p > 0.1). However, seven FOS functions were chosen
for subsequent modeling as the results were relatively better in terms of mean and
standard deviation.
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
58
12
%RM SE
10
8
6
4
2
4
5
6
7
Number of FOS functions
8
9
Figure 4.4: Distribution of the subject %RM SE results for different numbers of functions allowed in the FOS models. Seven FOS functions proved to give
better results, although not significant, in terms of mean and standard
deviation compared to the other numbers of FOS functions.
4.3.2
Effects of Calibration
Calibration coefficients for all seven joint angles were calculated from the constant
SEMG level calibration trial recorded for each subject. Figure 4.5 shows the distribution of calibration values at the seven joint angles for all subjects for the biceps
and triceps brachii muscles.
Figure 4.5: Distribution of the calibration values (α(θ)) for biceps brachii (solid black
lines) and triceps brachii (dotted grey lines) muscles over all subjects. The
calibration coefficients show an increase with joint angle for the triceps.
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
59
The distribution of the calibration coefficients shows a large inter-subject variability. However, some consistent patterns can be observed. For almost all subjects a
semi-linear ascending trend in calibration coefficient with increasing joint angle was
observed for the triceps brachii. A more variable pattern was observed across subjects for biceps brachii coefficients. The average patterns, however, are similar to the
published curves for the moment arms for both muscles [80]. Such an analogy is not
unexpected, because each calibration coefficient is representative of all joint angle dependent factors, including moment arm. Variability in subject anatomy, in particular
the IZ location in the biceps and triceps, may contribute to the large inter-subject
variability in the derived calibration coefficients.
The calibration coefficients were obtained for each of the joint angles tested, and
used to calibrate SEMG data recorded during constant force contractions at the corresponding joint angles. FOS-based SEMG-force models were trained and evaluated
using non-calibrated (scheme 1) and calibrated (scheme 2) SEMG data. The distributions of %RM SESubject values for scheme 1 and scheme 2 are shown in the first two
boxplots in Figure 4.6. The median %RM SE value for all models trained and evaluated with calibrated data (median = 4.98) was significantly lower than for models
trained with non-calibrated data (median = 10.28; p =< 0.001).
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
60
%RM SE
20
15
10
5
0
1
2
3
4
5
Scheme numbers
Figure 4.6: Distribution of the %RM SE for different approaches in choosing calibration joint angles. The first box-plot (scheme 1) represents the results for
non-calibrated datasets. In scheme 2 all calibration values at 7 joint angles were used to calibrate the datasets. Schemes 3 and 4 show the results
for models where the datasets were calibrated using calibration values at
4 joint angles. In scheme 5 calibration values at only 3 joint angles were
used to calibrate the datasets.
4.3.3
FOS Candidate Terms
Each FOS candidate term (see Appendix C) can be selected only once in a FOS model.
Therefore, the maximum number of times that a candidate term can be selected in all
models for all subjects is 45 (9*5). The frequency with which each candidate function
was selected over all FOS models was determined. The functions were ordered from
the most to the least frequently selected and given an index value as shown in Figure
4.7. The figure shows the consistency in choosing the FOS functions for non-calibrated
and calibrated datasets.
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
61
Percentage of usage (%)
100
Calibrated data
Non−calibrated data
80
60
40
20
0
0
10
20
30
40
Index of functions
50
60
Figure 4.7: FOS functions are sorted in descending order by the number of the times
they were selected in the models.
In terms of the FOS candidate functions selected for the SEMG-force models,
SEMG amplitudes for triceps, biceps and brachioradialis were selected most often
(over 80%) for both the non-calibrated and calibrated models. All other functions
contain a factor associated with the joint angle [sin(θ) or cos(θ)]. Models derived
using calibrated data contained 8% fewer functions dependent on joint-angle compared to models derived using non-calibrated data. This suggests less dependency on
joint angle and a more linear SEMG-force relationship when the calibration factors
are applied to SEMG data. The calibration method can be applied when using other
modeling procedures, e.g. parallel cascade identification, to potentially derive simpler
SEMG-force models.
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
4.3.4
62
Limited Number of Calibration Values
The joint angles at which the isometric constant force data were collected and the
joint angles at which the calibration values were obtained are defined as the “operational” and “calibration” joint angles, respectively. For practical recording situations,
it may be desirable to have fewer calibration angles than operational angles, and the
calibration and operational angles will not necessarily coincide. To investigate the performance of the calibration method under these conditions, three additional schemes
(schemes 3, 4 and 5) were defined:
• In scheme 3, the operational joint angles were the seven original angles:
15◦ , 30◦ , 45◦ , 60◦ , 75◦ , 90◦ and 105◦ and calibration joint angles were: 15◦ , 45◦ , 75◦
and 105◦ . Calibration coefficients for the intermediate operational angles were
obtained by averaging the values for two adjacent calibration angles.
• In scheme 4, the same operational and calibration joint angles were used as
in scheme 3 and calibration coefficients for the intermediate operational angles
were obtained using a second degree polynomial fitting procedure.
• In scheme 5, the operational joint angles were: 15◦ , 45◦ , 75◦ and 105◦ and the
calibration joint angles were: 30◦ , 60◦ and 90◦ . Calibration coefficients for joint
angles 15◦ and 105◦ were set equal to the coefficients for 30◦ and 90◦ respectively; calibration coefficients for 45◦ and 75◦ were obtained by averaging the
coefficients for the adjacent angles.
Figure 4.6 shows the %RM SESubject results obtained for all calibration schemes. In all
cases, models evaluated with calibrated datasets exhibited statistically better performance than those using non-calibrated datasets (p =< 0.05). Models calibrated using
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
63
coefficients measured at all seven operational joint angles, in general, showed better
performance than models for which fewer measured coefficients were used, but this
was not statistically significant (p > 0.05). The scheme where calibration and operational angles did not coincide, was expected to perform poorly compared to schemes
in which there was partial to full overlap between operational and calibration angles
(schemes 2, 3 and 4); however this was not the case. The comparable results for all
schemes show the effectiveness of interpolation for estimating calibration coefficients
from a subset of, or non-coincident operational joint angles.
In Figure 4.8, the measured and estimated calibration values for the different
calibration schemes and the corresponding force estimation errors at the seven operational joint angles are shown for the biceps brachii (top two plots) and triceps brachii
(bottom two plots) for a single subject. For both the biceps and triceps brachii muscles, the estimation errors increase sequentially for schemes 2, 5, 4, and 3 which is in
agreement with the results in Figure 4.6.
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
64
Calibration values, Biceps brachii, Subject 8
35
Scheme 2
α(θ)
30
25
Scheme 3
Scheme 4
Scheme 5
20
15
15
30
45
60
75
90
105
Calibration value estimation error, Biceps brachii, Subject 8
5
Error
0
−5
−10
15
30
45
60
75
90
105
90
105
Calibration values, Ticeps brachii, Subject 8
α(θ)
45
40
35
30
15
30
45
60
75
Calibration value estimation error, Ticeps brachii, Subject 8
Error
2
0
−2
15
30
45
60
75
90
105
Joint angle (θ)
Figure 4.8: The first and the third plots depict the measured and estimated α(θ) at
seven joint angles using schemes 3 to 5 in the biceps and triceps brachii
muscles for one subject. The second and fourth plots show the corresponding error (the difference between the measured and the estimated
wrist force values) for each of the estimation methods for the biceps and
triceps brachii muscles respectively.
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
4.3.5
65
Generalization of the Model and Calibration Values at
the Same Contraction Level
In this section, we investigate whether the calibration values and the calibrated models
generalize across recording sessions. Isometric constant force data were obtained
from four subjects, from the original subject group, in a subsequent recording session
(session 2). The following two cases were studied:
1. Calibration generalization: non-calibrated and calibrated models for session 2
were trained using data from session 2, and calibration values from session 1.
Figure 4.9(a) shows the distribution of the results for the non-calibrated and
calibrated datasets.
2. Model generalization: non-calibrated and calibrated models were trained using
datasets from session 1 and evaluated using data from session 2. Figure 4.9(b)
shows the distribution of the results for models evaluated using non-calibrated
and calibrated datasets.
%RM SE
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
45
45
45
40
40
40
35
35
35
30
30
30
25
25
25
20
20
20
15
15
15
10
10
10
5
5
5
0
0
Non−calibrated
(a)
Calibrated
Non−calibrated
(b)
Calibrated
0
66
Non−calibrated Calibrated
(c)
Figure 4.9: (a) Generalization of α(θ) at the same contraction level: α(θ) calculated
from the first recording session was used to calibrate datasets collected
in a subsequent session. (b) Generalization of the models at the same
contraction level: models were trained with calibrated data from the first
recording session and were evaluated by datasets from the second recording session. (c) Generalization of α(θ) at a higher contraction level: α(θ)
calculated from the first recording session was used to calibrate datasets
collected in the third session recorded at a higher contraction level.
In both cases the models evaluated with calibrated datasets had significantly (p <
0.001) better performance compared to those evaluated with non-calibrated datasets.
In Figure 4.9(a), there is a reduction of 70% in the median %RM SE for the calibrated
versus non-calibrated result, indicating that the calibration values obtained in one
session can be used for subsequent recordings. Evaluating the models trained in
session 1 using data from session 2 resulted in median %RM SE values of greater
than 20% for non-calibrated data, but less than 10% for calibrated data, indicating
that the models generalize significantly better across sessions with the calibrated data.
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
4.3.6
67
Generalization of the Model and Calibration Values at
a Higher Contraction Level
In the initial constant force recordings, a low target force level was used which reduced
the risk of fatigue and minimized the degree of agonist-antagonist co-contraction. For
these recordings the level of co-contraction was below 20% and the level did not change
significantly with joint angle for both muscles.
The possibility of using calibration values obtained in session 1 to calibrate data
recorded at a higher contraction level (40N) in a subsequent recording session (session
3) was assessed. Non-calibrated and calibrated models for session 3 were trained
using data from session 3 and the calibration values from session 1. Figure 4.9(c)
compares the distribution of the results for the non-calibrated and calibrated datasets.
The models evaluated with calibrated datasets had significantly (p < 0.001) better
performance compared to those evaluated with non-calibrated datasets.
For the 40 N recording session the average level of co-contraction in the biceps
brachii during extension regimes did not increase significantly compared to the 20 N
sessions, however the average level of co-contraction in the triceps brachii during flexion regimes increased to 40%, especially at angles between 75◦ and 105◦ . Brookham
et al. [9] found that incorporating co-contraction levels as constraints in a biomechanical muscle force prediction model improved model performance if appropriate values
for physiological cross-sectional area were used. In our case, where co-contraction is
present, FOS most likely includes appropriately weighted terms in the force prediction
model.
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
4.4
68
Summary
A method was developed to calibrate the amplitude of SEMG signals collected from
active bipolar sensors placed on the biceps and triceps brachii during isometric contractions at a range of elbow joint angles. SEMG calibration coefficients were calculated for each joint angle from constant SEMG level isometric recordings. The
calibration coefficients compensate for variations in SEMG amplitude due to changes
in muscle length, muscle moment arm and IZ displacement relative to the recording
electrodes. Non-parametric FOS-based SEMG-force models were trained and evaluated using both calibrated and non-calibrated SEMG data. The experimental results
show significant improvement in force prediction using calibrated data compared to
using non-calibrated data. It was also noted that fewer joint angle-dependent nonlinear functions are selected in the models for the calibrated SEMG datasets implying
more consistency and less dependency on joint angle in modeling the SEMG-force
relationship. Investigations using data from additional recording sessions from a subset of the original subject group, 6 to 12 months after the first session, suggest the
possibility of using a subject’s calibration values for future data recordings. The calibration procedure is model independent, and can be used with other SEMG-force
modeling techniques.
Our experiments focused on (static) isometric contractions over a range of joint
angles. The isometric constant EMG tests calibrate the EMG signals for their corresponding muscles by compensating for the angle-related effects (i.e. changing moment
arm, force-length curve, and the shift in muscle bulk) at the input channel. A dynamic
contraction represents the case where the number of operating points far exceeds the
CHAPTER 4. JOINT ANGLE BASED SEMG CALIBRATION
69
number of calibration points over the range of joint angles. Thus, for each calibration point, an angle zone can be defined. For any operational angle within a zone,
at any sampling iteration, the EMG can be calibrated using the corresponding calibration value or the interpolation of the calibration values of two neighboring zones.
As shown, the calibration values obtained from interpolation improve the force prediction results for static contractions. In dynamic contractions, e.g. isotonic and/or
isokinetic contractions, there are other factors that contribute to the measured output
force. These factors include the effects of muscle shortening or lengthening (forcevelocity curve), the viscous friction of the joint, and the inertia of the limb under
motion. These factors (f/v curve, friction, inertia), can be incorporated into the FOS
model as long as joint angular velocity and acceleration are included as inputs to the
model. Dynamic SEMG-force modeling with calibration is examined in Chapter 6.
Chapter 5
PCI Modeling
5.1
Overview
The SEMG-force relationship is nonlinear and dynamically changing even for isometric contractions. Use of advanced modeling techniques can capture the complexities of
the SEMG-force relationship and may not require time-consuming signal processing
techniques to achieve a reasonable estimation accuracy. Parallel cascade identification (PCI) can approximate any nonlinear system to an arbitrary degree of accuracy
by a sufficient number of linear dynamic and static nonlinear cascades in parallel [55].
In this chapter, the capacity of a PCI model to capture the nonlinear and dynamic
effects in the physiological behaviour of the muscles through the SEMG-force relationship is investigated. The effects of parameters and coefficients of the PCI model
on the accuracy of the force estimate are examined in order to find a model which best
represents upper-limb muscle behavior during sub-maximal isometric contractions at
two output force levels.
The results are compared to the results obtained from a physiologically motivated
70
CHAPTER 5. PCI MODELING
71
Hill-based parametric model applied on the same dataset [74]. Hill-based models require estimation of some physiological characteristics, such as muscle optimal length,
tendon slack length, maximum isometric force, physiological cross-sectional area, and
muscle-specific tension and there are different approaches for the determination of
these factors [113]. The Hill-based model developed by Mountjoy et al. uses FOS to
estimate the muscle optimal length [74]. The performance of the PCI model at higher
force levels is also evaluated.
In section 5.2 the data collection protocol and the principles of extending the PCI
method for multiple inputs are explained. Experimental results and discussion of
the observations are presented in Section 5.3. The contributions of this study are
summarized in the Section 5.4.
5.2
5.2.1
Methods
Data Collection
Data were collected from 10 subjects with no known neuromuscular deficit and all
subjects provided informed consent and the study was approved by the Health Sciences Research Ethics Board, Queen’s University. Subjects completed two recording
sessions on two different days. Each session included eight trials with an enforced
two minute rest between trials to avoid fatigue. In each trial, the subjects were asked
to generate a target force at the wrist by contracting the upper-arm muscles, first in
flexion and then in extension, at six elbow joint angles ranging from 30◦ to 105◦ in 15◦
intervals, taking full arm extension as an angle of 0◦ . In the first four trials of each
session, the target force was 10N and in the last four trials it was 20N. The 10 N and
CHAPTER 5. PCI MODELING
72
20 N wrist forces correspond to approximately 10 to 25 %MVC. These target forces
were used to insure that fatigue free data were collected from all subjects. In preliminary measurements, some subjects could not generate higher contraction forces
without the occurrence of fatigue during the experimental session. Visual feedback
of the measured wrist force was displayed to subjects in a real-time display on the
computer monitor. All contractions were isometric.
SEMG amplitude signals were estimated for the SEMG records, and were normalized using a sub-maximal normalization method. The SEMG recording for normalization was taken at a wrist force of 15 N (the mean of 10 N and 20 N). At the beginning
of each recording session, a 5 Nm torque (equal to 15 N wrist force) was applied to the
elbow joint, first in flexion, then in extension, while the subject maintained an elbow
angle of 75◦ . The linear envelope (LE) was computed and the average value was used
to normalize all recordings in the same session. The data were again normalized with
respect to variance i.e. the mean and standard deviation (STD) of data points were
calculated; the mean was subtracted from all data points and the result was divided
by the STD of the data to obtain a zero mean signal with unity STD. This made the
SEMG-force estimate invariant to the mean and variance of the input SEMG signal
which was assumed to have a normal distribution, for which mean and variance were
not known. Figure 5.1 shows the data collection procedure and how the data are used
to train and evaluate the force estimation models.
CHAPTER 5. PCI MODELING
73
Subject # x
(x=1 to 10)
Recording Session 1
10N constant
force trials
Recording Session 2
20N constant
force trials
10N constant
force trials
20N constant
force trials
Pre-processing
Repeated
Five times
Trained PCI models
(1 to 8)
Each PCI model is
evaluated by the
other 7 trials
Figure 5.1: Data collection and processing flowchart. The operations in the dashed
section were repeated five times.
In each data collection session, four 10N and four 20N trials were completed. A
PCI model was trained with the data in each trial and evaluated with the seven
remaining trials. As will be discussed in Section 5.2.2, different combinations of the
randomly selected input, cross-correlation function, and coefficients for each cascade,
can qualify the cascade to be added to the model. This means that two models
trained with the same data can have different structures. To avoid relying on results
from a single parallel structure, the training process was repeated five times for each
trial. For each subject, 40 (8x5) PCI models were trained resulting in 280 (40 x 7)
evaluation results per session.
CHAPTER 5. PCI MODELING
5.2.2
74
SEMG-force Mapping Using PCI
PCI is used to model the input/output relationship of dynamic systems. The PCI
method can approximate any time-invariant, causal, finite-memory, discrete-time nonlinear system to an arbitrary degree of accuracy by a sufficient number of linear and
static nonlinear cascades in parallel [55]. Additionally, the input to the system does
not have to be white or Gaussian or have any special autocorrelation properties.
Single Input PCI
A PCI model, as shown in Figure 5.2, consists of a sum of cascades in which a dynamic
linear element is followed by a static nonlinear element [55] where x(n) is the model
input(s) and y(n) is the measured output.
Figure 5.2: Structure of a PCI model. PCI mapping involves generating a parallel
connection of a series of linear dynamic and nonlinear static blocks. The
linear dynamic blocks are constructed from randomly selected functions
from the pool of cross-correlation functions of different orders between
the input x(n) and the residue yi−1 (n).
