Soft Computing Based Multilevel Strategy for Bridge Integrity Monitoring

Computer-Aided Civil and Infrastructure Engineering 25 (2010) 348–362

Soft Computing Based Multilevel Strategy for Bridge Integrity Monitoring S. 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 monitoring has become increasingly important in structural engineering and construction management. It represents an important 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 assessment 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 applying the Bayesian inference at four hierarchical levels: for training, optimization of the regularization terms, databased model selection, and evaluation of the relative importance of different inputs. In the second part of the article, 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 following level the specific damaged element is recognized and the intensity of damage is quantified. 1 INTRODUCTION The realization of high-cost and safety-critical constructions requires advanced approaches to take into account their intrinsic complexity (Ciampoli, 2005). The complexity of this kind of structures can be related to several aspects, as for example, nonlinear dynamic behavior (Adeli et al., 1978), various sources of uncertainties, both objective and cognitive, and strong interaction between components. ∗ To

whom correspondence should be addressed. E-mail: franco. [email protected].

 C 2010 Computer-Aided Civil and Infrastructure Engineering. DOI: 10.1111/j.1467-8667.2009.00644.x

Only by considering these aspects can a consistent evaluation of the structural performance be obtained. Therefore, it is necessary to evolve from the simplistic idealization of the structure as “device for channeling loads” to the analysis of the structural system as a whole, intended as “a set of interrelated components working together toward a common purpose” (NASA System Engineering Handbook, 2007). The correlation between different aspects can be taken into account by applying the principles and techniques of System Engineering, which is a robust approach to the creation, design, realization, and operation of an engineered system (Bontempi et al., 2008). If the entire design process needs to be reviewed in the System Engineering framework, one includes requirements concerning the construction phase and the operation and maintenance during the whole life-cycle (Sarma and Adeli, 2002). To this aim, data collected on site are important both for checking the accomplishment of the expected performance during the service life and for validating the original design (Smith, 2001). This approach requires the definition of the quality of a complex structural system in a comprehensive way by an integrated concept, like dependability. The concept of dependability has been originally developed in the field of Computer Science and it is extended to structural engineering as “the ability to deliver service that can justifiably be trusted” (Aviˇzienis et al., 2004). This definition stresses the need for justification of trust. The alternate definition considers dependable “a system that has the capability to avoid service failures which are more frequent and more severe than acceptable.” All these factors are connected to the integrity of the structural systems, considered as the completeness and consistency of the structural configuration. Specifically, structural integrity refers “to the safe operation of engineering components, structures and materials, and addresses the science and technology which is

Multilevel strategy for bridge integrity monitoring

used to assess the margin between safe operation and failure.” During the service life the integrity, and consequently the overall dependability, can be lowered by deterioration and damage. The structural monitoring represents 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 includes issues like definition and analysis of the structural performance, from regular exercise to out-of-service and collapse, assessment of the environmental conditions, choice of the sensor systems and their optimal placement, use of data transmission systems and signal processing techniques, and methods for damage identification and model updating (Jiang and Adeli, 2005; Adeli and Jiang, 2006; Psimoulis and Stiros, 2008). In case of complex structural systems it can be difficult to deal with the huge quantity of data coming from the monitoring process and various soft computing techniques have shown to be effective tools for data processing (Adeli and Jiang, 2006; Carden and Brownjohn, 2008; He et al., 2008; Jiang and Adeli, 2008a). In this article, a soft computing model, the Bayesian neural networks (Castillo et al., 2008; Adeli and Panakkat, 2009), is used to formulate a multilevel strategy for the assessment of the integrity of a long span suspension bridge subjected to wind actions and traffic loads. In the first step of the proposed strategy the occurrence of damage is detected and the damaged portion of the bridge is identified; in the second step the specific damaged element is recognized and the intensity of damage evaluated. In the following, the concept of integrity monitoring for dependability is explained with reference to structural systems and the multilevel strategy is illustrated.

