Soft Computing Based Multilevel Strategy for Bridge Integrity Monitoring

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Computer-Aided Civil and Infrastructure Engineering 25 (2010) 348362

Soft Computing Based Multilevel Strategy for Bridge

Integrity MonitoringS. Arangio & F. Bontempi

Department of Structural and Geotechnical Engineering, University of Rome La Sapienza,Via Eudossiana 18, Rome, Italy

Abstract: In recent years, structural integrity monitor-ing has become increasingly important in structural en-

gineering and construction management. It represents animportant tool for the assessment of the dependability of

existing complex structural systems as it integrates, in a

unified perspective, advanced engineering analyses and

experimental data processing. In the first part of this work

the concepts of dependability and structural integrity are

discussed and it is shown that an effective integrity assess-

ment needs advanced computational methods. For this

purpose, soft computing methods have shown to be very

useful. In particular, in this work the neural networks

model is chosen and successfully improved by apply-

ing the Bayesian inference at four hierarchical levels: for

training, optimization of the regularization terms, data-

based model selection, and evaluation of the relative im-portance of different inputs. In the second part of the ar-

ticle, Bayesian neural networks are used to formulate a

multilevel strategy for the monitoring of the integrity of

long span bridges subjected to environmental actions: in

a first level the occurrence of damage is detected; in a fol-

lowing level the specific damaged element is recognized

and the intensity of damage is quantified.

1 INTRODUCTION

The realization of high-cost and safety-critical construc-tions requires advanced approaches to take into ac-count their intrinsic complexity (Ciampoli, 2005). Thecomplexity of this kind of structures can be related toseveral aspects, as for example, nonlinear dynamic be-havior (Adeli et al., 1978), various sources of uncertain-ties, both objective and cognitive, and strong interactionbetween components.

To whom correspondence should be addressed. E-mail: franco.

[email protected].

Only by considering these aspects can a consistentevaluation of the structural performance be obtained.

Therefore, it is necessary to evolve from the simplis-tic idealization of the structure as device for channel-ing loads to the analysis of the structural system as awhole, intended as a set of interrelated componentsworking together toward a common purpose (NASASystem Engineering Handbook, 2007). The correlationbetween different aspects can be taken into account byapplying the principles and techniques of System Engi-neering, which is a robust approach to the creation, de-sign, realization, and operation of an engineered system(Bontempi et al., 2008).

If the entire design process needs to be reviewed inthe System Engineering framework, one includes re-

quirements concerning the construction phase and theoperation and maintenance during the whole life-cycle(Sarma and Adeli, 2002). To this aim, data collected onsite are important both for checking the accomplish-ment of the expected performance during the servicelife and for validating the original design (Smith, 2001).

This approach requires the definition of the quality ofa complex structural system in a comprehensive way byan integrated concept, like dependability. The conceptof dependability has been originally developed in thefield of Computer Science and it is extended to struc-tural engineering as the ability to deliver service that

can justifiably be trusted (Avizienis et al., 2004). Thisdefinition stresses the need for justification of trust. Thealternate definition considers dependable a system thathas the capability to avoid service failures which aremore frequent and more severe than acceptable.

All these factors are connected to the integrity ofthe structural systems, considered as the completenessand consistency of the structural configuration. Specif-ically, structural integrity refers to the safe opera-tion of engineering components, structures and mate-rials, and addresses the science and technology which is

C 2010 Computer-Aided Civil and Infrastructure Engineering.

DOI: 10.1111/j.1467-8667.2009.00644.x


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Multilevel strategy for bridge integrity monitoring 349

used to assess the margin between safe operation andfailure.

During the service life the integrity, and conse-quently the overall dependability, can be lowered bydeterioration and damage. The structural monitoringrepresents an essential tool to assess the evolution in

time of the dependability of existing structural systems(Soyoz and Fukuda, 2009; Li et al., 2006). It includesissues like definition and analysis of the structural per-formance, from regular exercise to out-of-service andcollapse, assessment of the environmental conditions,choice of the sensor systems and their optimal place-ment, use of data transmission systems and signal pro-cessing techniques, and methods for damage identifica-tion and model updating (Jiang and Adeli, 2005; Adeliand Jiang, 2006; Psimoulis and Stiros, 2008).