CHAPTER 5. PCI MODELING
75
The algorithm begins by approximating the nonlinear system with the first cascade. The difference between the desired output, y(n), and the first cascade output,
z1 (n), is called the residue, y1 (n). The residue is then treated as the output of a new
nonlinear system, which will be modeled by the second cascade. The residue of the
second cascade is computed, and another cascade is added. This process continues
until a desired approximation error is reached. The PCI model for a dynamic system
whose output depends on input delays from 0 to R, i.e. with a finite memory length
of R + 1, and an input length of T data points, is expressed as a summation of the
outputs from all of the cascades:
ỹ(n) =
M
∑
zi (n)
(5.1)
i=1
where M is the number of the cascades and ỹ(n) is the estimate of the output. For
the model structure shown in Figure 5.2, hi (j) is the impulse response of the dynamic
linear system in cascade “i” and is of arbitrary length R. The impulse response hi (j)
is constructed from a randomly selected function from the pool of cross-correlation
functions of different orders between the input x(n) and the residue yi−1 (n). The
cross-correlation functions are computed over a segment of the input and output
signals extending from n = R to n = T . This way the value of x(n) for negative
sample points (which does not exist) is not needed. Complete details about the PCI
method are provided in Appendix D.
Multiple Input PCI
In this study, the inputs to the PCI model are the SEMG signals collected from
three upper-arm muscles, biceps brachii, triceps brachii, and brachioradialis, and the
elbow joint angle. Consequently, instead of a single input PCI system, an extended
CHAPTER 5. PCI MODELING
76
version of PCI for multiple inputs has been used. In the multiple-input system, in
addition to the first, second, or higher order cross-correlation terms (Equations D.2D.3 in Appendix D), the pool of cross-correlation functions consists of second, third,
or higher order cross-correlation functions in which there is a contribution from more
than one input [55]:
ϕx1 ···x4 yi−1 (j1 , · · · , j4 ) =
T
∑
1
yi−1 (n)x1 (n − j1 ) · · · x4 (n − j4 ).
T − R + 1 n=R
(5.2)
The impulse transfer function is then constructed as:
hi (j) = ϕx1 ···x4 yi−1 (j, A2 , A3 , A4 )
(5.3)
where A2 , A3 , and A4 are selected randomly from 0, · · · , R. In adding each cascade to
the parallel structure, as illustrated in Figure 5.3, the algorithm selects one of the four
inputs at random, e.g. x1 , to be the input to the cascade. Then a cross-correlation
function is randomly selected from the pool of cross-correlation functions. Depending
on the chosen cross-correlation function the selected input can be treated in two
different ways: if the chosen function is constructed using only the selected input
(x1 ), such as in (D.2) or (D.3), hi (j) is constructed using the following equations:
hi (j) = ϕxyi−1 (j)
(5.4)
hi (j) = ϕxxyi−1 (j, A) ± Cδ(j − A)
(5.5)
if other inputs are included in the selected cross-correlation function, then hi (j) is
constructed using (5.3). However, one, two, or all other inputs, in this case x2 , x3 , and
x4 , can directly contribute as feedforward terms in the dynamic linear block output
that is fed to the static nonlinear block.
CHAPTER 5. PCI MODELING
77
Start
Add a cascade
Select an input
Pick ʔ function
from the pool
Construct h
No
ʔ
with
1 input
?
Yes
Calculate the output
of linear block
Construct h
Calculate the
output of the
linear block
Add contribution of
other inputs
Find the fit
coefficients
Find the output of
nonlinear block
Calculate the
cascade error
Reject the cascade
Increase threshold
Stop
Over
Under
Accept the cascade.
Calc. model error
No
Find residue
Threshold
Yes
Stop
Criteria
met
Figure 5.3: Flow diagram of the training process of a PCI model with multiple inputs.
In this scheme adding new cascades continues until one of the stopping
criteria is met. For this study, stopping criteria included reaching the
desired estimation %RM SE error or the maximum allowed number of
accepted or rejected cascades.
CHAPTER 5. PCI MODELING
78
For example, if all inputs contribute in a cascade, then the dynamic block output
is:
ui (n) =
R
∑
j=0
hi (j)x1 (n − j) + C
4
∑
±xk (n − Ak )
(5.6)
k=2
Here, C, A2 , A3 , and A4 are chosen as before. Since the input to the system, hi (n),
and the cascade coefficients are selected at random, there is no guarantee that the
selected cascade will be the only or the best possible cascade [55]. In other words,
many combinations of the randomly selected input, function, and coefficients can pass
the qualification threshold.
Model Identification
The pool of impulse response functions of the dynamic linear system was constructed
from cross-correlation functions of order 1 to 4, with 4, 16, 28 and 28 correlation
functions added to the pool of candidates, respectively. The four first-order correlation
functions are obtained by substituting x(n − j) in (D.2) with any of the four inputs
and the 16 second-order correlation functions are obtained by substituting x(n − j1 )
and x(n − j2 ) in (D.3) with any of the four inputs. For the third- and fourth-order
correlation functions a limited number of possible functions were added to the pool of
functions. The memory length of the system was chosen to be 2 lags. It was observed
that the fit between ui and zi diverges and may become unstable as polynomial degree
increases, thus 3rd-order polynomials were chosen as functions for the nonlinear block,
which has been noted in the literature as appropriate for SEMG-force modeling [7].
All inputs and outputs were normalized to have zero mean and unity variance.
The stopping criteria for the algorithm is as follows: if the reduction in %RM SE
by adding the ith cascade is less than an adaptive threshold value, the cascade is
CHAPTER 5. PCI MODELING
79
rejected and an attempt is made to find another cascade with a better contribution
to error reduction. The adaptive error threshold for accepting a cascade is linearly
decreased as candidate cascades are rejected. The algorithm is stopped if either the
maximum number of cascades allowed, the maximum number of rejected cascades
allowed, or a predefined %RM SE threshold (0.05), is reached.
5.3
Results and Discussion
The effects of each of the PCI model parameters and of specific data manipulations
on the %RM SE were investigated. As well, to understand the variability of the data
between different recording sessions, inter-session analysis for two of the subjects on
two datasets was performed. The results for inter-session analysis were compared with
results from the FOS method previously applied on the same dataset [74]. Results
for each force level were also separately reported, i.e. data were grouped into either
categorized (C) or not categorized (NCAT) sets based on the output force level (10N
or 20N).
5.3.1
Removing the Outliers
In constructing the PCI models, the inputs, transfer functions of the linear system,
and coefficients of the model are chosen at random. Therefore, extremely low or
high estimation errors might occur due to a random appropriate or inappropriate
initialization of the model. To avoid relying on random extreme results, the outliers
(very low and very high %RM SE values) were excluded. To discard the outliers, it
was initially assumed that the data are normally distributed. To preserve 99% (equal
CHAPTER 5. PCI MODELING
80
to 2.69*STD) of the data points any data point outside of the range of the median
±1.5 ∗ interquartile value was considered to be an outlier. However, as apparent in
the boxplots, the results are positively skewed in most cases. Therefore, accepting
data points within a range of mean±2.69∗STD would result in discarding almost
all of the data points from the upper extreme (high %RM SE values) due to the
positive skewness of the distribution. In order to avoid discarding only unsatisfactory
results, the ten best and ten worst data points were discarded, equivalent to keeping
approximately 95% of the data points for hypothetically normally distributed data.
Table 5.1 shows the %RM SE values averaged over 2800, and 2600 values across all
subjects. These results show that by omitting the ten best and ten worst values, the
mean error did not change considerably but the STD was significantly decreased as
expected. Wilcoxon signed-rank test was used to compare different groups of results.
Table 5.1: Effect of removing outliers on %RM SE for NCAT, C 10N, and C 20N data.
Ten data points from both extremes are discarded, resulting in keeping 95%
of the data points for each subject. Both mean and SD are reduced after
removing the data points. NCAT represents the non categorized data.
PCI
Evaluation % RMSE (STD)
Poly3
NCAT
C 10N
C 20N
Outliers kept
10.4 (19.2)
7.3 (4)
4.7 (3.1)
6.5 (1.3)
4.0 (1.1)
Outliers removed 8.5 (5.2)
5.3.2
SEMG Decimation
It is believed that lower time resolution results in more precise SEMG amplitude
estimates [95]. Decimating (down-sampling following lowpass filtering) was used to
CHAPTER 5. PCI MODELING
81
decrease time resolution and to reduce the number of data points thereby accelerating
the training process of the PCI models. It should be mentioned that since high-pass
filtering and rectification use the full bandwidth of the raw SEMG signal, decimation
must be performed after amplitude estimation.
However, there exists a risk that excessive decimation may eliminate valuable
information from the SEMG amplitude estimate, thus reducing the capacity of the
model to track the dynamics of the muscle force. To find an optimal decimation
factor all signals (force, angle, and amplitude estimate) were decimated by three
different factors (5, 10, and 15) and PCI models were trained and evaluated using the
decimated data for two subjects. It was observed that for both subjects the minimum
error was obtained for a decimation factor of 10. Although decimation smooths the
data records allowing for a better fit of the LE to the force, increasing the decimation
factor over a specific level increases the risk of losing useful information in the signal.
Therefore, a decimation factor of 10 was selected and subsequently all datasets were
decimated and the outliers were removed. Table 5.2 shows the results of the PCI
model evaluation averaged over 2600 %RM SE values from all subjects before and
after decimation. Although results for the decimated data are not significantly better
than the results for the non-decimated data, the 35% reduction in computation time
justified the use of decimation.
CHAPTER 5. PCI MODELING
82
Table 5.2: Effect of decimation by factor of 10 on %RMSE. Decimation was used
to decrease time resolution and to reduce the number of data points to
accelerate the training process for the PCI models. The %RMSE results
are not affected by decimation.
PCI
5.3.3
Evaluation % RMSE (STD)
NCAT
C 10N
C 20N
Non-decimated
8.5 (5.2)
6.5 (1.3)
4 (1.1)
Decimated
8.4 (5)
6.8 (1.4)
3.7 (0.9)
Effects of PCI Model Parameters on SEMG-based Force
Estimates
Two main parameters used in determining a PCI model are the value of the memory lag in the dynamic linear block and the degree of the polynomial in the static
non-linear block. To analyze the effects of changing these parameters on the force
estimation error, different models were trained with different parameter values and
the values which minimized the estimation errors were determined.
Polynomial Degree
It has been argued that a third degree polynomial will capture the nonlinearity in the
SEMG-force relationship [20]. Therefore, third degree polynomials were initially used
in the PCI structure. In order to determine the degree of polynomial which leads
to a PCI model that best represents the SEMG-force relationship, first to fourth
degree polynomials were used to train and evaluate 40 models for subject S4, chosen
because the data initially gave the worst %RM SE results. The averaged results for
CHAPTER 5. PCI MODELING
83
the different polynomial degrees were calculated. The average %RM SE values for
the first to third degree polynomials were similar. However, the results for a fourth
degree polynomial deteriorated drastically implying the occurrence of over fitting.
PCI models were generated for all subjects using first to third degree polynomials
and the averages of the resulting 2600 %RM SE values are given in Table 5.3. It
was observed that the polynomial degree which gave the lowest %RM SE varied from
subject to subject. However, for results averaged across all subjects, the performance
of models with second-degree polynomials was significantly better than with the first
or third degree polynomials for the NCAT data (p < 0.02). Figure 5.4 shows a box
plot comparing the distribution of the results for first to third degree polynomials for
all subjects.
Table 5.3: Effect of different polynomial degrees on %RMSE. First to third degree
polynomials were used to train and evaluate PCI models for all subjects.
Lowest%RMSE values were obtained for second degree polynomials.
PCI
Evaluation % RMSE (STD)
Polynomial
NCAT
C 10N
C 20N
1st degree
10.8 (3.7)
10.8 (1.6)
6.6 (0.7)
2nd degree 7.2 (3.6)
6.4 (1.1)
3.4 (0.8)
3rd degree
6.8 (1.4)
3.7 (0.9)
8.4 (5)
CHAPTER 5. PCI MODELING
84
Error (RMSE)
0.25
0.2
0.15
0.1
0.05
Poly1
Poly2
Poly3
Figure 5.4: Boxplots comparing RMSE error for different polynomial degrees used in
the PCI models for NCAT data from all subjects.
Memory Lag Magnitude
The delay between the input and the output of a system can be modeled by choosing
an appropriate magnitude for the memory lag in a PCI model. There is a dynamic in
the SEMG-force relationship due to the presence of the EMD. Applying a low-pass,
moving average filter in the SEMG signal amplitude estimation coarsely compensated
for the EMD by introducing 150ms of delay. However, EMD is affected by many
physiological factors and varies between different subjects [99]. Hence, the constant
delay introduced by the low-pass filtering may not accurately model the time delay
for all datasets.
In order to find the memory lag magnitude in the model that best represents the
time delay in the SEMG-force relationship, three different memory lags (2, 15, and
25 points) were tested and the results were averaged over 2600 %RM SE values as
reported in Table 5.4. Since the data were decimated by a factor of 10, each memory
lag represented 10 ms of time delay. A memory lag of 2 gave marginally better results
and lower computation time and, therefore, was selected for use in the PCI models.
CHAPTER 5. PCI MODELING
85
The resulting overall delay was 170 ms which was within the range of the reported
EMD values (47-244 ms) in the literature [74, 13, 20, 27, 45, 72, 97].
Table 5.4: Effect of memory lag magnitude on %RMSE for models developed using
2nd degree polynomials. Three different memory lags (2, 15, and 25 points)
were tested and the results were averaged over 2600 %RM SE values. Lowest %RM SE values were obtained for 2 memory lags .
PCI
5.3.4
Evaluation % RMSE (STD)
Poly2
NCAT
C 10N
C 20N
Mem 2
7.2 (5.8)
6.4 (3.1)
3.4 (1.4)
Mem 15
7.6 (5.9)
6.9 (3.3)
3.7 (1.5)
Mem 25
8 (6.2)
7 (3.2)
4 (1.4)
SEMG-force Mapping
Table 5.5 shows the final %RM SE values for the force estimation averaged over 260
values for each subject. The PCI models were trained using the decimated data, and
optimal parameters obtained from the previous analyses. The averaged results from
70 %RM SE values using the FOS method described in Mounjoy et al. [75] with
the same dataset are also reported in Table 5.5. The SEMG-force estimation error
averaged over all subjects was reduced by 44% for PCI modeling compared to the
FOS method. In some cases, e.g. subject S4, the error reduction was substantial.
This shows that dynamic modeling of the SEMG-force relationship can have superior performance in comparison to subject specific methods which must make use of
estimated physiological parameters for the Hill muscle model.
CHAPTER 5. PCI MODELING
86
Table 5.5: The %RMSE results obtained using optimal values for the PCI model
parameters: decimation factor of 10, polynomial degree of 2, and memory lag magnitude of 2. The results from the FOS model are shown for
comparison.
Poly2
NCAT
C 10N
C 20N
S1 PCI
6.3 (3.5)
4.8 (0.6)
3.1 (0.6)
S1 FOS
14.8 (10.7)
18.9 (16.1)
6.1(2.8)
S2 PCI
8.6 (4.1)
7.7 (1.6)
3.5 (0.6)
S2 FOS
9.4(5.0)
8.5 (2.3)
4.4 (1.3)
S3 PCI
6.6 (3.9)
7 (1.5)
3.1 (1.1)
S3 FOS
7.0 (3.6)
6.4 (2.5)
4.2 (2.3)
S4 PCI
18.5 (10)
13.3 (2.1)
4.8 (1.1)
S4 FOS
36.0 (22.5)
31.0 (22.0)
15.9 (9.4)
S5 PCI
5.1 (2)
5.9 (0.8)
3 (0.7)
S5 FOS
9.0 (4.5)
6.4 (1.5)
4.7 (1.4)
S6 PCI
5.9 (2.5)
5.6 (0.5)
2.7 (0.4)
S6 FOS
11.5 (7.5)
11.2 (5.6)
5.8 (3.3)
S7 PCI
6.3 (2.8)
8.3 (1.7)
2.8 (0.5)
S7 FOS
37.0 (28.4)
17.0 (10.1)
8.8 (3.9)
S8 PCI
4 (1.3)
3.9 (0.7)
3 (0.5)
S8 FOS
9.7 (6.0)
5.7 (2.3)
4.0 (1.1)
S9 PCI
6.5 (4)
3.1 (0.4)
5.7 (2.2)
S9 FOS
5.8 (3.3)
6.5 (4.2)
3.6 (1.5)
S10 PCI
4.5 (1.9)
4.2 (0.9)
2.2 (0.4)
S10 FOS
8.5 (5.8)
3.2 (0.8)
3.6 (1.0)
Average PCI
7.2 (3.6)
6.4 (1.1)
3.4 (0.8)
11.5 (6.7)
6.1 (2.8)
Average FOS 14.9 (9.7)
CHAPTER 5. PCI MODELING
87
Many factors in SEMG data collection such as subject characteristics, instrumentation, electrode placement and experimental protocol differ among studies and
affect the results. Thus, the best comparison between different modeling techniques
is obtained when they are applied to the same dataset. However, in order to assess
the value of our approach, the overall %RM SE value obtained from PCI (3.4 ± 0.8)
was compared to results from other studies. Clancy et al., [16] collected 50% MVC
constant posture contractions from 15 subjects and used the linear FIR method to
map the EMG-torque relationship in the biceps brachii. They reported a 22% error
with the error definition the same as for our experiment. Potvin and Brown [88] collected EMG data from the biceps brachii from 25 subjects and used an exponential
equation to map EMG to force. They reported a %RMSE error of 11% . Clancy
and Hogan [20] used third degree polynomials to map the EMG-torque relationship
and reported an error equal to 3% of the combined flexion/extension torque range.
These studies considered a more extended range of contraction level compared to our
experiment. As noted previously, we used lower force levels in order to collect fatiguefree data from all subjects. This is a limitation of our study since the SEMG-force
relationship is likely to appear linear at such low force levels. In order to evaluate
our method’s performance at higher levels of force, two subjects who could maintain
higher force level contractions, repeated the experiment at 40 N (50 %MVC). The
average %RMSE values for the resulting SEMG-force models were 7.1% and 6.7%
which are comparable to the values obtained for the 10 N contractions.
