Structural integrity monitoring for dependability
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Dependability of a structural system is a comprehensive concept that – by definition – describes the quality of the system as its ability to perform as expected in a way that can justifiably be ...

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

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  • 1. This article was downloaded by: [Universita Studi la Sapienza] On: 30 August 2013, At: 03:41 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Structure and Infrastructure Engineering: Maintenance, Management, Life-Cycle Design and Performance Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/nsie20 Structural integrity monitoring for dependability S. Arangio a , F. Bontempi a & M. Ciampoli a a Department of Structural and Geotechnical Engineering, Sapienza Università di Roma, Via Eudossiana 18, 00184, Roma, Italy Published online: 06 Apr 2010. To cite this article: S. Arangio , F. Bontempi & M. Ciampoli (2011) Structural integrity monitoring for dependability, Structure and Infrastructure Engineering: Maintenance, Management, Life-Cycle Design and Performance, 7:1-2, 75-86, DOI: 10.1080/15732471003588387 To link to this article: http://dx.doi.org/10.1080/15732471003588387 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions
  • 2. Structural integrity monitoring for dependability S. Arangio*, F. Bontempi and M. Ciampoli Department of Structural and Geotechnical Engineering, Sapienza Universita` di Roma, Via Eudossiana 18, 00184, Roma, Italy (Received 21 October 2008; final version received 16 December 2009; published online 6 April 2010) Dependability of a structural system is a comprehensive concept that – by definition – describes the quality of the system as its ability to perform as expected in a way that can justifiably be trusted. One of the attributes of dependability is integrity, which can be interpreted as the absence of improper alterations of the structural configuration. The assessment of the integrity during the whole life-cycle can be carried out efficiently by implementing a monitoring system able to detect and diagnose any fault at its onset. The essential feature of the monitoring system dealt with in the paper is the elaboration of data gathered on site by a combination of simulation and heuristics. In detail, the first part of the paper deals with the extension of the concept of dependability, as formulated in computer science, to structural engineering. The second part illustrates a two-step hierarchical strategy for the assessment of the integrity of a structure through monitoring of its response under ambient vibrations; Bayesian neural network models are used for fault detection and diagnosis from observable symptoms. In the first step, the occurrence of any fault is detected and the relevant portion of the structure identified; in the second step the specific element affected by the fault is recognised and the intensity of the alteration of the structural performance evaluated. The strategy is applied to assess the integrity of a long-span suspension bridge subjected to wind action and traffic loading. As the bridge is under design, measured data are simulated by analysing the response of a detailed FE model of the whole structural system. The final objective of the study is the optimal design of the integrity monitoring system for the bridge. Keywords: structural systems; dependability; integrity monitoring; fault detection; fault diagnosis; Bayesian neural network models 1. Introduction The design of a valuable and safety-critical construc- tion requires advanced approaches to take into account the intrinsic ‘complexity’ of the structural system. A relevant aspect of the complexity is the fact that structures are usually systems composed of strongly interacting components. Structural design cannot rely on a simplistic idealisation of the structure as a ‘device for channelling loads’, that allows safety checks carried out considering each structural element per se; it must be based on the analysis of the structural system as a whole, being interpreted as ‘a set of interrelated components working together toward a common purpose’ (NASA-SEH 1995). Another aspect that is worth mentioning is the fact that when subjected to accidental or exceptional actions, such as earthquakes and windstorms, or to deterioration mechanisms, structural systems may exhibit a non-linear behaviour, and a realistic evalua- tion of the structural performance during the whole life-cycle can be extremely cumbersome. Moreover, any structural response shall be evaluated by taking into account the influence of the several sources of uncertainty that characterise both the actions and the structural properties, as well as the efficiency and consistency of the model of structural response. In principle, the design process shall include requirements concerning the construction phase and the operation and maintenance during the whole life- cycle. To this aim, data collected on site (e.g. through a continuous monitoring) are essential both for checking the accomplishment of the expected performance during the service life, and for validating the original design. Only if the aforementioned features are properly considered, the structural response can be reliably evaluated, and the performance of the building construction ensured during the intended lifetime: System Engineering represents the robust approach that takes properly into account the different aspects related to conceptual and structural design, construc- tion and maintenance (Bontempi et al. 2008). The overall approach requires the definition of the quality of a complex structural system by a compre- hensive concept, like dependability. The concept of dependability has been originally developed in the field of computer science, where it is defined as ‘the ability *Corresponding author. Email: stefania.arangio@uniroma1.it Structure and Infrastructure Engineering Vol. 7, Nos. 1–2, January–February 2011, 75–86 ISSN 1573-2479 print/ISSN 1744-8980 online Ó 2011 Taylor & Francis DOI: 10.1080/15732471003588387 http://www.informaworld.com Downloadedby[UniversitaStudilaSapienza]at03:4130August2013
