Forensic assessment of a bridge downfall using Bayesian networks

Bayesian networks proved to be a useful tool in many technical fields as well as in forensic sciences. The present paper proposes a novel application of Bayesian networks in forensic engineering, focusing on the analysis of technical causes of a catastrophic bridge downfall. During repair a road bridge over important railway lines suddenly slipped down from temporary supports. Incidentally at the same time an intercity train approached the location and crashed into the collapsed bridge at a high speed. The accident resulted in great societal and economic consequences. Forensic investigation concerning causes of the bridge collapse was complicated due to the additional damage caused by the train. Moreover, the remaining structural elements of the collapsed bridge and temporary supports were shortly after the accident removed to renew railway traffic. Background materials of the investigation and additional detailed structural analyses did not reveal any convincing evidence of the initiation cause. Critical consideration of all possible causes including aerodynamic effects supplemented by a causal (Bayesian) network finally resulted in identification of the most significant causes including insufficient foundation and overall stiffness of temporary supports.     

考虑年均倒塌概率的结构倒塌安全储备可接受值

推导出结构年均倒塌概率与结构倒塌安全储备之间的关系,并提出依据年均倒塌概率可接受值计算可接受倒塌安全储备系数CMR的方法。利用全概率理论,将倒塌易损性与地震危险性进行耦合,得到结构年均倒塌概率,采用中值倒塌地震强度建立年均倒塌概率与结构倒塌安全储备系数CMR的关系。结合大震倒塌概率可接受值确定年均倒塌概率可接受值,进而计算结构可接受倒塌安全储备系数CMR。结合我国抗震规范规定的加速度反应谱建立CMR谱,给出了乙类、丙类结构在不同设防烈度下的可接受年均倒塌概率值以及可接受CMR值。研究表明:结构可接受年均倒塌风险越低,结构的倒塌安全储备可接受值越大,并呈现幂函数的数学关系,而可接受年均倒塌概率又与大震强度、地震危险性以及总倒塌不确定性有关。依据我国抗震设计规范背景建议的特定可接受年均倒塌概率下的可接受CMR谱,可以反映不同周期区间结构随总倒塌不确定性变化的规律,可用于结构倒塌安全储备的快速评估。基于CECS392建议的可接受大震倒塌概率计算得到乙类建筑的可接受年均倒塌概率远小于丙类建筑,均随着设防烈度的提高而下降,相应的CMR可接受值则呈现增加趋势。     

Controlled collapse of high-aspect-ratio nanostructures

Capillary-force-induced collapse of high-aspect-ratio (HAR) micro- and nanostructures is common in the evaporation-drying process and a number of applications based on the collapse have been proposed. However, the collapse of small HAR structures is usually uncontrollable, which has prevented it from being used in engineering applications. Here, the collapse of 10-nm-scale structures is separately controlled through engineering an asymmetric cross section, curvature, and tilt in the structures prior to collapse. It is shown that this deterministic-collapse approach can be used to create linear structures from collapsed pillars and planar rectangular structures from collapsed fencelike linear structures, and can further be used to create small gaps by controlling the collapse of nearby structures. These techniques could be used to improve the performance of beam-based lithography methods for certain types of patterns by increasing throughput and resolution, reducing the proximity effect, and reducing irradiation damage. In addition, this controlled-collapse concept provides a possible platform with which to study mechanical behavior at the 10-nm scale.     

Decision analysis for deteriorating structures

Measures that improve durability of a structure usually increase its initial cost. Thus, in order to make a decision about a cost-effective solution the life-cycle cost of a structure including cost of structural failure needs to be considered. Due to uncertainties associated with structural properties, loads and environmental conditions the cost of structural failure is a random variable. The paper derives probability distributions of the cost of failure of a single structure and a group of identical structures when single or multiple failures are possible during the service life of a structure. The probability distributions are based on cumulative probabilities of failure of a single structure over its service life. It is assumed that failures occur at discrete points in time, the cost of failure set at the time of decision making remains constant for a particular design solution and the discount rate is a deterministic parameter not changing with time. The probability distributions can be employed to evaluate the expected life-cycle cost or the expected utility, which is then used in decision making. An example, which considers the selection of durability specifications for a reinforced concrete structure built on the coast, illustrates the use of the derived probability distributions.     