In case of complex structural systems it can be diffi-cult to deal with the huge quantity of data coming from

the monitoring process and various soft computing tech-niques have shown to be effective tools for data pro-cessing (Adeli and Jiang, 2006; Carden and Brownjohn,2008; He et al., 2008; Jiang and Adeli, 2008a).

In this article, a soft computing model, the Bayesianneural networks (Castillo et al., 2008; Adeli andPanakkat, 2009), is used to formulate a multilevel strat-egy for the assessment of the integrity of a long spansuspension bridge subjected to wind actions and trafficloads. In the first step of the proposed strategy the oc-currence of damage is detected and the damaged por-tion of the bridge is identified; in the second step thespecific damaged element is recognized and the inten-

sity of damage evaluated.In the following, the concept of integrity monitoring

for dependability is explained with reference to struc-tural systems and the multilevel strategy is illustrated.

2 STRUCTURAL INTEGRITY MONITORINGFOR DEPENDABILITY

For complex structural systems, where there are signif-icant dependencies among elements or subsystems, it isimportant to have a solid knowledge of both how the

system works as a whole, and how the elements behaveindividually. In this contest, dependability is an inte-grated property that includes and describes the relevantaspects with reference to the system quality and its in-fluencing factors (Bentley, 1993). System dependabilitycan then be thought of as being composed of three ele-ments (Figure 1):

1. the attributes, that is, the properties thatquantify the dependability;

2. the threats, that is, the elements that can affect de-pendability;

ATTRIBUTES

THREATS

MEANS

MAINTAINABILITY

RELIABILITY

SAFETY

AVAILABILITY

FAILURE

ERROR

FAULT

FAULT TOLERANT

DESIGN

FAULT DETECTION

FAULT DIAGNOSIS

FAULT MANAGING

DEPENDABILITY

Fig. 1. Dependability: attributes, threats, and means.

3. the means, that is, the tools that can be used to in-crease dependability.

In structural engineering, relevant attributes are re-liability, safety, availability, and maintainability. Theseproperties are essential to guarantee the safety of thesystem under relevant hazard scenarios, the survivabil-ity under accidental or exceptional scenarios, and thefunctionality under operative conditions.

The threats for system dependability can be subdi-vided into faults, errors, and failures. According to thedefinition given in Avizienis et al. (2004), an active ordormant fault is a defect or an anomaly in the systembehavior that represents a potential cause of error; anerror is the cause for the system being in an incorrectstate and it may or may not cause failure; failure is a per-manent interruption of the system ability to perform arequired function under specified operating conditions.

The problem of conceiving and building a dependablestructural system can be considered at least by four dif-ferent points of view:

1. how to design a dependable system, that is a faulttolerant system;

2. how to detect faults, that is, anomalies in the sys-tem behavior;

3. how to localize and quantify (that is, diagnose) theeffects of faults and errors;

4. how to manage faults and errors to avoid failures.

This article is focused on points 2 and 3: fault de-tection and fault diagnosis. These aspects are strictlyrelated to the integrity monitoring of the structural sys-tem: an efficient integrity monitoring system is expected


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350 Arangio & Bontempi

to be able to preserve the structural dependability, diag-nosing deterioration and damage at their onset (Ou andLi, 2006).

Even if there is no general consensus on its defini-tion, in analogy with biological systems, an intelligentmonitoring system is expected to (Aktan et al., 1998;

Isermann, 2006):

1. sense the loading environment as well as the struc-tural response;

2. reason by assessing the structural condition andhealth; even small faults should be detected anddiagnosed;

3. communicate through proper interface with othercomponents and systems;

4. learn from experience as well as by interfacing withhumans for heuristic knowledge;

5. decide and take action for alerting controllers incase of accidental situations, or activate fault tol-

erant configurations in case of reconfigurable sys-tems.

Structural monitoring has a key role in the mainte-nance scheduling of the bridge structures and a great re-search effort has been devoted in the past 30 years to es-tablishing effective local and global methods for healthmonitoring in civil structures (Doebling et al., 1996; DeRoeck 2003; Sohn et al., 2004, 2008; Jiang and Adeli,2007; Li and Wu, 2008; Moaveni et al., 2008).

Analyzing the problem in terms of the expected pay-off, it comes out that, in cases of complex structures, likelong span bridges, for example, the monitoring process

should be planned during the design phase and shouldbe carried out during the entire life cycle to assess thestructural health and performance under in-service andaccidental conditions (Bontempi et al., 2008).

