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Neural Networks in short-term safety control for bridges
ROSA OSCURATO
Tirocinio svolto presso: LABORATÓRIO NACIONAL
(LNEC)
DE
ENGENHARIA CIVIL
Tutors universitari: PROF. MICHELE BRIGANTE – PROF. GIORGIO SERINO
Tutor aziendale: ENG. ANTÓNIO PAULO CAMPOS DA SILVEIRA
Co-Tutor aziendale: ENG. JOÃO PEDRO O. DIAS P. SANTOS
Abstract. Questo lavoro è stato sviluppato con l'obiettivo di mostrare come le
tecniche di Data Mining, in particolare le reti neurali basate su approcci
supervisionati Multi-Layer feed-forward, siano in grado di creare modelli di
grande ausilio per il monitoraggio strutturale e il controllo di sicurezza dei
ponti. Tali tecniche infatti, attraverso le misure delle azioni a cui le strutture
sono state in precedenza soggette, permettono la valutazione del
comportamento strutturale del ponte nel tempo per poter rilevare eventuali
anomalie e stabilire valori soglia e/o alerts. Particolari reti neurali,
implementate per un caso studio, relativo al ponte strallato autostradale
Salguiero Maia, che attraversa il fiume Tago nei pressi della città di Santarem,
in Portogallo, sono descritte ed i primi incoraggianti risultati prodotti
dall’applicazioni di questa tecnica sono presentati.
1. Introduction
Structural Health Monitoring (SHM) is the process of detecting damage in
structures with the goal to improve the structural safety control and
reliability. The safety control is supported by monitoring activities and is
based on models, which tend to predict the behavior of the structure, in
order to identify whether it is still similar to the past under the same loads
or if there is any difference. If indeed the evolution is divergent between
the model prediction and actual behavior, then the assumptions of the
models have changed and the reason for the change should be identified to
assess the consequences.
Among the different types of structures that can be subjected to the
practice of SHM, bridges represent a very significant case because of the
complexity and criticality of the construction techniques, because of their
great economical value and, finally, because of the importance that their
functionality has on the efficiency and safety of transportation networks.
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In general, the development of successful monitoring methods depends
on two key factors: sensing technology and the associated signal analysis
and interpretation algorithms. These two factors have been receiving a
great attention by researchers and, as result, sensors with very high level of
accuracy and precision are produced and several algorithms for structural
damage identification have been proposed. The latter is usually based on
dynamic techniques, but in the recent years also static-based procedures
have gained increasing importance.
Static-based techniques allow damage identification in bridges by
measuring changes in the static structural response (typically displacements
or strains under environmental and applied thermal loads), usually by
comparison with predictions from behavior models. However, models can
be expensive to create and may not accurately reflect undamaged behavior.
In order to overcome these limitations some studies have focused on
statistical techniques that discover anomalous behavior in data generated
by sensors without using behavior models.
Several authors suggest statistical techniques like Moving Principal
Components Analysis (MPCA) and Moving Correlation Analysis, that can
be involved in initial phase of SHM, called initialization, where the
monitored structure is assumed to behave in an undamaged condition. The
aim of this initialization period is to estimate the variability of the time
series and to define thresholds for detecting anomalous behavior. As
reported by Posenato et al. (2008), this period is normally one or two years
because in this manner all the expected variations in the behavior of health
structure, due to periodic environmental and load changes, is supposed to
be recorded. On the other hand, data corresponding to approximately two
years of acquisitions are not always available for some controlled
structures, as well as waiting two years for define threshold values, in some
cases may be excessive.
These limits can be overcome by the introduction of some Data Mining
techniques, such as Neural Networks, which can play a central role in this
field creating models for safety control of bridges, through data due to
actions to which the structures were previously subject, in order to
evaluate whether bridges’ structural behavior is developing according to
the trend or not, and to define thresholds for detecting anomalies.
2. Neural Networks
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Neural Networks in short-term safety control for bridges
A Neural Network (NN) is a powerful data modeling tool that is able to
capture and represent complex input/output relationships. Garrett (1994)
has given an interesting engineering definition of the NN as: “A
computational mechanism able to acquire, represent and compute mapping
from one multivariate space of information to another, given a set of data
representing that mapping”.
The motivation for the development of neural network technology
stemmed from the desire to develop an artificial system that could perform
“intelligent” tasks similar to those performed by the human brain. In fact, a
NN is an implementation of local behavior observed in our own brains
and, as the brains, it is composed of interconnected units, called artificial
neurons or simply neurons or nodes, which are the individual processing
elements. In a mathematical neural model, an external impulse is computed
as the weighted sum of input signals and transformed by an activation or
transfer function.
The learning capability of an artificial neuron is achieved by adjusting
the weights in accordance to the chosen learning algorithm.