  • 3. to deliver services that can justifiably be trusted’ (Avizˇ ienis et al. 2004): the dependability of a system reflects (i.e. represents, measures, . . .) the user’s degree of trust in that system, i.e. the user’s confidence that the system will operate as the user expects and will not fail in normal use during the whole lifetime (Sommer- ville 2000). The definition can be extended to Structural Engineering: the design process shall be aimed at justification of trust through the fulfilment of some ‘attributes’ of dependability, mainly reliability, safety, maintainability, and integrity. According to the original definitions given in Avizˇ ienis et al. (2004), reliability can be interpreted as the continuity of correct service for the whole service life; safety corresponds to the absence of catastrophic consequences of system operation on the users and the environment; maintainability is the ability to undergo modifications and repairs; integrity corresponds to the absence of improper system alterations and is some- times related to the completeness and consistency of the structural configuration (Bontempi and Giuliani 2008). Other attributes of dependability are the availabil- ity, originally defined as the readiness for correct service at a given point of time, and the security, that is a property that reflects the ability of the system to protect itself from accidental or deliberate external attack and is an essential pre-requisite for availability, reliability and safety. All attributes can be subdivided in high level or active performances (reliability, availability, maintain- ability) and low level or passive performances (safety, security and integrity); the latter are exclusive requirements, in the sense that they exclude undesir- able situations rather than specifying required performances. It is evident that the dependability specification of a structural system must include the requirements for the dependability attributes in terms of admissible fre- quency and severity of failures in a given environment; obviously, one or more attributes may not be required at all for a given system. The attributes can vary over the life-cycle; in particular, the integrity and conse- quently the overall dependability can be lowered by deterioration due to effects of wear during ordinary service, improper use and maintenance, as well as environmental and accidental events. Structural monitoring represents the tool for the assessment of the evolution in time of the integrity, thus of the dependability of an existing structural system. It integrates, in a unified framework, advanced engineering analyses and experimental data processing. Therefore it is a very complex task, and includes issues such as the definition and analysis of the structural performances, from regular exercise to out-of-service and collapse, the assessment of the environmental conditions, the choice of the sensor systems and their optimal placement, the use of data transmission systems and signal processing techniques, and the methods for damage identification, location and quantification and for structural model updating (Berthold and Hand 1999). Soft computing methods can be very useful to process data gathered by monitoring. In this paper, the Bayesian neural network models are used to formulate a two-step hierarchical strategy for structural integrity monitoring. In the first step the occurrence of abnormal alterations of the structural response is checked and eventually the damaged section of the structure identified; in the second step, the specific damaged element in the considered section is recog- nised and the intensity of damage evaluated. In the following, the dependability assessment is explained in detail with reference to structural systems and the two-step strategy for structural integrity monitoring illustrated. The strategy is applied to assess the integrity of a long-span suspension bridge sub- jected to wind action and traffic loading. As the bridge is under design, measured data are simulated by analysing the response of a detailed finite element model of the whole structural system. The final objective of the study is the optimal design of the integrity monitoring system for the bridge. 