2 STRUCTURAL INTEGRITY MONITORING FOR DEPENDABILITY For complex structural systems, where there are significant dependencies among elements or subsystems, it is important to have a solid knowledge of both how the system works as a whole, and how the elements behave individually. In this contest, dependability is an integrated property that includes and describes the relevant aspects with reference to the system quality and its influencing factors (Bentley, 1993). System dependability can then be thought of as being composed of three elements (Figure 1): 1. the attributes, that is, the properties that quantify the dependability; 2. the threats, that is, the elements that can affect dependability;

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RELIABILITY MAINTAINABILITY ATTRIBUTES SAFETY AVAILABILITY

FAILURE DEPENDABILITY

THREATS

ERROR FAULT

FAULT TOLERANT DESIGN FAULT DETECTION MEANS FAULT DIAGNOSIS FAULT MANAGING

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

3. the means, that is, the tools that can be used to increase dependability. In structural engineering, relevant attributes are reliability, safety, availability, and maintainability. These properties are essential to guarantee the safety of the system under relevant hazard scenarios, the survivability under accidental or exceptional scenarios, and the functionality under operative conditions. The threats for system dependability can be subdivided into faults, errors, and failures. According to the definition given in Aviˇzienis et al. (2004), an active or dormant fault is a defect or an anomaly in the system behavior that represents a potential cause of error; an error is the cause for the system being in an incorrect state and it may or may not cause failure; failure is a permanent interruption of the system ability to perform a required function under specified operating conditions. The problem of conceiving and building a dependable structural 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, that is, anomalies in the system behavior; 3. how to localize and quantify (that is, diagnose) the effects of faults and errors; 4. how to manage faults and errors to avoid failures. This article is focused on points 2 and 3: fault detection and fault diagnosis. These aspects are strictly related to the integrity monitoring of the structural system: an efficient integrity monitoring system is expected

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to be able to preserve the structural dependability, diagnosing deterioration and damage at their onset (Ou and Li, 2006). Even if there is no general consensus on its definition, in analogy with biological systems, an intelligent monitoring system is expected to (Aktan et al., 1998; Isermann, 2006): 1. sense the loading environment as well as the structural response; 2. reason by assessing the structural condition and health; even small faults should be detected and diagnosed; 3. communicate through proper interface with other components and systems; 4. learn from experience as well as by interfacing with humans for heuristic knowledge; 5. decide and take action for alerting controllers in case of accidental situations, or activate fault tolerant configurations in case of reconfigurable systems. Structural monitoring has a key role in the maintenance scheduling of the bridge structures and a great research effort has been devoted in the past 30 years to establishing effective local and global methods for health monitoring in civil structures (Doebling et al., 1996; De Roeck 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 payoff, it comes out that, in cases of complex structures, like long span bridges, for example, the monitoring process should be planned during the design phase and should be carried out during the entire life cycle to assess the structural health and performance under in-service and accidental conditions (Bontempi et al., 2008). This long-term monitoring of bridges, where longterm designates a period of time from 1 year to decades and desirably the entire life cycle, is a quite recent concept, enabled by recent advances in sensing, data acquisition, computing, communication, data, and information management (Ou and Li, 2006). Exploring longterm monitoring of structural responses was pioneered in China and in Japan (Abe and Amano, 1998; Lau et al., 1999; Wong et al., 2000). Nowadays several bridges are instrumented in Europe (Casciati, 2003), the United States (Aktan et al., 2002), Korea, and other countries, and the administration of the major countries have developed guidelines to explain the advantages of long-term monitoring and to help the engineers in 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 guidelines, long-term monitoring is based on the integration of different kinds of technologies (Figure 2): experimental, analytical, and information technologies.

EXPERIMENTAL TECHNOLOGIES

Non-destructive evaluation

Continuous monitoring

ANALYTICAL TECHNOLOGIES

Mathematical modeling

Finite Element modeling

INFORMATION TECHNOLOGIES

Data acquisition Communication Data processing

Interpretation

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

Fig. 3. Steps of the information technology.

Experimental technologies include nondestructive visual inspection and continuous monitoring. Analytical technologies include mathematical and finite-element modeling. The last one, the information technology, assumes a key role: it covers the entire spectrum of efforts related to the acquisition, communication, processing, and interpretation of the data (Figure 3). The entire monitoring process needs a team of experts in civil, mechanical, and electrical engineering and computer scientists working together to take full advantage of the data. In fact, the desired outcome of structural monitoring is not data collection, but it is the generation of information and the creation of a base of knowledge about potential and existent system symptoms that will enhance decision making for fault management.

