Estimation of the lower and upper bounds on the probability of failure using subset simulation and random set theory

被引:69
作者
Alvarez, Diego A. [1 ]
Uribe, Felipe [2 ]
Hurtado, Jorge E. [1 ]
机构
[1] Univ Nacl Colombia, Dept Ingn Civil, Sede Manizales, Carrera 27 64-60, Manizales 170004, Colombia
[2] Tech Univ Munich, Engn Risk Anal Grp, Arcisstr 21, D-80333 Munich, Germany
关键词
Lower and upper probabilities of failure; Imprecise probabilities; Random set theory; Copulas; Interval Monte Carlo; Subset simulation; Isoprobabilistic transformation; RELIABILITY-ANALYSIS; STRUCTURAL SYSTEMS; UNCERTAINTY; ALGORITHMS;
D O I
10.1016/j.ymssp.2017.07.040
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
Random set theory is a general framework which comprises uncertainty in the form of probability boxes, possibility distributions, cumulative distribution functions, Dempster-Shafer structures or intervals; in addition, the dependence between the input variables can be expressed using copulas. In this paper, the lower and upper bounds on the probability of failure are calculated by means of random set theory. In order to accelerate the calculation, a well-known and efficient probability-based reliability method known as subset simulation is employed. This method is especially useful for finding small failure probabilities in both low- and high-dimensional spaces, disjoint failure domains and nonlinear limit state functions. The proposed methodology represents a drastic reduction of the computational labor implied by plain Monte Carlo simulation for problems defined with a mixture of representations for the input variables, while delivering similar results. Numerical examples illustrate the efficiency of the proposed approach. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码:782 / 801
页数:20
相关论文
共 54 条
[1]  
Alvarez Diego A., 2014, Vulnerability, Uncertainty, and Risk. Quantification, Mitigation, and Management. Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA). Proceedings, P905
[2]  
Alvarez DA, 2007, THESIS
[3]   On the calculation of the bounds of probability of events using infinite random sets [J].
Alvarez, Diego A. .
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 2006, 43 (03) :241-267
[4]   Tighter bounds on the probability of failure than those provided by random set theory [J].
Alvarez, Diego A. ;
Hurtado, Jorge E. ;
Ramirez, Juliana .
COMPUTERS & STRUCTURES, 2017, 189 :101-113
[5]   An efficient method for the estimation of structural reliability intervals with random sets, dependence modeling and uncertain inputs [J].
Alvarez, Diego A. ;
Hurtado, Jorge E. .
COMPUTERS & STRUCTURES, 2014, 142 :54-63
[6]   Reduction of uncertainty using sensitivity analysis methods for infinite random sets of indexable type [J].
Alvarez, Diego A. .
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 2009, 50 (05) :750-762
[7]   A Monte Carlo-based method for the estimation of lower and upper probabilities of events using infinite random sets of indexable type [J].
Alvarez, Diego A. .
FUZZY SETS AND SYSTEMS, 2009, 160 (03) :384-401
[8]  
[Anonymous], 2004, Tech. Rep. SAND2004-3072
[9]  
[Anonymous], 1999, CISM COUR L
[10]  
[Anonymous], 2006, INTRO RANDOM SETS