Download Modeling Automotive Battery Diagnostics

Modeling Automotive
Battery Diagnostics
Neuro-fuzzy and statistical models can be used
to accurately model the state of charge and
state of health of a lead-acid battery, so that
these parameters may be displayed in real time
in a vehicle.
A
utomotive electrical systems are becoming
increasingly complex as more and more
electrical and electronic equipment is incorporated into new vehicles. With this trend,
the growing demand for electrical power is
placing greater demands on the automobile’s primary source
of electrical energy storage — the lead-acid battery.
Whether the vehicle relies on an internal combustion
engine, is a hybrid electric vehicle or is fully electric, the
reliability of the battery must be ensured. To do so requires
monitoring the car battery’s diagnostic parameters in the
system while the vehicle is running.
Even when not in active use, a battery discharges and its
health deteriorates. The task of identifying a faulty battery
for replacement or a depleted battery in need of recharging
is essential. If these actions are not performed in a timely
manner, a system breakdown is likely.
Although there are devices and methods for monitoring a
battery’s state of charge (SoC) and its state of health (SoH),
By Neeta Khare, Associate Professor in Electronics, and
Rekha Govil, Professor in Computer Science, Apaji Institute
of Mathematics and Applied Computer Technology, Banasthali
University, Banasthali, Rajasthan, India
they rarely operate in-system while the vehicle is running.
Consequently, they do not provide timely warning for corrective action.
A new approach to measuring these diagnostic parameters overcomes this limitation by indicating the SoC in
terms of the current-delivery capacity of the battery and
the SoH in terms of the remaining percentage of battery
life while the vehicle is operating with its various electrical
loads. By modeling the SoC and SoH of a lead-acid battery
using neuro-fuzzy and regression techniques, it’s possible
to display the battery charge status and battery health in
real time for the driver.
Indirect Measurement
In any automotive system, robustness is a necessity, and
a graceful degradation in system performance is preferred
over a sudden breakdown. Therefore, recording the battery
status in-system is a value-added feature for the driver, because it helps avoid a sudden breakdown of the vehicle due
to a battery malfunction.
Unfortunately, neither
Battery
SoC nor SoH are directly
measurable. Instead, these
Age
Fresh
Two years old
One year old
parameters need to be
inferred from other measurements. The model for
SoC described here uses
Real cranking
Slow discharge
a neuro-fuzzy approach
coupled with in-system
sensing of the charge status
State of charge
100%
75%
50%
100%
75%
50%
of the battery to provide a
Temp
Temp
Temp
Temp
Temp
Temp
timely detection and warnTemperature
ing of battery failure. SoC
0ºC 27ºC 40ºC 0ºC 27ºC 40ºC 0ºC 27ºC 40ºC
0ºC 27ºC 40ºC 0ºC 27ºC 40ºC 0ºC 27ºC 40ºC
is determined from measurable battery parameters
Fig. 1. A first step in modeling battery diagnostics is to measure a set of battery parameters for batteries of
varying age, at different discharge rates, states of charge and ambient temperatures.
such as terminal voltage,
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Power Electronics Technology March 2008
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discharge/charge current, internal resistance, discharge/
charge cycles, temperature as an input and specific gravity
(SG) of a lead-acid battery as an output through a neural
network model.
SoH can be expressed in terms of battery parameters using a regression equation. SoH is a function of the aging of
the battery and its run-time consumption. Therefore, the
regression equation for SoH is expressed as a function of
those battery parameters that affect the aging and run-time
consumption. The aging effect can be seen through various slopes of SG, terminal voltage
and internal resistance (IR) with
respect to discharge time. Runtime consumption can be observed
through the battery’s ampere-hour
(Ah) consumption. This work
also has an important application
in heavy mobile systems such as
rocket launchers, missile launchers,
submarines, satellites and trucks.
There are two major modes of
battery operation in an automobile:
slow discharge and engine cranking.[1] When the alternator voltage
is less than the battery voltage
(when the engine is not running),
the direction of the current flow
is from the battery to the load.