2. Dependability assessment and structural integrity monitoring As specified above, the dependability of a structural system is a comprehensive concept that includes and describes the relevant aspects with reference to the system quality and its influencing factors. The assess- ment of dependability requires the definition of three elements (Figure 1): the attributes, i.e. the properties that quantify the dependability; the threats, i.e. the elements that affect dependability; the means, i.e. the tools that can be used to increase dependability. In structural engineering, the relevant attributes are reliability, safety, maintainability and integrity. These properties are essential to guarantee, with reference to the whole life-cycle, the survivability of the system under the relevant accidental or exceptional hazard scenarios, considering also the security issue, and the system robustness, serviceability in operating condi- tions and durability. The threats to system dependability can be subdivided into faults, errors and failures. According to the definitions given in Avizˇ ienis et al. (2004), an active or dormant fault is a defect or an anomaly in the system behaviour that represents a potential cause of error; an error is the cause for the system being in an 76 S. Arangio et al. Downloadedby[UniversitaStudilaSapienza]at03:4130August2013
  • 4. incorrect state; failure is a permanent interruption of the system ability to perform a required function under specified operating conditions. For building constructions, possible faults are incorrect design, construction defects, improper use and maintenance, and damages due to accidental actions or deteriora- tion; errors may or may not cause failure, and may also activate a fault. Following the approach proposed in Isermann (2006), the design of a dependable structural system is basically the problem of the design of a fault-tolerant system: however, it includes also features like fault detection, that is detection of alterations of the system behaviour, fault diagnosis, that is, localisation and quantification of the effects of faults and errors, and, finally, the management of faults and errors aimed at avoiding failure. This paper is focused mainly on fault detection and diagnosis. These elements are strictly related to the monitoring of the integrity of the structural system: in fact an efficient monitoring programme is expected to be able to preserve the structural dependability, diagnosing alterations, that is deterioration and damage, at their onset (Li and Ou 2006). In analogy with biological systems, and even if there is no general consensus on its definition, an integrity monitoring system should (Aktan et al. 1998, Isermann 2006): sense the loading environment as well as the structural response; reason by assessing the structural condition and health; communicate through a proper interface with other components and systems, including controllers of the system behaviour; learn from experience as well as by interfacing with human for heuristic knowledge; be precise, so that even small faults should be detected and diagnosed; decide and take action for alerting controllers in case of accidental situations, or activate fault tolerant configurations in case of a reconfigurable system. An ‘optimal’ integrity monitoring system allows the control of the structural system in a proactive way: the circumstances that may eventually lead to deteriora- tion, damage and unsafe operations can be diagnosed and mitigated in a timely manner, and costly replace- ments can be avoided or delayed. Analysing the problem in terms of cost–benefit analysis, it comes out that, in case of complex structures, the integrity monitoring should be planned since the design phase and carried out during the entire life-cycle in order to assess the structural health and performance under in-service and accidental conditions (Aktan et al. 2002). Over the past 30 years a huge research effort has been devoted to developing effective methods for integrity monitoring of civil structures. An extensive survey of global methods (so-called because they are based on the analysis of the whole structure) has been presented in Doebling et al. (1996), and updated by Sohn et al. (2004), where it is observed that, usually, non-destructive global methods can be used for fault Figure 1. Dependability: attributes, threats and means (adapted from Avizˇ ienis et al. 2004). Structure and Infrastructure Engineering 77 Downloadedby[UniversitaStudilaSapienza]at03:4130August2013
  • 5. detection, whereas local inspections and pattern recognition approaches for fault diagnosis. Regarding the temporal extent of the measure- ments, continuous measurements are usually needed to capture environmental effects such as those due to wind and temperature; periodic inspections and measurements are needed to evaluate the response under operating conditions. Extensive use of long term continuous monitoring is quite new, enabled by recent advances in data acquisition, processing and manage- ment. Long term monitoring of the structural response was pioneered in China and Japan (Abe and Amano 1998, Wong et al. 2000, Ko and Ni 2005): nowadays, several bridges are instrumented in Europe (Casciati 2003), United States (Pines and Aktan 2002), Canada (Mufti 2001), Korea and other countries. Recent developments consist in formulating a general frame- work of asset management in a life-cycle perspective (Messervey and Frangopol 2008). 