CHAPTER 5. PCI MODELING
5.3.5
88
Inter-Session Performance Variability
Figure 5.5 and 5.6 show the distribution of results for individual subjects for two
different sessions. The variability of the results across subjects in each session is
apparent. A Wilcoxon signed-rank test comparing mean %RM SE indicated that in
subjects 1-9 there was a significant difference in the results between sessions (p <
0.02). In subject 10, there was no significant difference (p = 0.42) between sessions.
It can be concluded that there is significant variability in the force estimation results
across subjects and results also vary between recording sessions.
Error (%RM SE)
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10
Subjects
Figure 5.5: Boxplots comparing RMSE error for PCI models obtained for session 1
for individual subjects. In most subjects the results are positively skewed.
CHAPTER 5. PCI MODELING
89
Error (%RM SE)
70
60
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10
Subjects
Figure 5.6: Boxplots comparing RMSE error for PCI models obtained for session 2 for
individual subjects. Comparison between the two sessions for each subject reveals a significant difference between results from the two recording
sessions. It was attempted to minimize intersession variability by using
standard electrode placement and skin preparation protocols. The presence of significant intersession variability may indicate that more precise
electrode placement and skin preparation protocols are needed, or that
subject motivation varied between sessions.
The inter-session variability imposes a limitation to SEMG-force modeling and
should be avoided as much as possible. The main factors affecting inter-session variability are electrode placement and electrode-skin impedance. Careful attention to
electrode placement and skin preparation is required to alleviate the effects of the
inter-session variability.
5.4
Summary
A PCI structure was formulated to model the isometric SEMG-force relationship.
The linear part of the PCI structure captures the dynamics of the relationship by
constructing dynamic FIR filters based on cross-correlation of the system inputs and
CHAPTER 5. PCI MODELING
90
output, while the nonlinear component models the nonlinearity in the relationship.
In this study, PCI modeling was used to estimate force induced at the wrist from the
SEMG signals recorded from three upper arm muscles acting to flex and extend the
elbow. To improve the precision of the estimate, SEMG amplitude estimates were
decimated, thereby reducing the computational cost. Optimal model parameters
were determined by statistical analysis of the results for a range of parameter values.
The final results were compared to results obtained using the FOS method with Hill
muscle model parameters which was previously applied to the same dataset. Over
44% improvement in the average %RM SE for force estimation was achieved using
PCI. The inter-session variability analysis revealed a significant difference in results
for data recorded on two different days from the same subjects. This could be due to
factors such as different electrode placement and skin preparation in the two sessions.
This could also be a result of a learning effect since for most subjects the results were
better in the second recording session.
Our model has been developed and tested using SEMG data recorded at low force
levels. For the biceps and triceps brachii, it has been found that the SEMG-force
relationship was more nonlinear at lower contraction levels (0-30 %MVC) compared
to higher contraction levels (above 30%MVC) [110]. Other experimenters have suggested that more linear relationships between EMG and force are found where narrow
recruitment ranges are used [99]. We believe that the PCI method can be applied to
SEMG-force modeling at higher contraction levels. If the relationship becomes more
nonlinear, more cascades can be added or higher degree polynomials can be used.
This was shown on data from two subjects who performed the experiment at a force
level of 40 N (50 %MVC). The average %RMSE values for these two subjects were
CHAPTER 5. PCI MODELING
91
7.1% and 6.7% which were in the range of the values obtained for 10 N contractions.
PCI modeling is capable of modeling the SEMG-force relationship which is nonlinear and dynamic in nature. In the current work, only isometric isotonic contractions
were considered. In the next chapter, the performance of PCI modeling under more
complex contractions such as isometric varying force and dynamic contractions will
be assessed.
Chapter 6
Dynamic Force Estimation
6.1
Overview
To accurately estimate muscle forces using SEMG signals two fundamental steps are
necessary: first, a precise SEMG amplitude estimate must be obtained, and second
a modeling scheme capable of coping with the non-linearities and dynamics of the
SEMG-force relationship must be applied. In Chapter 4, we showed that angle-based
calibration can be used to improve SEMG based force estimation during isometric
contractions through minimization of the effects of joint angle related factors. Also,
in Chapter 5, we showed that PCI modeling captures both the nonlinear and dynamic
properties of the process being modeled.
In this work, angle-based SEMG amplitude calibration and PCI modeling are
combined to address the issue of SEMG force estimation in dynamic contractions including concentric and eccentric contractions of the biceps brachii and triceps brachii
muscles.
92
CHAPTER 6. DYNAMIC FORCE ESTIMATION
93
SEMG data recorded during constant force-constant velocity, and varying forcevarying velocity elbow flexion and extension trials were calibrated using calibration
values, which were obtained at specific elbow joint angles and then interpolated to
cover the range of joint angles under study. The calibrated data were then used in
PCI models to estimate the force induced at the wrist. The experimental results show
the effectiveness of the calibration scheme, and the choice of interpolation method,
in improving the force estimation accuracy and the superior performance of PCI
compared to the FOS method that does not explicitly model the system dynamics.
Force estimation accuracy was superior in concentric contractions in comparison to
eccentric contractions, which may be indicative of more non-linearity in the eccentric
SEMG-force relationship.
In Section 6.2, the data collection procedure and a brief description of the methods are presented. Section 6.3 presents experimental results and discussion on the
observations. In Section 6.4, the contributions of the this study are explained.
6.2
6.2.1
Methods
Data Collection
Data collection was done using the experimental set-up previously described in Chapter 3. Ten subjects (6 male and 4 female) with age range 25 to 30 years took part in
the study. The subjects had no known neuromuscular deficit and provided informed
consent. The study was approved by the Health Sciences Research Ethics Board,
Queen’s University. SEMG data were recorded from the biceps and triceps brachii
muscles of the right arm of each subject using the sensor patch described in Chapter
CHAPTER 6. DYNAMIC FORCE ESTIMATION
94
Sensor patch1
1 2 3
4 5 6
Sensor patch2
1 2 3
4 5 6
Figure 6.1: The SEMG sensor patch used to collect SEMG and force data. Adapted
from [39]
3. The intersection of the vertical and horizontal midline of the electrode patches was
placed on the locations suggested by SENIAM [39] for the biceps and triceps brachii
muscles measured with respect to anatomical landmarks for each subject as shown
in Figure 6.1. Initially, two MVC trials were collected from subjects at 90◦ elbow
joint angle and were used to normalize the recorded SEMG. Subjects then completed
three sets of flexion and extension trials: i) isometric, constant SEMG level trials;
ii) dynamic constant force-constant velocity trials; iii) dynamic varying force-varying
velocity trials. Figure 6.2 shows a flowchart of the data collection.
CHAPTER 6. DYNAMIC FORCE ESTIMATION
95
Subject # x
(x=1 to 10)
Constant EMG trial for
biceps brachii
Constant EMG trial for
triceps brachii
Calibration values for
biceps brachii
Calibration values for
triceps brachii
Constant force-constant
velocity trials (CF-CV)
Varying force-varying
velocity trial (VF-VV)
Pre-processing
Pre-processing
Calibrated CF-CV trials
Calibrated VF-VV trials
CONCENTRIC
PCI models
ECCENTRIC
Training
Segment
Trained PCI
model
PCI models
Repeated five times
Evaluation
Segment
Repeated ten times
Figure 6.2: Data collection flowchart.
In the isometric constant SEMG level trials, subjects performed isometric constant
SEMG contractions of the biceps brachii in flexion and the triceps brachii in extension.
Visual feedback of the SEMG amplitude from one recording channel (the middle
electrode of the first row) was provided. A constant SEMG amplitude level was
specified for each subject and each muscle such that for all joint angles the contraction
level remained in the range 10-50 % MVC. Subjects were asked to maintain the
specified SEMG level for 5 seconds at seven elbow joint angles from 15◦ to 105◦ at
15◦ intervals, taking full arm extension as an angle of 0◦ . A sample trial for a constant
SEMG level recording is shown in Figure 6.3(a).
Subsequently, subjects completed three trials of alternating concentric and eccentric constant force, constant velocity contractions at three force levels (20 N, 25 N and
CHAPTER 6. DYNAMIC FORCE ESTIMATION
96
30 N) sweeping through joint angles from 15◦ to 105◦ . During each sweep at each of the
three constant force levels the subjects were asked to overcome the motor-generated
force at the wrist while maintaining a constant velocity by tracking a trajectory of
joint angle which was displayed on the monitor. A five minute rest between trials
was enforced and a low target force (20 N to 30 N ) was used to avoid fatigue during
data collection. Figure 6.3(b) shows a sample constant velocity recording.
Subjects then completed an additional trial in which they performed random
movements of their forearm, in flexion and extension, at their choice of velocity for
60 seconds. A motor-generated torque proportional to the angular velocity and in a
direction opposing the movement of the arm, was applied at the wrist. The generated
torque satisfied the following equation: τ = k(θ).θ̇ where τ is torque, θ is elbow joint
angle and k is a scaling factor. The value of k was chosen to keep the generated torque
in the desired range (±20N ) and its sign ensured a concentric contraction in which
the applied force always opposed the hand movement. No specific constraints were
given to the subjects except that the maximum velocity (disregarding the direction)
had to be less than 200 degree/s to avoid excessive force to the force sensor at the
wrist.
CHAPTER 6. DYNAMIC FORCE ESTIMATION
Dynamic constant velocity
Full dynamic
0.4
0.4
0.4
0.2
0.2
0.2
0
0
0
50
100
0
50
100
150
0
0
20
40
60
0
20
40
60
0
20
40
60
0
20
40
60
0
20
40
60
20
40
Time (s)
60
0.4
0.2
0.1
0
0
50
100
0.2
0.1
0
0.2
0
50
100
150
0
100
100
100
50
50
50
0
0
0
50
100
200
0
50
100
150
200
0
200
0
0
0
−200
−200
−200
0
50
100
0
50
100
150
50
50
20
0
0
0
−50
Motor (Nm)
Force (N)
Velocity (θ’)
Angle (θ)
Triceps (V)
Biceps (V)
Isometric constant EMG
97
0
50
100
−50
0
50
100
150
5
5
5
−20
0
0
0
−5
−5
−5
0
50
Time (s)
(a)
100
0
50
100
Time (s)
(b)
150
0
(c)
Figure 6.3: Sample trial dataset for one subject for (a) isometric constant SEMG level
experiment for the biceps brachii, (b) dynamic (concentric and eccentric)
constant force-constant velocity experiment and (c) dynamic (concentric)
experiment with varying force and velocity. The first two rows show the
SEMG amplitude estimate from biceps brachii and triceps brachii for the
duration of the trial. The third row shows the joint-angles at which the
recordings were collected, the fourth row shows the velocity represented by
the derivative of the joint angle, the fifth row shows the measured force
at the wrist, and the last row shows the command given to the motor
in volts to generate the force at the wrist. A positive motor command
indicates a force which must be overcome by flexion and a negative motor
commands indicates a force which must be overcome by extension i.e. the
direction of the force is opposite to the direction of forearm motion.
CHAPTER 6. DYNAMIC FORCE ESTIMATION
98
This created a dynamic condition that was more analogous to an arbitrary operational condition where there were fewer limitations on the joint angle, contraction
level and velocity. Figure 6.3(c) shows a sample dynamic recording with varying force
and velocity.
6.2.2
Force Estimation in Dynamic Contractions
The isometric constant SEMG data from location 2 (L2) in the electrode patch (middle electrode, upper row) were used to obtain the calibration values for the biceps
brachii and triceps brachii at the 7 measurement joint angles. Calibration values at
intermediate joint angles were estimated using two interpolation methods: 3rd degree
polynomial fitting (POL) and piece-wise linear fitting (PWL).
Each of the three dynamic constant velocity trials consisted of alternating concentric and eccentric contractions at three force levels. For each recorded trial, the
concentric and eccentric segments (SEMG, force, joint angle) were extracted and concatenated to form a concentric (CON) and a eccentric (ECC) dataset. The SEMG
data from location 2 (middle electrode, upper row) for the biceps and triceps brachii
were calibrated using the corresponding calibration coefficients. The calibrated data
in a complete dataset (CON/ECC) were used to train a PCI model projecting the
inputs (SEMG, joint angle) to the output (measured force) and the two remaining
datasets (CON/ECC) were used for evaluation.
For each subject, three PCI models were trained with CON data and three models
for ECC data. Each model was evaluated with the remaining two trials resulting in
3x2 % RMSE values for each subject and each contraction type. Model generation was
CHAPTER 6. DYNAMIC FORCE ESTIMATION
99
repeated five times to avoid dependency on input selection, giving 5x6 % RMSE values. In total 10x30 % RMSE values were obtained for evaluating the force-estimation
performance. Initial PCI models incorporated second degree polynomials and a memory lag of 2 as these parameters previously gave best performance in modeling the
isometric SEMG-force relationship [37]. Subsequently, the effects of different PCI
model parameters were evaluated.
The PCI model was then tested using the calibrated data collected during the
varying force-varying velocity trials. The data recorded for each subject were partitioned into two segments. The first segment was used for training the model and the
second for evaluating the trained model. Different percentages of the data from 10 to
80% were used for the training segment to determine the optimal training length. For
this case, the PCI model was extended to accept up to 14 inputs including six SEMG
inputs from each of the biceps brachii and triceps brachii, velocity and joint angle,
i.e., all the SEMG channels were used. For each subject one model was trained using
a segment of the data and the model was evaluated using the remaining data resulting
in one % RMSE value for each subject. Model generation was repeated 10 times giving 1x10 % RMSE values per subject. In total 10x10 % RMSE values were obtained.
Statistical analysis on all %RM SE values was performed using the Wilcoxon signed
rank test as the data were not normally distributed. The significance level was set at
0.05 and it was adjusted when pairwise test was done on repeated measures data. To
adjust the significance level is was divided by the number of repeated measures.
CHAPTER 6. DYNAMIC FORCE ESTIMATION
6.3
6.3.1
100
Results and Discussion
Constant-force, constant-velocity trials
Effects of calibration
Figure 6.4(a) and 6.4(b) show boxplots comparing the % RMSE error for the force
estimation models for concentric and eccentric data, respectively, where model inputs
were: non-calibrated SEMG and joint angle; calibrated SEMG with polynomial fitting
of the calibration coefficients (CP OL ) and joint angle; calibrated SEMG with piecewise linear fitting of calibration coefficients CP W L and joint angle; CP W L data only.
The distribution of the calibration coefficients across subjects are shown in Figure 6.5
for the PWL and POL fitting methods.
%RMSE
Concentric contractions
Eccentric contraction
55
55
50
50
45
45
40
40
35
35
30
30
25
25
20
20
15
15
10
10
5
5
NC+JA
CPOL+JA CPWL+JA
(a)
C
PWL
NC+JA
CPOL+JA CPWL+JA
C
PWL
(b)
Figure 6.4: Boxplots comparing %RMSE error for models trained and tested with
non-calibrated (NC) SEMG data and joint angle (NC+JA), SEMG data
calibrated with values obtained from third degree polynomial fitting and
joint angle (CP OL +JA), SEMG data calibrated with values estimated
from piece-wise linear fitting and joint angle (CP W L +JA) and SEMG
data calibrated with values estimated from piece-wise linear fitting without joint angle (CP W L ). (a) concentric experiments and (b) eccentric
experiments.
CHAPTER 6. DYNAMIC FORCE ESTIMATION
Biceps brachii PWL
101
Triceps brachii PWL
3
30
20
α
2
10
1
0
0
1
2
3
4
5
6
7
−10
1
Biceps brachii POL3
2
3
4
5
6
7
Triceps brachii POL3
3
30
20
α
2
10
1
0
0
1
2
3
4
5
6
7
−10
Joint angle
1
2
3
4
5
6
7
Joint angle
Figure 6.5: Distribution of measured calibration coefficients at the 7 joint angles
shown among subjects for biceps (upper left) and triceps brachii (upper right), with PWL fitting and estimated calibration coefficients using
POL fitting for biceps (lower left) and triceps brachii (lower right). The
different patterns of the top and bottom plots indicate the estimation
error introduced due to interpolation.
The median % RMSE values for the concentric and eccentric contraction models
are similar for the NC data. However, a broader distribution was observed for the
eccentric case. For the concentric case, the calibrated data yield significantly better
results than the non-calibrated in terms of % RMSE with or without joint angle as
an input (p < 0.05). This is true for the eccentric data only when the joint angle
is included as a model input (p < 0.05) and model performance deteriorates when
joint angle is excluded. Comparing the two interpolation methods it is observed
that PWL interpolation led to better % RMSE values in comparison to POL. This
improvement is significant for concentric contractions (p < 0.05) where there is also
increased coherency represented by lower standard deviation. There is no significant
difference for eccentric contractions (p = 0.17).
The improvement in force estimation with calibration can be explained by the
CHAPTER 6. DYNAMIC FORCE ESTIMATION
102
compensation for joint angle-based factors (force-length, moment arm, and IZ shift)
since other factors such as velocity and contraction level were constant. However,
calibration does not fully compensate for joint angle based effects as even after calibration there is still joint angle dependency in the SEMG-force relationship. This is
particularly evident in the eccentric case where there are more substantial force contributions from passive elements (F P E ). The calibration coefficients were obtained from
isometric contractions, which have been shown to have an SEMG-force relationship
which is similar to that for concentric contractions [22, 63].
Effects of PCI parameters
The effects of using different PCI model parameters on % RMSE values were studied to
obtain an optimized SEMG-force model for the dynamic contractions. The mean and
standard deviation of the % RMSE values for concentric and eccentric contractions
are reported for different degrees of polynomial in the PCI model (Table 6.1) and for
different memory lags (Table 6.2).
CHAPTER 6. DYNAMIC FORCE ESTIMATION
103
Table 6.1: The mean and standard deviation of the 300 % RMSE values for both
concentric and eccentric contractions for different polynomial degrees used
in the PCI models for all subjects. The values are reported for both noncalibrated and calibrated data. 20 memory lags were used to train the PCI
models. * indicates a significant difference wrt the value in the row above.