3 FAULTS-SYMPTOMS RELATIONSHIP As mentioned in the previous section, to detect and diagnose a system fault, it is necessary to process the data

Multilevel strategy for bridge integrity monitoring

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Fig. 4. Fault–symptoms relationship.

coming from the monitoring process, that is, the system symptoms. However this is a complex task. The relationship between fault and symptoms can be represented graphically by a pyramid (Figure 4). The vertex represents the fault, and the lower levels the possible events generated by the fault; the base corresponds to the symptoms. The propagation of the fault to the observable symptoms follows a cause–effect relationship, and is a top–down forward process: a fault determines events that, as intermediate steps, influence the measurable or observable symptoms (Isermann, 2006). On the other hand, the fault diagnosis proceeds in the reverse way (Figure 4); it is a bottom–up inverse process that relates the observed symptoms to the faults. This implies the inversion of the causality principle. However, one cannot expect to rebuild the chain only by measured data because usually the causality is not reversible or the ¨ reversibility is ambiguous (Fussel, 2002): the underlying physical laws are often not known in analytical form, or are too complicated for explicit numerical calculation. Moreover, intermediate events between faults and symptoms are not always recognizable (Figure 4, righthand side). The solving strategy requires integrating different procedures, either forward or inverse: this mixed solving approach has been called total approach by Liu and Han (2004) and different computational techniques have been developed for this task (Adeli and Samant, 2000; Ghosh-Dastidar and Adeli, 2003).

4 KNOWLEDGE-BASED FAULT DETECTION AND DIAGNOSIS As shown in the previous section, fault diagnosis needs the integration of forward and inverse procedures with the heuristic knowledge coming from experience or qualitative information. For this task, a knowledge-based analysis can be applied (Adeli and

Fig. 5. Knowledge-based analysis for structural integrity monitoring.

Balasubramanyam, 1988; Paek and Adeli, 1990; Adeli and Hawkins, 1991; Shwe and Adeli, 1993; Waheed and Adeli, 2000; Aktan et al., 1998) (Figure 5). The results obtained by visual inspection or instrumented monitoring (the inverse diagnosis system of Figure 4) are processed and combined with the results coming from the analytical model (the forward physical system of Figure 4). Information technology provides the tool for such integration. The output of the information technology is then filtered by the available heuristic knowledge for decision making. An attractive aspect of the knowledge-based analysis is that it can cope with incomplete or uncertain data integrating qualitative and quantitative information, coming from modeling and heuristics. To carry out the various phases, different computational methods can be used. In several applications, inference models and soft computing techniques, like the Bayesian neural networks used in this work, have shown their effectiveness (Adeli and Park, 1995; Pandey and Barai, 1995; Masri et al., 1996; Faravelli and Pisano, 1997; Hajela, 1999; Topping et al., 1999; Kim et al., 2000; Adeli, 2001; Ni et al., 2002; Kao and Hung, 2003; Waszczyszyn and Ziemianski, 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 FAULT DETECTION AND DIAGNOSIS 5.1 The neural network model and the probability logic framework The neural network concept has its origins in attempts to find mathematical representations of information processing in biological systems. Actually, there is a definite probability model behind it: a neural network is an efficient statistical model for nonlinear regression (Cheng and Titterington, 1994). It can be described by a series of functional transformation working in different correlated layers (Bishop, 2006). For example, for two layers ⎛ ⎞  D  M   (2) (1) (1) (2) wkj g w ji xi + b j0 + bk0 ⎠ yk(x, w) = h ⎝ j=1

i=1

(1) where yk is the kth output variable in the output layer; x is the vector of the D input variables in the 1input layer; w is the matrix including the adaptive weight pa(1) (2) (1) (2) rameters w ji and wkj and the biases b j0 and bk0 (the superscript refer to the considered layer); M is the total number of units in the hidden layer. The quantities within the brackets are the so-called activations; each of them is transformed using a nonlinear activation function (h and g). The nonlinear activation functions are generally chosen to be sigmoidal or tanh functions because of the so-called universality property (Cybenko, 1989). In the traditional learning approach, the values of the parameters w are obtained during the training phase by minimizing an error function (Adeli and Hung, 1994), for example, the sum of squared errors with weight decay (Bishop, 1995) E=