3. Neural network models for fault detection and diagnosis In general, a fault causes events that, as intermediate steps, influence or determine measurable or observable symptoms. In order to detect, locate and quantify a system fault, it is necessary to process data obtained from monitoring and to interpret the symptoms. However, this is a very complex task, as explained in Figures 2 and 3. The relationship between fault and symptoms can be represented graphically by a pyramid (Figure 2); the vertex represents the fault, the lower levels the possible events generated by the fault and the base corresponds to the symptoms. The propagation of the fault to the symptoms follows a cause–effect relationship, and is a top-down forward process. The fault diagnosis proceeds in the reverse way; it is a bottom-up inverse process that relates the symptoms to the fault. To solve the problem implies the inversion of the causality principle. But one cannot expect to rebuild the fault–symptom chain only by measured data because the causality is not reversible or the reversibility is ambiguous (Fu¨ ssel 2002): the underlying physical laws are often not known in analytical form, or too complicated for numerical calculation. More- over, intermediate events between faults and symptoms are not always recognisable (as indicated in Figure 3). The solving strategy requires integrating different procedures, either forward or inverse; the mixed approach has been denoted as the total approach by Liu and Han (2004), and different computational methods have been developed for this task, that is, to interpret and integrate information coming from on site inspection, database and experience. In Figure 3 an example of knowledge-based analysis is shown. The results obtained by instrumented monitoring (the detection and diagnosis system on the right side) are processed and combined with the results coming from the analytical or 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 the output of the system (the measured symptoms: displacements, accel- eration, natural frequencies, etc) is known but the parameters of the structure have to be determined. Different computational methods can be used to this aim. In several applications, soft computing techni- ques, like the neural network models used in this study, have shown their effectiveness in processing informa- tion coming from monitoring. For a review on the subject, it is possible to refer to Adeli (2001), who illustrated the applications of neural networks to civil engineering during a decade, and to Waszczyszyn (1999), who collected in a book various papers on the use of neural networks for the analysis and design of structures. As concerns more specifically the problem of damage identification and structural health mon- itoring, Ni et al. (2002) presented a two-stage neural network-based damage detection method, where damage location is identified in a first stage and damage severity is estimated in a second stage; Ko Figure 2. Fault–symptoms relationship. 78 S. Arangio et al. Downloadedby[UniversitaStudilaSapienza]at03:4130August2013
  • 6. et al. (2002) used neural networks in a multi-stage identification scheme for detecting damage in a cable- stayed bridge in Hong Kong; Xu and Humar (2006) presented a two-step algorithm that uses a modal energy-based damage index to locate the damage and a neural network technique to determine its magnitude. The neural network concept has its origins in attempts to find mathematical representation of information processing in biological systems. Actually there is a definite probability model behind it; in fact a neural network is an efficient statistical model for nonlinear regression. It can be described by a series of functional transformations working in different corre- lated layers (Bishop 2006), that, in case of two layers, takes the form: yk x;wð Þ ¼ h XM j¼1 w ð2Þ kj g XD j¼1 w ð1Þ ji xi þb ð1Þ j0 ! þb ð2Þ k0 ! ð1Þ where yk is the k th output variable in the output layer, x is the vector of the D input variables in the input layer, w is the matrix including the adaptive weight parameters w 1ð Þ ji and w 2ð Þ kj and the biases b 1ð Þ j0 and b 2ð Þ k0 that are set during the training phase (the superscript refers 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, that are transformed using the activation functions h and g. The values of the components of w are obtained during the training phase by minimising a proper error function: in the considered case, the sum of squared errors with weight decay regularisation (Bishop 1995) given by: E ¼ 1 2 XN n ¼ 1 XNo k¼1 yk xn ; wð Þ À tn k È É2 þ a 2 XW i ¼ 1 wij j2 ð2Þ where yk is the k th neural network output correspond- ing to the n th realisation of x, tn k 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. Neural network learning can be interpreted in the framework of Bayesian inference (MacKay 1995), where probability is treated as a multi-valued logic that may be used to perform plausible inference (Jaynes 2003). Within this framework it is possible to solve a crucial problem of neural network application: the choice of the optimal model complexity, which is given by the number of units included in the hidden layers. This number has to be fixed before training, and affects significantly the generalisation performance of the network model. In general the number of hidden units is selected by experience or rule of thumb, and depends heavily on the subjective judgment of the designer: in this paper the optimal architecture of the network model for a given set of training data is selected by a Bayesian Figure 3. Knowledge-based analysis for structural integrity monitoring. Structure and Infrastructure Engineering 79 Downloadedby[UniversitaStudilaSapienza]at03:4130August2013
