Damage Detection in Water Distribution Pipe Network Using Bayesian Framework and System Reliability Analysis

Recent earthquake events evidenced that damage of structural components in a lifeline network may cause prolonged disruption of lifeline services, which eventually results in significant socio‐economic losses in the affected area. Despite recent advances in network reliability analysis, the complexity of the problem and various uncertainties still make it a challenging task to evaluate the post‐hazard performance and connectivity of lifeline networks efficiently and accurately. In order to overcome such challenges and take advantage of merits of multi‐scale analysis, this paper develops a multi‐scale system reliability analysis method by integrating a network decomposition approach with the matrix‐based system reliability (MSR) method. In addition to facilitating system reliability analysis of large‐size networks, the multi‐scale approach enables optimizing the level of computational effort on subsystems; identifying the relative importance of components and subsystems at multiple scales; and providing a collaborative risk management framework. The MSR method is uniformly applied for system reliability analyses at both the lower‐scale (for link failure) and the higher‐scale (for system connectivity) to obtain the probability of general system events, various conditional probabilities, component importance measures, statistical correlation between subsystem failures and parameter sensitivities. The proposed multi‐scale analysis method is demonstrated by its application to a gas distribution network in Shelby County of Tennessee. A parametric study is performed to determine the number of segments during the lower‐scale MSR analysis of each pipeline based on the strength of the spatial correlation of seismic intensity. It is shown that the spatial correlation should be considered at both scales for accurate reliability evaluation. The proposed multi‐scale analysis approach provides an effective framework of risk assessment and decision support for lifeline networks under earthquake hazards. Copyright © 2009 John Wiley & Sons, Ltd.

Over the last four decades, structural system reliability (SSR) has been an active research topic as engineering systems including structures and infrastructure networks become more complex, and the computational power has been remarkably advanced. Among many efforts to advance SSR technologies, the research by Prof. Armen Der Kiureghian in the early 2000s is considered to have built critical pathways to the development of next-generation SSR methods by revisiting the topic of SSR. As demonstrated in Der Kiureghian (Structural system reliability, revisited. Proceedings, 3rd ASRANet International Colloquium, Glasgow, UK, July 10-12, 2006), his research efforts led to new insights and perspectives on critical topics of structural system reliability. This has encouraged researchers to perform a variety of research activities to develop new SSR technologies that can address challenges and needs in risk management of real-world systems. This chapter provides a review on such efforts to reload the research community with SSR technologies, which were made possible by the revisit. The chapter reviews the following SSR methods: linear programming bounds, matrix-based system reliability method, sequential compounding method, cross-entropy-based adaptive importance sampling, selective recursive decomposition algorithm, branch-and-bound employing system reliability bounds, and genetic-algorithm-based selective search for dominant system failure modes. For each of the reviewed methods, their main concepts, applications and follow-up research activities are presented along with discussions on merits, remaining challenges, and future research needs.

Complex slopes are characterized by large numbers of failure modes, cut sets or link sets, or by statistical dependence between the failure modes. For such slopes, a systematic quantitative method, or matrix-based system reliability method, was described and improved for their reliability analysis. A construction formula of event vector cE was suggested to solve the difficulty of identifying any component E in sample space, and event vector c of system events can be calculated based on it, then the bounds of system failure probability can be obtained with the given probability information. The improved method was illustrated for four copper mine slopes with multiple failure modes, and the bounds of system failure probabilities were calculated by self-compiling program on the platform of the software MATLAB. Comparison in results from matrix-based system reliability method and two generic system methods suggests that identical accuracy could be obtained by all methods if there are only a few failure modes in slope system. Otherwise, the bounds by the Ditlevsen method or Cornell method are expanded obviously with the increase of failure modes and their precision can hardly satisfy the requirement of practical engineering while the results from the proposed method are still accurate enough.

Statistical Tolerance Analysis of a Mechanism with Gaps based on System Reliability Methods

In this paper, structural systems reliability analysis was used to estimate the system reliability of a typical semi-submersible based on the characteristic structure failure mechanisms under extreme wave loads. First, a three-dimensional simulation model was created for the chosen semi-submersible platform using an elastic-perfectly plastic material model, neglecting the effect of the strain hardening assumption. Then, under design wave conditions, and characteristic structural failure mechanisms of a semi-submersible platform were examined, and a system reliability model was developed based on the failure mechanism of the chosen platform. Finally, system reliability methods were used to determine the platform’s system reliability. It was discovered that the main node’s system reliability makes a significant contribution to the overall structure reliability, so it is strongly advised that the reliability of the main nodes be taken into account when determining the overall structure’s reliability. This research aims to apply reliability theory in offshore engineering and, ideally, to encourage the reliability-based design of semi-submersible platforms and other similar structures.