This long-term monitoring of bridges, where long-term designates a period of time from 1 year to decadesand desirably the entire life cycle, is a quite recentconcept, enabled by recent advances in sensing, dataacquisition, computing, communication, data, and infor-mation management (Ou and Li, 2006). Exploring long-term monitoring of structural responses was pioneeredin China and in Japan (Abe and Amano, 1998; Lau

et al., 1999; Wong et al., 2000). Nowadays severalbridges are instrumented in Europe (Casciati, 2003), theUnited States (Aktan et al., 2002), Korea, and othercountries, and the administration of the major coun-tries have developed guidelines to explain the advan-tages of long-term monitoring and to help the engineersin building effective monitoring systems (Aktan et al.,2002; Mufti, 2001; ISO, 2002; Task Group 5.3, 2002).

In accord with the concepts reported in these guide-lines, long-term monitoring is based on the integrationof different kinds of technologies (Figure 2): experimen-tal, analytical, and information technologies.

Mathematical modeling Finite Element modeling

ANALYTICAL TECHNOLOGIES

INFORMATION TECHNOLOGIES

EXPERIMENTAL TECHNOLOGIES

Non-destructive evaluation Continuous monitoring

Data acquisition Data processingCommunication Interpretation

Fig. 2. Issues in long-term monitoring implementation.

Fig. 3. Steps of the information technology.

Experimental technologies include nondestructive vi-sual inspection and continuous monitoring. Analyticaltechnologies include mathematical and finite-elementmodeling. The last one, the information technology,assumes a key role: it covers the entire spectrum ofefforts related to the acquisition, communication, pro-cessing, and interpretation of the data (Figure 3). Theentire monitoring process needs a team of experts incivil, mechanical, and electrical engineering and com-

puter scientists working together to take full advantageof the data. In fact, the desired outcome of structuralmonitoring is not data collection, but it is the generationof information and the creation of a base of knowledgeabout potential and existent system symptoms that willenhance decision making for fault management.

3 FAULTS-SYMPTOMS RELATIONSHIP

As mentioned in the previous section, to detect and di-agnose a system fault, it is necessary to process the data


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Fig. 4. Faultsymptoms relationship.

coming from the monitoring process, that is, the sys-tem symptoms. However this is a complex task. Therelationship between fault and symptoms can be repre-sented graphically by a pyramid (Figure 4). The vertexrepresents the fault, and the lower levels the possible

events generated by the fault; the base corresponds tothe symptoms. The propagation of the fault to the ob-servable symptoms follows a causeeffect relationship,and is a topdown forward process: a fault determinesevents that, as intermediate steps, influence the measur-able or observable symptoms (Isermann, 2006). On theother hand, the fault diagnosis proceeds in the reverseway (Figure 4); it is a bottomup inverse process thatrelates the observed symptoms to the faults. This im-plies the inversion of the causality principle. However,one cannot expect to rebuild the chain only by measureddata because usually the causality is not reversible or the

reversibility is ambiguous (Fussel, 2002): the underlyingphysical laws are often not known in analytical form,or are too complicated for explicit numerical calcula-tion. Moreover, intermediate events between faults andsymptoms are not always recognizable (Figure 4, right-hand side).

The solving strategy requires integrating differentprocedures, either forward or inverse: this mixed solv-ing approach has been called total approach by Liuand Han (2004) and different computational techniqueshave been developed for this task (Adeli and Samant,2000; Ghosh-Dastidar and Adeli, 2003).

4 KNOWLEDGE-BASED FAULT DETECTIONAND DIAGNOSIS

As shown in the previous section, fault diagnosisneeds the integration of forward and inverse proce-dures with the heuristic knowledge coming from ex-perience or qualitative information. For this task, aknowledge-based analysis can be applied (Adeli and

Fig. 5. Knowledge-based analysis for structural integritymonitoring.

Balasubramanyam, 1988; Paek and Adeli, 1990; Adeliand Hawkins, 1991; Shwe and Adeli, 1993; Waheed and

Adeli, 2000; Aktan et al., 1998) (Figure 5). The resultsobtained by visual inspection or instrumented monitor-ing (the inverse diagnosis system of Figure 4) are pro-cessed and combined with the results coming from theanalytical model (the forward physical system of Fig-ure 4). Information technology provides the tool forsuch integration. The output of the information technol-ogy is then filtered by the available heuristic knowledgefor decision making.

