Structural integrity monitoring for dependability

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Structural integrity monitoring for dependabilityS. Arangio a , F. Bontempi a & M. Ciampoli aa Department of Structural and Geotechnical Engineering, Sapienza Università di Roma, ViaEudossiana 18, 00184, Roma, ItalyPublished online: 06 Apr 2010.

To cite this article: S. Arangio , F. Bontempi & M. Ciampoli (2011) Structural integrity monitoring for dependability,Structure and Infrastructure Engineering: Maintenance, Management, Life-Cycle Design and Performance, 7:1-2, 75-86, DOI:10.1080/15732471003588387

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Structural integrity monitoring for dependability

S. Arangio*, F. Bontempi and M. Ciampoli

Department of Structural and Geotechnical Engineering, Sapienza Universita di Roma, Via Eudossiana 18, 00184, Roma, Italy

(Received 21 October 2008; final version received 16 December 2009; published online 6 April 2010)

Dependability of a structural system is a comprehensive concept that – by definition – describes the quality of thesystem as its ability to perform as expected in a way that can justifiably be trusted. One of the attributes ofdependability is integrity, which can be interpreted as the absence of improper alterations of the structuralconfiguration. The assessment of the integrity during the whole life-cycle can be carried out efficiently byimplementing a monitoring system able to detect and diagnose any fault at its onset. The essential feature of themonitoring system dealt with in the paper is the elaboration of data gathered on site by a combination of simulationand heuristics. In detail, the first part of the paper deals with the extension of the concept of dependability, asformulated in computer science, to structural engineering. The second part illustrates a two-step hierarchical strategyfor the assessment of the integrity of a structure through monitoring of its response under ambient vibrations;Bayesian neural network models are used for fault detection and diagnosis from observable symptoms. In the firststep, the occurrence of any fault is detected and the relevant portion of the structure identified; in the second step thespecific element affected by the fault is recognised and the intensity of the alteration of the structural performanceevaluated. The strategy is applied to assess the integrity of a long-span suspension bridge subjected to wind actionand traffic loading. As the bridge is under design, measured data are simulated by analysing the response of adetailed FE model of the whole structural system. The final objective of the study is the optimal design of theintegrity monitoring system for the bridge.

Keywords: structural systems; dependability; integrity monitoring; fault detection; fault diagnosis; Bayesian neuralnetwork models

1. Introduction

The design of a valuable and safety-critical construc-tion requires advanced approaches to take intoaccount the intrinsic ‘complexity’ of the structuralsystem. A relevant aspect of the complexity is the factthat structures are usually systems composed ofstrongly interacting components. Structural designcannot rely on a simplistic idealisation of the structureas a ‘device for channelling loads’, that allows safetychecks carried out considering each structural elementper se; it must be based on the analysis of the structuralsystem as a whole, being interpreted as ‘a set ofinterrelated components working together toward acommon purpose’ (NASA-SEH 1995).

Another aspect that is worth mentioning is the factthat when subjected to accidental or exceptionalactions, such as earthquakes and windstorms, or todeterioration mechanisms, structural systems mayexhibit a non-linear behaviour, and a realistic evalua-tion of the structural performance during the wholelife-cycle can be extremely cumbersome. Moreover,any structural response shall be evaluated by takinginto account the influence of the several sources of

uncertainty that characterise both the actions and thestructural properties, as well as the efficiency andconsistency of the model of structural response.

In principle, the design process shall includerequirements concerning the construction phase andthe operation and maintenance during the whole life-cycle. To this aim, data collected on site (e.g. through acontinuous monitoring) are essential both for checkingthe accomplishment of the expected performanceduring the service life, and for validating the originaldesign. Only if the aforementioned features areproperly considered, the structural response can bereliably evaluated, and the performance of the buildingconstruction ensured during the intended lifetime:System Engineering represents the robust approachthat takes properly into account the different aspectsrelated to conceptual and structural design, construc-tion and maintenance (Bontempi et al. 2008).