The significance level was adjusted by the number of repeated measures
(0.05/4).
Data:
Concentric
Eccentric
Polynomial degree
NC
CP W L
NC
CP W L
1st
21 (8.4)
15.4 (6.3)
30.1 (8.4)
18 (7.7)
2nd
15.8 (7.6)*
8.3 (3.2)*
16.5 (9.5)*
14.1 (4.3)*
3rd
14.1 (6)*
12.8 (5.2)*
15 (9.2)*
15.7 (5.3)*
4th
18 (8.2)*
16 (6)*
26.3 (9.7)*
18.3 (5.4)*
Table 6.2: The mean and standard deviation of the 300 % RMSE values for both
concentric and eccentric contractions for different numbers of memory lags
used in the PCI models for all subjects. Second degree polynomials were
used in the PCI models. * indicates a significant difference wrt the value
in the row above. The significance level was adjusted by the number of
repeated measures (0.05/5).
Data:
Calibrated
Memory lag
Concentric
Eccentric
2
8.3 (3.2)
14.1 (4.3)
5
8.3 (3.1)
13.5 (4.4)*
10
8 (3.3)
10.3 (3.7)*
20
7.2 (3.4)* 10.5 (5)*
30
11.2 (4.7)*
13.4 (6.7)*
CHAPTER 6. DYNAMIC FORCE ESTIMATION
104
Results for both calibrated and non-calibrated data are reported in Table 6.1.
In each column, the symbol * indicates a significant difference (measured by the
Wilcoxon test) with respect to the above row value. It is observed that second degree
polynomials give the best force estimation performance for calibrated data, while
third degree polynomials give the best estimation results for non-calibrated data. This
may indicate reduced non-linearity in the SEMG-force relationship with calibration.
Table 6.2 shows that 20 memory lags (∼ 20 ms) for concentric and 10 memory lags
(∼ 10 ms) for eccentric data led to lowest estimation errors. This implies an EMD
close to isometric contractions previously reported [37] for concentric contractions,
but a lower EMD for eccentric contractions. Similar findings have been reported in
the literature [13].
6.3.2
Varying-force, varying-velocity trials
SEMG-force models were obtained for the varying force-varying velocity trials where
there are fewer constraints on the elbow joint angle, contraction level and velocity.
The PCI model parameters obtained from the previous analysis for concentric contractions (2nd degree polynomial and 20 memory lags) were used. Model training
and testing were done using a single SEMG channel (electrode 2). Different segment
lengths of the data were used to train the model and the model was tested using the
remaining data. The %RMSE results are shown in Figure 6.6.
CHAPTER 6. DYNAMIC FORCE ESTIMATION
105
%RMSE vs Percentage of data used for training
NC
CPWL
80
70
%RMSE
60
50
40
30
20
0
10%
20%
30%
40%
50%
60%
70%
Figure 6.6: Distribution of 100 %RMSE values for models trained with different data
segment lengths for both calibrated (solid) and non-calibrated (dashed)
data. The lowest error is observed for models trained using 50% of the
data for when calibrated and 60% when not calibrated.
The average and standard deviation of the velocity and force were calculated over
the duration of each training and test segment. The results presented in Table 6.3
show that when 40% or more of the data are used for training, mean and standard
values of force and velocity are in the same range for the training and test data.
It is observed that using 50% and 60% of the data for training the PCI models
led to the lowest force estimation errors for NC and CP W L , respectively. Although in
some cases the models generated using CP W L data resulted in lower force estimation
error, there is no significant improvement in CP W L versus NC results. This may
be attributed to the higher variability of the data which could contribute to greater
non-stationarity.
CHAPTER 6. DYNAMIC FORCE ESTIMATION
106
Table 6.3: The mean and standard deviation of the 100 % RMSE values for models trained with different percentages of the varying force-varying velocity
data. * indicates a significant difference wrt the value in the row above.
The significance level was adjusted by the number of repeated measures
(0.05/8).On the right hand side of the table the mean (std) of velocity and
force are compared for training and test data.
%
%RMSE
NC
Velocity
Force
CP W L
Train
Test
Train
Test
10 65.4 (15)
62.8 (17.6)
28(20)
72(24)
2.9(1.1)
5.4(2.8)
20 58.7 (14.9)*
49.7 (23.9)*
55(24)
71(23)
4.6(2.4)
5.2(2.7)
30 51.7 (16.3)*
47 (18.2)*
61(23)
70(23)
4.9(2.7)
5.2(2.6)
40 46.5 (13.5)*
40.3 (12.9)*
69(23)
67(25)
5.2(2.8)
5.1(2.6)
50 39.2 (14.8)*
39 (13.7)
69(24)
67(26)
5.1(2.8)
5.2(2.6)
60 35.4 (15.1)* 33.3 (13)*
69(23)
66(26)
5.1(2.6)
5.2(2.7)
70 35 (14.3)
37.1 (16.5)*
69(22)
64(26)
5.1(2.6)
5.1(2.7)
80 38.9 (16.2)*
42.5 (16)*
68(22)
67(25)
5(2.6)
5.3(2.8)
The varying force-varying velocity data were used to compare the performance
of the PCI model and a FOS model in which dynamic elements are not explicitly
incorporated in the model. The list of the FOS candidate functions can be found
in Appendix C. In Figure 6.7 the distribution of the results for PCI and FOS models trained and evaluated with the varying force-varying velocity data are shown.
It is evident that these estimation results are not as promising as those for varying force-constant velocity data. This can be due to the addition of other factors
such as acceleration which affect the SEMG-force relationship. Better force estimation results may be obtained by providing signals such as acceleration to the model.
CHAPTER 6. DYNAMIC FORCE ESTIMATION
107
Significantly better performance is obtained using PCI modeling (p < 0.01). This
is further evidence of the superiority of a PCI model over FOS in dealing with the
dynamic situation [37].
FOS vs PCI
80
%RMSE
70
60
50
40
30
20
FOS
PCI
Figure 6.7: Boxplots comparing distribution of 100 %RMSE values for models trained
and evaluated with FOS and PCI.
In the next analysis, all 12 SEMG channels in addition to joint angle and the
velocity signals were used as inputs to the PCI model. In the first case the six biceps
and six triceps SEMG channels were averaged to represent the biceps and triceps
brachii muscle activity and used as input to the model. In the second case all 12
SEMG channels were used as input to the model. Figure 6.8 shows the distribution
of % RMSE values for the following four cases: 1) multi-channel SEMG non-calibrated
(MN) 2) multi-channel SEMG calibrated using values from PWL interpolation (MC)
3) averaged SEMG non-calibrated (AN) 4) averaged SEMG calibrated using values
from PWL interpolation (AC). In general calibration improved the results of force
estimation. The MC data resulted in lowest % RMSE values. For non-calibrated data
the performance of the multi-channel PCI model in force estimation was significantly
better than the model using averaged data (p < 0.01). However, for calibrated data,
although a lower error was achieved for AC, the difference between AC and MC is
CHAPTER 6. DYNAMIC FORCE ESTIMATION
108
not significant (p > 0.05).
70
%RMSE
60
50
40
30
20
10
MN
MC
AN
AC
Figure 6.8: Distribution of % RMSE values for using: 1) multi-channel SEMG noncalibrated (MN) 2) multi-channel SEMG calibrated 3) averaged SEMG
non-calibrated (AN) 4) averaged SEMG calibrated (AC).
The PCI models using the MN and MC data were analyzed to determine which
inputs were more frequently chosen to form the cascades. Since the maximum number
of allowed cascades (70) always stopped the training process, an equal number of
cascades were included for both MN and MC (70x10). The inputs were selected
and tested at random; therefore, the maximum number of times each input could be
selected was 700. The frequency of selected inputs is shown in Figure 6.9.
CHAPTER 6. DYNAMIC FORCE ESTIMATION
109
100
90
80
70
60
50
Non-calibrated
40
Calibrated
30
20
10
0
b1 b2 b3 b4 b5 b6 t1 t2 t3 t4 t5 t6 ja vel
Figure 6.9: The number of the times the inputs to the PCI were selected in the models
for non-calibrated and calibrated data. b1-b6 are SEMG channels 1 to
6 obtained from biceps brachii muscle. t1-t5 are SEMG channels 1 to 6
obtained from triceps brachii muscle. ja and vel represent joint angle and
velocity.
It is observed that joint angle was chosen as an input more frequently for the
non-calibrated data. Again, this is evidence that calibration does reduce joint angle dependency. As well, a more uniform selection of the inputs is evident for the
calibrated data especially in locations 4, 5 and 6. This may be due to the effect
of calibration on SEMG channels affected by IZ shift during the course of contraction. IZ shift affects the SEMG recording from each location differently i.e. there
should be a location (e.g., location 4) for which the recording is less influenced by
IZ shift and ,consequently, is superior to the others to be used for force estimation
using non-calibrated data. We believe that calibration reduces the sensitivity of the
SEMG-force estimation to the recording location by lowering the effects of IZ shift.
CHAPTER 6. DYNAMIC FORCE ESTIMATION
6.4
110
Summary
Applicability and performance of angle-based SEMG calibration and PCI modeling in
dynamic contractions of the elbow were assessed using single and multi-channel SEMG
recordings from the biceps and triceps brachii. Angle-based calibration reduced the
dependency of the SEMG-force relationship on joint angle. This is achieved by compensating for angle-dependent factors such as varying force-length, moment arm and
IZ shift under the recording site, which affect the force estimation results in dynamic
contractions. Improved force estimation results were achieved using SEMG calibration in dynamic contractions under constant velocity and constant force conditions.
Lower force estimation errors were obtained for concentric data, which may be
due to the presence of more non-linearity in eccentric contractions as reported in
the literature [22]. As well, different MU activation patterns have been reported
for concentric and eccentric contractions [22, 48, 60, 63]. Additionally, our results
indicate that the EMD for concentric contractions is similar to that for isometric
data; EMD for eccentric contractions is lower than that for isometric contractions,
similar to findings reported previously [13].
The improvement due to calibration was less significant in the free hand case where
a range of joint angle velocity and muscle contraction level was involved rather than
a few discrete levels. Under these conditions, the SEMG signals were nonstationary,
and the varying velocity and force affected the accuracy of force estimation. The
use of multiple SEMG channels led to lower estimation error in the free hand case.
As well, analysis of the channels selected by the PCI model confirmed a significant
decrease in selection of joint angle with calibrated data showing less joint angle dependency. More uniform selection of the inputs for the calibrated data can be a sign of
CHAPTER 6. DYNAMIC FORCE ESTIMATION
111
reduced sensitivity of the SEMG-force estimation to the recording location. The PCI
model showed superior performance compared to FOS model which could be linked
to its dynamic nature and capability in capturing the dynamics of the SEMG-force
relationship.
Chapter 7
Force Estimation Using Integrated
SEMG SMP signal
7.1
Overview
The focus of the work in Chapters 4 through 6, was to obtain better force estimates
by improving the SEMG amplitude estimate and applying a PCI modeling technique
using only SEMG signals. In this chapter, we explore the use of SMP signals as an
additional source of information to the SEMG for force estimation. It is hypothesized
that SMP signals will vary with changes in muscle tension and track changes in muscle
shape which vary with joint angle and contraction level. Unlike SEMG, SMP signals
are not affected by physiological (MUAP phase cancelation and the size principal) and
non-physiological (relative location of the electrode and signal sources and IZ shift
with changing force and/or joint angle) factors which affect the linearity of SEMGbased force estimation. Therefore, the integration of SMP and SEMG signals may
provide better force estimates.
112
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL113
SEMG and SMP data were obtained from four recordings of isometric contractions
of the biceps and triceps brachii muscles using two sensor patches each combining six
collocated SEMG-SMP sensors. The first three recordings were used for normalization
purposes. The fourth recording consisted of three repetitions (trials) which were split
into ramp data and isometric, isotonic data.
The linearity of the relationship between SEMG, SMP, force and joint angle was
assessed using cross-correlation analysis. Principal component analysis (PCA) was
done to find a subset of the inputs that can be used to accurately estimate the
measured force at the wrist. FOS-based force estimation models were derived for
different configurations of the input signals, where the total set of input signals comprised SEMG and SMP records from six locations on the two muscles and elbow joint
angle.
In Section 7.2, the data collection procedure and the proposed method are presented. Results of the study and discussion of the observations are given in Section
7.3. Section 7.4 summarizes the contributions of this study.
7.2
7.2.1
Methods
Data Collection
Data were collected from subjects with no known neuromuscular deficit and all subjects provided informed consent and the study was approved by the Health Sciences
Research Ethics Board, Queen’s University. Data were collected from 8 subjects in
four recordings with 5 to 15 minutes rest between recordings in each session. SEMG
and SMP data were recorded using the integrated sensor patches described in chapter
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL114
3. Sensor placement was done as described in chapter 6. Figure 7.1 shows a flowchart
of the data collection procedure and how each recording was used for processing.
Subject # x
(x=1 to 8)
Rest at 8 JA
(recording 1)
MVC at 8 JA biceps
(recording2)
MVC at 8 JA triceps
(recording 3)
Make target
force profile
Optimum input
subset using PCA
FOS models using
a subset of inputs
Ramp data
(varying force)
Isometric
Isotonic data
Isometric trials
(recording 4)
Normalization
Correlation
analysis
FOS models
using all inputs
Figure 7.1: Data collection and processing flowchart.
In the first recording SEMG and SMP data were collected during rest at 8 joint
angles from 0 to 105 degrees in 15 degree intervals. In the second recording SEMG
and SMP data from the biceps brachii and wrist force were recorded during flexion
MVC contractions at all joint angles. In the third recording the MVC procedure was
repeated for extension contractions of the triceps brachii muscle. From the two MVC
recordings force load equivalent to 50 %M V C was calculated for both flexion and
extension at each joint angle. These values were used to create a force profile for
each subject as shown in Figure 7.2. The last recording consisted of three repetitions
(trials) of the force profile with 10 minutes rest between each trial. In each trial the
force profile and measured wrist force were displayed on a computer monitor and
subjects were asked to follow the force profile. By doing so, each subject completed
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL115
consecutive 50 %M V C flexion and extension contractions at all 8 joint angles. Each
contraction consisted of three segments: 1- an isometric rest (0%MVC) to 50%M V C
ramp-up contraction with a constant slope; 2- a 5 second isometric, isotonic contraction at 50%MVC; 3- a ramp down from 50%M V C to rest. The data collected in
the three trials of the last recording were segmented based on joint angle and then
normalized with respect to values measured for rest and MVC contractions at the
corresponding joint angle. The normalization was performed according to following
equation:
Xθni =
Xθi
XθMi V C
− XθRest
i
(7.1)
The normalized data for individual trials were then segmented based on the type
of contraction. Data for the isometric, isotonic contractions at all joint angles were
extracted and concatenated. Ramp-up and ramp-down segments were also concatenated; this is referred to as ramp data hereafter.
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL116
Figure 7.2: A sample force profile. The profile comprises a flexion (positive) and extension (negative) portion at the eight joint angles. Joint angle increases
from 15◦ to 105◦ at 15◦ intervals, from left to right on the plot. The peak
forces are at 50% MVC for each joint angle.
7.2.2
Correlation analysis between Input and Output Modalities
It is hypothesized that SMP signals provide useful information, in addition to SEMG,
for estimating the muscle force, as the SMP signals will vary with muscle tension
and changing muscle shape which varies with joint angle and contraction level. The
change in SMP with joint angle was investigated for different locations on the biceps
and triceps brachii.
The SMP data points from the five second isotonic, isometric contraction at each
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL117
joint angle from each sensor on the biceps and triceps brachii were averaged resulting
in 8 values per subject per sensor. These averaged SMP values for all subjects were
grouped based on their locations and joint angle to assess the changes in SMP with
the location and the joint angle, correspondingly.
To investigate the degree of linearity in the relationship between input (SMP,
SEMG) and output (force induced at the wrist) signals, the SEMG and SMP signals
recorded from biceps brachii during isometric contractions were correlated with force
at each recording location and each joint angle. The maximum values of the crosscorrelations were used as a measure of the linearity between the two modalities. These
values were grouped based on sensor location and joint angle to assess the change in
linearity of the SEMG-force and SMP-force relationships at different locations and
joint angles.
7.2.3
Principal Component Analysis (PCA)
PCA maps a dataset with many variables to a smaller set of derived variables. Mathematically, PCA is an orthogonal linear transformation that maps the dataset to a
new coordinate system such that the greatest variance by any projection of the data
belongs to the first coordinate (the first principal component), the second greatest
variance on the second coordinate, and so on. In other words, PCA re-distributes
the total variance in the data in such a way that first K components explain as much
of the total variance as possible. PCA is mainly used for dimensionality reduction
where there are many independent variables which are highly correlated, as correlated
variables affect the accuracy and reliability of models.
If we define X, an n x 6 data matrix, where n data points from each of the six
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL118
recording locations are stored in the rows, the PCA transformation Y is given by:
Y T = XT W
(7.2)
where W is the m x m matrix of eigenvectors of the covariance matrix XX T . If we
substitute matrix X T with its singular value decomposition:
X = W ΣV T
(7.3)
we have:
T
Y T = (W ΣV T ) W = V ΣT
(7.4)
where the matrix Σ is an m x n rectangular diagonal matrix with non-negative real
numbers on the diagonal, and V is the n x n matrix of eigenvectors of X T X.
Each row of Y T is a linear transformation of the corresponding row of X T . The
first column of Y T is made up of the “scores” of the cases with respect to the “principal” component, the next column has the scores with respect to the “second principal” component, and so on. These scores represent the weight of each channel in
constructing the principal modes.
7.2.4
Force Estimation Using the Integrated Sensor
Each dataset (isometric or isometric, isotonic) included 12 SEMG channels, 12 SMP
channels, and 1 joint angle signal. The purpose of this analysis is to find a subset of
these inputs that can be used to accurately estimate the measured force at the wrist.