An attractive aspect of the knowledge-based analysisis that it can cope with incomplete or uncertain data in-tegrating qualitative and quantitative information, com-

ing from modeling and heuristics. To carry out the var-ious phases, different computational methods can beused. In several applications, inference models and softcomputing techniques, like the Bayesian neural net-works used in this work, have shown their effectiveness(Adeli and Park, 1995; Pandey and Barai, 1995; Masriet al., 1996; Faravelli and Pisano, 1997; Hajela, 1999;Topping et al., 1999; Kim et al., 2000; Adeli, 2001; Niet al., 2002; Kao and Hung, 2003; Waszczyszyn andZiemianski, 2005; Ko and Ni, 2005; Xu and Humar,2006; Lam et al. 2006; Jiang and Adeli, 2008a,b).


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5 BAYESIAN NEURAL NETWORK FOR FAULTDETECTION AND DIAGNOSIS

5.1 The neural network model and the probabilitylogic framework

The neural network concept has its origins in attemptsto find mathematical representations of informationprocessing in biological systems. Actually, there is a def-inite probability model behind it: a neural network isan efficient statistical model for nonlinear regression(Cheng and Titterington, 1994). It can be described by aseries of functional transformation working in differentcorrelated layers (Bishop, 2006). For example, for twolayers

yk(x,w) = h

M

j=1

w(2)kj g

D

i =1

w(1)ji xi + b

(1)j0

+ b

(2)k0

(1)where yk is the kth output variable in the output layer;x is the vector of the D input variables in the 1inputlayer; w is the matrix including the adaptive weight pa-

rameters w(1)ji and w

(2)kj and the biases b

(1)j0 and b

(2)k0 (the

superscript refer to the considered layer); M is the to-tal number of units in the hidden layer. The quantitieswithin the brackets are the so-called activations; each ofthem is transformed using a nonlinear activation func-tion (h and g). The nonlinear activation functions aregenerally chosen to be sigmoidal or tanh functions be-cause of the so-called universality property (Cybenko,

1989).In the traditional learning approach, the values of theparameters w are obtained during the training phase byminimizing an error function (Adeli and Hung, 1994),for example, the sum of squared errors with weight de-cay (Bishop, 1995)

E =1

2

Nn=1

Nok=1

yk (x

n;w) tnk2

+

2

Wi =1

|wi |2 (2)

where yk is the kth neural network output correspond-ing to the n-th realization ofx, tnk is the relevant targetvalue, N is the size of the considered data set, N0 is the

number of output variables, W is the number of param-eters in w, and is a regularization parameter. The sec-ond term in the right-hand side is a decay regularizationthat penalizes large weights.

Neural network learning can be framed as Bayesianinference, where probability is treated as a multival-ued logic that may be used to perform plausible infer-ence (Jaynes, 2003). The roots of this probability logicapproach are in the work by Bayes published in 1763(Bayes, 1763). He presented a method for updatingprobability distributions based on available data that

would come to be known as Bayes theorem, and thatforms the foundation of a framework for probabilis-tic inference. The power of this theorem was shownby Laplace (1812) and Jeffreys (1939) who applied itto the analysis of real data set. Although this frame-work had its origin in the 18th century, the practical

application of Bayesian methods was for a long timeseverely limited by the difficulties in carrying throughthe full Bayesian procedure. The developments of ap-proximation theories and stochastic sampling methods,along with dramatic improvements in the power of com-puters, have recently opened the door to the practi-cal use of Bayesian techniques in an impressive rangeof applications across all disciplines. In recent years incivil engineering, for example, the probability logic ap-proach has been successfully applied to system identifi-cation problems and structural health monitoring (Beckand Katafygiotis, 1998; Beck and Yuen, 2004; Muto and

Beck, 2008).Starting from the early works of MacKay (1992) andBuntine and Weigend (1991), there has been a growinginterest for the application of this framework in the fieldof neural networks methods (MacKay, 1994; Neal, 1996;Lampinen and Vethari, 2001; Barber, 2002; Lee, 2004;Nabney, 2004).

