Generalization of non-intrusive imprecise stochastic simulation for mixed uncertain variables

Jingwen Song, Pengfei Wei, Marcos Valdebenito, Sifeng Bi, Matteo Broggi, Michael Beer, Zuxiang Lei

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

Non-intrusive Imprecise Stochastic Simulation (NISS) is a recently developed general methodological framework for efficiently propagating the imprecise probability models and for estimating the resultant failure probability functions and bounds. Due to the simplicity, high efficiency, stability and good convergence, it has been proved to be one of the most appealing forward uncertainty quantification methods. However, the current version of NISS is only applicable for model with input variables characterized by precise and imprecise probability models. In real-world applications, the uncertainties of model inputs may also be characterized by non-probabilistic models such as interval model due to the extreme scarcity or imprecise information. In this paper, the NISS method is generalized for models with three kinds of mixed inputs characterized by precise probability model, non-probabilistic models and imprecise probability models respectively, and specifically, the interval model and distributional p-box model are exemplified. This generalization is realized by combining Bayes rule and the global NISS method, and is shown to conserve all the advantages of the classical NISS method. With this generalization, the three kinds of inputs can be propagated with only one set of function evaluations in a pure simulation manner, and two kinds of potential estimation errors are properly addressed by sensitivity indices and bootstrap. A numerical test example and the NASA uncertainty quantification challenging problem are solved to demonstrate the effectiveness of the generalized NISS procedure.

Original languageEnglish
Article number106316
JournalMechanical Systems and Signal Processing
Volume134
DOIs
StatePublished - 1 Dec 2019

Keywords

  • Bayes rule
  • Bootstrap
  • Imprecise probability
  • Interval model
  • Non-intrusive imprecise stochastic simulation
  • Non-probabilistic
  • Sensitivity
  • Uncertainty quantification

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