Treatment of uncertainties in space nuclear risk assessment with examples from Cassini mission applications

By means of several examples from a recent comprehensive space nuclear risk analysis of the Cassini mission, a scenario and consequence representational framework is presented for risk analysis of space nuclear power systems in the context of epistemic and aleatory uncertainties. The framework invites the use of probabilistic models for the calculation of both event probabilities and scenario consequences. Each scenario is associated with a frequency that may include both aleatory and epistemic uncertainties. The outcome of each scenario is described in terms of an end state vector. The outcome of each scenario is also characterized by a source term. In this paper, the source term factors of interest are number of failed clads in the space nuclear power system, amount of fuel released and amount of fuel that is potentially respirable. These are also subject to uncertainties. The 1990 work of Apostolakis is found to be a useful formalism from which to derive the relevant probabilistic models. However, an extension to the formalism was necessary to accommodate the situation in which aleatory uncertainty is represented by changes in the form of the probability function itself, not just its parameters. Event trees that show reasonable alternative accident scenarios are presented. A grouping of probabilities and consequences is proposed as a useful structure for thinking about uncertainties. An example of each category is provided. Concluding observations are made about the judgments involved in this analysis of uncertainties and the effect of distinguishing between aleatory and epistemic uncertainties.     

Matrix-based system reliability method and applications to bridge networks

Using a matrix-based system reliability (MSR) method, one can estimate the probabilities of complex system events by simple matrix calculations. Unlike existing system reliability methods whose complexity depends highly on that of the system event, the MSR method describes any general system event in a simple matrix form and therefore provides a more convenient way of handling the system event and estimating its probability. Even in the case where one has incomplete information on the component probabilities and/or the statistical dependence thereof, the matrix-based framework enables us to estimate the narrowest bounds on the system failure probability by linear programming. This paper presents the MSR method and applies it to a transportation network consisting of bridge structures. The seismic failure probabilities of bridges are estimated by use of the predictive fragility curves developed by a Bayesian methodology based on experimental data and existing deterministic models of the seismic capacity and demand. Using the MSR method, the probability of disconnection between each city/county and a critical facility is estimated. The probability mass function of the number of failed bridges is computed as well. In order to quantify the relative importance of bridges, the MSR method is used to compute the conditional probabilities of bridge failures given that there is at least one city disconnected from the critical facility. The bounds on the probability of disconnection are also obtained for cases with incomplete information.     

Safety analysis in process facilities: Comparison of fault tree and Bayesian network approaches

Safety analysis in gas process facilities is necessary to prevent unwanted events that may cause catastrophic accidents. Accident scenario analysis with probability updating is the key to dynamic safety analysis. Although conventional failure assessment techniques such as fault tree (FT) have been used effectively for this purpose, they suffer severe limitations of static structure and uncertainty handling, which are of great significance in process safety analysis. Bayesian network (BN) is an alternative technique with ample potential for application in safety analysis. BNs have a strong similarity to FTs in many respects; however, the distinct advantages making them more suitable than FTs are their ability in explicitly representing the dependencies of events, updating probabilities, and coping with uncertainties. The objective of this paper is to demonstrate the application of BNs in safety analysis of process systems. The first part of the paper shows those modeling aspects that are common between FT and BN, giving preference to BN due to its ability to update probabilities. The second part is devoted to various modeling features of BN, helping to incorporate multi-state variables, dependent failures, functional uncertainty, and expert opinion which are frequently encountered in safety analysis, but cannot be considered by FT. The paper concludes that BN is a superior technique in safety analysis because of its flexible structure, allowing it to fit a wide variety of accident scenarios.     