Otherwise, the current flows from
the alternator to the load and to
the battery (when the engine is
running). This situation is known
as the slow discharge of the battery
through the car’s electrical load.
The electrical load of a car consists of many different vehicle
subsystems such as sidelights, taillights, license-plate lights, headlights (main and dip), dashboard
lights, radio/cassette/CD, indicators, wipers, heater and other accessories. On average, the battery
is required to supply the electrical
load with 12 A of current when the
engine is off.
At engine startup, when the alternator is not running, the engine
requires an initial high torque of
about 100 rev/min (engine cranking). This high torque, in turn,
requires that the battery supply a
pulse of high current.
Again, the ability to reach this
high torque depends on several
factors, among which battery
characteristics play an important
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role along with the engine cranking resistance (torque
required at the starting limit temperature) and the voltage
drop between the battery and the starter. Thus, the battery
should be able to supply a heavy current for a very short
duration until the alternator can take over the function of
supplying electrical power to the load.
Battery parameters affecting SoC are voltage, current,
charge/discharge cycles (rate and method of charging),
temperature, internal resistance, internal pressure, grid
material (the grid refers to the frame of the battery’s elec-
37
Power Electronics Technology March 2008
Battery Diagnostics
more accurate results, it’s preferable to measure two additional parameters: the battery run-time and temperature.
Specific
gravity
A first step in designing the model was the selection of
1
State of charge
Artificial
2
an
actual battery from which data could be collected. The
Fuzzifier
•
Fully
charged
4
neural
3
• >Half charged
networks
4
present
study was made on an Exide model MF40sv/ 38
• Half charged
5
• <Half charged
LM
20
car
battery. For the purpose of the model design
• Fully discharged
it was necessary to measure sufficient data on the battery
under study.[3]
Data was collected while keeping the battery on a 12-A
Fig. 2. A schematic diagram of the SoC model illustrates how the
constant
load corresponding to a slow discharge rate and
artificial neural network simulates
the
discharge
process
of
a
battery,
0308PET24-Figure 2
and how that result is then translated using fuzzy logic into terms
drawing about 150 A of current for a few seconds to simurepresenting the various states of charge for the battery.
late real cranking. The latter action was simulated in the
laboratory by 15 seconds of constant
discharge at 150 A, followed by a rest
of 15 seconds. Several data sets were
LW{2,1}
LW{3,1}
LW{1,1}
taken for different environmental
temperatures, battery ages and states of
+
+
+
charge. Fig. 1 shows the activity chart
for a single set of data collection.
b{2}
b{3}
b{1}
As expected, the behavioral pattern
5
11
11
1
observed was similar in the two cases
of data collected on the MF40sv battery
Fig. 3. In this ANN model diagram, LW(ij) and b(i) refer to weights and biases of synapse of
for slow discharge and real cranking as
layer (i) and neuron (j), respectively. Each node outcome is given by a summation as S LW(ij)
summarized below.[3]
x(k) + b(i), where x(k) is the input to the neuron followed by the activation function. This box
Given a constant percentage of
defines a nonlinear sigmoidal activation function to limit the neuron output.
charge, the following occur as a result
trodes), electrode health, electrolytic strength, corrosion
of increasing ambient temperature:
(rate of corrosion), SG and consumption time.[2] Many
l The battery can run for a longer period of time
of these parameters are impossible
to measure3 while the
l The internal resistance of the battery decreases
0308PET24-Figure
battery is supplying current to the load. Furthermore, the
l A very small variation occurs in battery terminal voltage
dependence of SoC on these parameters is usually nonlinl The value of the SG decreases.
ear, making mathematical modeling of the behavior of a
Conversely, when the ambient temperature was held conbattery a prohibitive task.
stant and the battery’s SoC was varied, it was seen that:
The SG of a battery is an indirect indicator of its SoC. Its
l A battery with a high SoC runs longer
direct measurement is based on a chemical process whereby
l The battery’s internal resistance increases with a dean electrolyte is siphoned from the battery into a digital or
crease in charged state
analog hygrometer — a technique that is impractical when
l The SG of the battery decreases along with a decrease
the battery is operating in the system.
