Design Knowledge Gain by Structural Health Monitoring

Chapter 4

Design Knowledge Gain by StructuralHealth Monitoring

Stefania Arangio and Franco BontempiDepartment of Structural and Geotechnical Engineering, Sapienza University of Rome,Rome, Italy

Abstract

The design of complex structures should be based on advanced approaches able to takeinto account the behavior of the constructions during their entire life-cycle. Moreover,an effective design method should consider that the modern constructions are usuallycomplex systems, characterized by strong interactions among the single componentsand with the design environment. A modern approach, capable of adequately consider-ing these issues, is the so-called performance-based design (PBD). In order to profitablyapply this design philosophy, an effective framework for the evaluation of the overallquality of the structure is needed; for this purpose, the concept of dependability canbe effectively applied. In this context, structural health monitoring (SHM) assumesthe essential role to improve the knowledge on the structural system and to allowreliable evaluations of the structural safety in operational conditions. SHM should beplanned at the design phase and should be performed during the entire life-cycle of thestructure. In order to deal with the large quantity of data coming from the continu-ous monitoring various processing techniques exist. In this work different approachesare discussed and in the last part two of them are applied on the same dataset. It isinteresting to notice that, in addition to this first level of knowledge, structural healthmonitoring allows obtaining a further more general contribution to the design knowl-edge of the whole sector of structural engineering. Consequently, SHM leads to twolevels of design knowledge gain: locally, on the specific structure, and globally, on thegeneral class of similar structures.

Keywords

ANCRiSST benchmark problem, complex structural systems, dependability, enhancedfrequency domain decomposition, neural networks, performance-based design, softcomputing, structural health monitoring, structural identification, system engineering,Tianjin Yonghe bridge.

4.1 Introduction

In recent years more and more demanding structures and infrastructures, like tall build-ings or long span bridges, are designed, built and operated to satisfy the increasing

DOI: 10.1201/b17073-5http://dx.doi.org/10.1201/b17073-5

96 Maintenance and Safety of Aging Infrastructure

needs of society. These constructions require high performance levels and should bedesigned taking into account their durability and their behavior in accidental con-ditions (Koh et al., 2010; Petrini & Bontempi, 2011; Crosti et al., 2011; 2012;Petrini & Palmeri, 2012). Their design should be able to consider their intrinsiccomplexity that can be related to several aspects, such as for example the strong non-linear behavior in case of accidental actions and the fact that, while safety checksare carried out considering each structural element per sé, structures are usually sys-tems composed by deeply interacting components. Moreover the structural responseshall be evaluated taking into account the influence of several sources of uncertainty,both stochastic and epistemic, that characterize either the actions or the structuralproperties, as well as the efficiency and consistency of the adopted structural model(Frangopol & Tsompanakis, 2009; Elnashai & Tsompanakis, 2012, Biondini et al.,2008; Bontempi & Giuliani, 2010). Only if these aspects are properly considered, thestructural response can be reliably evaluated, and the performance of the constructionsensured.

Furthermore, the recent improvement in data measurement and in elaborationtechnologies has created the proper conditions to improve the decisional tools basedon the performance on site, leading to a system design philosophy based on the per-formance, known as performance-based design (PBD). In order to apply the PBDapproach, an effective framework for the evaluation of the overall quality of a struc-ture is needed. For this purpose, a specific concept has been proposed: the so-calledstructural dependability. This is a global concept that was originally developed in thefield of computer science but that can be extended to civil engineering systems (Arangioet al., 2010).

In this context, structural health monitoring assumes an essential role to improvethe knowledge on the structural system and to allow reliable evaluations. It should beplanned since the design phase and carried out during the entire life-cycle because it rep-resents an effective way to control the structural system in a proactive way (Frangopol,2011): the circumstances that may eventually lead to deterioration, damage and unsafeoperations can be diagnosed and mitigated in a timely manner, and costly replacementscan be avoided or delayed.

Different approaches exist for assessing the structural performance starting from themonitoring data: they are based on deterministic indexes or on sophisticated proba-bilistic evaluations and they can be developed at different levels of accuracy, accordingto the considered situation. In the last part of the work, a case study is analyzed byusing two different approaches, the structural identification in the frequency domainand a neural network-based damage detection strategy, and the results are compared.The concepts discussed above are schematized in the flow chart in Figure 4.1 anddetailed in the following paragraphs.

4.2 Knowledge and Design

It is well known, and perhaps it is an abused slogan, that we are in the Era of Knowl-edge. This is of course true in the field of structural design. Generally speaking, theknowledge of the people involved in structural design can be schematically representedby the large rectangle shown in Figure 4.2. But this actual knowledge usually does notcover all the design necessities and there are areas of knowledge that are not expected

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Design Knowledge Gain by Structural Health Monitoring 97

Figure 4.1 Logical process for an innovative design by exploiting the knowledge gained bystructural health monitoring.

Figure 4.2 Knowledge gain process.

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at the beginning of the project. According to the required additional knowledge, designcan be classified as:

I. evolutive design (small rectangle at the bottom) that does not require a largeamount of new knowledge because well-known concepts, theories, schemes, toolsand technologies are employed;

II. innovative design (small rectangle at the top) that does need new expertise becausesomething new is developed and introduced.