Energy-based collapse assessment of concrete structures subjected to random damage evolutions

The assessment of structural capacity against collapse is conducive to the optimal design of new structures as well as checking the safety of existing structures. However, the evaluation cannot be typically carried out by means of destructive tests on prototype or reduced scale structures. In this regard, the numerical models that adequately represent the prototype structures can be alternatively used. Specifically, both the nonlinearities and randomness as well as their coupling effect of materials need to be represented in a unified manner in structural analysis. The present paper aims at providing an effective approach to incorporate the stochastic nature of damage constitutive relationships in collapse analysis and assessment of concrete structures subjected to earthquake ground motions. Within the framework of stochastic damage mechanics, the spatial variability of concrete is represented by a two-scale stationary random fields. The concept of covariance constraint is introduced to bridge the two-scale random fields such that the scale-of-fluctuation of the random material property is satisfied at both scales. Random damage evolution induced structural collapse analysis is achieved via the nonlinear stochastic finite element method. To address the randomness propagation across scales, the probability density evolution method is employed. By exerting the absorbing boundary condition associated with an energy-based collapse criterion on the generalized probability density evolution equation, the anti-collapse reliability of concrete structures can be evaluated with fair accuracy and efficiency. Numerical investigation regarding an actual high-rise reinforced concrete frame-shear wall structure indicates that the random damage evolution of concrete dramatically affects the structural nonlinear behaviors and even leads to entirely different collapse modes. The proposed method provides a systematic treatment of both uncertainties and nonlinearities in collapse assessment of complex concrete structures.     

Failure analysis of transmission towers

This paper advocates the use of nonlinear methodology for structural failure analysis. This approach is used for structural failure prediction rather than forensic analysis. Failure prediction has been confirmed by the expensive full-scale testing of a new transmission tower design that collapsed during the test. Using this approach, tower designs can be easily modified and upgraded, which results in substantial savings in time and resources.     

Dependent failure modeling in highly redundant structures—Application to BWR safety valves

Common cause failures and other dependences dominate the failure probability of a group of identical components, particularly when a large number of redundant components are concerned. The currently used models suffer from inconsistencies and practical difficulties at least when structures of more than four redundant components need to be analyzed.This paper will introduce the extension of the common load model (CLM) developed because of the practical need to realistically assess the failure probability of the pressure relief function in the TVO/PRA study. There are twelve safety/relief valves with the success criteria varying from 4/8 to 1–9/12 depending upon the transient case and event scenario. The model is defined through the subgroup failure probabilities, which means that simple but yet exact and consistent expressions for different success criteria are derived. The otherwise-needed truncations and approximations for higher order combinations are avoided. The underlying physical stress-strength model provides understandable interpretations for the model parameters. The paper describes the application on the electromagnetic pilot valves which are critical for the depressurization function, including analysis and utilization of operating experience.     

不完整结构系统同时考虑强度和刚度的可靠性分析

基于结构强度可靠性分析理论的基础之上,提出了不完整结构(结构系统中有部分元件已失效,但结构未变成机构仍具有一定的承载能力)强度、刚度可靠性的分析方法。该方法考虑了元件因强度失效对不完整结构系统强度、刚度可靠性的影响,同时导出了等效安全余量的形式,进而计算结构系统在失效各阶段的总体失效概率。并结合算例对结构系统在失效各阶段进行了强度、刚度的可靠性分析。算例表明,这样分析符合结构在使用各阶段可靠性的真实情况,从而为结构的合理利用起指导性作用。     

Wind speed estimation uncertainties: effects of climatological and micrometeorological parameters

To achieve structures that are risk-consistent, structural reliability methods must be used that account for uncertainties with respect to the relevant parameters affecting the estimation of wind effects. In this paper, we obtain measures of uncertainties in the estimation of the wind speeds upwind of structures. These uncertainties are due to incomplete knowledge with respect to the relevant extreme climatological and micrometeorological parameters. Advances in wind engineering and improvements in computational capabilities now make it possible to improve upon earlier estimates available in the literature. The work presented in this paper is a phase of a broader NIST project aimed at developing user-friendly software for the estimation of probabilities of failure of low-rise structures subjected to wind loads.     