To pose the neural network model within theBayesian framework, the learning process needs to beinterpreted probabilistically: the network output can beconsidered as the conditional average of the target data(Bishop, 1995). Because the model does not reproducethe data set exactly, the error = t y(x; w) between

the target value t and the network output y needs tobe interpreted probabilistically using a prediction-errorprobability model: a Gaussian distribution with meanzero and constant inverse variance = 1/D

2 is a modelsupported by the principle of maximum differential en-tropy (Jaynes, 2003). Thus, modeling the predictions asindependent and identically distributed (i.i.d.), the like-lihood function for a data set D = xn, \ ,tn is given by

p(D | w,, M)

=

2 NN0

exp

2

N

n=1No

k=1 yk (xn;w) tnk

2

(3)

where Mdenotes the Bayesian model class that specifiesthe forms of the likelihood function and the prior prob-ability distribution discussed next. Although the like-lihood function does take into account the uncertainprediction error, it does not quantify the uncertainty inthe values of the parameters w. In the Bayesian frame-work, this can be represented by a prior PDF p(w | M)over the parameters w, which expresses the relative


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Fig. 6. Learning as inference.

plausibility of each value. Because generally there is alittle idea of what the values should be, it is usual to se-lect the prior as a rather broad distribution. Using onceagain the principle of maximum differential entropy,this requirement suggests a Gaussian prior distributionwith zero mean of the form

p(w | , M) =

2

W/2exp

2|w|2

(4)

where = 1/2W represents the inverse variance of thedistribution. Using available data, Bayes theorem up-dates the prior probability distribution over the parame-ters p(w |, M) to give the posterior PDF p(w | D, , ,M):

p(w | D,,, M) =p (D | w,, M) p (w | , M)

p (D | ,, M).

(5)

This posterior distribution is always more compactthan the prior distribution if the data informs the model,as indicated schematically in Figure 6, expressing thefact that something has been learned. Therefore, bymaximizing the posterior, the most plausible values ofthe parameters wMAP can be found.

Instead of finding a maximum of the posterior prob-ability in Equation (5), it is usually more convenientto seek instead a minimum of its negative logarithm.As shown in Figure 6, for the chosen prior distributionand likelihood function, the negative log probability is

just the usual sum of squares function in Equation (2).Therefore, the conventional learning approach can bederived as a particular approximation of the Bayesianframework where only the MAP (maximum a posteri-ori) parameter values are utilized.

5.2 Bayesian enhancements for neural networks

The optimization of the parameters w, that is, the so-called model fitting, is only one level of inference whereBayesian approach can be applied to neural networks.The potential enhancements that can be obtained by ap-plying this framework at further levels in a hierarchicalfashion are often not appreciated. The various levels canbe summarized as follows (Arangio, 2008):

1. Level 1: Model fitting: task of inferring appropriatevalues for the model parameters, given the model

and the data.2. Level 2: Optimization of the regularization terms and that make level 1 a better conditioned in-verse problem.

3. Level 3: Model class selection: the Bayesian ap-proach allows an objective comparison betweenmodels using alternative network architectures.

4. Level 4: Automatic relevance determination(ARD): the relative importance of different inputscan be determined using separate regularizationcoefficients.


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Regarding the first two levels, the traditional andthe Bayesian framework usually give equivalent results(MacKay, 1992). The addition of the third level, themodel class selection, has shown to be very effective.In fact, the number of adaptive parameters of the net-work model, that is, the model class, has to be fixed in

advance, and this choice has a fundamental importance.It is not correct to choose simply the model that fitsthe data better: more complex models will always fit thedata better but they may be over-parameterized and sothey make poor predictions for new cases.

The problem of finding the optimal number of param-eters provides an example of Ockhams razor, which isthe principle that one should prefer simpler models tomore complex models, and that this preference shouldbe traded off against the extent to which the models fitthe data (Sivia, 1996). The best generalization perfor-mance is achieved by the model whose complexity is

neither too small nor too large.The third level of inference mentioned above dealswith this task: the Bayesian framework provides anobjective and structured framework for dealing withthe issue of model complexity, and allows an objec-tive comparison between models with alternative net-work architectures (Beck and Yuen, 2004). The mostplausible model class among a set M of NM candi-date ones is obtained by applying Bayes Theorem asfollows:

p(Mj | D,M) p (D | Mj) p (Mj | M) . (6)

The factor p(D | Mj) is known as the evidence for the

model class Mj provided by the data D. Equation (6)shows that the most plausible model class is the one thatmaximizes p(D | Mj)p(Mj) with respect to j. If there isno particular reason a priori to prefer one model overanother, they can be treated as equally plausible a prioriand a noninformative prior, that is, p(Mj) = 1/NM, canbe assigned; then different models can be compared justby evaluating their evidence (MacKay, 1992).

