Failure probability estimation through high-dimensional elliptical distribution modeling with multiple importance sampling

• Published in: Reliability engineering & system safety Vol. 235; p. 109238
• Main Authors: Chiron, Marie, Genest, Christian, Morio, Jérôme, Dubreuil, Sylvain
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2023; Elsevier
• Subjects: Computer Science; Data Structures and Algorithms; Elliptical distribution; Engineering Sciences; High dimension; Mathematics; Multiple importance sampling; Other; Probability; Reliability analysis; Simulation method; Multiple importance sampling; Reliability analysis; High dimension; Simulation method; Elliptical distribution; stochastic system; loi de probabilité; échantillonnage d'importance; méthode numérique; numerical method; probability distribution; importance sampling; système stochastique
• ISSN: 0951-8320; 1879-0836; 1879-0836
• DOI: 10.1016/j.ress.2023.109238

This paper addresses the challenge of performing importance sampling in high-dimensional space (several hundred inputs) in order to estimate the failure probability of a physical system subject to randomness. It is assumed that the failure domain defined in the input space can possibly include multiple failure regions. A new approach is developed to construct auxiliary importance sampling densities sequentially for each failure region identified as part of the failure domain. The search for failure regions is achieved through optimization. A stochastic decomposition of the elliptically distributed inputs is exploited in the structure of the auxiliary densities, which are expressed as the product of a parametric conditional distribution for the radial component, and a parametric von Mises–Fisher distribution for the directional vector. The failure probability is then estimated by multiple importance sampling with a mixture of the densities. To demonstrate the efficiency of the proposed method in high-dimensional space, several numerical examples are considered involving the multivariate Gaussian and Student distributions, which are commonly used elliptical distributions for input modeling. In comparison with other simulation methods, the numerical cost of the proposed approach is found to be quite low when the gradient of the performance function defining the failure domain is available. •Importance sampling in high-dimensional space for elliptical distributions.•Auxiliary distribution based on a stochastic decomposition of the inputs.•Failure probability estimated by multiple importance sampling.•Adaptive search for the multiple failure regions of the failure domain.