PCA was applied to four sets of data i.e. 6 SEMG channels from the biceps brachii,
6 SEMG channels from the triceps brachii, 6 SMP channels from biceps brachii and
6 SMP channels from triceps brachii. Each channel was used as a variable in the
PCA and each data point was treated as an observation. The PCA converted the
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL119
six variables into a set of values of linearly uncorrelated variables called principal
components. The first three principal components and the projection of the input
channels on these components were considered for further analysis. The coefficients
of the input constructing the principal components were analyzed to determine which
inputs had the highest contribution. These inputs were then selected to train FOS
models.
An initial analysis to predict the wrist force was done using a subset of inputs
in the ramp data from two randomly selected subjects to determine the optimum
number of functions to include in the FOS model for a candidate pool of 243 functions
(See Appendix C for a list of functions). Then, three FOS models were trained per
subject using the 3 isometric force varying trials collected in recording 4. These
models were evaluated using the leave one out method (3 models each evaluated by
2 trials) resulting in 6 %RM SE evaluation values per subject.
Lastly, the optimum number of functions to be included in the FOS models was
determined using all the possible inputs in the ramp data from two randomly selected subjects. Since FOS models were trained and evaluated having all the possible
channels as input, 647 functions were included in the pool (See Appendix C for a
list of functions). The results were compared with those of previous FOS models.
A histogram analysis was done on the selected inputs to find out which inputs were
chosen more frequently and whether these were the same inputs as those found in the
initial analysis.
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL120
7.3
7.3.1
Results and Discussion
SMP variations with the joint angle
The SMP signal was analyzed for the isometric, isotonic portion of the data to investigate how SMP changes with joint angle.
The variation in SMP recorded over the biceps brachii with joint angle is presented
in Figure 7.3 where the distribution of averaged normalized SMP data points are
shown for the isometric, isotonic flexion data at each of the eight joint angles for
each of the six locations averaged across subjects. The SMP increases with joint
angle at all locations for the biceps brachii. This was expected since with increasing
joint angle the muscle bulk pushes the sensor patch against the blood pressure cuff
and increases the amplitude of the SMP signal. Figure 7.4 shows the distribution
of averaged normalized SMP data points from the triceps brachii for the isometric,
isotonic extension data at each of the eight joint angles and each of the six locations
averaged across subjects. There is no overall trend in SMP with joint angle in this
case. This may be due to anatomical differences between the biceps and triceps
brachii and that the muscle bulk of the triceps is not shifting under the sensor to
the same extent as for the biceps. Cross-talk from the changing shape of the biceps
brachii, which is transferred through the non-elastic material in the sensor patch and
cuff may also contribute to the large variance in Figure 7.4.
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL121
BP Location#6
1.5
1
1
0.5
0.5
0
0
0
2
4
6
BP Location#4
1.5
1
0.5
0
-0.5
0
2
4
6
-0.5
8
8
Normalized SMP wrt max value for each sensor
-0.5
Normalized SMP wrt max value for each sensor
BP Location#5
1.5
0
2
1
0.5
0
-0.5
0
2
1
1
0.5
0.5
0
0
4
6
Joint angle
4
6
8
BP Location#1
1.5
2
8
BP Location#3
BP Location#2
0
6
1.5
1.5
-0.5
4
8
-0.5
0
2
4
6
Joint angle
8
Figure 7.3: Distribution of the averaged normalized SMP data points from the biceps
brachii for isometric data at each of the eight joint angles. Labels on the
x-axis represents the joint angles from 15◦ (JA1) to 105◦ (JA8) at 15◦
intervals.
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL122
TP Location#6
1.5
1
1
0.5
0.5
0
0
0
2
4
6
TP Location#4
1.5
1
0.5
0
-0.5
0
2
4
6
-0.5
8
8
Normalized SMP wrt max value for each sensor
-0.5
Normalized SMP wrt max value for each sensor
TP Location#5
1.5
0
2
1
0.5
0
-0.5
0
2
1
1
0.5
0.5
0
0
4
6
Joint angle
4
6
8
TP Location#1
1.5
2
8
TP Location#3
TP Location#2
0
6
1.5
1.5
-0.5
4
8
-0.5
0
2
4
6
Joint angle
8
Figure 7.4: Distribution of the averaged normalized SMP data points from triceps
brachii for isometric data at each of the eight joint angles. Labels on the
x-axis represents the joint angles from 15◦ (JA1) to 105◦ (JA8) at 15◦
intervals.
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL123
7.3.2
SMP variations with force
As noted previously muscle shape and tension (represented by SMP signals) change
with contraction level (represented by the measured force). Using the ramp data
for the biceps and triceps brachii, where a range of force levels from 0%M V C to
50%M V C were included, the variation of the recorded SMP signals and the contraction level (represented by the measured force at the wrist) was investigated using
cross-correlation.
Figure 7.5 shows the distribution of the maximum cross-correlation values between
SMP and measured force at the wrist for ramp data from the biceps and triceps
brachii for all subjects, locations at all joint angles (p < 0.05). Eight maximum crosscorrelation values from 8 ramp segments available at each trial were obtained. It can
be observed that SMP from the biceps brachii is more linearly related to the wrist
force compared to triceps brachii. Again, this can be due to the different anatomy of
the triceps brachii and the likely presence of cross-talk.
Correlation
1
0.9
0.8
0.7
Max Xcor
0.6
0.5
Biceps
Triceps
Figure 7.5: Cross-correlation analysis between SMP and the measured force at wrist
for ramp data for biceps and triceps brachii for all subjects.
The rest of the correlation analysis was performed on the SMP recorded from
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL124
the biceps brachii since more robust results were observed. Figure 7.6 shows the
distribution of maximum cross-correlation values between SMP and force signals for
each location on the biceps brachii over all joint angles, trials and subjects and pvalues from the Wilcoxon test comparing the data in each of the boxplots are given
in Table 7.1. The significance level of the test was adjusted based on the number of
repeated measures(0.05/6).
1
Correlation
0.95
0.9
0.85
0.8
0.75
L11
L2
2
L3
3
L4
4
L5
5
L6
6
Figure 7.6: Distribution of maximum cross-correlation values between SMP and force
signals for each location (L1 to L6) over all joint angles, trials and subjects
for ramp data from biceps brachii.
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL125
Table 7.1: p-values from the Wilcoxon test comparing the data in each of the boxplots
shown in Figure 7.6. The significance level of the test was adjusted based
on the number of repeated measures(0.05/6).
p-value L1
L2
L3
L4
L5
L6
L1
0
0
0
0.01
0
NA
0.01
0
0
0
NA
0
0
0.01
L2
L3
NA
L4
NA 0.01
0
L5
NA
0
L6
NA
Among locations 1 to 3 and 4 to 6, the middle sensor (sensors 2 and 5) had the
highest SMP-force correlation. This could be due to more prominent bulging of the
biceps brachii under locations 2 and 5 compared to other locations. A similar trend in
SMP-force linearity is observed from location 1 to 3 and 4 to 6. The repeated pattern
may suggest that the SMP data collected from locations 1, 2 and 3 (the top row of
sensors) are correlated with data recorded from locations 4, 5 and 6 (the bottom row
of sensor). One factor that may have caused the apparent correlation between signals
from adjacent locations is the blood pressure cuff used for data collection (see chapter
3), where the cuff may transfer the pressure due to bulging of the muscle from one
location to another.
To analyze the variation in linearity of the SMP-force relationship due to varying
joint angle the maximum cross-correlation values between SMP and force were regrouped. Figure 7.7 shows the maximum cross-correlation values between SMP and
force signals for each joint angle over all locations, trials and subjects and Table 7.2
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL126
gives the p-values from the Wilcoxon test comparing the data in each of the boxplots.
1
Correlation
0.95
0.9
0.85
0.8
0.75
0.7
JA1
JA2
JA3
JA4
JA5
JA6
JA7
JA8
Figure 7.7: Distribution of maximum cross-correlation values between SMP and force
signals for each joint angle over all locations, trials and subjects for ramp
data. Labels on the x-axis represents the joint angles from 15◦ (JA1) to
105◦ (JA8) at 15◦ intervals.
Table 7.2: Mutual p-values for the distribution of maximum cross-correlation values
between SMP and force signals for 8 joint angles as shown in Figure 7.7.
p-value JA1
JA2
JA3
JA4
JA5
JA6
JA7
JA8
JA1
0
0
0
0
0
0
0
NA
0.02
0
0
0
0
0
NA
0.16
0.05
0
0
0
NA
0.57
0.03
0
0.08
NA
0.08
0.01
0.22
NA
0.29
0.61
NA
0.12
JA2
JA3
JA4
JA5
JA6
JA7
JA8
NA
NA
The highlighted p-values in the Table 7.2 represent a significant difference in mean
values of the two compared groups. The significance level was adjusted based on the
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL127
number of repeated measures(0.05/8). In general, an increase in the linearity of the
SMP-force relationship was observed with increasing joint angle (from more extended
to more flexed positions). This may be because in more flexed joint angles the bulging
of the biceps brachii generates a pressure on the SMP sensors, which acts as a bias
and shifts the pressure into the linear range of the SMP sensors.
7.3.3
SEMG-force linearity analysis
Cross-correlation between SEMG amplitudes from the biceps brachii and force at
the wrist for each location over the full ramp dataset including all subjects and joint
angles were calculated. The maximum cross-correlation value between the two signals
was used as a measure of the linearity of their relationship. Figure 7.8 shows the
distribution of maximum cross-correlation values and Table 7.3 shows the p-values
from the Wilcoxon test comparing the data in each of the boxplots. The significance
level of the test was adjusted based on the number of repeated measures(0.05/6).
Correlation
0.99
0.98
0.97
0.96
p=0
L1
p=0.002
L2
p=0
L3
p=0
L4
p=0
L5
L6
Figure 7.8: Distribution of maximum cross-correlation values between SEMG and
force signals for each location (L1 to L6) over all joint angles, trials and
subjects.
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL128
Table 7.3: p-values from the Wilcoxon test comparing the data in each of the boxplots
for 6 locations shown in Figure 7.8. The significance level of the test was
adjusted based on the number of repeated measures(0.05/6).
p-value L1
L2
L3
L4
L5
L6
L1
0
0
0.49
0
0
NA
0
0
0.35
0
NA
0
0
0.12
NA
0
0
NA
0
L2
NA
L3
L4
L5
L6
NA
The linearity between SEMG and force was highest in locations 3 and 6 (see Figure
6.1). An increasing trend in linearity is observed from location 1 to 3 and also 4 to 6.
The repeated pattern may suggest that the SEMG data collected from locations 1,
2 and 3 are correlated with data recorded from locations 4, 5 and 6. This is evident
in Table 7.3 where the difference in mean for the data from location pairs (L1, L4),
(L2, L5) and (L3, L6) was not statically significant.
To analyze the variation in linearity of the SEMG-force relationship with varying
joint angle the maximum cross-correlation values between SEMG and force were regrouped to show their distribution for each joint angle over all locations, trials and
subjects. Figure 7.9 shows the maximum cross-correlation values between SEMG and
force signals for each joint angle over all locations, trials and subjects and Table 7.4
presents the mutual p-values from Wilcoxon test comparing the data in each of the
boxplots in Figure 7.9. The significance level of the test was adjusted based on the
number of repeated measures(0.05/8).
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL129
0.995
Correlation
0.99
0.985
0.98
0.975
0.97
0.965
JA2
JA1
1
JA3
3
2
JA4
4
JA5
5
JA6
6
JA7
7
JA8
8
Figure 7.9: Distribution of maximum cross-correlation values between SEMG and
force signals for each joint angle over all locations, trials and subjects.
Labels on the x-axis represents the joint angles from 15◦ (JA1) to 105◦
(JA8) at 15◦ intervals.
Table 7.4: p-values from the Wilcoxon test comparing the data in each of the boxplots
for 8 joint angles shown in Figure 7.9. The significance level of the test
was adjusted based on the number of repeated measures(0.05/8)
p-value JA1
JA2
JA3
JA4
JA5
JA6
JA7
JA8
JA1
0.21
0.34
0.06
0
0
0.03
0
NA
0.02
0
0
0
0
0
NA
0.29
0.01
0
0.14
0.03
NA
0.08
0.01
0.56
0.30
NA
0.33
0.35
0.42
NA
0.08
0.08
NA
0.79
JA2
JA3
JA4
JA5
JA6
JA7
JA8
NA
NA
From Table 7.4 it is evident that, while a significant change in linearity occurs
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL130
between some of the joint angles (p − value < 0.006), no specific pattern in SEMGforce linearity (either increasing or decreasing) is observed across joint angles (JA1
to JA8).
7.3.4
Training FOS models with a subset of the inputs
Different subsets of the inputs were used as inputs to train FOS models using the
ramp segments of the recorded trials for each subject. These subsets were: i) SEMG
recordings from all six locations on biceps and triceps brachii and joint angle; ii) SMP
recordings from all six locations on biceps and triceps brachii and joint angle. Three
FOS models were trained using the ramp data in each of the three trials and each
model was evaluated with the ramp data from the remaining two trials resulting in
3x2 %RM SE values for each subject. Seven FOS candidate functions were added
in both cases. Table 7.5 summarizes the modeling results for the different input
modalities.
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL131
Table 7.5: Mean ± standard deviation of %RM SE values for all results obtained
from different input modalities.
Methods
6 SEMG
6 SMP
Sub1
6.04 ± 1.05
50.43 ± 42.89
Sub2
11.80 ± 4.01
18.90 ± 5.07
Sub3
44.83 ± 18.90
71.57 ± 22.59
Sub4
16.10 ± 8.83
94.47 ± 40.56
Sub5
11.95 ± 2.71
95.15 ± 53.34
Sub6
14.18 ± 3.52
74.95 ± 34.49
Sub7
16.21 ± 3.65
93.84 ± 77.56
Sub8
13.93 ± 6.99
8.72 ± 1.11
Average (all)
16.88 ± 13.42
63.50 ± 50.48
Results from SEMG recordings were superior to those of SMP recordings.
7.3.5
Using PCA to select a subset of the inputs
Figure 7.10 shows a histogram of the coefficients of the channels constructing the
first three principal components with highest variance for SEMG recordings from
biceps and triceps brachii. Each plot represents the distribution of coefficients of
each location (L1 to L6) used for constructing the first three principal components
with highest variance for biceps brachii (plots on the left) and triceps brachii (plots
on the right). Figure 7.11 shows the same plots for SMP recordings.
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL132
L6
L5
L4
L3
L2
L1
SEMG data from biceps brachii
20
10
0
20
10
0
20
10
0
20
10
0
20
10
0
20
10
0
SEMG data from triceps brachii
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
0.8
1
10
5
0
10
5
0
10
5
0
10
5
0
10
5
0
10
5
0
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
0.8
1
L1
10
5
0
L2
10
5
0
L3
10
5
0
L4
10
5
0
L5
10
5
0
L6
Figure 7.10: Histogram of the coefficients of the channels constructing the first three
principal components for SEMG recordings from biceps (left) and triceps
brachii (right) muscles.
10
5
0
SMP data from biceps brachii
0
0.2
0.4
0.6
0.8
0
0.2
0.4
0.6
0.8
0
0.2
0.4
0.6
0.8
0
0.2
0.4
0.6
0.8
0
0.2
0.4
0.6
0.8
0
0.2
0.4
0.6
0.8
10
5
0
10
5
0
10
5
0
10
5
0
−1
10
5
0
10
5
0
SMP data from triceps brachii
−0.5
0
0.5
1
−0.5
0
0.5
1
−0.5
0
0.5
1
−0.5
0
0.5
1
−0.5
0
0.5
1
−0.5
0
0.5
1
Figure 7.11: Histogram of the coefficients of the channels constructing the first three
principal components for SMP recordings from biceps (left) and triceps
brachii (right) muscles.
In general, it is evident that locations 4, 5, and 6 had the highest coefficients
among all the locations. Therefore, these locations were used for further analysis.
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL133
In order to find the optimum number of FOS functions to include in the model, an
initial investigation was performed on the data from two randomly selected subjects.
SEMG, SMP from locations 4, 5 and 6 on the biceps and triceps brachii, and joint
angle (13 inputs) from the ramp data were used to train three FOS models (1 model for
each of the three trials collected in session 4). Figure 7.12 shows the %RM SE results
for different numbers of functions included in the FOS model. It is observed that 30
functions had the lowest %RM SE error for the two selected subjects. Therefore, this
was used for our analysis for the rest of the experiments. Table 7.6 gives the mean
and standard deviation of 6 %RM SE results for the three FOS models trained and
evaluated with the ramp dataset.
%RMSE estimation error
100
95
90
85
80
75
70
8
12
16
19
22
25
Number of functions included in the model
30
35
40
Figure 7.12: Results of the analysis performed to determine the optimum number of
functions to include in the FOS model. SEMG and SMP ramp data from
locations 4, 5 and 6 on the biceps and triceps brachii, and joint angle
(13 inputs) were used to train and evaluate the models. The points are
connected with straight lines to visualize the trend of decrease in the
error. Each point represent an average of 6 %RM SE evaluation values
obtained from two subjects.
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL134
Table 7.6: The mean and standard deviation of 6 %RM SE results for the three FOS
models trained and evaluated with SEMG and SMP ramp data from locations 4, 5 and 6 on the biceps and triceps brachii, and joint angle (13
inputs)
Subjects S1
S2
S3
Mean
8.01
11.59
STD
2.44
5.53
S4
S8
S1-8
13.96 10.45 10.69 21.83 13.43
13.08
12.88
2.00
11.17
6.58
3.69
S5
6.74
S6
6.76
S7
5.04
Figure 7.13 shows a histogram of the selected inputs. Each number on the X axis
represents a function in the pool of available FOS candidate functions, where the list
of the functions can be found in Appendix C. The four most selected functions were
input signals in the following order: i) SEMG from triceps brachii ii) SEMG from
Number of times that each
function was selected
biceps brachii iii) SMP from biceps and iv) SMP from triceps.
40
20
30
15
20
10
5
10
0
100
100
150
150
200
200
250
250
300
300
350
350
Index of selected functions
Portion 1
Portion 2
Figure 7.13: Histogram of the functions selected in the FOS models for all subjects.
Each number on the x-axis represents an index of one of the FOS functions in the pool.
