Evaluating small failure probabilities of multiple limit states by parallel subset simulation

• Published in: Probabilistic engineering mechanics Vol. 25; no. 3; pp. 291 - 304
• Main Authors: Hsu, Wei-Chih, Ching, Jianye
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.07.2010; Elsevier
• Subjects: Algorithms; Computer simulation; Estimating; Estimators; Exact sciences and technology; Failure; Fundamental areas of phenomenology (including applications); High dimensions; Limit states; Monte Carlo methods; Monte Carlo simulation; Physics; Reliability analysis; Samples; Solid mechanics; Stochastic simulation; Structural and continuum mechanics; Subset simulation; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Subset simulation; Reliability analysis; Stochastic simulation; High dimensions; Monte Carlo simulation; Monte Carlo method; Parallel algorithm; Statistical analysis; Probabilistic approach; Rupture; Reliability; Modeling
• ISSN: 0266-8920; 1878-4275
• DOI: 10.1016/j.probengmech.2010.01.003

A novel subset simulation algorithm, called the parallel subset simulation, is proposed to estimate small failure probabilities of multiple limit states with only a single subset simulation analysis. As well known, crude Monte Carlo simulation is inefficient in estimating small probabilities but is applicable to multiple limit states, while the ordinary subset simulation is efficient in estimating small probabilities but can only handle a single limit state. The proposed novel stochastic simulation approach combines the advantages of the two simulation methods: it is not only efficient in estimating small probabilities but also applicable to multiple limit states. The key idea is to introduce a “principal variable” which is correlated with all performance functions. The failure probabilities of all limit states therefore could be evaluated simultaneously when subset simulation algorithm generates the principal variable samples. The statistical properties of the failure probability estimators are also derived. Two examples are presented to demonstrate the effectiveness of the new approach and to compare with crude Monte Carlo and ordinary subset simulation methods.