The overall approach requires the definition of thequality of a complex structural system by a compre-hensive concept, like dependability. The concept ofdependability has been originally developed in the fieldof computer science, where it is defined as ‘the ability

*Corresponding author. Email: [email protected]

Structure and Infrastructure Engineering

Vol. 7, Nos. 1–2, January–February 2011, 75–86

ISSN 1573-2479 print/ISSN 1744-8980 online

� 2011 Taylor & Francis

DOI: 10.1080/15732471003588387

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to deliver services that can justifiably be trusted’(Avizienis et al. 2004): the dependability of a systemreflects (i.e. represents, measures, . . .) the user’s degreeof trust in that system, i.e. the user’s confidence thatthe system will operate as the user expects and will notfail in normal use during the whole lifetime (Sommer-ville 2000). The definition can be extended toStructural Engineering: the design process shall beaimed at justification of trust through the fulfilment ofsome ‘attributes’ of dependability, mainly reliability,safety, maintainability, and integrity.

According to the original definitions given inAvizienis et al. (2004), reliability can be interpretedas the continuity of correct service for the whole servicelife; safety corresponds to the absence of catastrophicconsequences of system operation on the users and theenvironment; maintainability is the ability to undergomodifications and repairs; integrity corresponds to theabsence of improper system alterations and is some-times related to the completeness and consistency ofthe structural configuration (Bontempi and Giuliani2008).

Other attributes of dependability are the availabil-ity, originally defined as the readiness for correctservice at a given point of time, and the security, that isa property that reflects the ability of the system toprotect itself from accidental or deliberate externalattack and is an essential pre-requisite for availability,reliability and safety.

All attributes can be subdivided in high level oractive performances (reliability, availability, maintain-ability) and low level or passive performances(safety, security and integrity); the latter are exclusiverequirements, in the sense that they exclude undesir-able situations rather than specifying requiredperformances.

It is evident that the dependability specification of astructural system must include the requirements for thedependability attributes in terms of admissible fre-quency and severity of failures in a given environment;obviously, one or more attributes may not be requiredat all for a given system. The attributes can vary overthe life-cycle; in particular, the integrity and conse-quently the overall dependability can be lowered bydeterioration due to effects of wear during ordinaryservice, improper use and maintenance, as well asenvironmental and accidental events.

Structural monitoring represents the tool for theassessment of the evolution in time of the integrity,thus of the dependability of an existing structuralsystem. It integrates, in a unified framework, advancedengineering analyses and experimental data processing.Therefore it is a very complex task, and includes issuessuch as the definition and analysis of the structuralperformances, from regular exercise to out-of-service

and collapse, the assessment of the environmentalconditions, the choice of the sensor systems and theiroptimal placement, the use of data transmissionsystems and signal processing techniques, and themethods for damage identification, location andquantification and for structural model updating(Berthold and Hand 1999).

Soft computing methods can be very useful toprocess data gathered by monitoring. In this paper, theBayesian neural network models are used to formulatea two-step hierarchical strategy for structural integritymonitoring. In the first step the occurrence ofabnormal alterations of the structural response ischecked and eventually the damaged section of thestructure identified; in the second step, the specificdamaged element in the considered section is recog-nised and the intensity of damage evaluated.

In the following, the dependability assessment isexplained in detail with reference to structural systemsand the two-step strategy for structural integritymonitoring illustrated. The strategy is applied to assessthe integrity of a long-span suspension bridge sub-jected to wind action and traffic loading. As the bridgeis under design, measured data are simulated byanalysing the response of a detailed finite elementmodel of the whole structural system. The finalobjective of the study is the optimal design of theintegrity monitoring system for the bridge.

2. Dependability assessment and structural integrity

monitoring

As specified above, the dependability of a structuralsystem is a comprehensive concept that includes anddescribes the relevant aspects with reference to thesystem quality and its influencing factors. The assess-ment of dependability requires the definition of threeelements (Figure 1): the attributes, i.e. the propertiesthat quantify the dependability; the threats, i.e. theelements that affect dependability; the means, i.e. thetools that can be used to increase dependability.

In structural engineering, the relevant attributes arereliability, safety, maintainability and integrity. Theseproperties are essential to guarantee, with reference tothe whole life-cycle, the survivability of the systemunder the relevant accidental or exceptional hazardscenarios, considering also the security issue, and thesystem robustness, serviceability in operating condi-tions and durability.