in charged state
An alternative method for determining the SG is an
l The initial voltage decreases with a decrease in charged
indirect measurement of SoC using the dependence of SG
state.
on load conditions and other battery parameters. These
parameters include temperature, current drawn, voltage
SoC Model
(load), internal resistance, corrosion rate and the time
Artificial neural networks (ANNs) are well known for
duration for which the battery has been used.
simulating nonlinear physical processes, and ANNs coupled
In-system measurement of these input parameters is
with fuzzy logic provide a powerful mechanism to linguisticentral to any modeling technique. However, measuring
cally translate the behavior of a complex physical process.
all these parameters will be costly given the amount of
The nonlinear adaptive-learning capability of ANNs is used
hardware required. Therefore, a careful selection of the most
here to simulate the discharging process of a battery, which
critical parameters for determining SoC is needed to make
is translated linguistically using fuzzy logic to represent
SoC modeling cost effective. The selected parameters can be
the charged state of the battery for maneuvering battery
used to estimate the cost of the instrumentation required
operations. The term linguistically refers to the fact that
for modeling SoC.
the battery’s SoC is expressed in relative terms such as fully
In the present work, we have experimented with optimizcharged, half charged or fully discharged.
ing the number of input parameters to determine the SG for
A schematic of the model[4] is shown in Fig. 2. In this
SoC indication. The three essential parameters turn out to
schematic, 1 through 5 represent the in-system inputs to
be internal resistance, voltage and current consumption. For
be given to the ANN to generate the output in terms of
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Battery Diagnostics
Result of training of complete model
1.28
1.26
1.30
Specific gravity
1.22
Specific gravity
Trained output
Target output
1.35
1.24
1.20
1.18
1.16
1.14
1.25
1.20
1.15
1.10
1.12
1.05
1.10
1.08
Simulated results of completed model
1.40
Trained output
Target output
0
200
400
600
Reference
800
1000
1200
1.00
0
50
100
150
Reference
200
250
Fig. 4. Training the ANN model with a complete set of input and output data for the battery under test provides the specific gravity data
shown (left). The ANN model is then tested using external input data from batteries of different ages, varying operating temperatures
and different states of charge (right).
battery behavior. Therefore, simulation was
first performed on training the ANN with
0308PET24-Figure 4
separate sets of data for slow discharge and
1
One year old
4645
0.000499
99.96%
real cranking functions of a car battery of dif2
New + one year old +
1481
0.005337
99.597%
ferent ages.[3] (This data appears in a figure in
two year old (mixed)
the online version of this article.) Then the same
ANN was trained with the combined data of
Table 1. Results of training the ANN with mixed data of RC and SD on mixed SoC
slow discharge and real cranking at all ages at
and with mixed temperatures.
different environmental temperatures.
SoC. These inputs are directly measurable in-system battery
The loss in accuracy due to generalization was found to
parameters. These parameters include terminal voltage, cur- be not more than 0.4%. Here we have seen that there is no
rent drawn, internal resistance, internal battery temperature loss of accuracy when training is done with mixed data
and time of battery consumption.
of various charged states, but it does take a longer time to
The ANN output is the SG, which along with temperature learn to converge. The loss of accuracy further increases if
is the input to a “fuzzifier” outputting the SoC of the battery training is performed with data on batteries of various ages
in linguistic form such as very high, high, half, low and very as shown in Table 1.
low. The ANN architecture and weights have to be obtained
After training the ANN with an input-output dataset, it
with the battery out of the system using a prior training of needs to be tested with given data. Fig. 4 shows the results
the ANN on the specific battery under study.
of both training and testing when the data of batteries of
different ages, different SoCs and different operating temANN Modeling
peratures is employed.
The design of an ANN and its training are done using the
Fuzzy logic was employed for the purpose of transforming
Neural Network Toolbox of MATLAB version 6.0. The back the ANN output SG to the target output (i.e., battery SoC).[7]
propagation learning algorithm in a fully connected multi- The complete process is shown in Fig. 5.
layer architecture of neurons was employed for supervised
In this module all three parameters — input parameters
learning in ANN.[5] With standard steepest descent, the SG and temperature, and output parameter percentage of
learning rate was held constant throughout the training.