N No W

2 α  1  |wi |2 yk (x n ; w) − tkn + 2 2 n=1 k=1

(2)

i=1

where yk is the kth neural network output corresponding to the n-th realization of x, tkn is the relevant target value, N is the size of the considered data set, N0 is the number of output variables, W is the number of parameters in w, and α is a regularization parameter. The second term in the right-hand side is a decay regularization that penalizes large weights. Neural network learning can be framed as Bayesian inference, where probability is treated as a multivalued logic that may be used to perform plausible inference (Jaynes, 2003). The roots of this probability logic approach are in the work by Bayes published in 1763 (Bayes, 1763). He presented a method for updating probability distributions based on available data that

would come to be known as Bayes’ theorem, and that forms the foundation of a framework for probabilistic inference. The power of this theorem was shown by Laplace (1812) and Jeffreys (1939) who applied it to the analysis of real data set. Although this framework had its origin in the 18th century, the practical application of Bayesian methods was for a long time severely limited by the difficulties in carrying through the full Bayesian procedure. The developments of approximation theories and stochastic sampling methods, along with dramatic improvements in the power of computers, have recently opened the door to the practical use of Bayesian techniques in an impressive range of applications across all disciplines. In recent years in civil engineering, for example, the probability logic approach has been successfully applied to system identification problems and structural health monitoring (Beck and Katafygiotis, 1998; Beck and Yuen, 2004; Muto and Beck, 2008). Starting from the early works of MacKay (1992) and Buntine and Weigend (1991), there has been a growing interest for the application of this framework in the field of neural networks methods (MacKay, 1994; Neal, 1996; Lampinen and Vethari, 2001; Barber, 2002; Lee, 2004; Nabney, 2004). To pose the neural network model within the Bayesian framework, the learning process needs to be interpreted probabilistically: the network output can be considered as the conditional average of the target data (Bishop, 1995). Because the model does not reproduce the data set exactly, the error ε = t – y(x; w) between the target value t and the network output y needs to be interpreted probabilistically using a prediction-error probability model: a Gaussian distribution with mean zero and constant inverse variance β = 1/σ D 2 is a model supported by the principle of maximum differential entropy (Jaynes, 2003). Thus, modeling the predictions as independent and identically distributed (i.i.d.), the likelihood function for a data set D = xn , \ ,tn  is given by p(D | w, β, M)

  N·N0 N No

β  β 2 yk (x n ; w) − tkn exp − = 2π 2 n=1 k=1

(3) where M denotes the Bayesian model class that specifies the forms of the likelihood function and the prior probability distribution discussed next. Although the likelihood function does take into account the uncertain prediction error, it does not quantify the uncertainty in the values of the parameters w. In the Bayesian framework, this can be represented by a prior PDF p(w | M) over the parameters w, which expresses the relative

Multilevel strategy for bridge integrity monitoring

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Fig. 6. Learning as inference.

plausibility of each value. Because generally there is a little idea of what the values should be, it is usual to select the prior as a rather broad distribution. Using once again the principle of maximum differential entropy, this requirement suggests a Gaussian prior distribution with zero mean of the form   α  α W/2 (4) exp − |w|2 p(w | α, M) = 2π 2 where α = 1/σ 2 W represents the inverse variance of the distribution. Using available data, Bayes’ theorem updates the prior probability distribution over the parameters p(w | α, M) to give the posterior PDF p(w | D, α, β, M): p(w | D, α, β, M) =

p (D | w, β, M) p (w | α, M) . p (D | α, β, M) (5)

This posterior distribution is always more compact than the prior distribution if the data informs the model, as indicated schematically in Figure 6, expressing the fact that something has been learned. Therefore, by maximizing the posterior, the most plausible values of the parameters w MAP can be found. Instead of finding a maximum of the posterior probability in Equation (5), it is usually more convenient to seek instead a minimum of its negative logarithm. As shown in Figure 6, for the chosen prior distribution and likelihood function, the negative log probability is

just the usual sum of squares function in Equation (2). Therefore, the conventional learning approach can be derived as a particular approximation of the Bayesian framework where only the MAP (maximum a posteriori) parameter values are utilized. 5.2 Bayesian enhancements for neural networks The optimization of the parameters w, that is, the socalled model fitting, is only one level of inference where Bayesian approach can be applied to neural networks. The potential enhancements that can be obtained by applying this framework at further levels in a hierarchical fashion are often not appreciated. The various levels can be summarized as follows (Arangio, 2008): 1. Level 1: Model fitting: task of inferring appropriate values for the model parameters, given the model and the data. 2. Level 2: Optimization of the regularization terms α and β that make level 1 a better conditioned inverse problem. 3. Level 3: Model class selection: the Bayesian approach allows an objective comparison between models using alternative network architectures. 4. Level 4: Automatic relevance determination (ARD): the relative importance of different inputs can be determined using separate regularization coefficients.