The threats to system dependability can besubdivided into faults, errors and failures. Accordingto the definitions given in Avizienis et al. (2004), anactive or dormant fault is a defect or an anomaly in thesystem behaviour that represents a potential cause oferror; an error is the cause for the system being in an

76 S. Arangio et al.

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incorrect state; failure is a permanent interruption ofthe system ability to perform a required functionunder specified operating conditions. For buildingconstructions, possible faults are incorrect design,construction defects, improper use and maintenance,and damages due to accidental actions or deteriora-tion; errors may or may not cause failure, and mayalso activate a fault.

Following the approach proposed in Isermann(2006), the design of a dependable structural systemis basically the problem of the design of a fault-tolerantsystem: however, it includes also features like faultdetection, that is detection of alterations of the systembehaviour, fault diagnosis, that is, localisation andquantification of the effects of faults and errors, and,finally, the management of faults and errors aimed atavoiding failure.

This paper is focused mainly on fault detection anddiagnosis. These elements are strictly related to themonitoring of the integrity of the structural system: infact an efficient monitoring programme is expected tobe able to preserve the structural dependability,diagnosing alterations, that is deterioration anddamage, at their onset (Li and Ou 2006).

In analogy with biological systems, and even ifthere is no general consensus on its definition, anintegrity monitoring system should (Aktan et al. 1998,Isermann 2006): sense the loading environment as wellas the structural response; reason by assessing the

structural condition and health; communicate througha proper interface with other components and systems,including controllers of the system behaviour; learnfrom experience as well as by interfacing with humanfor heuristic knowledge; be precise, so that even smallfaults should be detected and diagnosed; decide andtake action for alerting controllers in case of accidentalsituations, or activate fault tolerant configurations incase of a reconfigurable system.

An ‘optimal’ integrity monitoring system allows thecontrol of the structural system in a proactive way: thecircumstances that may eventually lead to deteriora-tion, damage and unsafe operations can be diagnosedand mitigated in a timely manner, and costly replace-ments can be avoided or delayed. Analysing theproblem in terms of cost–benefit analysis, it comesout that, in case of complex structures, the integritymonitoring should be planned since the design phaseand carried out during the entire life-cycle in orderto assess the structural health and performance underin-service and accidental conditions (Aktan et al. 2002).

Over the past 30 years a huge research effort hasbeen devoted to developing effective methods forintegrity monitoring of civil structures. An extensivesurvey of global methods (so-called because they arebased on the analysis of the whole structure) has beenpresented in Doebling et al. (1996), and updated bySohn et al. (2004), where it is observed that, usually,non-destructive global methods can be used for fault

Figure 1. Dependability: attributes, threats and means (adapted from Avizienis et al. 2004).

Structure and Infrastructure Engineering 77

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detection, whereas local inspections and patternrecognition approaches for fault diagnosis.

Regarding the temporal extent of the measure-ments, continuous measurements are usually needed tocapture environmental effects such as those due towind and temperature; periodic inspections andmeasurements are needed to evaluate the responseunder operating conditions. Extensive use of long termcontinuous monitoring is quite new, enabled by recentadvances in data acquisition, processing and manage-ment. Long term monitoring of the structural responsewas pioneered in China and Japan (Abe and Amano1998, Wong et al. 2000, Ko and Ni 2005): nowadays,several bridges are instrumented in Europe (Casciati2003), United States (Pines and Aktan 2002), Canada(Mufti 2001), Korea and other countries. Recentdevelopments consist in formulating a general frame-work of asset management in a life-cycle perspective(Messervey and Frangopol 2008).

3. Neural network models for fault detection and

diagnosis

In general, a fault causes events that, as intermediatesteps, influence or determine measurable or observablesymptoms. In order to detect, locate and quantify asystem fault, it is necessary to process data obtainedfrom monitoring and to interpret the symptoms.However, this is a very complex task, as explained inFigures 2 and 3. The relationship between fault andsymptoms can be represented graphically by a pyramid(Figure 2); the vertex represents the fault, the lowerlevels the possible events generated by the fault and thebase corresponds to the symptoms. The propagation ofthe fault to the symptoms follows a cause–effectrelationship, and is a top-down forward process. Thefault diagnosis proceeds in the reverse way; it is abottom-up inverse process that relates the symptoms tothe fault. To solve the problem implies the inversion ofthe causality principle. But one cannot expect torebuild the fault–symptom chain only by measured

data because the causality is not reversible or thereversibility is ambiguous (Fussel 2002): the underlyingphysical laws are often not known in analytical form,or too complicated for numerical calculation. More-over, intermediate events between faults and symptomsare not always recognisable (as indicated in Figure 3).