At the end of each project the design team gains further areas of knowledgeand this is an important point in engineering: one acquires expertise making thingsdirectly. Also, the order of the knowledge, meaning having the right thing at theright place, is an a-posteriori issue: sense-making is often organized after, looking atthe past.

A rational question can be raised looking at Figure 4.2: generally speaking, is thenecessity for the designers of an innovative structure so well-founded, to have already astrong experience in this kind of structures? This question seems, but only superficially,very provocative. In fact, if one is framed by its self-experience and culture, it isreasonable to expect him to be caged in ideas and schemes securely useful in evolutivesituations, where only small changes are expected, whereas a largely innovative contextneeds new frameworks that cannot be extrapolated from the past.

This concept is presented also in Figure 4.3 where the trend of the structural qualityvs. the design variables is shown for both types of design. In the case of evolutivedesigns, the variables are few and it is possible to obtain the optimal structural con-figuration with a local optimization. On the other hand, innovative design allowsreaching higher values of structural quality but needing a global optimization thatinvolves numerous variables.

Figure 4.3 Structural quality or performance vs. design variables for evolutive and innovativedesign.

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4.3 System Engineering Approach & Performance-basedDesign

In order to define an appropriate procedure for dealing with complex structures, itis interesting to define first the aspects that make a construction complex. They canbe understood looking at the plot in Figure 4.4 (adapted from Perrow (1984)) thatshows in an ideal but general way a three dimensional Cartesian space where the axesindicate:

1 the nonlinearities of the system. In the structural field the nonlinearities affect thebehavior at different levels: at a detailed micro-level, for example, they affectthe mechanical properties of the materials; at a macro-level they influence thebehavior of single elements or even the entire structure as in the case of instabilityphenomena;

2 the interactions and connections between the various parts;3 the intrinsic uncertainties; they could have both stochastic and epistemic nature.

In this reference system the overall complexity of the system increases as the valuesalong each of the axes increase.

In order to adequately face all these aspects, complex structures require high per-formance levels and should be designed taking into account their durability duringthe entire life cycle and their behavior in accidental situations. All these requirementsare often in contrast with the simplified formulations that are still widely applied instructural design.

It is possible to handle these aspects only evolving from the simplistic idealization ofthe structure as a device for channeling loads to the more complete idea of the struc-tural system, intended as a set of interrelated components working together toward acommon purpose (NASA – SE Handbook, 2007), and acting according System Engi-neering, which is a robust approach to the creation, design, realization and operationof an engineered system. It has been said that the notion of structural systems is a‘marriage of Structural Engineering and Systems Science’ (Skelton, 2002).

Figure 4.4 Aspects that increase the complexity of a system (adapted by Perrow, 1984).

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Figure 4.5 Functional/hierarchical breakdown of a system/problem.

In the System Engineering framework, an operational tool that can be useful for deal-ing with complex systems is the breakdown. The hierarchical/functional breakdownof a system (or a problem) can be represented graphically (as shown in Figure 4.5) by apyramid, set up with various objects positioned in a hierarchical manner. The peak ofthe pyramid represents the goal (the whole system), the lower levels represent a descrip-tion of fractional objects (the sub-systems/problems in which it can be divided), and thebase corresponds to basic details. By applying a top-down approach, a problem can bedecomposed by increasing the level of details one level at a time. On the other hand, inthose situations where the details are the starting point, a bottom-up approach is usedfor the integration of low-level objectives into more complex, higher-level objectives.In common practice, however, actual problems are unclear and lack straightforwardsolutions. In this case, the strategy becomes a mixed recipe of top-down and bottom-up procedures that may be used alternately with reverse-engineering approaches andback analysis techniques.

The whole structural design process can be reviewed within this system view,considering also that the recent improvement in measurement and elaboration datatechnologies have created the proper conditions to integrate the information on theperformance on site in the design process, leading to the so-called performance-baseddesign (PBD) (Smith, 2001; Petrini & Ciampoli, 2012). The flow chart in Figure 4.6summarizes the concepts at the base of the PBD. The first five steps in the figureare those considered in the traditional design approach and lead to the “as built’’construction; they are:

1 formulation of the problem;2 synthesis of the solution;3 analysis of the proposed solution;4 evaluation of the solution performances;5 construction.

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Figure 4.6 Steps of the Performance Based Design (PBD) approach (adapted from Smith,2001).

Difficulties associated with this kind of approach are evident: the as built structurecould be very different from the as designed one for various reasons, as fabrication mis-takes or unexpected conditions during the construction phase, or also non-appropriatedesign assumptions. In order to evaluate the accomplishment of the expected perfor-mance, a monitoring system can be used. Under this perspective, three further stepswill be added to the aforementioned traditional ones:

6 monitoring of the real construction;7 comparison of monitored and expected results;8 increase of the accuracy of the expectation.