Once the optimal architecture has been determined,the last issue that should be considered is the relativeimportance of each input variable. If the available datacomes from real systems it could be difficult to separate

the relevant variables from the redundant ones. In theBayesian framework, this problem can be addressed bythe ARD method, proposed by Mackay (1994) and Neal(1996). To use this technique, a separate hyperparame-ter i is associated with each input variable: this valuerepresents the inverse variance of the prior distributionof the parameters related to that input. In this way, ev-ery hyperparameter explicitly represents the relevanceof one input: a small value means that large parametersare allowed and the corresponding input is important;on the contrary, a large value means that the parameters

are constrained near zero, and hence the correspondinginput is less important.

The ARD allows a fourth level of inference to be ap-plied to the neural networks model. Once the architec-ture of the model is defined, the importance of every in-put is evaluated: if some hyperparameter is very large,

the related input will be dropped from the model andthe optimal architecture for the new model will be re-estimated.

The four levels of inference are summarized in theflowchart in Figure 7. Starting from the simple processof model fitting, further steps have been added to in-clude the other three levels of inference: evaluation ofthe hyperparameters, model class selection, and ARD.More details can be found in Arangio (2008).

The improvements that can be obtained by applyingthe first three levels are well documented in the exist-ing literature (MacKay, 1992, 1994). On the contrary,

the fourth level is usually applied independently andin this way the benefits of an integrated approach arenot fully exploited. In this work the evaluation of therelative importance of each input is included in the it-erative process. In this way, once the optimal architec-ture of the model is defined, it is possible to recognizeeventual redundant parameters and drop them from themodel.

6 MULTILEVEL STRATEGY FOR BRIDGEINTEGRITY ASSESSMENT

The Bayesian neural networks discussed in the previoussection is applied in a multi-step strategy for the assess-ment of the integrity of the long suspension bridge inFigure 8 (Arangio, 2008). The considered bridge has amain span of 3,300 m and it carries six road lanes in theexternal box girders and two railway tracks in the cen-tral one; detailed information on the bridge project andits history can be found in Bontempi (2006).

A multi-step approach has been followed because ithas been shown that is more effective to consider inde-pendently the tasks of damage detection, location, and

quantification (Ceravolo et al., 1995; Ko et al., 2002). Inthe first step of the strategy the occurrence of damageor anomalies in the bridge is detected, and the damagedportion of the structure is identified. If some damage isdetected, the second step of the procedure is initiated:using a pattern recognition approach, the specific dam-aged member within the whole area is identified, andthe extent of damage is evaluated. The entire procedurehas been carried out working on a finite-element modelof the bridge but it could be applied in the same way toan existent structure.


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Fig. 7. Hierarchical Bayesian framework for neural networks.

Fig. 8. Steps of the damage identification strategy.

6.1 Step 1: Damage detection

In the first step of the proposed strategy, the responseof the structure is monitored at various measurementpoints, located at groups of three (A, B, and C) every30 m along the bridge deck. One neural network foreach intermediate point (B) is built and trained using

the time-histories of the response of the structure sub-jected to wind actions and traffic loads (due to the pas-sage of a train) in the undamaged situation. The time-histories of selected structural response parameters aresampled at regular intervals, thus generating series ofdiscrete values. A set of such values from the instant t k to t is used as input for the network models, and thevalue at the instant t + 1 is used as the target output(left-hand side of Figure 9).

Then, the trained models are tested on new input pat-terns, corresponding to different time intervals and to


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Fig. 9. Flowchart of the chart of the Step 1 procedure for damage detection.

both undamaged and damaged situations. For each pat-tern, the set of values from ft+nk to ft+n1 is used asinput, and the value ft+n is predicted and compared with

the target one.If the error in the prediction is negligible, the struc-

ture is considered as undamaged; if the error is higherthan a threshold value (eventually defined according toexpert opinion), the presence of an anomaly is detected(Figure 10).