Aircraft structures are subjected to random loading conditions while the material properties vary around their nominal values. Despite recent advances, finite element (FE) reliability analysis is mostly performed for individual failure modes or parts represented by single limit-state functions. For risk-quantified design of complex aircraft structural systems, however, it is essential to quantify the risk of complex “system” events, i.e. logical functions consisting of multiple “component” events representing the failures of physical components or the occurrences of various failure modes. This paper proposes a new framework for FE “system” reliability analysis based on a Matrix-based System Reliability (MSR) method, which was recently developed to estimate the probabilities of general system events and their sensitivities with respect to the design parameters by efficient matrix calculations. A numerical example of an aircraft wing torque box demonstrates the proposed framework of FE system reliability analysis.

This study proposes a system reliability analysis of rack storage facilities subjected to forklift colliding events. The proposed system reliability analysis consists of two steps: the first step is to identify dominant failure modes that most contribute to the failure of the whole rack facilities, and the second step is to evaluate the system failure probability. In the first step, dominant failure modes are identified by using a simulation-based selective searching technique where the contribution of a failure mode to the system failure is roughly estimated based on the distance from the origin in the space of the random variables. In the second step, the multi-scale system reliability method is used to compute the system reliability where the first-order reliability method (FORM) is initially used to evaluate the component failure probability (failure probability of one member), and then the probabilities of the identified failure modes and their statistical dependence are evaluated, which is called as the lower-scale reliability analysis. Since the system failure probability is comprised of the probabilities of the failure modes, a higher-scale reliability analysis is performed again based on the results of the lower-scale analyses, and the system failure probability is finally evaluated. The illustrative example demonstrates the results of the system reliability analysis of the rack storage facilities subjected to forklift impact loadings. The numerical efficiency and accuracy of the approach are compared with the Monte Carlo simulations. The results show that the proposed two-step approach is able to provide accurate reliability assessment as well as significant saving of computational time. The results of the identified failure modes additionally let us know the most-critical members and their failure sequence under the complicated configuration of the member connections.

Damage detection in an offshore platform using incomplete noisy FRF data by a novel Bayesian model updating method

In this study, a two-stage damage detection procedure using a new approximation of modal strain energy (MSE) value is developed to boost the accuracy of structural damage localization in plate-type structures. The MSE is calculated using the center differential method for both intact and damaged states. The new formulas to approximate MSE are developed based on the nine-node isometric quadrilateral element that eliminates boundary conditions’ effect on damage detection results. The modal assurance criteria (MAC) is used as an indicator to choose the mode shapes with the best damage detection results. A global and a local MSE are proposed to enhance the accuracy of detecting the location of structural damage. An aluminum plate is used to verify the effectiveness of the proposed procedure with several damage scenarios. The results show that the new estimation of MSE value combined with MAC and the two-step MSE procedure can improve the accuracy of identifying the damage location compared to the original MSE procedure.KeywordsDamage detectionModal assurance criteriaModal strain energyPlate-type structureStructural health monitoring

Unsupervised learning methods are effective and suitable tools for damage detection. The main reason for the popularity of these methods in structural health monitoring originates from the fact that the process of learning can be implemented by information of the only normal condition called training data. In contrast, supervised learning methods require information of both normal and current conditions for the process of interest. Because civil engineering structures are expensive and complex, it is not reasonable and economical to impose intentional damage on providing training data. Hence, it is not simple to directly exploit supervised learning techniques in structural health monitoring. To deal with this limitation, this article proposes a novel two-level strategy including three algorithms for using the concepts of both unsupervised learning and supervised learning. The major contribution of this strategy is to consider supervised learning as a validation tool for damage detection. First, the results of damage detection are obtained from two unsupervised learning methods developed by Mahalanobis squared distance and a deep autoencoder neural network in the first two algorithms of the proposed strategy. The main objective is to separate accurate and confusing results of damage detection based on Type I and Type II errors. Second, the confusing results are fed into the third algorithm to train a classifier and compute their classification margins for making the final decision and validating damage detection. The effectiveness and applicability of the proposed strategy are assessed by a numerical concrete beam and an experimental laboratory frame. Results show that this strategy with the aid of the Naive Bayes classifier enables the unsupervised learning methods to make accurate decisions.