These three additional steps are the starting point of the PBD and lead to otherfollowing steps devoted to the possible modification of the project in order to fulfillthe expected performance:

9 reformulation: development of advanced probabilistic methods for a moreaccurate description of the required performance;

10 weak evaluation, that assumes that the analysis is exact and all the actions areknown, from the probabilistic point of view;

11 improvement of the model;12 strong evaluation that is carried out when the improvement (see point 11) aims

at assigning more accurate values to the assigned parameters.

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Looking at the flow chart in Figure 4.6, it is possible to make two observations:

I. the structural monitoring plays a key role in the PBD approach because it is thetool that allows the first comparison between the ‘as designed’ structure with the‘as built’ one. If it is managed in the right way, it can lead to a significant gain ofdesign knowledge that can assure the long term exploitation of the structure;

II. in order to evaluate the quality of the structure it is necessary to take into accountnumerous aspects and to consider at the same time how the system works as awhole, and how the elements behave singularly. For a comprehensive evaluationof the overall performance a new concepts should be used, as for example that ofstructural dependability discussed in the next section.

Finally, step 10, weak evaluation, can lead to a local specific increase of knowledge,while step 12, strong evaluation, can lead to a global – general increase of knowledgereferring to a whole class of structures or even to a whole sector of the structuralengineering. If these knowledge step increases are recognized and organized by thedesign team, the overall scheme reported in Figure 4.1 is developed.

4.4 Structural Dependability

As anticipated, for the purpose of evaluation of the overall quality of structural systemsa new concept has been recently proposed: the structural dependability. It can be intro-duced looking at the scheme in Figure 4.7, where the various aspects discussed in theprevious section are ordered and related to this concept (Arangio, 2012). It has beensaid that a modern approach to structural design requires evolving from the simplisticidea of ‘structure’ to the idea of ‘structural system’, and acting according to the SystemEngineering approach; in this way it is possible to take into account the interactionsbetween the different structural parts and between the whole structure and the designenvironment. The grade of non-linearity and uncertainty in these interactions deter-mines the grade of complexity of the structural system. In case of complex systems,it is important to evaluate how the system works as a whole, and how the elementsbehave singularly.

In this context, dependability is a global concept that describes the aspects assumedas relevant to describe the quality of a system and their influencing factors (Bentley,1993). This concept has been originally developed in the field of computer sciencebut it can be reinterpreted in the civil engineering field (Arangio et al., 2010). Thedependability reflects the user’s degree of trust in the system, i.e., the user’s confidencethat the system will operate as expected and will not ‘fail’ in normal use: the systemshall give the expected performance during the whole lifetime.

The assessment of dependability requires the definition of three elements(Figure 4.8):

• the attributes, i.e. the properties that quantify the dependability;• the threats, i.e. the elements that affect the dependability;• the means, i.e. the tools that can be used to obtain a dependable system.

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Figure 4.7 Roadmap for the analysis and design of complex structural systems (Arangio, 2012).

In structural engineering, relevant attributes are reliability, safety, security, main-tainability, availability, and integrity. Note that not all the attributes are required forall the systems and they can vary over the life-cycle.

The various attributes are essential to guarantee:

• the ‘safety’ of the system under the relevant hazard scenarios, that in currentpractice is evaluated by checking a set of ultimate limit states (ULS);

• the survivability of the system under accidental scenarios, considering also thesecurity issues; in recent guidelines, this property is evaluated by checking a set of‘integrity’ limit states (ILS);

• the functionality of the system under operative conditions (availability), that incurrent practice is evaluated by checking a set of serviceability limit states (SLS);

• the durability of the system.

The threats to system dependability can be subdivided into faults, errors and fail-ures. According to the definitions given in (Avižienis et al., 2004), an active or dormantfault is a defect or an anomaly in the system behavior that represents a potential causeof error; an error is the cause for the system being in an incorrect state; failure isa permanent interruption of the system ability to perform a required function underspecified operating conditions. Error may or may not cause failure or activate a fault.

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Figure 4.8 Dependability: attributes, threats and means (from Arangio et al., 2010).

In case of civil engineering constructions, possible faults are incorrect design, construc-tion defects, improper use and maintenance, and damages due to accidental actions ordeterioration.

With reference to Figure 4.5, the problem of conceiving and building a dependablestructural system can be considered at least by four different points of view:

1 how to design a dependable system, that is a fault-tolerant system;2 how to detect faults, i.e., anomalies in the system behavior (fault detection);3 how to localize and quantify the effects of faults and errors (fault diagnosis);4 how to manage faults and errors and avoid failures (fault management).

In general, a fault causes events that, as intermediate steps, influence or determinemeasurable or observable symptoms. In order to detect, locate and quantify a systemfault, it is necessary to process data obtained from monitoring and to interpret thesymptoms.

A system is taken as dependable if it satisfies all requirements with regards to variousdependability performance and indices, so the various attributes, such as reliability,safety or availability, which are quantitative terms, form a basis for evaluating thedependability of a system. Dependability evaluation is a complex task because this isa term used for a general description of the quality of a system and it cannot be easily

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expressed by a single measure. The approaches for its evaluation can be qualitativeor quantitative and usually are related to the phase of the life cycle that it is consid-ered (design or assessment). In the early design phase a qualitative evaluation is moreappropriate than a detailed one, as some of the subsystems and components are notcompletely conceived or defined.

