Adaptive importance sampling based on fault tree analysis for piecewise deterministic Markov process

TL;DR

This paper introduces an adaptive importance sampling method for simulating piecewise deterministic Markov processes, leveraging fault tree analysis concepts to improve efficiency in complex industrial system reliability assessments.

Contribution

It proposes novel families of approximations for the committor function based on fault tree analysis, tailored for high-dimensional industrial systems.

Findings

Significant variance reduction in simulations.

Effective application to nuclear industry systems.

Improved efficiency over standard Monte Carlo methods.

Abstract

Piecewise deterministic Markov processes (PDMPs) can be used to model complex dynamical industrial systems. The counterpart of this modeling capability is their simulation cost, which makes reliability assessment untractable with standard Monte Carlo methods. A significant variance reduction can be obtained with an adaptive importance sampling (AIS) method based on a cross-entropy (CE) procedure. The success of this method relies on the selection of a good family of approximations of the committor function of the PDMP. In this paper original families are proposed. They are well adapted to high-dimensional industrial systems. Their forms are based on reliability concepts related to fault tree analysis: minimal path sets and minimal cut sets. The proposed method is discussed in detail and applied to academic systems and to a realistic system from the nuclear industry.