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL135
7.3.6
Training with all inputs
In order to evaluate the selected inputs compared to selection of other inputs, we performed another analysis where all the available SEMG and SMP channels were given
to the FOS models as inputs. Figure 7.14 shows the average %RM SE estimation
error versus the number of functions included in the model for two subjects, where
all 25 inputs (12 SEMG and 12 SMP signals from biceps and triceps brachii and the
joint angle) were given to the model. It is observed that 16 functions gave the lowest
averaged %RM SE values for the two subjects. Therefore, this parameter was set to
%RMSE estimation error
16 for the rest of analysis in this section.
14
12
10
8
6
8
12
16
19
22
Number of FOS functions in the model
Figure 7.14: Results of the analysis performed to determine the optimum number of
functions to include in the FOS model. SEMG and SMP ramp data from
all 6 locations (L1-L6) on the biceps and triceps brachii, and joint angle
(25 inputs) were used to train and evaluate the models. The points are
connected with straight lines to visualize the trend of decrease in the
error. Each point represent an average of 6 %RM SE evaluation values
obtained from two subjects.
Table 7.7 shows the mean and standard deviation of 6 %RM SE results for the
three FOS models trained and evaluated with the ramp dataset having all 25 channels
as input.
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL136
Table 7.7: The mean and standard deviation of 6 %RM SE results for the three FOS
models trained and evaluated with the ramp dataset having all 25 channels
(6 SEMG, 6 SMP and the joint angle) as input. Last row (on the left)
shows the previous results where only locations L4, L5 and L6 were used.
Subjects S1
S2
S3
S4
S5
S6
S7
S8
S1-8
S1-8
(L4,L5,L6)
Mean
7.63 7.56 8.18
6.67 9.50
13.29
10.43
7.16 8.80
12.88
STD
4.02 3.61 8.50
4.32 2.40
9.22
1.82
6.85 4.68
6.58
The last two columns of the Table 7.7 show the mean and standard deviation of the
results averaged over all subjects for the case of using all inputs and using only three
selected inputs. It is evident that the results are improved by using all possible inputs.
Figure 7.15 shows the number of times that each FOS function was selected in the
models generated for all subjects. Each number on the x-axis represents an index of
one of the FOS functions in the pool. The list of FOS functions can be found in Table
C.1 of Appendix C. The maximum number of times a function could be selected was
equal to the number of trained models for all subjects which was 24 (8x3).
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL137
Number of times that each
function was selected
20
15
10
5
0
100
200
300
400
500
600
700
Index of the selected functions
Figure 7.15: The number of times that each FOS function was selected in the models
generated for all subjects for the case where SEMG and SMP ramp data
from all 6 locations (L1-L6) on the biceps and triceps brachii, and joint
angle (25 inputs) were included in the model.
Table 7.8 lists the functions which were selected more than 5 (20% of total possible)
times in descending order.
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL138
Table 7.8: List of the functions selected more than 5 (20% of total possible) times in
descending order.
Rank Function name
Number chosen
1
SEMG from Biceps brachii from L4
21
2
SEMG from Biceps brachii from L2
19
3
SEMG from Triceps brachii from L5
19
4
SEMG from Biceps brachii from L3
13
5
SMP from Biceps brachii from L4
12
6
SMP from Triceps brachii from L5
12
7
SEMG from Biceps brachii from L5
11
8
SMP from Triceps brachii from L3
11
9
SMP from Triceps brachii from L6
11
10
SEMG from Biceps brachii from L6
8
11
SEMG from Triceps brachii from L4
8
12
SMP from Biceps brachii from L2
8
13
SMP from Biceps brachii from L6
8
14
SMP from Triceps brachii from L1
8
15
SEMG from Triceps brachii from L3
7
16
SMP from Triceps brachii from L4
7
17
SMP from Biceps brachii from L3
6
18
SEMG from Triceps brachii from L1
5
19
SMP from Biceps brachii from L4
5
It is observed that among all possible functions in the pool, mostly functions
without modifying angle-dependant terms such as cos(θ) and sin(θ) were selected.
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL139
The selected functions for all models were also analyzed to find out which locations
were selected more often. Table 7.9 shows the the number of times that each signal
(SEMG or SMP) from different locations (L1 to L6) on the biceps and triceps brachii
were selected. It is evident that locations 4, 5 and 6 were selected most often. The
same locations were previously selected as optimal subset of inputs using PCA in
Sections 7.3.5.
Table 7.9: The number of times that functions from each location (L1 to L6) were
selected based on their location and type.
7.4
Modalities
LOC1
LOC2
LOC3
LOC4
LOC5
LOC6
Sum
SEMG Bi
12
8
14
24
11
8
77
SEMG Tr
6
7
9
10
9
7
48
SMP Bi
6
11
6
8
16
14
61
SMP Tr
10
2
14
10
16
18
70
Total
34
28
43
52
52
47
256
Summary
The objective of developing and testing enhanced muscle activation sensing was to
include information which was not, or at least less, influenced by physiological (phase
cancelation and size principal) and non-physiological (relative location of electrode
and signal sources and shift in IZ) factors affecting the linearity of the force estimation.
This was accomplished by using two sensor patches each combining six SEMG and
six SMP sensors. Since the SMP signals are not affected by the above-mentioned
factors, they were used as additional inputs to the model.
CHAPTER 7. FORCE ESTIMATION USING INTEGRATED SEMG SMP SIGNAL140
The assumption that the SMP signal is a function of joint angle and contraction
level was verified for the biceps brachii muscle. SMP from the triceps brachii muscle
does not follow a specific pattern in different locations on the muscle. The hypothesis
that SMP is, to some extent, linearly related to contraction level was also validated
for the biceps brachii. The linearity of the SMP-joint angle relationship for the SMP
collected from triceps was significantly less than for the biceps. An issue with the
SMP recordings, especially for the triceps brachii, was the presence of cross-talk
between adjacent recording locations. Use of elastic materials to connect the two
sensor patches for the biceps and triceps and in the cuff may reduce this problem.
The modeling results show that forces are statistically predicted more accurately
using both SEMG and SMP than just using SEMG amplitude data by itself. These
results show that SMP data has the potential to provide additional useful information for force estimation. To reduce the computational cost of adding more inputs
to the system, an optimal subset of the inputs was found by PCA analysis. The
superiority of this subset over the other inputs was validated with an experiment providing all possible inputs to the FOS model. Analyzing the histogram of the chosen
inputs showed that primarily non-modified SEMG and SMP signals were selected to
construct the model.
Chapter 8
Conclusions and Future Work
8.1
Summary and Conclusions
SEMG-force estimation is a non-invasive and inexpensive means of obtaining estimates of individual muscle forces and is of great interest for many different applications. However, the SEMG-force relationship is nonlinear and dynamically changing
due to presence of complicating factors, and thus development of an accurate and
robust force estimation procedure is a challenging problem.
The goal of this research was to develop novel methods to obtain more accurate
and reliable SEMG based muscle force estimates for isometric, isotonic and dynamic
(concentric and eccentric) contractions. This was achieved by proposing a joint angle
based calibration method, utilizing dynamic and non-linear modeling methods including PCI and FOS and using SMP signals as an additional source of information. The
results presented in this thesis provide evidence that the proposed methods are able
to cope with both the non-linearity and dynamics in the SEMG-force relationship
and generate more accurate force estimates.
141
CHAPTER 8. CONCLUSIONS AND FUTURE WORK
142
A shift in the relative location of the IZ and the recording SEMG electrode affects the SEMG amplitude and increases the nonlinearity in the SEMG-force relationship. Closely spaced multi-channel SEMG recordings can be used to locate and
track the IZs. However, they are not computationally efficient and require collection
and processing of many data channels. Thus, there is a need for a standard normalization/calibration protocol that can compensate for the IZ shift with changing
joint angle. A joint angle based calibration procedure is proposed which compensates
for variations in SEMG amplitude due to changes in muscle length, muscle moment
arm and IZ displacement relative to the recording electrodes. Non-parametric FOSbased SEMG-force models were trained and evaluated using both calibrated and
non-calibrated SEMG data. The experimental results show significant improvement
in force prediction with calibration. It was also noted that fewer joint angle dependent nonlinear functions are selected in the models for the calibrated SEMG datasets,
implying more consistency and less dependency on joint angle in modeling the SEMGforce relationship. Investigations using data from additional recording sessions from
a subset of the original subject group, 6 to 12 months after the first session, suggest
the possibility of using a subject’s calibration values for future data recordings. The
calibration procedure is model independent, and can be used with other SEMG-force
modeling techniques.
The use of dynamic linear and static nonlinear models, independently, in SEMGforce modeling has been reported in the literature. These methods lack the ability
to simultaneously capture the dynamics of the system and cope with the inherent
nonlinearities in the SEMG-force relationship. We applied PCI modeling in which
the model structure is a cascade of dynamic linear and static non-linear functions.
CHAPTER 8. CONCLUSIONS AND FUTURE WORK
143
The linear blocks of the PCI structure are able to capture the dynamics of the
SEMG-force relationship by constructing dynamic FIR filters based on the crosscorrelation of the system inputs and output, while the nonlinear blocks model the
nonlinearity of the system. Optimal model parameters were determined by statistical
analysis of the results for a range of parameter values. The final results were compared
to results obtained using FOS with Hill muscle model parameters previously applied
to the same dataset. Improved SEMG-force estimation was achieved using PCI. The
significant difference in results for data recorded on two different days from the same
subjects revealed a high inter-session variability.
Applicability and performance of angle-based SEMG calibration and PCI modeling in dynamic flexion and extension of the elbow were assessed using single and
multi-channel SEMG recordings from the biceps and triceps brachii. Better force estimation results were achieved for dynamic contractions at constant velocity and force
level. Lower force estimation errors were obtained for concentric versus eccentric data,
which may be due to the presence of more non-linearity in eccentric contractions as
reported in the literature [22]. As well, different motor unit activation patterns have
been reported for concentric and eccentric contractions [22, 48, 60, 63]. Additionally, our results indicate that the EMD for concentric contractions is similar to that
for isometric data; EMD for eccentric contractions is lower than that for isometric
contractions, similar to findings reported by [13].
The improvement in force estimation accuracy with calibration was less significant
in the free hand case where subjects randomly moved their forearms within a range
of joint velocity and muscle contraction levels. Under these conditions, the SEMG
signals were non-stationary, and the varying velocity and force affected the accuracy
CHAPTER 8. CONCLUSIONS AND FUTURE WORK
144
of force estimation. However, force estimation was improved with the use of multiple
SEMG channels. Analysis of the channels selected by the PCI model confirmed a
significant decrease in selection of joint angle for the calibrated data indicating less
joint angle dependency. The PCI model showed superior performance compared to
a FOS model which could be linked to its capacity to capture the dynamics of the
SEMG-force relationship. The addition of other signal modalities as inputs to the
force estimator can improve the force estimation accuracy, especially if the additional
signal contains information that cannot be obtained from SEMG recordings. An
example is the contribution of passive forces to the muscle force, which occurs for
muscle lengths greater than the optimal length. It has been claimed that these forces
are reflected in the SMP [112]. Thus, the simultaneous recording of co-located SEMG
and SMP signals provides complimentary information about the generated force.
A novel sensor patch combining six SEMG and six collocated SMP channels was
designed and constructed. The SMP signals are not (or at least are less) influenced by
physiological (phase cancelation and size principal) and non-physiological (IZ shift)
factors affecting the linearity of SEMG-based force estimation. To reduce the computational cost of using the SMP signals as additional inputs to the system, an optimal
subset of the inputs was found using PCA. The superiority of this subset over the
other inputs was shown by training FOS models with all possible inputs and analyzing
the histogram of the chosen inputs. The modeling results show that force prediction
is statistically more accurate using both SEMG and SMP than using only SEMG
amplitude data.
CHAPTER 8. CONCLUSIONS AND FUTURE WORK
8.2
145
Future Work
Our models have been developed and tested using SEMG data obtained from 8 to
10 subjects in a number of experiments. These methods should be evaluated with a
larger number of subjects. As well, increasing the number of recording sessions can
reduce the risk of fatigue, can enable us to include more joint angles in one trial, and
can permit evaluation of the ability of the methods to generalize over experimental
sessions. Also, recording from other upper arm muscles which contribute to flexion
and extension can increase the accuracy of force estimation, and allow us to examine
muscle synchronization during dynamic tasks. Direct comparison of the proposed
joint angle based calibration method with similar methods, such as multiple MVC
normalization, which was claimed to reduce the joint angle related effects, needs to
be performed.
Our model has been developed and tested using SEMG data recorded at low force
levels. We believe that the PCI method can be applied to SEMG-force modeling at
higher contraction levels. If the relationship becomes more nonlinear, more cascades
can be added or higher degree polynomials can be used. However, evaluating the PCI
model at higher contraction levels is of great interest. As well, more general models
can be created by combining segments of data collected from different subjects using
the data concatenation procedures.
It has been claimed that SMP is proportional to intra-muscle-pressure (IMP)
which is a function of the passive force element of the muscle (F SE ) [112]. SMP
can provide additional information, for any force estimator, particularly when there
are substantial passive forces, as in eccentric contractions. In addition, it may be
possible to use the relationship between the SMP recorded over the biceps brachii
CHAPTER 8. CONCLUSIONS AND FUTURE WORK
146
and joint angle to estimate the joint angle from the SMP signal in applications such
as control of a powered prosthetic arm, where the joint angle measurement is not
possible. However, this would require mapping the SMP signal from the residual
muscle of an amputee to joint angle. It might also be useful to estimate the joint
angle using SMP in normally limbed subjects, and use this information to weight the
SEMG-force relationship.
Bibliography
[1] A.A. Amis, D. Dowson, and V. Wright. Muscle strengths and musculoskeletal
geometry of the upper limb. Eng. Med., 8(1):41–48, 1979.
[2] K.N. An, F.C. Hui, B.F. Morrey, R.L. Linscheid, and E.Y. Chao. Muscles across
the elbow joint: a biomechanical analysis. J. Biomech., 14(10):659–661, 1981.
[3] K.N. An, K. Takahashi, T.P. Harrigan, and E.Y. Chao. Determination of muscle
orientations and moment arms. J. Biomech. Eng., 106:280–282, 1984.
[4] J.V. Basmajian and A. Latif. Integrated actions and functions of the chief
flexors of the elbow a detailed electromyographic analysis. J. Bone Jt. Surg.
(Am.), 39(5):1106–1118, 1957.
[5] T.W. Beck, T.J. Housh, J.T. Cramer, M.O.H.H. Malek, M. Mielke, R. Hendrix,
and J.P. Weir. Electrode shift and normalization reduce the innervation zone’s
influence on EMG. Med. Sci. Sports Exercise, 40(7):1314–1322, 2008.
[6] T.W. Beck, T.J. Housh, J.T. Cramer, J.R. Stout, E.D. Ryan, T.J. Herda, P.B.
Costa, and J.M. Defreitas. Electrode placement over the innervation zone affects
the low-, not the high-frequency portion of the EMG frequency spectrum. J.
Electromyogr. Kinesiol., 19:660–666, 2009.
147
BIBLIOGRAPHY
148
[7] O. Bida, D. Rancourt, and E.A. Clancy. Electromyogram (EMG) amplitude
estimation and joint torque model performance. In Northeast Conf. Bioeng.,
pages 229–230. IEEE, 2005.
[8] J.H. Blok, J.P. Van Dijk, G. Drost, M.J. Zwarts, and D.F. Stegeman. A highdensity multichannel surface electromyography system for the characterization
of single motor units. Rev. Sci. Instrum., 73(4):1887–1898, 2002.
[9] R.L. Brookham, E.E. Middlebrook, Grewal T., and C.R. Dickerson. The utility
of an empirically derived co-activation ratio for muscle force prediction through
optimization. J. Biomech., 44(8):1582–1587, 2011.
[10] S.H.M. Brown and S.M. McGill. Co-activation alters the linear versus nonlinear impression of the EMG-torque relationship of trunk muscles. J. Biomech.,
41(3):491–497, 2008.
[11] C. Castellini and P. van der Smagt. Surface EMG in advanced hand prosthetics.
Biological Cybernetics, 100(1):35–47, 2009.
[12] E.E. Cavallaro, J. Rosen, J.C. Perry, and S. Burns. Real-time myoprocessors
for a neural controlled powered exoskeleton arm. IEEE Trans. Biomed. Eng.,
53(11):2387–2396, 2006.
[13] P.R. Cavanagh and P.V. Komi. Electromechanical delay in human skeletal
muscle under concentric and eccentric contractions. Eur. J. Appl. Physiol.
Occup. Physiol., 42(3):159–163, 1979.
[14] Y.W. Chang, F.C. Su, H.W. Wu, and K.N. An. Optimum length of muscle
contraction. Clin. Biomech., 14(8):537–542, 1999.
BIBLIOGRAPHY
149
[15] J. Cholewicki and S.M. McGill. EMG assisted optimization: a hybrid approach for estimating muscle forces in an indeterminate biomechanical model.
J. Biomech., 27(10):1287–1289, 1994.
[16] E.A. Clancy, O. Bida, and D. Rancourt. Influence of advanced electromyogram
(EMG) amplitude processors on EMG-to-torque estimation during constantposture, force-varying contractions. J. Biomech., 39(14):2690–2698, 2006.
[17] E.A. Clancy, S. Bouchard, and D. Rancourt. Estimation and application of emg
amplitude during dynamic contractions. IEEE Eng. Med. Biol., 20(6):47–54,
2001.
[18] E.A. Clancy and K.A. Farry. Adaptive whitening of the electromyogram to
improve amplitude estimation. IEEE Trans. Biomed. Eng., 47(6):709–719, 2000.
[19] E.A. Clancy and N. Hogan. Estimation of joint torque from the surface emg.
IEEE Eng. Med. Biol. Soci., 13(1):877–878, 1991.
[20] E.A. Clancy and N. Hogan. Relating agonist-antagonist electromyograms to
joint torque during isometric, quasi-isotonic, nonfatiguing contractions. IEEE
Trans. Biomed. Eng., 44(10):1024–1028, 1997.
[21] E.A. Clancy, E.L. Morin, and R. Merletti. Sampling, noise-reduction and amplitude estimation issues in surface electromyography. J. Electromyogr. Kinesiol.,
12(1):1–16, 2002.