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Regarding the first two levels, the traditional and the Bayesian framework usually give equivalent results (MacKay, 1992). The addition of the third level, the model class selection, has shown to be very effective. In fact, the number of adaptive parameters of the network 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 fits the data better: more complex models will always fit the data better but they 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 of Ockham’s razor, which is the principle that one should prefer simpler models to more complex models, and that this preference should be traded off against the extent to which the models fit the data (Sivia, 1996). The best generalization performance is achieved by the model whose complexity is neither too small nor too large. The third level of inference mentioned above deals with this task: the Bayesian framework provides an objective and structured framework for dealing with the issue of model complexity, and allows an objective comparison between models with alternative network architectures (Beck and Yuen, 2004). The most plausible model class among a set M of NM candidate ones is obtained by applying Bayes’ Theorem as follows: 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 that maximizes p(D | Mj )p(Mj ) with respect to j. If there is no particular reason a priori to prefer one model over another, they can be treated as equally plausible a priori and a noninformative prior, that is, p(Mj ) = 1/NM , can be assigned; then different models can be compared just by evaluating their evidence (MacKay, 1992). Once the optimal architecture has been determined, the last issue that should be considered is the relative importance of each input variable. If the available data comes from real systems it could be difficult to separate the relevant variables from the redundant ones. In the Bayesian framework, this problem can be addressed by the ARD method, proposed by Mackay (1994) and Neal (1996). To use this technique, a separate hyperparameter α i is associated with each input variable: this value represents the inverse variance of the prior distribution of the parameters related to that input. In this way, every hyperparameter explicitly represents the relevance of one input: a small value means that large parameters are allowed and the corresponding input is important; on the contrary, a large value means that the parameters

are constrained near zero, and hence the corresponding input is less important. The ARD allows a fourth level of inference to be applied to the neural networks model. Once the architecture of the model is defined, the importance of every input is evaluated: if some hyperparameter is very large, the related input will be dropped from the model and the optimal architecture for the new model will be reestimated. The four levels of inference are summarized in the flowchart in Figure 7. Starting from the simple process of model fitting, further steps have been added to include the other three levels of inference: evaluation of the hyperparameters, model class selection, and ARD. More details can be found in Arangio (2008). The improvements that can be obtained by applying the first three levels are well documented in the existing literature (MacKay, 1992, 1994). On the contrary, the fourth level is usually applied independently and in this way the benefits of an integrated approach are not fully exploited. In this work the evaluation of the relative importance of each input is included in the iterative process. In this way, once the optimal architecture of the model is defined, it is possible to recognize eventual redundant parameters and drop them from the model.

6 MULTILEVEL STRATEGY FOR BRIDGE INTEGRITY ASSESSMENT The Bayesian neural networks discussed in the previous section is applied in a multi-step strategy for the assessment of the integrity of the long suspension bridge in Figure 8 (Arangio, 2008). The considered bridge has a main span of 3,300 m and it carries six road lanes in the external box girders and two railway tracks in the central one; detailed information on the bridge project and its history can be found in Bontempi (2006). A multi-step approach has been followed because it has been shown that is more effective to consider independently the tasks of damage detection, location, and quantification (Ceravolo et al., 1995; Ko et al., 2002). In the first step of the strategy the occurrence of damage or anomalies in the bridge is detected, and the damaged portion of the structure is identified. If some damage is detected, the second step of the procedure is initiated: using a pattern recognition approach, the specific damaged member within the whole area is identified, and the extent of damage is evaluated. The entire procedure has been carried out working on a finite-element model of the bridge but it could be applied in the same way to an existent structure.

Multilevel strategy for bridge integrity monitoring

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Fig. 7. Hierarchical Bayesian framework for neural networks.