A typical artificial neuron is shown in Fig. 1. It has n input, denoted as
, , …, . To each line connecting these inputs to the neuron is assigned a
weight, which are denoted as , ,.., respectively, and can take any real
value.
Fig. 1. Artificial neuron
The net input, or activation of the i-th neuron is the sum of all
weighted inputs from presynaptic neuron j (Eq. 1):
Eq.
1
The output value of the neuron is a function of the net input and of a
neuron threshold. The latter in artificial neuron is usually represented by
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θ and it is usually referred as bias (Bishop, 2006). The output value is
express as reported in Eq. 2:
Eq.
2
where f(⋅) is the activation function that influences the speed and capacity
of the network to adapt to the data. It describes the response profile of the
neuron and there are different types, such as threshold, bipolar, linear or
sigmoidal activation function.
Sometimes, the threshold is combined for simplicity into the
summation part by assuming an imaginary input =+1 and a connection
weight =θ. This is the case of the neural model represented in Fig. 1.
In particular, for the present work a Neural Network based on MultiLayer feed-forward perceptron is considered.
In this model the neurons, organized in the form of layers, get input
from the previous layer and feed their output to the next layer. This kind
of network is made up by an input layer, one or more hidden layer(s) and
an output layer and connections between neurons in the same or previous
layers are not permitted. The best possible architecture of adopted Neural
Network is strictly related not only to the considered dataset and its the
aim of implementation, but also to the number of input and outputs. Fig. 2
shows the Multi-Layer Perceptron neural network structure considered for
the study.
Fig. 2. Scheme of MLP Neural Network implemented with n input units, m hidden
neurons (characterized by sigmoid activation function), and the only output unit (with
linear activation function).
Actually, the major architectural decision regards the number of hidden
layers and hidden units. Sadly, there is not a precise procedure to follow
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Neural Networks in short-term safety control for bridges
for making these decisions, but only some "rules of thumb" have been
proposed during the years. However, the choice of optimal size of NN
represents an fundamental aspect to consider, in order to control the two
main limitations of neural model: local minima and overfitting. Especially
the latter can reduce drastically the network performance, due to a lost of
generalization, and for this reason this problem has been carefully
considered in this work, implementing an iterative procedure to obtain the
optimal size of neurons and applying the regularization technique of weight
decay (Gnecco & Sanguineti, 2008).
3. Case study: Salgueiro Maia Bridge
The reported case study refers to the development and implementation, of
a supervised model based on Multi-Layer feed-forward Network, with a
dataset characterized by measurements obtained from the continuous
monitoring over the years of the Salgueiro Maia Bridge, a cable-stayed
bridge that crosses the Tagus River near the city of Santarem, in Portugal
(Fig. 3).
Fig. 3. Salgueiro Maia Bridge, Santarem (Portugal) - (From Santos et al., 2004)
3.1. Description of dataset. The first major step to apply the Neural
Network technique is related to the constitution of a well organized
dataset, which must be carefully chosen and prepared. Accuracy of the
results can greatly depend on the accurate is the choice of data to use.
Different studies about Data Mining point out some rules to follow for a
correct data preparation, especially outliears and data missing, which are
also considered in the present work for the involved dataset (Bigus, 1996);
the latter is made up by measures obtained from the continuous
monitoring of the Salgueiro Maia Bridge over the years related to strains,
temperatures, vertical displacements and hangers’ forces.
The bridge, in fact, is monitored by Observation of Structures Division
of LNEC (Laboratório Nacional de Engenharia Civil) since its construction
phase, in 1998. Moreover, before it was opened to the traffic, the bridge
was subjected to static and dynamic load tests (Santos et al., 2004).
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As reported by Marecos et al. (2006), during and after bridge
construction, several sections were instrumented. Over 200 sensors
(acoustical strain-gages and resistance thermometers) were installed inside
the concrete, both at the pylons and at the bridge deck, to monitor strains,
temperature as well as the evolution of time dependent effects, such as
creep or shrinkage; approximately 50 electrical strain gauges were installed
at the deck steel ties. In addition to this, the SHM system includes weather
stations to measure air temperature and its relative humidity, air-bubble
clinometers to evaluate rotations, an hydrostatic leveling system to
measure deck’s vertical displacements and load cells to monitor the force
on several hangers.
3.2. Training the network and prediction. Two groups of NNs
implementations have been carried out, based on types of inputs/output
considered:
1. the temperatures inside the concrete have been considered as
inputs of the system while the output of the network, from time
to time, has been represented by the various structural parameters;
2. the structural parameters have entered, in the model both, as
inputs and as output.