The solving strategy requires integrating differentprocedures, either forward or inverse; the mixedapproach has been denoted as the total approach byLiu and Han (2004), and different computationalmethods have been developed for this task, that is, tointerpret and integrate information coming from onsite inspection, database and experience. In Figure 3 anexample of knowledge-based analysis is shown. Theresults obtained by instrumented monitoring (thedetection and diagnosis system on the right side) areprocessed and combined with the results coming fromthe analytical or numerical model of the structuralresponse (the physical system on the left side).

Information technology provides the tool for suchintegration. The processing of experimental data is thebottom-up inverse process, where the output of thesystem (the measured symptoms: displacements, accel-eration, natural frequencies, etc) is known but theparameters of the structure have to be determined.Different computational methods can be used to thisaim. In several applications, soft computing techni-ques, like the neural network models used in this study,have shown their effectiveness in processing informa-tion coming from monitoring. For a review on thesubject, it is possible to refer to Adeli (2001), whoillustrated the applications of neural networks to civilengineering during a decade, and to Waszczyszyn(1999), who collected in a book various papers on theuse of neural networks for the analysis and design ofstructures. As concerns more specifically the problemof damage identification and structural health mon-itoring, Ni et al. (2002) presented a two-stage neuralnetwork-based damage detection method, wheredamage location is identified in a first stage anddamage severity is estimated in a second stage; Ko

Figure 2. Fault–symptoms relationship.


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et al. (2002) used neural networks in a multi-stageidentification scheme for detecting damage in a cable-stayed bridge in Hong Kong; Xu and Humar(2006) presented a two-step algorithm that uses amodal energy-based damage index to locate thedamage and a neural network technique to determineits magnitude.

The neural network concept has its origins inattempts to find mathematical representation ofinformation processing in biological systems. Actuallythere is a definite probability model behind it; in fact aneural network is an efficient statistical model fornonlinear regression. It can be described by a series offunctional transformations working in different corre-lated layers (Bishop 2006), that, in case of two layers,takes the form:

yk x;wð Þ¼ hXMj¼1

wð2Þkj g

XDj¼1

wð1Þji xiþb

ð1Þj0

!þb

ð2Þk0

!ð1Þ

where yk is the k th output variable in the outputlayer, x is the vector of the D input variables in theinput layer, w is the matrix including the adaptiveweight parameters w

1ð Þji and w

2ð Þkj and the biases b

1ð Þj0 and

b2ð Þk0 that are set during the training phase (the

superscript refers to the considered layer), M isthe total number of units in the hidden layer, thequantities within the brackets are the so calledactivations, that are transformed using the activationfunctions h and g.

The values of the components of w are obtainedduring the training phase by minimising a proper errorfunction: in the considered case, the sum of squarederrors with weight decay regularisation (Bishop 1995)given by:

E ¼ 1

2

XNn¼ 1

XNo

k¼1yk xn;wð Þ � tnk� �2 þ a

2

XWi¼ 1

wij j2 ð2Þ

where yk is the k th neural network output correspond-ing to the n th realisation of x, tnk is the relevant targetvalue, N is the size of the considered data set, N0 is thenumber of output variables, W is the number ofparameters in w.

Neural network learning can be interpreted in theframework of Bayesian inference (MacKay 1995),where probability is treated as a multi-valued logicthat may be used to perform plausible inference(Jaynes 2003). Within this framework it is possible tosolve a crucial problem of neural network application:the choice of the optimal model complexity, which isgiven by the number of units included in the hiddenlayers. This number has to be fixed before training, andaffects significantly the generalisation performance ofthe network model.

In general the number of hidden units is selected byexperience or rule of thumb, and depends heavily onthe subjective judgment of the designer: in this paperthe optimal architecture of the network model for agiven set of training data is selected by a Bayesian

Figure 3. Knowledge-based analysis for structural integrity monitoring.