  • 7. model class selection approach (Beck and Yuen 2004). As a result, the selection of the neural network model class is mathematically rigorous and systematic; the Bayesian approach allows an objective comparison among alternative solutions and eliminates reliance on the judgment of the neural network designer (MacKay 1995). The mathematical approach for neural network model class selection is illustrated in detail in Arangio and Beck (2010), where the most plausible model class among a set of candidate ones is obtained by applying Bayes’ Theorem and maximising the posterior prob- ability of the model class given a set of training data. In this respect, let us remember that it is not correct to choose simply the model that better fits data: more complex models will always fit the data in a better way, but they may be over-parameterised and give poor prediction for new cases. 4. A two-level strategy for bridge integrity assessment Bayesian neural network models have been used to formulate the two-step hierarchical strategy for the integrity assessment of the bridge that is schematically represented in Figure 4. It is a long span suspension bridge that was recently reconsidered in Italy: a preliminary design scheme elaborated in 2005 has been considered for numerical calculations. The main span is 3300 m long, while, including the two side spans, the total length is 3666 m. The towers are 383 m high and the bridge suspension system relies on two pairs of steel cables, each with a diameter of 1.24 m and a total length, between the anchor blocks, of approximately 5000 m; the secondary suspension system consists of 121 pairs of rope hangers. The cross section of the deck is composed of three box elements supported every 30 m by transversal beams; the deck carries six road lanes in the external portions of the deck and two railway tracks in the central one. More detailed information on the bridge design can be found, for example, in Bontempi (2006). The two-step strategy considers the tasks of damage detection, location, and quantification. As shown in Figure 5, in the first step the occurrence of anomalies in the bridge response is detected: if the anomalies correspond to possible alterations of the bridge response due to any damage, the damaged portion of the whole structural system is identified. If some damage has been detected, the second step is initiated: by using a pattern recognition approach, the specific damaged member within the whole section is identified and the intensity of damage evaluated. The two steps are illustrated in detail in the following. 4.1. Step 1: Damage detection As shown in Figure 5, it is assumed that the response of the structure, represented by the time-histories of the displacements, is monitored by sensors at various measurement points. In the example case, they are located in groups of three (A–B–C) every 30 m along the bridge deck; each group individuates a test section. Different Bayesian neural network models are trained; in this step, one for each intermediate point (B). The models are built and trained using the time- histories of the displacements of the structure subjected to wind action and traffic loads (that correspond, in the examined case, to the passage of one train) in the undamaged situation. The procedure for network training is shown in Figure 6: the time-history of the response parameter f is sampled at regular intervals, generating a series of discrete values ft. A set of d such values: ft-dþ1, . . ., ft, is used as input of the network model, while the next value ftþ1 is used as the target output. By stepping along the time axis, a training data set consisting of many sets of input vectors with the corresponding output values is built, and the network models are trained. The trained models are then tested with a set of observed values ftþn-d, . . . , ftþn, to predict the value of ftþnþ1, according to the procedure of one- step ahead forecast (Bishop 1995). After the initial training phase, new input sets, corresponding to both undamaged and damaged situations, are tested on the trained models. For each set, the one-step ahead value of the parameter is forecast and compared with the target. Figure 4. Scheme of the considered bridge. 80 S. Arangio et al. Downloadedby[UniversitaStudilaSapienza]at03:4130August2013
  • 8. The results of the training and test phases are elaborated as shown in Figure 7. The two plots show the difference err between the network output value y and the target value t at several time steps for both training and test in undamaged and damaged condi- tions. It is possible to note that the mean values of err (indicated by a straight line) obtained both in training and test are comparable if the structure remains undamaged. On the contrary, in case of anomalies that may correspond to damages, there is a difference De between the mean values of err corresponding to the damaged and undamaged conditions in the test phase. It has to be noted that the detected anomaly may correspond to a damage state or simply to a change of the characteristics of the excitation. To individuate the actual cause of the anomaly, the intensity of De is checked in different test sections, according to the procedure that is schematically represented in the flow chart shown in Figure 8. In the left side of Figure 8, the start-up of the procedure is shown: given a data set, the optimal neural network model is selected according to the Bayesian approach, that is, the model with the highest posterior probability is chosen and