Reliability analysis—a review and some perspectives

Rackwitz, R.

doi:10.1016/s0167-4730(02)00009-7

Cited by 659 publications

(287 citation statements)

References 53 publications

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“…(5) is equivalent to that of traditional reliability problems solved adopting reliability methods. Indeed, various strategies for the solution of this integral are available in the literature, such as numerical integration techniques, Monte Carlo simulations (Hammersley and Handscomb 1964) and asymptotic Laplace expansions (Rackwitz 2001). Common approximate solutions largely adopted in practice are First-Order and Second-Order Reliability Methods (Hasofer and Lind 1974), which ensure low computational costs but generally perform poorly in high dimensional spaces or in the case of strongly non-linear domains.…”

Section: Bayesian Network Enhanced With System Reliability Methodsmentioning

confidence: 99%

Robust vulnerability analysis of nuclear facilities subject to external hazards

Tolo

Patelli

Beer

2016

Stoch Environ Res Risk Assess

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Natural hazards have the potential to trigger complex chains of events in technological installations leading to disastrous effects for the surrounding population and environment. The threat of climate change of worsening extreme weather events exacerbates the need for new models and novel methodologies able to capture the complexity of the natural-technological interaction in intuitive frameworks suitable for an interdisciplinary field such as that of risk analysis. This study proposes a novel approach for the quantification of risk exposure of nuclear facilities subject to extreme natural events. A Bayesian Network model, initially developed for the quantification of the risk of exposure from spent nuclear material stored in facilities subject to flooding hazards, is adapted and enhanced to include in the analysis the quantification of the uncertainty affecting the output due to the imprecision of data available and the aleatory nature of the variables involved. The model is applied to the analysis of the nuclear power station of Sizewell B in East Anglia (UK), through the use of a novel computational tool. The network proposed models the direct effect of extreme weather conditions on the facility along several time scenarios considering climate change predictions as well as the indirect effects of external hazards on the internal subsystems and the occurrence of human error. The main novelty of the study consists of the fully computational integration of Bayesian Networks with advanced Structural Reliability Methods, which allows to adequately represent both aleatory and epistemic aspects of the uncertainty affecting the input through the use of probabilistic models, intervals, imprecise random variables as well as probability bounds. The uncertainty affecting the output is quantified in order to attest the significance of the results and provide a complete and effective tool for riskinformed decision making.

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Section: Bayesian Network Enhanced With System Reliability Methodsmentioning

confidence: 99%

Robust vulnerability analysis of nuclear facilities subject to external hazards

Tolo

Patelli

Beer

2016

Stoch Environ Res Risk Assess

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show abstract

“…6 are available such numerical integration techniques, Monte Carlo simulations [5] and asymptotic Laplace expansions [16]. Other common solutions (e.g.…”

Section: Structural Reliability Methodsmentioning

confidence: 99%

A Computational Tool for Bayesian Networks Enhanced With Reliability Methods

Tolo¹,

Patelli²,

Beer³

et al. 2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. A computational framework for the reduction and computation of Bayesian Networks enhanced with structural reliability methods is presented. During the last decades, the inner flexibility of the Bayesian Network method, its intuitive graphical structure and the strong mathematical background have attracted increasing interest in a large variety of applications involving joint probability of complex events and dependencies. Furthermore, the fast growing availability of computational power on the one side and the implementation of robust inference algorithms on the other, have additionally promoted the success of this method. Inference in Bayesian Networks is limited to only discrete variables (with the only exception of Gaussian distributions) in case of exact algorithms, whereas approximate approach allows to handle continuous distributions but can either result computationally inefficient or have unknown rates of convergence.This work provides a valid alternative to the traditional approach without renouncing to the reliability and robustness of exact inference computation. The methodology adopted is based on the combination of Bayesian Networks with structural reliability methods and allows to integrate random and interval variables within the Bayesian Network framework in the so called Enhanced Bayesian Networks. In the following, the computational algorithms developed are described and a simple structural application is proposed in order to fully show the capability of the tool developed.

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“…With the failure region F = {x|g(x) < a}, the probability of failure is p f = Pr{X ∈ F} = ∫ F p(ξ)dξ, where p(·) is the joint probability density function of X (Melchers 1999). This integral is generally difficult to calculate analytically and various approximate calculation methods have been developed, among which FORM (First Order Reliability Method) is very popular for its simplicity and efficiency (Hohenbichler et al 1987;Zhao and Ono 1999;Rackwitz 2001). In FORM, the random vector X is first transformed into an uncorrelated Gaussian random vector U in the standard normal space U by the transformation U = T(X).…”

Section: The Fundamentals Of Measure Theory For Aleatory Uncertaintymentioning

confidence: 99%

An extended probabilistic method for reliability analysis under mixed aleatory and epistemic uncertainties with flexible intervals

Chen

Yao

Zhao

et al. 2016

Struct Multidisc Optim

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The reliability analysis approach based on combined probability and evidence theory is studied in this paper to address the reliability analysis problem involving both aleatory uncertainties and epistemic uncertainties with flexible intervals (the interval bounds are either fixed or variable as functions of other independent variables). In the standard mathematical formulation of reliability analysis under mixed uncertainties with combined probability and evidence theory, the key is to calculate the failure probability of the upper and lower limits of the system response function as the epistemic uncertainties vary in each focal element. Based on measure theory, in this paper it is proved that the aforementioned upper and lower limits of the system response function are measurable under certain circumstances (the system response function is continuous and the flexible interval bounds satisfy certain conditions), which accordingly can be treated as random variables. Thus the reliability analysis of the system response under mixed uncertainties can be directly treated as probability calculation problems and solved by existing welldeveloped and efficient probabilistic methods. In this paper the popular probabilistic reliability analysis method FORM (First Order Reliability Method) is taken as an example to illustrate how to extend it to solve the reliability analysis problem in the mixed uncertainty situation. The efficacy of the proposed method is demonstrated with two numerical examples and one practical satellite conceptual design problem.

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Reliability analysis—a review and some perspectives

Cited by 659 publications

References 53 publications

Robust vulnerability analysis of nuclear facilities subject to external hazards

Robust vulnerability analysis of nuclear facilities subject to external hazards

A Computational Tool for Bayesian Networks Enhanced With Reliability Methods

An extended probabilistic method for reliability analysis under mixed aleatory and epistemic uncertainties with flexible intervals

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