Rare event modelling for stochastic dynamic systems approximated by the probability density evolution method

authored by: Marius Bittner, Matteo Broggi, Michael Beer
Abstract: The Probability Density Evolution Method (PDEM) is a relatively novel tool to approximate the time-dependent joint Probability Distribution Function of multidimensional stochastic systems. The PDEM enables the possibility to give a statement about the time-dependent behaviour of a target physical quantity acquired from a deterministically solvable system. This has been utilized to assess the performance of systems in the face of reliability statements, specifically first passage problems. For now, the PDEM requires a solving strategy that includes the selection of points of interest that cover a large area in the random space, based on direct Monte Carlo simulation and Sobol set establishment. This approach often neglects the existence of rare events which could trigger critical behaviours of the system. This neglection can lead to a system assessment that is too much generalized. A new approach is presented that utilizes the features of the advanced Monte Carlo method Subset sampling (SuS) with regard to a first passage failure criteria. This enables the identification of random parameter configurations that result in rare event behaviour which lead to a failure. This combination and the novel formulation of the selected points that cover a rare event space could lead to further understandings of rare event behaviour of specific systems and additionally increase the PDEM efficiency and accuracy when dealing with a higher order of random dimensions.
Organisation(s): Institute for Risk and Reliability
Type: Conference contribution
Pages: 2719-2726
No. of pages: 8
Publication date: 2019
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Safety, Risk, Reliability and Quality, Safety Research
Electronic version(s): https://doi.org/10.3850/978-981-11-2724-3_0735-cd (Access: Open)