First-passage probability estimation of high-dimensional nonlinear stochastic dynamic systems by a fractional moments-based mixture distribution approach

authored by: Chen Ding, Chao Dang, Marcos A. Valdebenito, Matthias G.R. Faes, Matteo Broggi, Michael Beer
Abstract: First-passage probability estimation of high-dimensional nonlinear stochastic dynamic systems is a significant task to be solved in many science and engineering fields, but remains still an open challenge. The present paper develops a novel approach, termed ‘fractional moments-based mixture distribution’, to address such challenge. This approach is implemented by capturing the extreme value distribution (EVD) of the system response with the concepts of fractional moment and mixture distribution. In our context, the fractional moment itself is by definition a high-dimensional integral with a complicated integrand. To efficiently compute the fractional moments, a parallel adaptive sampling scheme that allows for sample size extension is developed using the refined Latinized stratified sampling (RLSS). In this manner, both variance reduction and parallel computing are possible for evaluating the fractional moments. From the knowledge of low-order fractional moments, the EVD of interest is then expected to be reconstructed. Based on introducing an extended inverse Gaussian distribution and a log extended skew-normal distribution, one flexible mixture distribution model is proposed, where its fractional moments are derived in analytic form. By fitting a set of fractional moments, the EVD can be recovered via the proposed mixture model. Accordingly, the first-passage probabilities under different thresholds can be obtained from the recovered EVD straightforwardly. The performance of the proposed method is verified by three examples consisting of two test examples and one engineering problem.
Organisation(s): Institute for Risk and Reliability
External Organisation(s): Universidad Adolfo Ibanez
TU Dortmund University
Type: Article
Journal: Mechanical Systems and Signal Processing
Volume: 185
ISSN: 0888-3270
Publication date: 15.02.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Control and Systems Engineering, Signal Processing, Civil and Structural Engineering, Aerospace Engineering, Mechanical Engineering, Computer Science Applications
Electronic version(s): https://doi.org/10.15488/12761 (Access: Open)
https://doi.org/10.1016/j.ymssp.2022.109775 (Access: Closed)