Qualitative evaluations can be performed, for example, by means of failure modeanalyses approaches, as the Failure Mode Effects and Criticality Analysis (FMECA)or the failure tree analysis (FTA), or by using reliability block diagrams. On the otherhand, in the assessment phase, numerous aspects should be taken into account andall of them are affected by uncertainties and interdependencies, so quantitative evalu-ations, based on probabilistic methods, are more suitable. It is important to evaluatewhether the failure of a component may affect other components, or whether a recon-figuration is involved upon a component failure. These stochastic dependencies can becaptured for example by Markov chains models, which can incorporate interactionsamong components and failure dependence. Other methods are based on Petri Netsand stochastic simulation. At the moment, most of the applications are on electricalsystems (e.g., Nahman, 2002) but the principles can be applied in the civil engineeringfield. When numerous different factors have to be taken into account and dependabil-ity cannot be described by using analytical functions, linguistic attributes by means ofthe fuzzy logic reasoning could be helpful (Ivezic et al., 2008).

4.5 Structural Health Monitoring

As aforementioned, structural monitoring has a fundamental role in the PBD because itis the tool that allows the comparison between the expected behavior and the observedone in order to verify the accomplishment of the expected performance and guaranteea dependable system. Moreover, the recent technological progresses, the reductionof the price of hardware, the development of accurate and reliable software, not tomention the decrease in size of the equipment have laid the foundations for a widelyuse of monitoring data in the management of civil engineering systems (Spencer et al.,2004).

However, it is also important to note that the choice of the assessment methodand level of accuracy is strictly related to the specific phase of the life-cycle and tothe complexity and importance of the structure (Bontempi, 2006; Casas, 2010). Theuse of advanced methods is not justified for all structures; the restriction in terms oftime and cost is important: for each structural system a specific assessment process,which would be congruent with the available resources and the complexity of thesystem, should be developed. In Bontempi et al. (2008) for example, the structuresare classified for monitoring purposes in the following categories: ordinary, selected,special, strategic, active and smart structures. The information needed for an efficientmonitoring, shown in Figure 4.9 by means of different size circles, increases with thecomplexity of the structure.

For those structural systems subjected to long term monitoring, data processing isa crucial step because, as said earlier, they represent the measurable symptoms of thepossible damage (fault). However, the identification of the fault from the measurementdata is a complex task, as explained in Figure 4.10. The relationship between fault andsymptoms can be represented graphically by a pyramid: the vertex represents the fault,

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Figure 4.9 Relationship between classification of structures and characteristics of the monitoringprocess.

Figure 4.10 Knowledge-based analysis for structural health monitoring.

the lower levels the possible events generated by the fault and the base correspondsto the symptoms. The propagation of the fault to the symptoms follows a cause-effectrelationship, and is a top-down forward process. The fault diagnosis proceeds in thereverse way. To solve the problem implies the inversion of the causality principle; but

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one cannot expect to rebuild the fault-symptom chain only by measured data becausethe causality is not reversible or the reversibility is ambiguous: the underlying physicallaws are often not known in analytical form, or too complicated for numerical cal-culation. Moreover, intermediate events between faults and symptoms are not alwaysrecognizable (as indicated in Figure 4.3).

The solution strategy requires integrating different procedures, either forward orinverse; this mixed approach has been denoted as the total approach by Liu and Han(2004), and different computational methods have been developed for this task, thatis, to interpret and integrate information coming from on site inspection, databaseand experience. In Figure 4.10 an example of knowledge-based analysis is shown. Theresults obtained by instrumented monitoring (the detection and diagnosis system onthe right side) are processed and combined with the results coming from the analyticalor numerical model of the structural response (the physical system on the left side).Information Technology provides the tool for such integration.

The processing of experimental data is the bottom-up inverse process, where theoutput of the system (the measured symptoms: displacements, acceleration, naturalfrequencies, etc.) is known but the parameters of the structure have to be determined.For this purpose different methods can be used; a great deal of research in the past30 years has been aimed at establishing effective local and global assessment meth-ods (Doebling et al., 1996; Sohn et al., 2004). The traditional global approaches arebased on the analysis of the modal parameters obtained by means of structural iden-tification. On the other hand, in recent years, also other approaches based on softcomputing techniques have been widely applied. These methods, as for example theneural networks applied in this work, have proved to be useful in such case where con-ventional methods may encounter difficulties. They are robust and fault tolerant andcan effectively deal with qualitative, uncertain and incomplete information, makingthem highly promising for smart monitoring of civil structures. In the sequence bothapproaches are briefly presented and, in the last part of the work, they are applied onthe same dataset and the results are compared.

4.5.1 Structural Identification

Structural identification of a civil structure includes the evaluation of its modal param-eters, which are able to describe its dynamic behavior. The basic idea behind thisapproach is that modal parameters (natural frequencies, mode shapes, and modaldamping) are functions of the physical properties of the structure such as mass, damp-ing and stiffness. Therefore, changes in the physical properties, as for example thereductions of stiffness due to damage, will cause detectable changes in the modalproperties. During the last three decades extensive research has been conducted invibration-based damage identification and significant progress has been achieved (seefor example: Doebling, 1996; Sohn et al. 2004; Gul & Catbas 2008; Frangopol et al.,2012; Li et al., 2006; Ko et al., 2009).