基于离散单元法和物理引擎的结构连续倒塌可视化模拟

目前强离散性、大位移、大变形的倒塌全过程求解是结构计算分析的瓶颈,而离散单元法以理论力学为基础,基于刚体运动学和动力学方程,可有效实现结构全过程倒塌可视化模拟。运用Blender平台实现建筑结构的三维可视化建模及倒塌场景的可视化渲染;BCB(Bullet Constraints Builder)完成结构梁板柱构件的离散及刚体间约束的建立;物理引擎计算刚体间碰撞过程并"实时"更新刚体运动轨迹,三者协同作用实现倒塌全过程可视化模拟。模拟结果表明:所用方法适用于结构大变形模拟,可实现结构从弹性、弹塑性直至倒塌破坏的全过程可视化模拟,后续研究可为结构连续倒塌破坏机理的分析及人员逃生路径和搜救人员营救路线的选择提供科学指导。     

Uncertainties and quantification of common cause failure rates and probabilities for system analyses

Simultaneous failures of multiple components due to common causes at random times are modelled by constant multiple-failure rates. A procedure is described for quantification of common cause failure (CCF) basic event probabilities for system models using plant-specific and multiple-plant failure-event data. Methodology is presented for estimating CCF-rates from event data contaminated with assessment uncertainties. Generalised impact vectors determine the moments for the rates of individual systems or plants. These moments determine the effective numbers of events and observation times to be input to a Bayesian formalism to obtain plant-specific posterior CCF-rates. The rates are used to determine plant-specific common cause event probabilities for the basic events of explicit fault tree models depending on test intervals, test schedules and repair policies. Three methods are presented to determine these probabilities such that the correct time-average system unavailability can be obtained with single fault tree quantification. Recommended numerical values are given and examples illustrate different aspects of the methodology.     

Extensions of the uncertainty quantification of common cause failure rates

Uncertainties in common cause event observation, documentation and interpretation are taken into account by conditional probabilities and generalized impact vector weights that separate single and double events of a specific multiplicity in a single observation. Distributions and moments of common cause failure (CCF) rates of a system are obtained in terms of the weights by using probability generating functions, combining assessment uncertainties and statistical uncertainties. These results are then used to generate effective plant-specific input data to general empirical Bayes estimation methods to combine data from many plants. The posterior output yields CCF probabilities for standby safety system fault tree analysis or probabilistic safety assessments of a target plant.     

Engineering forensics at Youngstown State University

Buildings collapse, vehicles crash, cranes and bridges collapse. Why? Who is responsible? Forensic engineers must analyze failures to determine causes, origins, and legal responsibilities of accidents, fires, and explosions. This is the subject of a new course offered in spring 2005 at Youngstown State University (YSU) entitled Engineering Forensics Using the Scanning Electron Microscope. The course included a lab in which undergraduate students conducted failure analysis investigations involving the use of the scanning electron microscope and the energy-dispersive X-ray spectrometer. The creation of this course was a collaborative effort between the Forensic Science and the Materials Engineering Programs at YSU. This paper describes how this course was forged from a combination of the principles of forensic science with engineering failure analysis techniques.     

A study on damage assessment of the scoured bridges

Abstract

Throughout the past decade, scoured bridges in Taiwan have frequently collapsed as a result of heavy rainfall during typhoon seasons. To mitigate the bridge damage caused by scouring, an improved warning system is required. Three fundamental parameters including the water level, the flow velocity, and the scouring depth (SD) are significant for the structural safety of a scoured bridge. Nowadays, these parameters can be successfully detected by advanced monitoring instruments and serve as a database for a damage assessment system to carry out the function of early warning. Therefore, this article aims at developing the damage assessment system for scoured bridges as the core of a warning system.

We have proposed an analytical process as an assessment system. Through finite element analysis with respect to water level and flow velocity, the critical scouring depth with a specific degree of safety factor for a bridge foundation can be determined by choosing among different failure modes. Accordingly, the relationships between various possible sets of water levels, flow velocities and critical SD are established to present the surfaces of structural safety corresponding to different levels of safety factor. The surfaces obtained can then be applied to the warning system.