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model class selection approach (Beck and Yuen 2004).As a result, the selection of the neural network modelclass is mathematically rigorous and systematic; theBayesian approach allows an objective comparisonamong alternative solutions and eliminates reliance onthe judgment of the neural network designer (MacKay1995). The mathematical approach for neural networkmodel class selection is illustrated in detail in Arangioand Beck (2010), where the most plausible model classamong a set of candidate ones is obtained by applyingBayes’ Theorem and maximising the posterior prob-ability of the model class given a set of training data. Inthis respect, let us remember that it is not correct tochoose simply the model that better fits data: morecomplex models will always fit the data in a better way,but they may be over-parameterised and give poorprediction for new cases.

4. A two-level strategy for bridge integrity assessment

Bayesian neural network models have been used toformulate the two-step hierarchical strategy for theintegrity assessment of the bridge that is schematicallyrepresented in Figure 4. It is a long span suspensionbridge that was recently reconsidered in Italy: apreliminary design scheme elaborated in 2005 hasbeen considered for numerical calculations. The mainspan is 3300 m long, while, including the two sidespans, the total length is 3666 m. The towers are 383 mhigh and the bridge suspension system relies on twopairs of steel cables, each with a diameter of 1.24 mand a total length, between the anchor blocks, ofapproximately 5000 m; the secondary suspensionsystem consists of 121 pairs of rope hangers. The crosssection of the deck is composed of three box elementssupported every 30 m by transversal beams; the deckcarries six road lanes in the external portions of thedeck and two railway tracks in the central one. Moredetailed information on the bridge design can befound, for example, in Bontempi (2006).

The two-step strategy considers the tasks ofdamage detection, location, and quantification. Asshown in Figure 5, in the first step the occurrence of

anomalies in the bridge response is detected: if theanomalies correspond to possible alterations of thebridge response due to any damage, the damagedportion of the whole structural system is identified. Ifsome damage has been detected, the second step isinitiated: by using a pattern recognition approach,the specific damaged member within the wholesection is identified and the intensity of damageevaluated. The two steps are illustrated in detail inthe following.

4.1. Step 1: Damage detection

As shown in Figure 5, it is assumed that the responseof the structure, represented by the time-histories ofthe displacements, is monitored by sensors at variousmeasurement points. In the example case, they arelocated in groups of three (A–B–C) every 30 m alongthe bridge deck; each group individuates a test section.

Different Bayesian neural network models aretrained; in this step, one for each intermediate point(B). The models are built and trained using the time-histories of the displacements of the structure subjectedto wind action and traffic loads (that correspond, in theexamined case, to the passage of one train) in theundamaged situation. The procedure for networktraining is shown in Figure 6: the time-history of theresponse parameter f is sampled at regular intervals,generating a series of discrete values ft. A set of d suchvalues: ft-dþ1, . . ., ft, is used as input of the networkmodel, while the next value ftþ1 is used as the targetoutput. By stepping along the time axis, a training dataset consisting of many sets of input vectors with thecorresponding output values is built, and the networkmodels are trained. The trained models are then testedwith a set of observed values ftþn-d, . . . , ftþn, to predictthe value of ftþnþ1, according to the procedure of one-step ahead forecast (Bishop 1995). After the initialtraining phase, new input sets, corresponding to bothundamaged and damaged situations, are tested on thetrained models. For each set, the one-step ahead valueof the parameter is forecast and compared with thetarget.

Figure 4. Scheme of the considered bridge.


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The results of the training and test phases areelaborated as shown in Figure 7. The two plots showthe difference err between the network output value yand the target value t at several time steps for bothtraining and test in undamaged and damaged condi-tions. It is possible to note that the mean values of err(indicated by a straight line) obtained both in trainingand test are comparable if the structure remainsundamaged. On the contrary, in case of anomalies

that may correspond to damages, there is a differenceDe between the mean values of err corresponding to thedamaged and undamaged conditions in the test phase.