The methods for structural identification belong to two main categories: Experimen-tal Modal Analysis (EMA) and Operational Modal Analysis (OMA or output-onlyanalysis). The first class of methods requires knowledge of both input and output,which are related by a transfer function that describes the system. This means thatthe structure has to be artificially excited in such a way that the input load can be

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measured. In case of large structures, to obtain satisfactory results, it is necessary togenerate a certain level of stress to overcome the ambient noise, but this is difficultand expensive and moreover could create undesired nonlinear behavior. Operationalmodal analysis, on the other hand, requires only measurement of the output response,since the excitation system consists of ambient vibrations, such as wind and traffic.

For these reasons, in recent years, output-only modal identification techniques havebeing largely used. This can lead to a considerable saving of resources, since it is notnecessary any type of equipment to excite the structure. In addition, it is not necessaryto interrupt the operation of the structure, which is very important in case of strategicinfrastructures that, in case of closure, will strongly affect the traffic. Another keyaspect is that the measurements are made under real operating conditions. In this work,the used approach belongs to this latter category: the identification was carried outby using an output only approach in the frequency domain, the Enhanced FrequencyDomain Decomposition (EFDD) technique (Brincker et al., 2001).

4.5.2 Neural Network-based Data Processing

Whenever a large quantity of noisy data need to be processed in short time thereare other methods, based on soft computing techniques, that have proven to be veryefficient (see for example: Adeli, 2001; Arangio & Bontempi, 2010; Ceravolo et al.,1995; Choo et al., 2009; Dordoni et al., 2010; Freitag et al., 2011; Ni et al., 2002; Kimet al., 2000; Ko et al., 2002; Sgambi et al., 2012; Tsompanakis et al., 2008) and haveattracted the attention of the research community. In particular, in this work a neuralnetwork-based approach is applied for the assessment of the structural condition of acable-stayed bridge.

The neural network concept has its origins in attempts to find mathematical repre-sentations of information processing in biological systems, but a neural network canalso be viewed as a way of constructing a powerful statistical model for nonlinearregression. It can be described by a series of functional transformations working indifferent correlated layers (Bishop, 2006):

yk(x, w) = h

⎛⎝ M∑

j=1

w(2)kj g

⎛⎝ D∑

j=1

w(1)ji xi + b(1)

j0

⎞⎠+ b(2)

k0

⎞⎠ (4.1)

where yk is the k-th neural network output; x is the vector of the D variables inthe input layer; w consists of the adaptive weight parameters, w(1)

ji and w(2)kj , and the

biases, b(1)j0 and b(2)

k0 ; H is the number of units in the hidden layer; and the quantities inthe brackets are known as activations: each of them is transformed using a nonlinearactivation function (h and g).

Input–output data pairs from a system are used to train the network by ‘learning’ or‘estimating’ the weight parameters and biases. Usually, the values of the componentsof w are estimated from the training data by minimizing a proper error function. Theestimation of these parameters, i.e. the so called model fitting, can be also derived asa particular approximation of the Bayesian framework (MacKay, 1992; Lampinen &Vethari, 2001). More details are given in (Arangio & Beck, 2012).

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A key aspect in the use of neural network models is the definition of the optimalinternal architecture that is the number of weight parameters needed to adequatelyapproximate the required function. In fact, it is not correct to choose simply the modelthat fits the data better: more complex models will always fit the data better butthey may be over–parameterized and so they make poor predictions for new cases.The problem of finding the optimal number of parameters provides an example ofOckham’s razor, which is the principle that one should prefer simpler models to morecomplex models, and that this preference should be traded off against the extent towhich the models fit the data (Sivia, 1996). The best generalization performance isachieved by the model whose complexity is neither too small nor too large.

The issue of model complexity can be solved in the framework of Bayesian proba-bility. In fact, the most plausible model class among a set M of NM candidate ones canbe obtained by applying Bayes’ Theorem as follows:

p(Mj|D, M) ∝ p(D|M j

)p(Mj|M

)(4.2)

The factor p(D/Mj) is known as the evidence for the model class Mj provided by thedata D. Equation (4.2) illustrates that the most plausible model class is the one thatmaximizes p(D/Mj)p(Mj) with respect to j. If there is no particular reason a priori toprefer one model over another, they can be treated as equally plausible a priori and anon informative prior, i.e. p(Mj) = 1/NM, can be assigned; then different models withdifferent architectures can be objectively compared just by evaluating their evidence(MacKay, 1992; Lam et al., 2006).