trained (Arangio and Beck 2010). Then, as shown in the right side of Figure 8, the model is tested with new input data sets. If the difference De of the errors between training and test is different from zero in several test sections, it can be concluded that the characteristics of the excitation are probably different from those hypothesised. The adopted neural network models are thus unable to represent the actual time-histories of the response parameters, and have to be updated and trained according to the modified characteristics of the excitation. If De is different from zero only in one or few test sections and generally decreases with the distance from the selected section, it can be concluded that the considered section of the structure is damaged and the second step of the procedure is actuated. Figure 5. Sketch of the two-step strategy for the assessment of the structural integrity. Figure 6. Procedure for network training. Structure and Infrastructure Engineering 81 Downloadedby[UniversitaStudilaSapienza]at03:4130August2013
  • 9. In real applications, not all cases in which De is different from zero should be considered as relevant; also, because it is essential to take properly into account the noise corrupting the signals and the accuracy of the measuring instruments, the choice of the threshold value for initiating the second step must be left to the experience of the operator. In the numerical applications illustrated below, all cases in which De is different from zero have been considered. In the considered example, data are simulated by analysing the dynamic response of a FE model of the suspension bridge. Damage is modeled as a reduction Figure 7. Difference err between output y and target t values as a function of time for training and test in undamaged and damaged conditions in a case example (considered damage: 5% reduction of stiffness in one cable). Figure 8. Flow-chart of the first step of the procedure. 82 S. Arangio et al. Downloadedby[UniversitaStudilaSapienza]at03:4130August2013
  • 10. of stiffness of a structural element in a test section and the following damage scenarios are considered: . Hangers: reduction of stiffness from 5% to 80%. . Cables: reduction of stiffness from 1% to 10%. . Transverse beam: reduction of stiffness from 5% to 30%. Data adopted for training every network model consist of 1000 samples of the time-histories of the response parameters that were found to be the more sensitive to a stiffness reduction (Arangio and Petrini 2007): the deck twist in case of wind actions, and the vertical displacement of the centroid of the deck cross section in case of traffic loads. The number of samples has been chosen after some trials, where it has been noticed that no significant improvements in the generalisation capacity of the network are obtained for a higher number. 4.2. Step 2: Identification of damage location and intensity Having recognised that a test section is damaged, the second step of the procedure is start up. It is aimed at identifying the specific damaged element (Figure 5: one of the two cables – the transverse beam – one of the two hangers), and at evaluating the intensity of damage. A pattern recognition approach is used: in order to improve the quality of the procedure, the mean values of the errors err in the prediction of the response time-histories for all three measurement points (A, B and C) in the considered test section are taken as input of the selected neural network model. As shown in Figure 5, each damage scenario is described by a vector of five components: each component indicates the state (represented by a number denoting the presence – if different from zero – and the intensity) of damage of a structural element in the test section. Simulated damage scenarios have been assumed as output of the neural network model in numerical calculations. The data set for the second step has been gathered by simulating 400 damage scenarios (corre- sponding to different positions and intensities of damage): 370 out of them have been used for network training, the remaining 30 for testing the network generalisation performance. 5. The case example: Results of the procedure for the integrity assessment 5.1. Results of step 1: Damage detection The optimal model for the prediction of the time- histories of the response parameters has been selected by considering the structural response in the unda- maged condition, and exploiting the procedure for Bayesian model selection that is fully explained in Arangio and Beck (2010); it consists of 2, 2 and 1 units in, respectively, the input, hidden and output layers. The model optimised in this way is also the most efficient in terms of sensitivity to changes in structural behavior: it corresponds to the lowest error in the training phase and to the highest error in the approximation of the signal when anomalies are detected (Arangio 2008). In Figure 9 (a), (b), (c), the differences between the mean values of the errors De in the damaged and undamaged conditions are shown for different inten- sities of damage (that is, of stiffness reduction) respectively to the cables, the transverse beam, and the hangers. Looking at the plots in Figure 9, it is evident that the adopted strategy is more effective when responses to high speed excitations (like traffic loads) are considered instead of responses to slow speed excita- tions (like wind actions). Thus, in the following step, only the structural response due to the transit of train is considered. The possibility of detecting the damages is different for the various elements, as expected: in fact, a small damage to the cables determines a much higher value of De than strong damages to the transverse beam and the hangers. Nonetheless, the strategy allows detecting even small damages, and is characterised by a high level of precision. 