The anomaly may correspond to a damage state orsimply to a change of the characteristics of the exci-tation. To distinguish the changes in the structural re-sponse due to variations in the excitation from those dueto damage, the prediction errors are checked in all mea-surement points, according to the procedure schemati-

cally represented in the flowchart of Figure 9.If the prediction is wrong in several locations, that isthe difference e between the mean value of the errorsin training and testing is different from zero in differentmeasurement points, it can be concluded that the char-acteristics of the excitation are probably different fromthose assumed, and the trained neural network modelsare unable to represent the actual time-history of the re-sponse parameters. In this case, the models need to beupdated according to the new excitation. On the otherhand, if the difference e is large only at one or a few

points and generally decreases with the distance fromthose points, it can be concluded that the consideredportion is damaged.

To illustrate the proposed approach, data is simu-lated using a dynamic model of the suspension bridgewhere damage is implemented as a reduction of stiff-ness of a structural element. The following scenarios areconsidered:

1. Hangers: reduction of stiffness from 5% to 80%;2. Cables: reduction of stiffness from 1% to 10%;3. Transverse beam: reduction of stiffness from 5%

to 30%.

The training data set for every network model in-cludes 1,000 samples of the time-history of the response

parameters that were found to be the most sensitive toa stiffness reduction (Arangio and Petrini, 2007), that isthe rotation of the deck around the longitudinal axis incase of wind actions, and the vertical displacements ofthe deck in case of traffic loads.

6.2 Step 2: Identification of damage location andseverity

Having recognized that a portion of the structure isdamaged, the second step of the procedure is initiated;it is aimed at identifying the specific damaged element


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Fig. 10. Location of the measurement points on the bridge deck and identification of the damaged portion by considering theerrors in the approximation; also shown the potentially damaged elements of each portion.

Fig. 11. Neural network for the identification of damage location and intensity.

(a hanger, the cable, or a transverse beam), and at eval-uating the damage intensity. A pattern recognition ap-proach is used.

To create the training data set, the errors in Step 1obtained by the neural network approximation of theresponse time-histories at three different points of thedamaged portion (A, B, and C in Figure 11) are col-lected, by considering different damage scenarios.

For each damage scenario, the training data set has as

input the mean values of the errors in A, B, and C, and,as output, a vector including the five possible locationsof damage and its intensity (Figure 11).

7 RESULTS OF THE INTEGRITY ASSESSMENTPROCEDURE

7.1 Results of step 1: Damage detection

The different network models were trained using thetime-histories of the response of the bridge in undam-

aged conditions. The network architecture has been de-termined by the Bayesian approach discussed in Sec-tion 5: the optimal network models consist of 2, 2 and1 nodes in the input, hidden and output layers, respec-tively.

An example of the evolution in time of the differencesbetween the predicted and the target values in the setsof training and test data is reported in Figures 12 and13; both undamaged and damaged conditions are con-

sidered. It is possible to notice that when time-historiesrelated to various damage scenarios are proposed to thetrained networks the errors in the approximation in-crease. There is a difference e between the mean val-ues of the error in undamaged and damaged conditions.

In Figures 14 to 16 the increments e of the meanvalues of the error with respect to the undamaged situ-ation are shown for different levels of damage in the ca-bles, the hangers, and the transverse beam. Both windactions and traffic loads are considered and the resultsare compared.


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0.0

0.3

0.6

0.9

0 20 40 60 80

Training error Test error (undamaged)

err

t[s]

Fig. 12. Differences between the network values and thecorrect value in case of undamaged structure.

0.0

0.3

0.6

0.9

0 20 40 60 80

Training error Test error (damaged)

err

t[s]

emean -damaged

mean -undamaged

Fig. 13. Differences between the network values y and thecorrect value tin damaged conditions in a case example

(considered damage: 5% reduction of stiffness in one cable).

(a) Damage intensity (%) cable (pos 1/5)

0.0

0.3

0.6

0.9

1.0% 3.0% 5.0% 10%

train

wind

e

Fig. 14. Increment of the error in the approximation of theresponse time-history of the cable under wind actions and

traffic load.

0.00

0.03

0.06

0.09

20% 40% 50% 80%

train

wind

(c) Damage intensity (%) hanger (pos 2/4)

e

Fig. 15. Increment of error in the approximation of theresponse time-history of the hanger under wind actions and

traffic load.