[22] P.A. Dalton and M.J. Stokes. Acoustic myography reflects force changes during dynamic concentric and eccentric contractions of the human biceps brachii
muscle. Eur. J. Appl. Physiol. Occup. Phys., 63(6):412–416, 1991.
BIBLIOGRAPHY
150
[23] C.J. De Luca. The use of surface electromyography in biomechanics. J. Appl.
Biomech., 13:135–163, 1997.
[24] N.A. Dimitrova, G.V. Dimitrov, and O.A. Nikitin. Neither high-pass filtering
nor mathematical differentiation of the EMG signals can considerably reduce
cross-talk. J. Electromyogr. Kinesiol., 12(4):235–246, 2002.
[25] G. Drost, D.F. Stegeman, B.G.M. van Engelen, and M.J. Zwarts. Clinical
applications of high-density surface EMG: a systematic review. J. Electromyogr.
Kinesiol., 16(6):586–602, 2006.
[26] G. Drost, D.F. Stegeman, B.G.M. van Engelen, and M.J. Zwarts. Clinical
applications of high-density surface EMG: a systematic review. J. Electromyogr.
Kinesiol., 16(6):586–602, 2006.
[27] B.F.B. Falk, C.U.C. Usselman, R.D.R. Dotan, L.B.L. Brunton, P.K.P. Klentrou,
J.S.J. Shaw, and D.G.D. Gabriel. Child-adult differences in muscle strength and
activation pattern during isometric elbow flexion and extension. Appl. Physiol.
Nutrition Metabolism, 34(4):609–615, 2009.
[28] D. Farina. Interpretation of the surface electromyogram in dynamic contractions. Exercise Sport Sci. R., 34(3):121–127, 2006.
[29] D. Farina, R. Merletti, and R.M. Enoka. The extraction of neural strategies
from the surface EMG. J. Appl. Physiol., 96(4):1486–1495, 2004.
[30] D. Farina, R. Merletti, M. Nazzaro, and I. Caruso. Effect of joint angle on EMG
variables in leg and thigh muscles. IEEE Eng. Med. Biol. Mag., 20(6):62–71,
2001.
BIBLIOGRAPHY
151
[31] D. Farina, L. Mesin, S. Martina, and R. Merletti. A surface emg generation
model with multilayer cylindrical description of the volume conductor. IEEE
Trans. Biomed. Eng., 51(3):415–426, 2004.
[32] A.J. Fuglevand, D.A. Winter, and A.E. Patla. Models of recruitment and rate
coding organization in motor-unit pools. J. Neurophysiol., 70(6):2470–2475,
1993.
[33] G.A. Garcia, R. Okuno, and K. Azakawa. A decomposition algorithm for surface
electrode-array electromyogram. Eng. Med. .Biol. Mag., 24(4):63–72, 2005.
[34] B. A. Garner and M. G. Pandy. Estimation of musculotendon properties in the
human upper limb. Ann. Biomed. Eng., 31:207–220, 2003.
[35] M. Gazzoni, D. Farina, and R. Merletti. A new method for the extraction and
classification of single motor unit action potentials from surface EMG signals.
J. Neurosci. Meth., 136(2):165–177, 2004.
[36] E. A. Hansen, H. D. Lee, K. Barrett, and W. Herzog. The shape of the forceelbow angle relationship for maximal voluntary contractions and sub-maximal
electrically induced contractions in human elbow flexors. J. Biomech., 36:1713–
1718, 2003.
[37] J. Hashemi, E. Morin, P. Mousavi, K. Mountjoy, and K. Hashtrudi-Zaad. EMG–
force modeling using parallel cascade identification. J. Electromyogr. Kinesiol.,
22(3):469–477, 2012.
[38] E. Henneman. Relation between size of neurons and their susceptibility to
discharge. Science, 126(3287):1345–1347, 1957.
BIBLIOGRAPHY
152
[39] H.J. Hermens, B. Freriks, C. Disselhorst-Klug, and G. Rau. Development of
recommendations for SEMG sensors and sensor placement procedures. J. Electromyogr. Kinesiol., 10(5):361–374, 2000.
[40] H.J. Hermens, B. Freriks, R. Merletti, D.F. Stegeman, J. Blok, G. Rau, and
C. Disselhorst-Klug. European recommendations for surface electromyography:
results of the SENIAM project. Roessingh Research and Development, 1999.
[41] A.V. Hill. The heat of shortening and the dynamic constants of muscle. Proc.
R. Soc. Lond. B Biol. Sci., 126(843):136–195, 1938.
[42] A.L. Hof, C.N.A. Pronk, and J.A. Van Best. Comparison between emg to
force processing and kinetic analysis for the calf muscle moment in walking and
stepping. J. Biomech., 20(2):167–178, 1987.
[43] A.L. Hof and J.W. Van Den Berg. EMG to force processing I: an electrical
analogue of the Hill muscle model. J. Biomech., 14(11):747–753, 1981.
[44] A. Holtermann, K. Roeleveld, and J.S. Karlsson. Inhomogeneities in muscle
activation reveal motor unit recruitment. J. Electromyogr. Kinesiol., 15(2):131–
137, 2005.
[45] G. Howatson. The impact of damaging exercise on electromechanical delay in
biceps brachii. J. Electromyogr. Kinesiol., 20(3):477–481, 2010.
[46] J.C. Jamison and G.E. Caldwell. Muscle synergies and isometric torque production: influence of supination and pronation level on elbow flexion. J. Neurophysiol., 70(3):947–960, 1993.
BIBLIOGRAPHY
153
[47] Yasuo Kawakami, Kimitaka Nakazawa, Toshiro Fujimoto, Daichi Nozaki, Mitsumasa Miyashita, and Tetsuo Fukunaga. Specific tension of elbow flexor and
extensor muscles based on magnetic resonance imaging. Eur. J. Appl. Physiol.,
68(2):139–147, 1994.
[48] D. Kay, A. St Clair Gibson, M.J. Mitchell, M.I. Lambert, and T.D. Noakes.
Different neuromuscular recruitment patterns during eccentric, concentric and
isometric contractions. J. Electromyogr. Kinesiol., 10(6):425–432, 2000.
[49] K.G. Keenan and F.J. Valero-Cuevas. Epoch length to accurately estimate the
amplitude of interference EMG is likely the result of unavoidable amplitude
cancellation. Biomed. Signal Process. Control, 3(2):154–162, 2008.
[50] T. K. K. Koo, A. F. T. Mak, and L. K. Hung. In vivo determination of subjectspecific musculotendon parameters: applications to the prime elbow flexors in
normal and hemiparetic subjects. Clinical Biomechanics, 17:390–399, 2002.
[51] T.K. Koo and A.F. Mak. Feasibility of using EMG driven neuromusculoskeletal
model for prediction of dynamic movement of the elbow. J. Electromyogr.
Kinesiol., 15(1):12–26, 2005.
[52] M. J. Korenberg. A robust orthogonal algorithm for system identification. Biol.
Cybern., 60:267–276, 1989.
[53] M.J. Korenberg. Fast orthogonal identification of non-linear difference equation
and function expansion models. In Proc. 28th Midwest Symposium on Circuits
and Systems, volume 1, pages 270–276, 1985.
BIBLIOGRAPHY
154
[54] M.J. Korenberg. Identifying nonlinear difference equation and functional expansion representations: the fast orthogonal algorithm. Ann. Biomed. Eng.,
16:123–142, 1988.
[55] M.J. Korenberg. Parallel cascade identification and kernel estimation for nonlinear systems. Ann. Biomed. Eng., 19(4):429–455, 1991.
[56] A. Kossev and P. Christova. Discharge pattern of human motor units during
dynamic concentric and eccentric contractions. Electroencephalogr. Clin. Neurophysiol., 109(3):245–255, 1998.
[57] J. Langenderfer, S.A. Jerabek, V.B. Thangamani, J.E. Kuhn, and R.E. Hughes.
Musculoskeletal parameters of muscles crossing the shoulder and elbow and the
effect of sarcomere length sample size on estimation of optimal muscle length.
Clin. Biomech., 19(7):664–670, 2004.
[58] M. A. Lemay and P. E. Crago. A dynamic model for simulating movements of
the elbow, forearm and wrist. J. Biomech., 29(10):1319–1330, 1996.
[59] Dorling
Kindersley
Limited.
http://www.dkimages.com/discover/
previews/740/60417.JPG, 2008.
[60] V. Linnamo, T. Moritani, C. Nicol, and PV Komi. Motor unit activation patterns during isometric, concentric and eccentric actions at different force levels.
J. Electromyogr. Kinesiol., 13(1):93–101, 2003.
[61] D.G. Lloyd and T.F. Besier. An EMG-driven musculoskeletal model to estimate
muscle forces and knee joint moments in vivo. J. Biomech., 36(6):765–776, 2003.
BIBLIOGRAPHY
155
[62] J.J. Luh, G.C. Chang, C.K. Cheng, J.S. Lai, and T.S. Kuo. Isokinetic elbow
joint torques estimation from surface EMG and joint kinematic data: using an
artificial neural network model. J. Electromyogr. Kinesiol., 9(3):173–183, 1999.
[63] P. Madeleine, P. Bajaj, K. Søgaard, and L. Arendt-Nielsen. Mechanomyography and electromyography force relationships during concentric, isometric and
eccentric contractions. J. Electromyogr. Kinesiol., 11(2):113–121, 2001.
[64] C. N. Maganaris. Force-length characteristics of in vivo human skeletal muscle.
Acta physiologica Scandinavica, 172(4):279–285, 2001.
[65] C.N. Maganaris. Force–length characteristics of in vivo human skeletal muscle.
Acta Physiol. Scand., 172(4):279–285, 2001.
[66] S. Martin and D. MacIsaac. Innervation zone shift with changes in joint angle
in the brachial biceps. J. Electromyogr. Kinesiol., 16(2):144–148, 2006.
[67] R. Merletti, D. Farina, and M. Gazzoni. The linear electrode array: a useful tool with many applications. Journal of electromyography and kinesiology:
official journal of the International Society of Electrophysiological Kinesiology,
13(1):37–47, 2003.
[68] R. Merletti and P.A. Parker. Electromyography: Physiology, engineering, and
noninvasive applications. Wiley-IEEE Press, Piscataway, NJ., 2004.
[69] Roberto Merletti and P Di Torino. Standards for reporting emg data. J.
Electromyogr. Kinesiol., 9(1):3–4, 1999.
[70] HS Milner-Brown and RB Stein. The relation between the surface electromyogram and muscular force. J. Physiol., 246(3):549–569, 1975.
BIBLIOGRAPHY
156
[71] D.L. Misener and E.L. Morin. An EMG to force model for the human elbow derived from surface EMG parameters. In IEEE Eng. Med. Biol. Soci., volume 2,
pages 1205–1206. IEEE, 1995.
[72] F. Mobasser, J.M. Eklund, and K. Hashtrudi-Zaad.
Estimation of elbow-
induced wrist force with EMG signals using fast orthogonal search. IEEE Trans.
Biomed. Eng., 54(4):683–693, 2007.
[73] M. Moradi. Force control for prosthetic arms using an emg-based wrist force
observer. Master’s thesis, Bremen Universitat, July 2007.
[74] K. Mountjoy, E. Morin, and K. Hashtrudi-Zaad. Contraction-based variations
in upper limb EMG-force models under isometric conditions. In Eng. Med. Biol.
Soc. Ann., pages 2955–2959. IEEE, 2009.
[75] K. Mountjoy, E. Morin, and K. Hashtrudi-Zaad. Use of the fast orthogonal
search method to estimate optimal joint angle for upper limb hill-muscle models.
IEEE Trans. Biomed. Eng., 57(4):790–798, 2010.
[76] K.C. Mountjoy, K. Hashtrudi-Zaad, and E.L. Morin. Fast orthogonal search
method to estimate upper arm hill-based muscle model parameters. In Eng.
Med. Biol. Soci. Ann., pages 3720–3725. IEEE, 2008.
[77] M. Mulas, M. Folgheraiter, and G. Gini. An EMG-controlled exoskeleton for
hand rehabilitation. In 9th Int. Conf. Rehab. Robot., 2005.
[78] W. M. Murray, S. L. Delp, and T. S. Buchanan. Variation of muscle moment
arms with elbow and forearm position. J. Biomech., 28:513–525, 1995.
BIBLIOGRAPHY
157
[79] W.M. Murray, T.S. Buchanan, and S.L. Delp. The isometric functional capacity
of muscles that cross the elbow. J. Biomech., 33(8):943–952, 2000.
[80] W.M. Murray, T.S. Buchanan, and S.L. Delp. Scaling of peak moment arms of
elbow muscles with upper extremity bone dimensions. J. Biomech., 35(1):19–26,
2002.
[81] K. Ollivier, P. Portero, O. Maı̄setti, and J.Y. Hogrel. Repeatability of surface
EMG parameters at various isometric contraction levels and during fatigue using bipolar and laplacian electrode configurations. J. Electromyogr. Kinesiol.,
15(5):466–473, 2005.
[82] A. Philippou, G. C. Bogdanis, A. M. Nevill, and M. Maridaki. Changes in
the angle-force curve of human elbow flexors following eccentric and isometric
exercise. Eur. J. Appl. Physiol., 93:237–244, 2004.
[83] P. Pigeon, L. Yahia, and A. G. Feldman. Moment arms and lengths of human
upper limb muscles as functions of joint angles. J. Biomech., 29(10):1365–1370,
1996.
[84] H. Piitulainen, R. Bottas, V. Linnamo, P. Komi, and J. Avela. Effect of electrode location on surface electromyography changes due to eccentric elbow flexor
exercise. Muscle & Nerve, 40(4):617–625, 2009.
[85] H. Piitulainen, A. Botter, R. Merletti, and J. Avela. Multi-channel electromyography during maximal isometric and dynamic contractions. J. Electromyogr.
Kinesiol., 23(2):302–310, 2012.
BIBLIOGRAPHY
158
[86] H. Piitulainen, T. Rantalainen, V. Linnamo, P. Komi, and J. Avela. Innervation
zone shift at different levels of isometric contraction in the biceps brachii muscle.
J. Electromyogr. Kinesiol., 19(4):667–675, 2009.
[87] R. Plonsey. Bioelectric phenomena. Wiley Online Library, 1969.
[88] J.R. Potvin and S.H. Brown. Less is more: high pass filtering, to remove up
to 99% of the surface EMG signal power, improves EMG-based biceps brachii
muscle force estimates. J. Electromyogr. Kinesiol., 14(3):389–399, 2004.
[89] T. Rantalainen, A. Klodowski, and H. Piitulainen. Effect of innervation zones in
estimating biceps brachii force–EMG relationship during isometric contraction.
J. Electromyogr. Kinesiol., 22(1):80–87, 2011.
[90] H. Reucher, G. Rau, and J. Silny. Spatial filtering of noninvasive multielectrode EMG: Part i-introduction to measuring technique and applications. IEEE
Trans. Biomed. Eng., 34(2):98–105, 1987.
[91] H. Reucher, J. Silny, and G. Rau. Spatial filtering of noninvasive multielectrode
EMG: Part ii-filter performance in theory and modeling. IEEE Trans. Biomed.
Eng., 34(2):106–113, 1987.
[92] A. Ridderikhoff, C.L.E. Peper, R.G. Carson, and P.J. Beek. Effector dynamics
of rhythmic wrist activity and its implications for (modeling) bimanual coordination. Hum. Movement Sci., 23(3):285–313, 2004.
[93] I.C.N. Sacco, A.A. Gomes, M.E. Otuzi, D. Pripas, and A.N. Onodera. A method
for better positioning bipolar electrodes for lower limb EMG recordings during
dynamic contractions. J. Neurosci. Methods, 180(1):133–137, 2009.
BIBLIOGRAPHY
159
[94] M. Solomonow, A. Guzzi, R. Baratta, H. Shoji, and R. D’Ambrosia. EMG-force
model of the elbows antagonistic muscle pair. the effect of joint position, gravity
and recruitment. Am. J. Phys. Med. Rehab., 65(5):223–230, 1986.
[95] D. Staudenmann, A. Daffertshofer, I. Kingma, D.F. Stegeman, and J.H. van
Dieen. Independent component analysis of high-density electromyography in
muscle force estimation. IEEE Trans. Biomed. Eng., 54(4):751–754, 2007.
[96] D. Staudenmann, I. Kingma, A. Daffertshofer, D.F. Stegeman, and J.H.
Van Dieën. Improving EMG-based muscle force estimation by using a highdensity EMG grid and principal component analysis. IEEE Trans. Biomed.
Eng., 53(4):712–719, 2006.
[97] D. Staudenmann, I. Kingma, D.F. Stegeman, and J.H. van Dieėn. Towards
optimal multi-channel EMG electrode configurations in muscle force estimation:
a high density emg study. J. Electromyogr. Kinesiol., 15(1):1–11, 2005.
[98] D. Staudenmann, J.R. Potvin, I. Kingma, D.F. Stegeman, and J.H. van Dieën.
Effects of EMG processing on biomechanical models of muscle joint systems:
sensitivity of trunk muscle moments, spinal forces, and stability. J. Biomech.,
40(4):900–909, 2007.
[99] D. Staudenmann, K. Roeleveld, D.F. Stegeman, and J.H. van Dieėn. Methodological aspects of SEMG recordings for force estimation-A tutorial and review.
J. Electromyogr. Kinesiol., 20(3):375–387, 2010.
BIBLIOGRAPHY
160
[100] DF Stegeman, MJ Zwarts, C. Anders, and T. Hashimoto. Multi-channel surface EMG in clinical neurophysiology. Supplements to Clinical neurophysiology,
53:155–162, 2000.
[101] A.A.M. Tax, J.J.D. Gon, C. Gielen, and C.M.M. Tempel. Differences in the
activation of m. biceps brachii in the control of slow isotonic movements and
isometric contractions. Exp. Brain Res., 76(1):55–63, 1989.
[102] D.G. Thelen, A.B. Schultz, S.D. Fassois, and J.A. Ashton-Miller. Identification
of dynamic myoelectric signal-to-force models during isometric lumbar muscle
contractions. J. Biomech., 27(7):907–919, 1994.