The model considered is characterized by a supervised approach, where
a dataset for training, or training set, includes examples of inputs and
outputs and plays the role of “teacher” for the system. This means that, in
the training phase, the network, knowing a priori the values of inputs and
output, learns the relationship between these data through the
backpropagation algorithm, which allows to change weights and other
parameters of the network in order to minimize the error for the whole
training. In fact, using the backpropagation algorithm, the errors are
propagated backwards through the network and in the second stage, the
weights are adjust using the technique of gradient descent (Bishop, 1995;
2006). Once the Neural Network is “successfully trained”, it is therefore able
to make predictions even when the output is not known a priori.
In practice, the procedure adopted to implement a NN model starts
with the choice, from the complete prepared dataset, of a time windows
increasing on a weekly basis (growing from 1 to 20 weeks). In this way
training sets with progressively greater number of observations are defined
for each application and, by the evaluation of the committed Absolute
Mean Error, it is possible to assert each time if the Network is well trained
or not.
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Neural Networks in short-term safety control for bridges
Subsequently the results of the trained NN, in terms of weights that
connect inputs and output, are used to predict the evolution of the
monitored variables over the time (for instance the present work refers to
the week after the period of observation considered for the training set). Of
course, in order to demonstrate the reliability of the results obtained, the
predictions are made assuming a fixed time interval during the monitoring
of the bridge, where the measurements are available for a comparison
between predicted and real values. In addition, the Absolute Mean Error
for the prediction and the ratio between the latter and AME in training
phase are evaluated.
3.3. Results. From the analysis of obtained result, it is possible to point
out some important aspects about Neural Network technique applied to
safety control for bridges. Firstly, considering a very small training set (1
or 2 weeks of measurements), a Neural model is able to reproduce perfectly
the relationship between inputs and outputs with errors tending to zero.
However, the model does not reproduce structural behaviour since
subsequent predictions are performed with significant errors. Increasing
the number of weeks that make up the training set, the results tend to be
more accurate, due to the fact that the algorithm has more data as example
for “teaching”; the network is trained gradually better than in the previous
cases and learns more properly the relationship between inputs and output.
Excellent results can be achieved with 20 weeks of data available, but even
with a smaller training set (5 to 7 weeks), the results are very satisfactory,
without generating great errors, both for training and for predictions, and,
primarily, without incurring in the problem of overfitting, as shown in the
examples reported in Fig. 4 where the AME of predictions are normalized
with respect to the AME for trainings. a consequence, the model can be
considered “successfully trained”.
These results appear very useful for bridges safety control, and in
general for Structural Heath Monitoring, especially during the phase of
initialization, where the monitored structure is assumed to behave in an
undamaged condition. In this phase, unlike other statistical techniques,
Neural Networks allow to estimate the structural trends and to define
thresholds for detecting anomalous behaviors, even when one or two years
of acquisitions are not available. In fact, very reliable results can be
obtained even if the training set is made up of monitoring data for only few
months.
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Fig. 4. Example of NN results : in connection with the number of weeks of monitoring,
smaller the training set, lower the Absolute Mean Error during the training of the
Network, greater the AME for prediction phase, and, as a consequence, greater the ratio
between the latter and the training error.
In addition to this, the neural models are implemented considering as
inputs temperature (mean distributions and gradients) or structural
parameters (strains and hangers’ forces). The obtained results are
characterized by curves showing the ratio AMEprediction/AMEtraining
with trends and values perfectly comparable (Fig. 5), or even with more
accurate predictions in the second case, which means that a Neural
Network can be well trained in both applications.
Fig. 5. NN results : AMEprediction/AMEtraining for the main strain in a pier section,
considering as input the forces in the cables(green) and the temperatures (violet)
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Neural Networks in short-term safety control for bridges
Also these results have interesting and important implications about the
Bridge Health Monitoring. In fact, relying more on Neural Networks,
with structural parameters considered both as inputs and as outputs, the
sensors’ number to measure temperatures may be reduced, with
consequent significant savings, from an economic point of view, but also in
terms of computation due to a lower data production to manage.
4. Conclusions
The analysis of obtained results show that a supervised Multi-Layer feedforward Neural Network seem a suitable method to model structural
behavior. In order to confirm and generalize this assertion, much more
applications should be carried out, considering also other bridges
typologies or using different structural parameters both as inputs and as
outputs.
Moreover, interesting results could be obtained developing Neural
models which provide several outputs as well as more hidden layers in
order to better analyze the structural response of bridges, obtaining more
accurate and reliable results than those achieved with the “simple” model
implemented for this work.
Finally, a Multi-layer Neural Network, such as that presented in this
paper, may be subject to further research, to develop, for example, a model
that allows to set thresholds and alerts even on a daily scale, or that can be
also useful for structural damage identification.
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BISHOP C., Pattern Recognition, Clarendon Press, Oxford, 1995.
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GARRETT J.H., Where and why artificial neural networks are applicable in
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GNECCO G. & SANGUINETI M., The weight-decay technique in learning
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MARECOS V.M., SANTOS L.O. & BRANCO F., Data Processing for Safety
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