It has to be noted that the detected anomaly maycorrespond to a damage state or simply to a change ofthe characteristics of the excitation. To individuate theactual cause of the anomaly, the intensity of De ischecked in different test sections, according to theprocedure that is schematically represented in the flowchart shown in Figure 8. In the left side of Figure 8, thestart-up of the procedure is shown: given a data set, theoptimal neural network model is selected according tothe Bayesian approach, that is, the model with thehighest posterior probability is chosen and trained(Arangio and Beck 2010). Then, as shown in the rightside of Figure 8, the model is tested with new inputdata sets. If the difference De of the errors betweentraining and test is different from zero in several testsections, it can be concluded that the characteristics ofthe excitation are probably different from thosehypothesised. The adopted neural network modelsare thus unable to represent the actual time-histories ofthe response parameters, and have to be updated andtrained according to the modified characteristics of theexcitation. If De is different from zero only in one orfew test sections and generally decreases with thedistance from the selected section, it can be concludedthat the considered section of the structure is damagedand the second step of the procedure is actuated.

Figure 5. Sketch of the two-step strategy for the assessment of the structural integrity.

Figure 6. Procedure for network training.


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In real applications, not all cases in which De isdifferent from zero should be considered as relevant;also, because it is essential to take properly intoaccount the noise corrupting the signals and theaccuracy of the measuring instruments, the choice ofthe threshold value for initiating the second step must

be left to the experience of the operator. In thenumerical applications illustrated below, all cases inwhich De is different from zero have been considered.

In the considered example, data are simulated byanalysing the dynamic response of a FE model of thesuspension bridge. Damage is modeled as a reduction

Figure 7. Difference err between output y and target t values as a function of time for training and test in undamaged anddamaged conditions in a case example (considered damage: 5% reduction of stiffness in one cable).

Figure 8. Flow-chart of the first step of the procedure.


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of stiffness of a structural element in a test section andthe following damage scenarios are considered:

. Hangers: reduction of stiffness from 5% to 80%.

. Cables: reduction of stiffness from 1% to 10%.

. Transverse beam: reduction of stiffness from 5%to 30%.

Data adopted for training every network modelconsist of 1000 samples of the time-histories of theresponse parameters that were found to be the moresensitive to a stiffness reduction (Arangio and Petrini2007): the deck twist in case of wind actions, and thevertical displacement of the centroid of the deck crosssection in case of traffic loads. The number of sampleshas been chosen after some trials, where it has beennoticed that no significant improvements in thegeneralisation capacity of the network are obtainedfor a higher number.

4.2. Step 2: Identification of damage location andintensity

Having recognised that a test section is damaged, thesecond step of the procedure is start up. It is aimed atidentifying the specific damaged element (Figure 5: oneof the two cables – the transverse beam – one of thetwo hangers), and at evaluating the intensity ofdamage. A pattern recognition approach is used: inorder to improve the quality of the procedure, themean values of the errors err in the prediction of theresponse time-histories for all three measurementpoints (A, B and C) in the considered test section aretaken as input of the selected neural network model.As shown in Figure 5, each damage scenario isdescribed by a vector of five components: eachcomponent indicates the state (represented by anumber denoting the presence – if different from zero– and the intensity) of damage of a structural elementin the test section.

Simulated damage scenarios have been assumed asoutput of the neural network model in numericalcalculations. The data set for the second step has beengathered by simulating 400 damage scenarios (corre-sponding to different positions and intensities ofdamage): 370 out of them have been used for networktraining, the remaining 30 for testing the networkgeneralisation performance.

5. The case example: Results of the procedure for the

integrity assessment

5.1. Results of step 1: Damage detection

The optimal model for the prediction of the time-histories of the response parameters has been selected

by considering the structural response in the unda-maged condition, and exploiting the procedure forBayesian model selection that is fully explained inArangio and Beck (2010); it consists of 2, 2 and 1 unitsin, respectively, the input, hidden and output layers.The model optimised in this way is also the mostefficient in terms of sensitivity to changes in structuralbehavior: it corresponds to the lowest error inthe training phase and to the highest error in theapproximation of the signal when anomalies aredetected (Arangio 2008).

In Figure 9 (a), (b), (c), the differences between themean values of the errors De in the damaged andundamaged conditions are shown for different inten-sities of damage (that is, of stiffness reduction)respectively to the cables, the transverse beam, andthe hangers.

Looking at the plots in Figure 9, it is evident thatthe adopted strategy is more effective when responsesto high speed excitations (like traffic loads) areconsidered instead of responses to slow speed excita-tions (like wind actions). Thus, in the following step,only the structural response due to the transit of trainis considered. The possibility of detecting the damagesis different for the various elements, as expected: infact, a small damage to the cables determines a muchhigher value of De than strong damages to thetransverse beam and the hangers. Nonetheless, thestrategy allows detecting even small damages, and ischaracterised by a high level of precision.