4.6 Knowledge Gain by Structural Health Monitoring:A Case Study

4.6.1 Description of the Considered Bridge and Its Monitoring System

In the following it is presented a case study that shows the key role of structuralmonitoring for increasing our knowledge on the operational behavior of the structures,allowing the detection of anomalies in a timely manner. The considered structure is areal bridge, the Tianjin Yonghe Bridge, proposed as benchmark problem by the Asian-Pacific Network of Centers for Research in Smart Structure Technology (ANCRiSSTSHM benchmark problem, 2011) (see Figure 4.11). In October 2011 they shared somedata of the long term monitoring of the bridge with the Structural Health Monitoringcommunity. The benchmark data included also an ANSYS finite element model of thestructure that was at the base of the numerical analyses carried out in this work.

The Tianjin Yonghe Bridge is one of the earliest cable-stayed bridges constructed inmainland China. It has a main span of 260 m and two side spans of 25.15 + 99.85 meach. The full width of the deck is about 13.6 m, including a 9 m roadway andsidewalks. The bridge was opened to traffic since December 1987 and significantmaintenance works were carried out 19 years later. In that occasion, for ensuring thefuture safety of the bridge, a sophisticated SHM system has been designed and imple-mented by the Research Center of Structural Health Monitoring and Control of theHarbin Institute of Technology (Li et al., 2013).

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Figure 4.11 Skyline of the Tianjin Yonghe bridge with the main dimensions (top); cross section(bottom). The distribution of the sensors is indicated.

The continuous monitoring system designed for the bridge includes 14 uniaxialaccelerometers permanently installed on the bridge deck and 1 biaxial accelerometerthat was fixed on the top of one tower to monitor its horizontal oscillation. Ananemometer was attached on the top of the tower to measure the wind speed in threedirections and a temperature sensor were installed at the mid-span of the girder tomeasure the ambient temperature. The accelerometers of the deck were placed halfdownstream and half upstream. The skyline of the bridge with the main dimensionsof the structure and the scheme of the distribution of the sensor is shown in Fig-ure 4.11. While it was monitored, the bridge experienced some damages, thus, thedata that were made available for the researchers regard both health and damagedconditions.

Data in the health condition include time histories of the accelerations recordedby the 14 deck sensors and environmental information (wind and temperature). Theyconsist in registrations of 1 hour that have been repeated for 24 hours on January 17th,2008. The sampling frequency is 100 Hz. The second part of available data includesother measurements recorded at the same locations after some months, on July 31st,2008. The damage observed in the meantime regarded cracking at the closure segmentof both side spans and damage at the piers (partial loss of the vertical supports dueto overloading). The dataset includes again registrations of 1 hour repeated for the 24hours at the same sampling frequency (100 Hz). The available data have been processedby using both a structural identification approach and a neural network-based strategy.In the following the results are presented and compared.

4.6.2 Application of the Enhanced Frequency DomainDecomposition

In this work the structural identification has been carried out by using the EnhancedFrequency Domain Decomposition (EFDD) technique that is based on the analysis ofthe frequency content of the response by using the auto-cross power spectral density

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Figure 4.12 Averaged Singular Values Decompositions (health condition – left; damagedcondition – right).

(PSD) functions of the measured time series of the responses. The PSD matrix is thendecomposed by using the Singular Value Decomposition (SVD) tool. The singularvalues contain information from all spectral density functions and their peaks indicatethe existence of different structural modes, so they can be interpreted as the autospectral densities of the modal coordinates, and the singular vectors as mode shapes(Brincker et al., 2001).

It should be noted that this approach is exact when the considered structure is lightlydamped and excited by a white noise, and when the mode shapes of closed modesare geometrically orthogonal (Ewins, 2000). If these assumptions are not completelysatisfied, the SVD is an approximation, but the obtained modal information is stillenough accurate (Brincker et al., 2003). The first step of the FDD is to construct a PSDmatrix of the ambient responses G(f ):

G(f ) = E[A(f )AH(f )] (4.3)

where the vector A(f ) collects the acceleration responses in the frequency domain, thesuperscript H denotes the Hermitian transpose operation and E denotes the expectedvalue. In the considered case, the spectral matrix G(f ) was computed by using theWelch’s averaged modified periodogram method (Welch, 1967). In addition, an over-lapping of 50% between the various segments was considered and a periodic Hammingwindowing was applied to reduce the leakage.

After the evaluation of the spectral matrix, the FDD technique involves the SingularValue Decomposition (SVD) of G(f ) at each frequency and the inspection of the curvesrepresenting the singular values (SV). The SVD have been carried out for the 24 hourregistrations carried out on January 17th, 2008. The consistency of the spectral peaksand the time invariance of resonant frequencies has been investigated by analyzing theauto-spectra of the vertical accelerations acquired at different time of the day and byevaluating the corresponding average auto-spectral estimates.

The averaged SVD plot in health conditions is shown in the left side of Figure 4.12.The attention was focused on the frequencies below 2 Hz. The selection of this rangehas been done for two reasons: first, because the most important modes for the dynamic

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Figure 4.13 FEM model of the bridge (left); Comparison of the frequencies of the first sixmodes obtained from the Finite Element Model (FEM) and from the vibration-basedidentification in undamaged and damaged conditions (right).

description of large structural systems generally are below 2 Hz; in addition, the avail-able data included the measurements of 14 stations (7 downstream and 7 upstream)that made difficult to identify clearly higher frequency. Looking at the plot, is possibleto note that the fourth mode is not characterized by a single well-defined peak on theSV line, but by different close peaks around the frequency 1 Hz, suggesting a nonlinearbehavior of the bridge.