5.2. Results of step 2: Identification of damage location and severity Once a damaged section is detected, the specific damaged element and the intensity of damage are identified by using the pattern recognition approach. The optimal network model, that is the most efficient in terms of localisation and quantification of damage (Arangio and Beck 2010), is selected by the Bayesian approach on the base of the 370 patterns considered for training. It consists of three input variables, that is, the errors err evaluated at A, B, and C, five output variables, that is, the possible locations (coincident with a structural element) and intensities of damage, and two hidden layers with 11 units (obtained by the Bayesian selection process). After the training phase, the network is tested with the remaining 30 patterns. To evaluate the efficiency of the assessment, two quantities are defined and evaluated for each test pattern: the position, which gives a measure of the prediction error made in any damaged location, and the intensity, which gives a measure of the error made in estimating the damage intensity. These quantities are obtained by comparing the vectors of the output Structure and Infrastructure Engineering 83 Downloadedby[UniversitaStudilaSapienza]at03:4130August2013
  • 11. variables corresponding to the evaluated y and the target t damage scenarios, and are expressed by: pos ¼ t  y tj j Á yj j ð3Þ int ¼ tj j yj j ð4Þ where 6 denotes the inner product and jÁj is the norm of the vector. If pos and int are (approximately) equal to 1, it can be assumed that the damage is well localised and its intensity correctly estimated. The results of the numerical application are shown in Figure 10: the damaged element is correctly located in almost 90% of the considered cases, and the intensity is correctly estimated in approximately 66% of the considered cases. Therefore, it appears that the proposed strategy is more efficient in locating the damage than in quantifying it. 6. Final remarks In the first part of the paper, the concept of dependability, originally developed in the field of computer science, has been extended to structural engineering, in order to define and measure the quality of a complex structural system. The whole design process is then understood as aimed at ‘justification of trust’ through the fulfilment of some ‘attributes’ of dependability, mainly reliability, safety, maintainabil- ity and integrity. As a further development of the concept of dependability, it seems useful to add the attribute of sustainability: a structure should be acceptable for its environment and ‘meet present needs without com- promising the ability of future generations to meet their needs’, as indicated in a 1987 UN Conference. This aspect will be dealt with in future studies. In the second part of the paper, a two-step strategy for structural integrity monitoring has been discussed. Figure 9. Differences between the mean errors De in training and test for different intensities of damage in (a) one of the two cables, (b) the transverse beam, and (c) one of the two hangers. Figure 10. Accuracy of the estimation of the position and intensity of damage in a bridge section (30 tests). 84 S. Arangio et al. Downloadedby[UniversitaStudilaSapienza]at03:4130August2013
  • 12. It represents an essential tool for the assessment of existing structural systems as it allows controlling the structural system in a proactive way: the circumstances that may eventually lead to deterioration, damage and unsafe operations can be diagnosed and mitigated in a timely manner, and costly replacements avoided or delayed. Fundamental tasks of integrity monitoring are fault detection and diagnosis. It has been observed that the diagnosis from experimental data is an inverse problem and the backwards assessment of the fault- symptom chains cannot be done solely from measured data, since the causality is not reversible or the reversibility is ambiguous. The problem has been solved by developing and applying a knowledge-based procedure that integrates forward and inverse solving methods with the heuristic knowledge coming from experience or qualitative information. More specifi- cally, the Bayesian neural network model has been proposed to formulate the two-step hierarchical strategy for integrity assessment. The strategy has been applied to the case of a long-span suspension bridge subjected to wind actions and traffic loadings, and the capability of detecting the location and intensity of damages to the main structural elements of the superstructure has been examined. Acknowledgements This paper is dedicated to Professor Giuliano Augusti who always gave, and still gives, impetus to the research of the authors with stimulating suggestions. Thanks are due to Professors Pier Giorgio Malerba, Dan Frangopol and Fabio Biondini for fruitful discussions and comments on the manuscript, and to James L. Beck, who introduced the first author to the exciting subject of Bayesian neural networks. 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