6.1 Step 1: Damage detection

Fig. 8. Steps of the damage identification strategy.

In the first step of the proposed strategy, the response of the structure is monitored at various measurement points, located at groups of three (A, B, and C) every 30 m along the bridge deck. One neural network for each intermediate point (B) is built and trained using the time-histories of the response of the structure subjected to wind actions and traffic loads (due to the passage of a train) in the undamaged situation. The timehistories of selected structural response parameters are sampled at regular intervals, thus generating series of discrete values. A set of such values from the instant t – k to t is used as input for the network models, and the value 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 patterns, 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 pattern, the set of values from ft+n−k to f t+n−1 is used as input, and the value ft+n is predicted and compared with the target one. If the error in the prediction is negligible, the structure is considered as undamaged; if the error is higher than a threshold value (eventually defined according to expert opinion), the presence of an anomaly is detected (Figure 10). The anomaly may correspond to a damage state or simply to a change of the characteristics of the excitation. To distinguish the changes in the structural response due to variations in the excitation from those due to damage, the prediction errors are checked in all measurement points, according to the procedure schematically represented in the flowchart of Figure 9. If the prediction is wrong in several locations, that is the difference e between the mean value of the errors in training and testing is different from zero in different measurement points, it can be concluded that the characteristics of the excitation are probably different from those assumed, and the trained neural network models are unable to represent the actual time-history of the response parameters. In this case, the models need to be updated according to the new excitation. On the other hand, if the difference e is large only at one or a few

points and generally decreases with the distance from those points, it can be concluded that the considered portion is damaged. To illustrate the proposed approach, data is simulated using a dynamic model of the suspension bridge where damage is implemented as a reduction of stiffness of a structural element. The following scenarios are considered: 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 includes 1,000 samples of the time-history of the response parameters that were found to be the most sensitive to a stiffness reduction (Arangio and Petrini, 2007), that is the rotation of the deck around the longitudinal axis in case of wind actions, and the vertical displacements of the deck in case of traffic loads. 6.2 Step 2: Identification of damage location and severity Having recognized that a portion of the structure is damaged, 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 the errors 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 evaluating the damage intensity. A pattern recognition approach is used. To create the training data set, the errors in Step 1 obtained by the neural network approximation of the response time-histories at three different points of the damaged portion (A, B, and C in Figure 11) are collected, 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 locations of damage and its intensity (Figure 11). 7 RESULTS OF THE INTEGRITY ASSESSMENT PROCEDURE 7.1 Results of step 1: Damage detection The different network models were trained using the time-histories of the response of the bridge in undam-

aged conditions. The network architecture has been determined by the Bayesian approach discussed in Section 5: the optimal network models consist of 2, 2 and 1 nodes in the input, hidden and output layers, respectively. An example of the evolution in time of the differences between the predicted and the target values in the sets of training and test data is reported in Figures 12 and 13; both undamaged and damaged conditions are considered. It is possible to notice that when time-histories related to various damage scenarios are proposed to the trained networks the errors in the approximation increase. There is a difference e between the mean values of the error in undamaged and damaged conditions. In Figures 14 to 16 the increments e of the mean values of the error with respect to the undamaged situation are shown for different levels of damage in the cables, the hangers, and the transverse beam. Both wind actions and traffic loads are considered and the results are compared.

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Training error

0.9

Test error (undamaged)

0.09

Δe

err

0.06

0.6

train wind

0.03

0.3 0.00 5%

0.0

10%

30%

50%

(b) Damage intensity (%) – transverse beam (pos 3) 0

20

40

t [s]

60

80

Fig. 12. Differences between the network values and the correct value in case of undamaged structure. Training error

Test error (damaged)

0.9

err 0.6 0.3

Δe

mean -damaged mean -undamaged

0.0 0

20

40

t [s]

60

0.9

Δe train wind

0.3 0.0 1.0%

3.0%

5.0%

10%

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

Fig. 14. Increment of the error in the approximation of the response time-history of the cable under wind actions and traffic load. 0.09