The same procedure has been applied for processing the time series of the responsein damaged conditions. In the plot on the right of Figure 4.12 the related averagedSVD is shown. It is possible to note three singular values coming up around 1.1 and1.3 Hz that indicate the presence of three modes in this range. The other modes arereasonable separated.

The results of the vibration-based identification have been compared with the outputof the modal analysis carried out with the finite element model of the structure. For thiscomparison it has to be considered that the FE model represents the “as built’’ bridgewhere the mechanical properties and the cross sections were assigned as reported inthe original project, while the monitored data represent the behavior of the bridgeafter years of operation. The comparison of the first six frequencies is summarized inthe table on the right side of Figure 4.13 and the first three mode shapes are shownin Figure 4.14. More details are given in (Arangio et al., 2013; Arangio & Bontempi,2014).

Looking at the plots in Figure 4.14, it is possible to note that the mode shapes iden-tified using the time series recorded in undamaged condition are in good agreementwith those given by the finite element model. The mode shapes remains similar alsoafter damage because probably it affects the higher modes. The deterioration of thestructure during time and the occurrence of damage are suggested by the decrement ofthe frequencies: those of the FEM model, which represent the “as built’’ structure arehigher of those obtained from the signal recorded in January 2008, showing that the

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Figure 4.14 Comparison of the first three mode shapes obtained from the Finite ElementModel (FEM) and from the vibration-based identification in undamaged and damagedconditions.

years of operation have reduced the overall stiffness of the structure. This phenomenonis even more evident looking at the decrement of the frequencies in the damagedcondition.

4.6.3 Application of a Neural Networks-based Approach

The results obtained with the structural identification have been cross validated withthose obtained by applying a neural network-based strategy. The proposed methodconsists in building different neural network models, one for each measurement pointand for each hour of measurements (that is, the number of network models is equalto 14 (sensor locations) × 24 (hours) = 336). The neural network models are built andtrained using the time-histories of the accelerations recorded in the selected points inthe undamaged situation. The purpose of these models is to approximate the behaviorof the undamaged bridge taking into account the variation of the traffic during thedifferent hours of the day.

The procedure for network training is shown in Figure 4.15. The time-history ofthe response f is sampled at regular intervals, generating series of discrete values ft.In order to obtain signals that could be adequately reproduced, the time series needed

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Figure 4.15 Scheme of the proposed damage detection strategy.

to be pre-processed by applying appropriate scaling and smoothing techniques. Afterthat, a set d of values of the processed time series, ft−d+1, . . . , ft, is used as input ofthe network model, while the next value ft+1 is used as target output. By steppingalong the time axis, a training data set consisting of many sets of input vectors withthe corresponding output values is built, and the network models are trained.

The architecture of the model is chosen by applying the Bayesian approach discussedin section 4.2 and the models with the highest evidence have been selected. Theyhave four inputs and three internal units. The performance of the models is tested byproposing to the trained networks input patterns of values recorded some minutes afterthose used for training ft+n−d . . . ft+n, and by predicting the value of ft+n+1. The modelsare considered well trained when they show to be able to reproduce the expected valueswith a small error. Subsequently, these trained neural networks models are tested withdata recorded in the following days. The testing patterns include time series recordedin both undamaged and damaged conditions.

For each pattern of four inputs, the next value is predicted and compared with thetarget output. If the error in the prediction is negligible the models show to be able toreproduce the monitoring data and the bridge is considered undamaged; if the errorin one or more points is large, the presence of an anomaly (that may represent ormay not represent damage) is detected. The results of the training and test phases areelaborated as shown in Figure 4.16. The two plots show the difference err between thenetwork output value y and the target value t at several time steps for both trainingand testing, in undamaged (left) and damaged (right) conditions. It is possible to note

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Figure 4.16 Error in the approximation for training and test in health and damaged conditions.

that the mean values of err (indicated by the straight lines) obtained in training and testare comparable (�e ∼= 0) if the structure remains undamaged. In contrast, in case ofanomalies that may correspond to damage, there is a significant difference �e betweenthe values of the error in testing and training.

To distinguish the actual cause of the anomaly, the intensity of �e is checked atdifferent measurement points: if �e is large in several points, it can be concluded thatthe external actions (wind, traffic) are probably changed. In this case, the trained neuralnetwork models are unable to represent the time-histories of the response parameters,and they have to be updated and re-trained according to the modified characteristicsof the action. If �e is large only in one or few points it can be concluded that the bridgeexperienced some damage.

In the following the results of the strategy are shown. As previously mentioned, 14groups of neural networks have been made, one group for each measurement point,which have been trained with the time histories of the accelerations in health conditions(data recorded on January 17th, 2008). In order to take into account the change in thevibrations of the structures caused by the different use during the day, one networkmodel for each hour of monitoring has been created (24 network models for eachpoint). For the training phase of each model, 4 steps of the considered time historyare given as input and the following step as output. The training set of each networkmodel includes 5000 examples chosen randomly in the entire set.