[103] A. Troiano, F. Naddeo, E. Sosso, G. Camarota, R. Merletti, and L. Mesin.
Assessment of force and fatigue in isometric contractions of the upper trapezius
muscle by surface EMG signal and perceived exertion scale. Gait and Posture,
28(2):179–186, 2008.
[104] T. Tsuji and M. Kaneko. Estimation and modeling of human hand impedance
during isometric muscle contraction. In ASME Dynamics Sys. Control Division,
volume 58, pages 575–582, 1996.
[105] JG van Dijk and JP van Vugt. The reduction of crosstalk (from a clinical
point of view). Future Applications of Surface Electromyography. Enschede,
The Netherlands: Roessingh Research and Development, pages 110–113, 1999.
[106] John G Webster. Reducing motion artifacts and interference in biopotential
recording. IEEE Trans. Biomed. Eng., 31(12):823–826, 1984.
BIBLIOGRAPHY
161
[107] T.G. Welter, M.F. Bobbert, B.M. van Bolhuis, S.C. Gielen, L.A. Rozendaal,
and D.H. Veeger. Relevance of the force-velocity relationship in the activation
of mono-and bi-articular muscles in slow arm movements in humans. Motor
Control, 4(4):420–38, 2000.
[108] D.T. Westwick and R.E. Kearney. Identification of nonlinear physiological systems. Wiley-IEEE Press, Piscataway, NJ., 2003.
[109] M. Wininger, N. Kim, and W. Craelius. Pressure signature of the forearm as a
predictor of grip force. J. Rehabil. Res. Dev., 45(6):883–892, 2008.
[110] J.J. Woods and B. Bigland-Ritchie. Linear and non-linear surface EMG/force
relationships in human muscles. An anatomical/functional argument for the
existence of both. Am. J. Phys. Med., 62(6):287–295, 1983.
[111] J.F. Yang and D.A. Winter. Electromyographic amplitude normalization methods: improving their sensitivity as diagnostic tools in gait analysis. Arch. Phys.
Med. Rehab., 65(9):517–525, 1984.
[112] D.A. Yungher, M.T. Wininger, JB Barr, W. Craelius, and A.J. Threlkeld. Surface muscle pressure as a measure of active and passive behavior of muscles
during gait. Med. Eng. Phys., 33(4):464–471, 2011.
[113] F.E. Zajac et al. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit. Rev. Biomed. Eng., 17(4):359–
411, 1989.
BIBLIOGRAPHY
[114] L.Q. Zhang and G.W. Nuber.
162
Moment distribution among human elbow
extensor muscles during isometric and submaximal extension. J. Biomech.,
33(2):145–154, 2000.
Appendices
163
Appendix A
Data Sheets
A.1
Invenium AE100 datasheet
164
APPENDIX A. DATA SHEETS
165
APPENDIX A. DATA SHEETS
A.2
166
Flexiforce A201 Datasheet
FlexiForce
®
Standard Force & Load Sensors Model # A201
Actual size of sensor
Sensing area
Physical Properties
Thickness
Length
Width
Sensing Area
Connector
Substrate
Pin Spacing
0.208 mm (0.008 in.)
197 mm (7.75 in.)*
optional trimmed lengths: 152 mm (6 in.), 102 mm (4 in.), 51 mm (2 in.)
14 mm (0.55 in.)
9.53 mm (0.375 in.) diameter
3-pin Male Square Pin (center pin is inactive)
Polyester (ex: Mylar)
2.54 mm (0.1 in.)
ROHS Compliant
* Length does not include pins, please add 31.75 mm (0.25 in.) for pin length to equal a total length of 203.2 mm (8 in.).
Standard Force Ranges (as tested with circuit shown below)
0 - 1 lb. (4.4 N)
0 - 25 lb. (110 N)
0 - 100 lb. (440 N)*
Recommended Circuit
In order to measure forces above 100 lb
(up to 1000 lb), apply a lower drive
voltage (-0.5 V, -0.10 V, etc.) and reduce the
resistance of the feedback resistor (1k min.)
Conversely, the sensitivity can be increased for
measurement of lower forces by increasing the
drive voltage or resistance of the feedback resistor.
Typical Performance
Evaluation Conditions
Linearity (Error)
Repeatability
Hysteresis
Drift
Response Time
< ±3%
< ±2.5% of full scale
< 4.5 % of full scale
< 5% per logarithmic time scale
< 5µsec
Operating Temperature
-40°F - 140°F (-40°C - 60°C)
Line drawn from 0 to 50% load
Conditioned sensor, 80% of full force applied
Conditioned sensor, 80% of full force applied
Constant load of 25 lb (111 N)
Impact load, output recorded on oscilloscope
Time required for the sensor to respond to an input force
Tekscan, Inc. 307 West First Street South Boston, MA 02127-1309 USA tel: 617.464.4500/800.248.3669 fax: 617.464.4266
e-mail: [email protected]
URL: www.tekscan.com
Rev M_5.23.13
Appendix B
Fast Orthogonal Search (FOS)
The Fast Orthogonal Search (FOS) method [54, 52] is a nonlinear identification
method that forms a sum of M linear or nonlinear basis functions pm (n) and coefficient terms am and aims to minimize the mean square error between the estimate
and the system output. The FOS model takes the form:
y(n) =
M
∑
am pm (n) + e(n)
(B.1)
m=1
The FOS method is based on the principals of Gram-Schmidt orthogonal identification, whereby orthogonal basis functions wm (n) would be generated from the
candidate basis functions pm (n) and coefficients found to minimize the MSE of the
estimate, therefore taking the form
y(n) =
M
∑
gm wm (n) + e(n)
(B.2)
m=1
where the gm terms are the coefficients of the orthogonal basis functions wm (n), which
are orthogonal over the entire data record such that:
wi (n)wj (n) = 0, i, jϵ[1, M ], i ̸= j
167
(B.3)
APPENDIX B. FAST ORTHOGONAL SEARCH (FOS)
168
Here the overline represents the average over the entire data record. The orthogonal functions are found by subtracting from each pm (n) the components which are
“parallel” to the previously found orthogonal function wj (n), where j < m.
w1 (n) = p1 (n) = 1
w2 (n) = p2 (n) − α21 w1 (n)
..
.
wm (n) = pm (n) −
m−1
∑
αmr wr (n)
(B.4)
r=1
where αmr represents the projection of wr on pm as:
αmr =
wr (n)pm (n) m = 2, . . . , M
,
wr2 (n)
r = 1, . . . , m − 1
(B.5)
Since the error can be represented as mean square error (MSE):
e2 (n) = [y(n) − yb(n)]2
then,
[
(
e2 (n) = y(n) −
M
∑
(B.6)
)]2
gi wi (n)
i=1
=
y 2 (n)
− 2y(n)
M
∑
gi wi (n) +
i=1
M
∑
gi2 wi2 (n)
i=1
Since the basis functions wi (n) are orthogonal, the error can be written as:
e2 (n)
=
y 2 (n)
−
M
∑
gi2 wi2 (n)
(B.7)
i=1
The coefficients gi that minimize the MSE of the model estimate can be found as:
gi =
y(n)wi (n)
wi2 (n)
(B.8)
APPENDIX B. FAST ORTHOGONAL SEARCH (FOS)
169
From equation C.7, the iterative reduction in error of the model estimate can be
measured as a term Q(m) as:
Q(m) = gi2 wi2 (n)
(B.9)
Therefore, the method can select the best candidate functions to include in the
model, selecting iteratively, the one that maximizes the value of Q(m). However, in
order to calculate Q(m), both the coefficient values gi and orthogonal basis functions
wi (n) need to be found. Calculating the orthogonal functions can be time-consuming
and computationally expensive.
The benefit of the Fast Orthogonal Search method is that there is a way in which
to circumvent the calculation of the actual orthogonalized basis functions wi (n) using
only a few variables, and simply find the coefficients of the orthogonalized basis
functions gi . To do this, a number of orthogonal expansion coefficients are given.
gm =
C(m)
, for m = 0, . . . , M
D(m, m)
(B.10)
where
D(0, 0) = 1
(B.11)
D(m, 0) = pm (n), for m = 1, . . . , M
(B.12)
D(m, r) = pm (n)pr (n) −
r−1
∑
αri D(m, i), for m = 1, . . . , M and r = 0, . . . , m − 1
i=0
(B.13)
αmr =
D(m, r)
, for m = 1, . . . , M and r = 0, . . . , m − 1
D(r, r)
(B.14)
APPENDIX B. FAST ORTHOGONAL SEARCH (FOS)
C(0) = y(n)
C(m) = y(n)pm (n) −
m−1
∑
170
(B.15)
αmr C(r), for m = 1, . . . , M
(B.16)
r=0
The algorithm implemented in MATLAB to develop the FOS models was based on
the following pseudocode [54, 52]. For more details on the MATLAB codes used to
calculated the FOS models, refer to [73].
D(0,0)=1
for m = 1, . . . , M
Calculate D(m,0) using equation C.12
for m = 1, . . . , M
for r = 0, . . . , M − 1
Calculate αmr using equation C.14
Calculate D(m,r +1) using equation C.13
Recall that the term Q(m) in equation C.9 represents the iterative reduction in
model error. This error reduction for the addition of the m-th candidate function
pm (n) can be written as
2
D(m, m) =
Q(m) = gm
C 2 (m)
D(m, m)
(B.17)
As the FOS model moves through its iterative process, selecting candidate functions pm (n) which produce a maximum Q(m), the selected pm is removed from the
pool of candidates so that it will not be selected again. The FOS method continues
APPENDIX B. FAST ORTHOGONAL SEARCH (FOS)
171
to select pm terms until m = M . The model coefficient terms am from equation C.1
can then be calculated using
am =
M
∑
gi vi
(B.18)
i=M
where
vm = 1
vi = −
i=1
∑
r=m
αir vr for i = m, . . . , M
(B.19)
(B.20)
Appendix C
List of Candidate Functions
The pool of FOS candidate functions was constructed using the input signals with
modifying mathematical terms as shown in Table C.1. The modifying mathematical
terms were: quadratic functions, limited square functions and square root functions.
The functions were constructed with the modified version of the input signals and
their cross-terms adjusted by an angle-dependent factor which was either cos(θ) or
sin(θ). The total number of functions in the pool depends on the number of inputs
used.
In Table C.1, the functions are listed for the case in chapter 4 where SEMG signals
from biceps brachii (EBi ), triceps brachii (ET r ) and brachioradialis (ERa ) were used
as inputs to the FOS model along with the joint angle (θ). In this case 59 functions
were included to the model. For chapter 6 similar functions were used for three inputs
(EBi , ET r and θ). This resulted in 32 inputs. In chapter 7, different scenarios with
different number of inputs were examined. In the cases where 6 SEMG or 6 SMP
inputs from biceps brachii and 6 SEMG for triceps brachii were used, the functions in
the Table C.1 were added for each of the 6 recording location to the pool of functions.
172
APPENDIX C. LIST OF CANDIDATE FUNCTIONS
173
In the case where SEMG and SMP signals were used together, SEMG input signals
and their cross terms and SMP signals and their cross terms were included separately
i.e. no cross term between SEMG and SMP signals was included in the pool.
APPENDIX C. LIST OF CANDIDATE FUNCTIONS
174
Table C.1: List of the used FOS candidate functions for the case where SEMG signals
from biceps brachii (EBi ), triceps brachii (ET r ) and brachioradialis (ERa )
were used as inputs to the FOS model along with the joint angle (θ).
Common functions:
offset
θ
ERa
ET r
EBi
cosθ ∗ EBi
sinθ ∗ EBi
cosθ ∗ ET r
sinθ ∗ ET r
cosθ ∗ ERa
sinθ ∗ ERa
cosθ ∗ ERa ∗ ET r
sinθ ∗ ERa ∗ ET r
cosθ ∗ EBi ∗ ERr
sinθ ∗ EBi ∗ ERr
cosθ ∗ EBi ∗ ET r
sinθ ∗ EBi ∗ ET r
Quadratic functions:
cosθ ∗ (ERa )2
sinθ ∗ (ERa )2
2
cosθ ∗ (ET r )
sinθ ∗ (ET r )2
cosθ ∗ (EBi )2
sinθ ∗ (EBi )2
Limited square functions:
2Lim
2Lim
cosθ ∗ EBi
∗ ET2Lim
sinθ ∗ EBi
∗ ET2Lim
r
r
2Lim
2Lim
2Lim
cosθ ∗ ERa
∗ ET2Lim
sinθ
∗
E
∗
E
r
Ra
Tr
2Lim
2Lim
2Lim
2Lim
cosθ ∗ EBi
∗ ERa
sinθ ∗ EBi
∗ ERa
cosθ ∗ (ET r )2Lim
sinθ ∗ (ET r )2Lim
cosθ ∗ (ERa )2Lim
sinθ ∗ (ERa )2Lim
2Lim
cosθ ∗ (EBi )
sinθ ∗ (EBi )2Lim
√ Square root functions:
√
cosθ ∗ √EBi
sinθ ∗ √EBi
cosθ ∗ √ ET r
sinθ ∗ √ ET r
cosθ√∗ ERa
sinθ√∗ ERa
cosθ ∗ √ERa ∗ ET r
sinθ ∗ √ERa ∗ ET r
cosθ ∗ √EBi ∗ ERr
sinθ ∗ √EBi ∗ ERr
cosθ ∗ EBi ∗ ET r
sinθ ∗ EBi ∗ ET r
Sigmoid functions:
cosθ ∗ sigm(EBi )
sinθ ∗ sigm(EBi )
cosθ ∗ sigm(ET r )
sinθ ∗ sigm(ET r )
cosθ ∗ sigm(ERa )
sinθ ∗ sigm(ERa )
cosθ ∗ sigm(ERa ) ∗ sigm(ET r ) sinθ ∗ sigm(ERa ) ∗ sigm(ET r )
cosθ ∗ sigm(EBi ) ∗ sigm(ERr ) sinθ ∗ sigm(EBi ) ∗ sigm(ERr )
cosθ ∗ sigm(EBi ) ∗ sigm(ET r ) sinθ ∗ sigm(EBi ) ∗ sigm(ET r )
Appendix D
Parallel Cascade Identification
(PCI)
PCI is used to model the input/output relationship of dynamic systems. The PCI
method can approximate any time-invariant, causal, finite-memory, discrete-time nonlinear system to an arbitrary degree of accuracy by a sufficient number of linear and
static nonlinear cascades in parallel [55]. Additionally, the input to the system does
not have to be white or Gaussian or have any special autocorrelation properties. For
more detail on the PCI algorithm refer to [55] and [108].
A PCI model, as shown in Figure 5.2, consists of a sum of cascades in which
a dynamic linear element is followed by a static nonlinear element [55] where x(n)
is the model input(s) and y(n) is the measured force. The algorithm begins by
approximating the nonlinear system with the first cascade. The difference between
the desired output, y(n), and the first cascade output, z1 (n), is called the residue,
y1 (n). The residue is then treated as the output of a new nonlinear system, which will
be modeled by the second cascade. The residue of the second cascade is computed,
175
APPENDIX D. PARALLEL CASCADE IDENTIFICATION (PCI)
176
and another cascade is added. This process continues until a desired approximation
error is reached. The PCI model for a dynamic system whose output depends on
input delays from 0 to R, i.e. with a finite memory length of R + 1, and an input
length of T data points, is expressed as a summation of the outputs from all of the
cascades:
ỹ(n) =
M
∑
zi (n)
(D.1)
i=1
where M is the number of the cascades and ỹ(n) indicates the estimate of the output. For the model structure shown in Figure 5.2, hi (j) is the impulse response of the
dynamic linear system in cascade “i” and is of length R. The impulse response hi (j)
is constructed from a randomly selected function from the pool of cross-correlation
functions of different orders between the input x(n) and the residue yi−1 (n). The
cross-correlation functions are computed over a segment of the input and output signals extending from n = R to n = T . This way the value of x(n) for negative sample
points (which does not exist) is not needed. For randomly selected first-order and
second-order correlation functions
T
∑
1
yi−1 (n)x(n − j)
ϕxyi−1 (j) =
T − R + 1 n=R
(D.2)
ϕxxyi−1 (j1 , j2 ) =
T
∑
1
yi−1 (n)x(n − j1 )x(n − j2 )
T − R + 1 n=R
(D.3)
the impulse response hi (j) is, respectively, constructed as:
hi (j) = ϕxyi−1 (j)
(D.4)
hi (j) = ϕxxyi−1 (j, A) ± Cδ(j − A)
(D.5)
APPENDIX D. PARALLEL CASCADE IDENTIFICATION (PCI)
177
Here, the integer A is selected randomly from 0, · · · , R, and the parameter C is chosen
according to:
2
(n)
yi−1
C=
(D.6)
y 2 (n)
The overbar denotes the time-average over the portion of the signal extending from
n = R to n = T . The parameter C is initialized to one and then decreases to zero as
more cascades are added, and consequently the residue, yi−1 (n), approaches zero. The
sign of the δ function term is also chosen at random. It should be noted that third
or higher-order cross-correlations can also be used provided that the corresponding δ
functions be added or subtracted to the equation constructing the impulse response
hi (j). The output of the dynamic linear system is then determined as:
ui (n) =
R
∑
hi (j)x(n − j)
(D.7)
j=0
The static nonlinearity, Fi (.), is found by fitting a polynomial from the input ui (n)
to the residue yi−1 (n) over n = R, · · · , T . The cascade output is then obtained from:
zi (n) = Fi (ui ) =
P
∑
aij uji
(D.8)
j=0
where P is the degree of the polynomial and aij are the polynomial coefficients minimizing the percent relative-mean-square error (%RM SE) of the estimation in each
cascade calculated as:
n
∑
%RM SE =
i=1
(y(t) − ỹ(t))2
n
∑
× 100
(D.9)
y(t)2
i=1
The new residue, used as a desired output for the next cascade, is:
yi (n) = yi−1 (n) − zi (n)
(D.10)
APPENDIX D. PARALLEL CASCADE IDENTIFICATION (PCI)
178
Adding new cascades is stopped when the desired estimation %RM SE error for the
PCI model is reached.