0.00

0.03

0.06

0.09

5% 10% 30% 50%

train

wind

(b) Damage intensity (%) transverse beam (pos 3)

e

Fig. 16. Increment of error in the approximation of theresponse time-history of the transverse beam under wind

actions and traffic load.

Looking at the results shown in Figures 14 to 16, it ispossible to note that the proposed method is more ef-fective when responses from high speed excitation (liketraffic) are considered instead of responses due to slow

speed excitation (like wind). Thus, in the following step,only the structural response due to the passage of onetrain is considered.

7.2 Results of step 2: Identification of damage locationand intensity

Once the damaged portion of the whole structure is rec-ognized, the specific damaged element and the intensityof damage are identified using a pattern recognition ap-proach. Various damage scenarios, corresponding to thereduction of the stiffness in the hangers, the cables, andthe transverse beam in the identified damaged portion

is simulated, and a training set consisting of 370 exam-ples is created. The network architecture is always de-termined by the Bayesian approach discussed in Section5. The optimal network model has 11 units in the hiddenlayers.

After the training phase the network is tested with 30new input vectors that are not included in the trainingset, and the related damage scenarios are obtained andcompared with the target ones. To give a global and in-tuitive representation of the results, two quantities aredefined:

1. The position, which gives a measure of the error in

the location:

pos(i) =t y

|t| |y|(7)

2. The intensity, which gives a measure of the errorin the quantification:

int(i) =|t|

t|y|. (8)

If these quantities are equal to one, the damage is welllocalized and its intensity is correctly estimated. These


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0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 10 20 30

Test number

pos

Fig. 17. Identification of the damage position in the testexamples.

0.0

0.3

0.5

0.8

1.0

1.3

1.5

0 10 20 30

Test number

int

Fig. 18. Identification of the intensity in the test examples.

quantities are evaluated for each of the 30 test samplesand the results are shown in Figures 17 and 18. The lo-cation can be detected in almost 90% of the considered

cases and the intensity is correctly estimated in 66% ofthe cases.

8 CONCLUSIONS

In this work the concept of dependability has been dis-cussed and its original meaning has been extended tothe structural engineering field. It has been shown thatthis term describes the overall quality performance of acomplex structural system and its influencing factors inan integrated way.

The different aspects related to dependability are

strictly connected with the concept of structural in-tegrity. During the service life the integrity, and conse-quently the dependability, can be lowered by damages.The structural monitoring represents an essential toolto assess the evolution in time of the dependability ofexisting structural systems.

Fundamental tasks of integrity monitoring are faultdetection and diagnosis. Fault diagnosis from experi-mental data is an inverse problem and the reconstruc-tion of the fault-symptom chain can be very difficult.A solution can be achieved by applying a knowledge-

based procedure that integrates the solving procedureswith the heuristic knowledge coming from experienceor qualitative information. For this task, different softcomputing methods can be suitable. In particular, inthis work, the Bayesian neural network model has beenused to formulate a hierarchical integrity assessment

strategy.The proposed approach has been applied for the anal-

ysis of the time-history of the response of a long spansuspension bridge subjected to ambient excitations. Thestrategy could be useful for damage identification oflarge structural systems instrumented with on-line mon-itoring systems. The presented example case has beendeveloped on a numerical model of the structure butthe strategy can be applied on real structural systems aswell: various neural networks models could be selectedand trained in a continuous way using the time-historiesof the structural response; in this way the occurrence of

anomalies can be detected almost in real time. Whenan anomaly is recognized, numerical simulations can becarried out to create the data set to develop the secondstep of the strategy. In this way experimental data areused for damage detection and the results of the numer-ical analyses can help to identify the damaged elementand to quantify the intensity of damage.

ACKNOWLEDGMENTS

The authors wish to thank Professors H. Li (Harbin In-stitute of Technology), J.L. Beck (California Institute

of Technology), F. Casciati, and L. Faravelli (Univer-sity of Pavia) for discussions related to this study. Thereviewers of the article are acknowledged for the care-ful reading and the very useful suggestions. The sup-port of Prof. H. Adeli is also recognized. The financialsupport of University of Rome La Sapienza is alsoacknowledged. The opinions and the results presentedhere are however the responsibility only of the authorsand cannot be assumed to reflect the ones of Universityof Rome La Sapienza.

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