Δe 0.06

7.2 Results of step 2: Identification of damage location and intensity Once the damaged portion of the whole structure is recognized, the specific damaged element and the intensity of damage are identified using a pattern recognition approach. Various damage scenarios, corresponding to the reduction of the stiffness in the hangers, the cables, and the transverse beam in the identified damaged portion is simulated, and a training set consisting of 370 examples is created. The network architecture is always determined by the Bayesian approach discussed in Section 5. The optimal network model has 11 units in the hidden layers. After the training phase the network is tested with 30 new input vectors that are not included in the training set, and the related damage scenarios are obtained and compared with the target ones. To give a global and intuitive representation of the results, two quantities are defined: 1. The position, which gives a measure of the error in the location: t×y (7) pos(i) = |t| · |y|

train wind

0.03

0.00 20%

Looking at the results shown in Figures 14 to 16, it is possible to note that the proposed method is more effective when responses from high speed excitation (like traffic) 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 one train is considered.

80

Fig. 13. Differences between the network values y and the correct value t in damaged conditions in a case example (considered damage: 5% reduction of stiffness in one cable).

0.6

Fig. 16. Increment of error in the approximation of the response time-history of the transverse beam under wind actions and traffic load.

40%

50%

80%

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

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

2. The intensity, which gives a measure of the error in the quantification: int(i) =

|t| . t|y|

(8)

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

Multilevel strategy for bridge integrity monitoring

pos

1.2 1.0 0.8 0.6 0.4 0.2 0.0 0

10

20

30

Test number Fig. 17. Identification of the damage position in the test examples.

int

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Test number

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based procedure that integrates the solving procedures with the heuristic knowledge coming from experience or qualitative information. For this task, different soft computing methods can be suitable. In particular, in this work, the Bayesian neural network model has been used to formulate a hierarchical integrity assessment strategy. The proposed approach has been applied for the analysis of the time-history of the response of a long span suspension bridge subjected to ambient excitations. The strategy could be useful for damage identification of large structural systems instrumented with on-line monitoring systems. The presented example case has been developed on a numerical model of the structure but the strategy can be applied on real structural systems as well: various neural networks models could be selected and trained in a continuous way using the time-histories of the structural response; in this way the occurrence of anomalies can be detected almost in real time. When an anomaly is recognized, numerical simulations can be carried out to create the data set to develop the second step of the strategy. In this way experimental data are used for damage detection and the results of the numerical analyses can help to identify the damaged element and to quantify the intensity of damage.

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

ACKNOWLEDGMENTS quantities are evaluated for each of the 30 test samples and the results are shown in Figures 17 and 18. The location can be detected in almost 90% of the considered cases and the intensity is correctly estimated in 66% of the cases. 8 CONCLUSIONS In this work the concept of dependability has been discussed and its original meaning has been extended to the structural engineering field. It has been shown that this term describes the overall quality performance of a complex structural system and its influencing factors in an integrated way. The different aspects related to dependability are strictly connected with the concept of structural integrity. During the service life the integrity, and consequently the dependability, can be lowered by damages. The structural monitoring represents an essential tool to assess the evolution in time of the dependability of existing structural systems. Fundamental tasks of integrity monitoring are fault detection and diagnosis. Fault diagnosis from experimental data is an inverse problem and the reconstruction of the fault-symptom chain can be very difficult. A solution can be achieved by applying a knowledge-

The authors wish to thank Professors H. Li (Harbin Institute of Technology), J.L. Beck (California Institute of Technology), F. Casciati, and L. Faravelli (University of Pavia) for discussions related to this study. The reviewers of the article are acknowledged for the careful reading and the very useful suggestions. The support of Prof. H. Adeli is also recognized. The financial support of University of Rome “La Sapienza” is also acknowledged. The opinions and the results presented here are however the responsibility only of the authors and cannot be assumed to reflect the ones of University of Rome “La Sapienza.” REFERENCES Abe, K. & Amano, K. (1998), Monitoring system of the Akashi Kaikyo Bridge, Honshi Technical Report, 22(86), 29–34. Adeli, H. (2001), Neural networks in civil engineering: 1989– 2000, Computer-Aided Civil and Infrastructure Engineering, 16(2), 126–42. Adeli, H. & Balasubramanyam, K. V. (1988), A novel approach to expert systems for design of large structures, AI Magazine, pp. 54–63. Adeli, H., Gere, J. & Weaver, W., Jr. (1978), Algorithms for nonlinear structural dynamics, Journal of Structural Division, ASCE, 104(ST2), 263–80.

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