In general, a system is understood as a technical arrangement of clearly identifiable (system—) components whose functioning depends on the proper functioning of all or a subset of its components. For a reliability analysis, a number of idealizations are convenient if not necessary. It is assumed that the components can attain only two states, i.e. one functioning (safe, working, active,...) and one failure (unsafe, defect, inactive,...) state. This is a simplification which is not always appropriate but we will maintain it throughout the text. If there is a natural multi—state description of a component or a system we shall assume that this is reduced to a two-state description in a suitable manner. In practice, this step of modeling might be not an easy task. It is, nevertheless, mandatory in practical system reliability analyses. Several attempts have been made to establish concepts for analyzing systems with multi—state components (see, for example, Caldarola, 1980; Fardis and Cornell, 1981). It should be clear that systems then have also multiple states and the definition of safe or failure states requires great care. Such relatively recent extensions of the classical concepts cannot be dealt with herein.

Monte Carlo simulation (MCS) provides a conceptually simple and robust method to evaluate the system reliability of slope stability, particularly in spatially variable soils. However, it suffers from a lack of efficiency at small probability levels, which are of great interest in geotechnical design practice. To address this problem, this paper develops a MCS-based approach for efficient evaluation of the system failure probability Pf,s of slope stability in spatially variable soils. The proposed approach allows explicit modeling of the inherent spatial variability of soil properties in a system reliability analysis of slope stability. It facilitates the slope system reliability analysis using representative slip surfaces (i.e., dominating slope failure modes) and multiple stochastic response surfaces. Based on the stochastic response surfaces, the values of Pf,s are efficiently calculated using MCS with negligible computational effort. For illustration, the proposed MCS-based system reliability analysis is applied to two slope examples. Results show that the proposed approach estimates Pf,s properly considering the spatial variability of soils and improves the computational efficiency significantly at small probability levels. With the aid of the improved computational efficiency offered by the approach, a series of sensitivity studies are carried out to explore the effects of spatial variability in both the horizontal and vertical directions and the cross-correlation between uncertain soil parameters. It is found that both the spatial variability and cross-correlation affect Pf,s significantly. The proposed approach allows more insights into such effects from a system analysis point of view.

According to the deficiency of traditional Markov chain approach in dynamic fault tree analysis, a new modular method for system reliability analysis is proposed. This paper focuses on dividing the fault tree of system into independent subtrees using a linear-time algorithm, and the processing method for different subtrees: Binary decision diagram solution for static subtrees and Bayesian Network solution for dynamic subtrees, respectively. In addition, an approach is also provided for mapping some dynamic logic gates into discrete-time Bayesian network. At last, the modular method has been applied to assess the reliability of a satellite key device and the results have shown that the proposed method can overcome the state explosion problem, and is useful for assessing the reliability of large and complex systems.

The flow capacity of a transportation network can be reduced significantly if its constituent bridges are damaged by natural or man-made hazards. For rapid risk-informed decision making on hazard mitigation and response, it is therefore essential to have a capability to predict the post-hazard flow capacity of the network efficiently and accurately. However, this is a challenging task due to the uncertainty in hazards and structural damage, and the complex nature of the network flow analysis. Moreover, the bridge structures may experience significant deterioration over their life cycle, which requires time-varying network reliability analysis. This paper proposes a new non-sampling-based approach to estimate the time-varying post-hazard flow capacity of a bridge transportation network considering structural deterioration of bridges. The proposed approach evaluates the probabilities of structural damage scenarios efficiently using the matrix-based system reliability method and rapidly computes the corresponding flow capacities using a maximum flow capacity analysis algorithm. The matrix-based framework facilitates the integration of these results to obtain the probabilistic distributions and statistical moments of the network flow capacity. It also enables computing various measures useful for risk-informed decision making, such as the conditional mean and standard deviation of flow capacity given observed structural damage, and component importance measures. In the proposed approach, probability calculation and network flow analysis are performed separately, which renders time-varying post-hazard flow capacity analysis efficient. The proposed approach is demonstrated by a numerical example based on the Sioux Falls network under multiple bridge-deterioration scenarios simulating the progress of deterioration.

This paper addresses the problem of damage detection in suspension bridge hangers, with an emphasis on the modal flexibility method. It aims at evaluating the capability and the accuracy of the modal flexibility method to detect and locate single and multiple damages in suspension bridge hangers, with different level of severity and various locations. The study is conducted numerically and experimentally on a laboratory suspension bridge mock-up. First, the covariance-driven stochastic subspace identification is used to extract the modal parameters of the bridge from experimental data, using only output measurements data from ambient vibration. Then, the method is demonstrated for several damage scenarios and compared against other classical methods, such as: Coordinate Modal Assurance Criterion (COMAC), Enhanced Coordinate Modal Assurance Criterion (ECOMAC), Mode Shape Curvature (MSC) and Modal Strain Energy (MSE). The paper demonstrates the relative merits and shortcomings of these methods which play a significant role in the damage detection of suspension bridges.