Non-intrusive stochastic analysis with parameterized imprecise probability models: II. Reliability and rare events analysis

Pengfei Wei, Jingwen Song, Sifeng Bi, Matteo Broggi, Michael Beer, Zhenzhou Lu, Zhufeng Yue

Research output: Contribution to journalArticlepeer-review

40 Citations (Scopus)


Structural reliability analysis for rare failure events in the presence of hybrid uncertainties is a challenging task drawing increasing attentions in both academic and engineering fields. Based on the new imprecise stochastic simulation framework developed in the companion paper, this work aims at developing efficient methods to estimate the failure probability functions subjected to rare failure events with the hybrid uncertainties being characterized by imprecise probability models. The imprecise stochastic simulation methods are firstly improved by the active learning procedure so as to reduce the computational costs. For the more challenging rare failure events, two extended subset simulation based sampling methods are proposed to provide better performances in both local and global parameter spaces. The computational costs of both methods are the same with the classical subset simulation method. These two methods are also combined with the active learning procedure so as to further substantially reduce the computational costs. The estimation errors of all the methods are analyzed based on sensitivity indices and statistical properties of the developed estimators. All these new developments enrich the imprecise stochastic simulation framework. The feasibility and efficiency of the proposed methods are demonstrated with numerical and engineering test examples.

Original languageEnglish
Pages (from-to)227-247
Number of pages21
JournalMechanical Systems and Signal Processing
Early online date22 Feb 2019
Publication statusPublished - 1 Jul 2019


  • aleatory uncertainty
  • epistemic uncertainty
  • failure probability
  • high-dimensional model representation
  • imprecise probability
  • imprecise stochastic simulation
  • sensitivity analysis
  • subset simulation
  • uncertainty quantification


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