SoC — are taken to be fuzzy. While the fuzzy membership
The performance of the algorithm is very sensitive to the for the temperature and percentage of SoC parameters are
proper setting of the learning rate. If the learning rate is defined with five linguistic variables, the SG parameter is
too high, the algorithm will oscillate and become unstable, represented by seven fuzzy states. The fuzzy states for each
while if too low, the algorithm takes longer to converge.[6] The of the three fuzzy variables are given here:
activation functions used are log sigmoid in the hidden layer
l Temperature (input variable) — very low, low, medium,
and purelin at the output layer. A block diagram of the ANN high and very high
model employed in the present study is shown in Fig. 3.
l SG (input variable) — very very low, very low, low,
This work aimed to obtain a generalized ANN model of medium, high, very high and very very high
Age of battery
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Epochs Surface error
Accuracy
at 1.240 SG
39
Power Electronics Technology March 2008
Battery diagnostiCS
regression[9] on the aging effect and the on-time consumpSpecific gravity
tion of the battery. The values of various slopes for the Exide
Fuzzification
Implication
Temperature
car battery under study are given in tabular form with difDegree of
ferent SoC conditions at different temperatures for ages of
membership
Multiple
batteries in the face of real cranking and slow discharge,
function
rules
respectively. (This data is available in a table in the online
version of this article.)
It is seen that the slopes of parameters like SG, terminal
Defuzzification
Aggregation
voltage and internal resistance indicate the effect of age on
battery performance. SG and terminal voltage decrease
Crisp percentage of SoC
Fuzzy percentage of SoC
with discharge duration, and internal resistance increases
with the discharge of the battery. The negative slope of
Fig. 5. The “fuzzifier module” transforms the specific gravity data
SG and terminal voltage has a sharper decrease with age,
generated by the ANN into a state of charge for the battery.
and the positive slope of internal resistance also shows an
l Percentage of SoC (output variable) — flat, less than half,
incremental rise with age.
half, greater than half and full.
From the online table it can also be observed that smaller
For temperature0308PET24-Figure
and SG, the 5membership function is values of slopes of SG and terminal voltage were not as sigchosen to be Gaussian with extreme states open. For per- nificant as values of the IR slope. This fact is verified later
centage of SoC, the fuzzy membership function is taken to with the results that internal resistance affects the SoH more
be bell shaped.
than SG and terminal voltage.
If-then rules are defined to specify the relationship beInitially, the regression technique had been applied to only
tween the input and the output. For each input, some rules two factors on which the SoH depends: SG and open circuit
are fired. For each rule being fired, the degree of membership voltage (OCV). The various slopes of the SG and OCV have
of the percentage of SoC is implied. Then the membership been used to obtain a formula. The results obtained were
value of all the outputs is aggregated to produce the final not very satisfactory, so we realized that internal resistance
output.
is also an important factor on which SoH depends. ThereThe fuzzy rule base[8] employed for the case under study fore, internal resistance should be included in the formula
is given in Table 2. Implementation of fuzzy logic is done developed to model SoH.
using MATLAB’s Fuzzy Logic Toolbox. The inputs and
The formula obtained after applying the multiple regresoutputs are designated in the Fuzzy Inference System (FIS) sion technique is:
editor window in the Fuzzy Logic Toolbox.
SoH = 1.0043 + 0.0088(TT × C) + 3.8925 m(SG) +
The fuzzy rules defined in Table 2 are verified with 0.2444m9(OCV) – 0.0863m0(IR),
the observed data. For different sets of data on SG and
where TT is the run-time of the battery and C is the distemperatures, the percentage of SoC is thus computed. A charge rate and IR is the internal resistance. TT × C gives
typical result of fuzzy inference is demonstrated in Fig. 6, the ampere-hour consumption of the battery and m(SG),
where temperature equals 45°C (very high), SG equals 1.178 m9 (OCV), m0(IR) are slopes.