5.2. Results of step 2: Identification of damagelocation and severity

Once a damaged section is detected, the specificdamaged element and the intensity of damage areidentified by using the pattern recognition approach.The optimal network model, that is the most efficientin terms of localisation and quantification of damage(Arangio and Beck 2010), is selected by the Bayesianapproach on the base of the 370 patterns consideredfor training. It consists of three input variables, that is,the errors err evaluated at A, B, and C, five outputvariables, that is, the possible locations (coincidentwith a structural element) and intensities of damage,and two hidden layers with 11 units (obtained by theBayesian selection process). After the training phase,the network is tested with the remaining 30 patterns.

To evaluate the efficiency of the assessment, twoquantities are defined and evaluated for each testpattern: the position, which gives a measure of theprediction error made in any damaged location, andthe intensity, which gives a measure of the error madein estimating the damage intensity. These quantitiesare obtained by comparing the vectors of the output


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variables corresponding to the evaluated y and thetarget t damage scenarios, and are expressed by:

pos ¼ t� y

tj j � yj j ð3Þ

int ¼ tj jyj j ð4Þ

where 6 denotes the inner product and j�j is the normof the vector. If pos and int are (approximately) equalto 1, it can be assumed that the damage is well localisedand its intensity correctly estimated.

The results of the numerical application are shownin Figure 10: the damaged element is correctly locatedin almost 90% of the considered cases, and theintensity is correctly estimated in approximately 66%of the considered cases. Therefore, it appears that theproposed strategy is more efficient in locating thedamage than in quantifying it.

6. Final remarks

In the first part of the paper, the concept ofdependability, originally developed in the field ofcomputer science, has been extended to structuralengineering, in order to define and measure the qualityof a complex structural system. The whole designprocess is then understood as aimed at ‘justification oftrust’ through the fulfilment of some ‘attributes’ ofdependability, mainly reliability, safety, maintainabil-ity and integrity.

As a further development of the concept ofdependability, it seems useful to add the attribute ofsustainability: a structure should be acceptable for itsenvironment and ‘meet present needs without com-promising the ability of future generations to meettheir needs’, as indicated in a 1987 UN Conference.This aspect will be dealt with in future studies.

In the second part of the paper, a two-step strategyfor structural integrity monitoring has been discussed.

Figure 9. Differences between the mean errors De in training and test for different intensities of damage in (a) one of the twocables, (b) the transverse beam, and (c) one of the two hangers.

Figure 10. Accuracy of the estimation of the position and intensity of damage in a bridge section (30 tests).


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It represents an essential tool for the assessment ofexisting structural systems as it allows controlling thestructural system in a proactive way: the circumstancesthat may eventually lead to deterioration, damage andunsafe operations can be diagnosed and mitigated in atimely manner, and costly replacements avoided ordelayed.

Fundamental tasks of integrity monitoring arefault detection and diagnosis. It has been observedthat the diagnosis from experimental data is an inverseproblem and the backwards assessment of the fault-symptom chains cannot be done solely from measureddata, since the causality is not reversible or thereversibility is ambiguous. The problem has beensolved by developing and applying a knowledge-basedprocedure that integrates forward and inverse solvingmethods with the heuristic knowledge coming fromexperience or qualitative information. More specifi-cally, the Bayesian neural network model has beenproposed to formulate the two-step hierarchicalstrategy for integrity assessment. The strategy hasbeen applied to the case of a long-span suspensionbridge subjected to wind actions and traffic loadings,and the capability of detecting the location andintensity of damages to the main structural elementsof the superstructure has been examined.

Acknowledgements

This paper is dedicated to Professor Giuliano Augusti whoalways gave, and still gives, impetus to the research of theauthors with stimulating suggestions. Thanks are due toProfessors Pier Giorgio Malerba, Dan Frangopol and FabioBiondini for fruitful discussions and comments on themanuscript, and to James L. Beck, who introduced the firstauthor to the exciting subject of Bayesian neural networks. Apartial support from the Italian National Ministry forUniversity and Research (in the framework of PRIN 2007– Research Project Wi-POD) is gratefully acknowledged.

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