Work

iCE-NGM: Improved cross-entropy importance sampling with non-parametric adaptive Gaussian mixtures and budget-informed stopping criterion

Year: 2025

Type: article

Abstract: Estimating the failure probability is an essential task in engineering reliability analysis, which can be challenging for applications featuring small failure probabilities and complex numerical models. Cross entropy (CE) importance sampling is a promising strategy to enhance the estimation efficiency, by searching for the proper proposal density that resembles the theoretically optimal choice. This paper introduces iCE-NGM, an approach that enriches the recently proposed improved cross entropy (iCE) method by a non-parametric adaptive Gaussian mixture model and a budget-informed stopping criterion. An over-parameterized Gaussian mixture model will be identified with a kernel density estimation-inspired initialization and a constrained Expectation-Maximization fitting procedure. A novel budget-informed stopping criterion quantitatively balances between further refining proposal and reserving computational budget for final evaluation. A set of numerical examples demonstrate that the proposed approach performs consistently better than the classical distribution families and the existing stopping criteria.

Source: Reliability Engineering & System Safety

DOI: 10.1016/j.ress.2025.111322

Authors: Tianyu Zhang, Jize Zhang

Institution: Hong Kong University of Science and Technology

Language: English

Topic: Probabilistic and Robust Engineering Design

Subfield: Statistics, Probability and Uncertainty

Field: Decision Sciences

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $4,830

Funder: Research Grants Council, University Grants Committee