Based on the proposed assessment process, the collapse of the Shuang-Yuan Bridge caused by Typhoon Morakot in 2009 is discussed in detail. The consequence of bridge collapse is reasonably explained by the analytical surfaces of structural safety based on the reported parameters at the bridge site. In addition, the Dia-Jia-Hsi Bridge, which has implemented advanced monitoring instruments serves as the second case study. The surfaces of structural safety obtained have been used in conjunction with real-time observations of sensitive parameters to display the situation of structural safety at any time. The results obtained in this article benefit bridge engineers, giving a safety-management platform to speed up the decision making process during an emergency.     

桥梁结构地震易损性研究进展述评

随着基于性能的地震工程全概率决策框架的提出,要求从概率的角度对桥梁结构的抗震性能进行评估,结合结构地震响应分析和结构损伤分析的地震易损性分析受到广泛关注。为了促进国内桥梁结构地震易损性研究的发展,首先回顾了易损性研究的历史阶段与发展过程,评述了国内外桥梁结构地震易损性的研究现状;在此基础上介绍了地震易损性分析的基本原理和研究方法:分别从经验型、理论型以及经验-理论相结合的角度详细介绍了常用的易损性分析方法和一般过程,指出了当前研究中遇到的问题以及存在的局限性;最后,对桥梁结构地震易损性的应用前景和发展方向进行了展望。总结既有研究成果表明,环境因素、地震动、场地条件以及桥梁自身参数等的不确定性问题,地震动强度参数和结构能力指标的合理选择问题,各主要构件之间的相关性及其对桥梁结构整体抗震性能的贡献问题等都是桥梁结构地震易损性研究领域的重要内容。此外,对于更为复杂的情况,包括液化或特殊场地以及特殊大跨度桥梁等的研究,都将对桥梁抗震工程领域的发展具有重要意义。     

A polynomial dimensional decomposition framework based on topology derivatives for stochastic topology sensitivity analysis of high-dimensional complex systems and a type of benchmark problems

In this paper, a new computational framework based on the topology derivative concept is presented for evaluating stochastic topological sensitivities of complex systems. The proposed framework, designed for dealing with high dimensional random inputs, dovetails a polynomial dimensional decomposition (PDD) of multivariate stochastic response functions and deterministic topology derivatives. On one hand, it provides analytical expressions to calculate topology sensitivities of the first three stochastic moments which are often required in robust topology optimization (RTO). On another hand, it offers embedded Monte Carlo Simulation (MCS) and finite difference formulations to estimate topology sensitivities of failure probability for reliability-based topology optimization (RBTO). For both cases, the quantification of uncertainties and their topology sensitivities are determined concurrently from a single stochastic analysis. Moreover, an original example of two random variables is developed for the first time to obtain analytical solutions for topology sensitivity of moments and failure probability. Another 53-dimension example is constructed for analytical solutions of topology sensitivity of moments and semi-analytical solutions of topology sensitivity of failure probabilities in order to verify the accuracy and efficiency of the proposed method for high-dimensional scenarios. Those examples are new and make it possible for researchers to benchmark stochastic topology sensitivities of existing or new algorithms. In addition, it is unveiled that under certain conditions the proposed method achieves better accuracies for stochastic topology sensitivities than for the stochastic quantities themselves.     

Common cause failure probabilities in standby safety system fault tree analysis with testing—scheme and timing dependencies

Modelling and quantification of common cause failures (CCFs) in redundant standby safety systems can be implemented by implicit or explicit fault tree techniques. Common cause event probabilities are derived for both methods for systems with time-related CCFs modelled by general multiple failure rates. The probabilities are determined so that the correct time-average risk can be obtained by a single computation. The impacts of test intervals and test staggering are included. Staggered testing is best with a certain extra-testing rule, although extra testing is not important for 1-out-of-n:G systems. An economic model provides insights into the impacts of various parameters: the optimal test interval increases with increasing redundancy and testing cost, and it decreases with increasing accident cost and initiating event rate. Staggered testing with extra tests allows for the longest optimal test intervals. A practical technique is outlined for incorporating assessment uncertainties in the estimation of multiple failure rates based on data from many plants or systems.