(medium) and the corresponding percentage of SoC is 50%
The regression results, from the data collected from the
(half charged).
car battery, show that the current consumption affects 60%
(for real cranking of a car for 15 sec), the IR slope affects
SoH Modeling
30% and the remaining two paremeters — the SG slope and
The SoH of a battery is defined as the remaining life of the terminal voltage slope—affect only 10% of the battery’s
the battery given a specific load. The cause of battery health SoH. The SG in-system measurement is difficult and its slope
deterioration is the effect of aging on the grid, electrodes, values also are not significant, so it can be ignored.
contacts, corrosion and charging /discharging cycles.
This work concentrates on an intelligent modeling of the
The SoH of a battery is modeled using multivariate linear nonlinear behavior of a battery, not through mathematical/ algorithmic
Temperature
Specific gravity
ap p r o a c h l i k e
Very very low Very low
Low
Medium
High Very high Very very high prior work in this
field, but through
Very low
Flat
Flat
Flat
Flat
Flat
<Half
<Half
a simulation of
Low
Flat
Flat
Flat
Flat
<Half
Half
>Half
the entire process based on real
Medium
Flat
Flat
Flat
Flat
>Half
>Half
>Half
data, using battery
High
Flat
<Half
<Half
<Half
>Half
>Half
Full
parameters meaVery High
<Half
<Half
<Half
Half
>Half
Half
Full
sured in-system.
A nonlinear beTable 2. The fuzzy rule base for percentage of SoC output.
40
Power Electronics Technology March 2008
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Battery Diagnostics
havior mapping of the battery
has been conducted using an
ANN and the regression technique. This has been found to
provide a more-reliable and
accurate estimation of SoC
and SoH than previous methods. A relative indication of
SoC is implemented through
the use of fuzzy logic and SoH
is expressed as a remaining
percentage of battery life.
The objective of the study
was also to achieve a desired
accuracy with an optimized
hardware model (i.e., highly
accurate and low cost). The Fig. 6. Fuzzy inference indicates that the battery status is half charged.
process model has the potential to be implemented in product form as a panel display Neural Network, 5(3), May 1994, pp. 342-353.
in automobiles. While preferred model parameters have 7. Zadeh, L.A., “Quantitive Fuzzy Semantics,” Information
been given and described, various modifications may be Science, 3(2), 1971, pp. 159-176
made without departing from the spirit and scope of the 8. Pritpal, S. “Development of Fuzzy Logic Based Lead Acid
process. The hardware used to implement these models can Battery Management Techniques with Applications to 42V
be a low-cost, easy-to-build module consisting of a DSP or Systems.” U.S. patent 6,668,247.
microcontroller and signal-conditioning circuits. PETech 9. Draper, N.R., and Smith, H. Applied Regression Analysis,
3rd edition, John Wiley & Sons, 1998.
Acknowledgement
We gratefully acknowledge the assistance provided by Exide, R&D Lab, Kolkata, Exide Industries Ltd. India in terms
of financing the project and facilitating
the experimentation in their laboratory
without which this research work could
not have been accomplished.
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References
1. Crompton, T.R., Battery Reference
Book, Butterworth-Heinemann, March
1990 edition.
2. Vinal, G.W., Storage Batteries, John Wiley & Sons, 4th rev. edition, pp.130-336.
3. Khare, N., “Intelligent Battery Monitoring.” Thesis work under Prof. Rekha
Govil, Banasthali Vidyapith, Rajasthan,
India, 2006.
4. Khare, N.; Govil, R.; and Mittal, S.K.,
“A Process of Determining State of Charge
and State of Health of a Battery,” Indian
patent 813/KOL/2005.
5. Haykin, S., Neural Networks: A Comprehensive Foundation, 2nd edition, Prentice
Hall, 1998.
6. Hwang, J.N.; Lay, S.R.; Maechlar, M.;
Martin, D.; and Schimert, J., “Regression
Modeling in Back-Propagation and Projection Pursuit Learning,” IEEE Trans. on
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