The trained networks have been tested by using the time histories of the accelerationsrecorded at the same points and at the same time some month after, on July 31st 2008.The difference between the root mean squares of the error, ERMS, calculated in thetwo dates for each point is shown in Figures 4.17 and 4.18. Each plot represents onehour of the day (H1, H3, etc.) and has on the x-axis the measurement points and onthe y-axis the value of the difference of the errors ERMS; the results every two hoursare shown. The measurement points are represented on two rows: the first one (deepgrey) represents the results of the downward sensors (#1, 3, 5, 7, 9, 11, 13) while thesecond one (light grey) represents the results of the upward sensors (#2, 4, 6, 8, 9, 10,12, 14) (see also Figure 4.11 for the location of the sensors).

Looking at the plots, it is possible to notice that, apart from some hours of the daythat look difficult to reproduce, the neural networks models are able to approximatethe time history of the acceleration with a small error in almost all the measurementpoints, except that around sensor #10. Considering that in the undamaged situation

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Figure 4.17 Root mean square of the error in the 14 locations of the sensors (from H1 to H11).

Figure 4.18 Root mean square of the error in the 14 locations of the sensors (from H13 to H23).

the error was small in all the points, this difference is interpreted as the presence of ananomaly (damage) in the structure. Between 6 a.m. and 9 a.m. and around 9 p.m. theerror is larger in various sensors but it is possible that this depends on the additionalvibrations given by the traffic in the busiest hours of operation of the bridge.

Note that there is another factor which was not examined in this study, but whichcould have partially influenced the results: the dependence on the temperature, asstated by (Li et al., 2010). Actually, the two signals have been recorded in two differentperiods of the year that are characterized by significant climatic differences. However,the results obtained with the two methods suggest that the detected anomalies donot depend only on the temperature, but they could be related to the presence ofdeterioration or damage.

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4.7 Conclusions

The design of complex structural systems requires an accurate definition of the projectrequirements and a detailed verification of the expected performance. In this sense,structural health monitoring is an essential tool that allows the comparison betweenthe as built structure and the as designed one and enriches the engineer’s knowledgeon the structure, making the required modifications possible.

A key aspect is the interpretation of the monitoring data and the assessment ofthe structural conditions. It has been shown that different approaches exist, rangingfrom the traditional identification procedures up to the application of advanced softcomputing technique. For each situation it will be necessary to choice the appropriateapproach. Where possible, additional information can be gained by using differentstrategies and by cross-validating the obtained results.

To illustrate this process a characteristic bridge has been analyzed. In particular,the available time histories of the acceleration have been processed by using first anidentification procedure in the frequency domain and then a neural network-basedstrategy. Both methods detected the occurrence of an anomaly but were not able toidentify clearly where. Those results have been compared also with those obtained fromthe finite element model of the bridge and the comparison highlights the difference ofthe behavior between as built conditions and the current state after several years ofoperation.

Acknowledgments

Prof. Hui Li and Prof. Wensong Zhou of the Harbin Institute of Technology, Eng. SilviaMannucci, the team www.francobontempi.org from Sapienza University of Rome aregratefully acknowledged. Prof. Jim Beck of Caltech is acknowledged for his contribu-tion to the development of the Bayesian framework for neural networks models. Thisresearch was partially supported by StroNGER s.r.l. from the fund “FILAS – PORFESR LAZIO 2007/2013 – Support for the research spin off’’.

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w w w . c r c p r e s s . c o m CRC Press Taylor & Francis Group

Just released in the Series Structures and Infrastructures

FREE standard shipping when you order online.To view our full range of books and order online visit www.crcpress.com

About the Structures and Infrastructures Series :The scope of this book series covers the entire spectrum of structures and infrastructures. Thus it includes, but is not restricted to, mathematical modeling, computer and experimental methods, practical applications in the areas of assessment and evaluation, construction and design for durability, decision making, deterioration modeling and aging, failure analysis, field testing, structural health monitoring, financial planning, inspection and diagnostics, life-cycle analysis and prediction, loads, maintenance strategies, management systems, nondestructive testing, optimization of maintenance and management, specifications and codes, structural safety and reliability, system analysis, time-dependent performance, rehabilitation, repair, replacement, reliability and risk management, service life prediction, strengthening and whole life costing.

Maintenance and Safety of Aging InfrastructureEdited by: Dan Frangopol, Lehigh University, Bethlehem, PA, USA and

Yiannis Tsompanakis, Department of Applied Sciences, Technical University of Crete, Chania, Greece

This book presents the latest research findings in the field of maintenance and safety of aging infrastructure. The invited contributions provide an overview of the use of advanced computational and/or experimental techniques in damage and vulnerability assessment as well as maintenance and retrofitting of aging structures and infrastructures such as buildings, bridges, lifelines and ships. Cost-efficient maintenance and management of civil infrastructure requires balanced consideration of both structural performance and the total cost accrued over the entire life-cycle considering uncertainties.

ISBN: 978-0-415-65942-0 | October 2014 | HB | 746pp. http://www.crcpress.com/product/isbn/9780415659420