Bayesian improved cross entropy method for network reliability assessment

TL;DR

This paper introduces the Bayesian improved cross entropy (BiCE) method, enhancing network reliability assessment by using Bayesian updating to improve importance sampling accuracy in multi-state systems.

Contribution

The paper proposes a novel Bayesian updating approach for the improved cross entropy method, addressing convergence issues in multi-state network reliability analysis.

Findings

BiCE improves estimation accuracy over standard iCE.

The method demonstrates higher efficiency in numerical examples.

BiCE effectively mitigates zero-probability convergence issues.

Abstract

We propose a modification of the improved cross entropy (iCE) method to enhance its performance for network reliability assessment. The iCE method performs a transition from the nominal density to the optimal importance sampling (IS) density via a parametric distribution model whose cross entropy with the optimal IS is minimized. The efficiency and accuracy of the iCE method are largely influenced by the choice of the parametric model. In the context of reliability of systems with independent multi-state components, the obvious choice of the parametric family is the categorical distribution. When updating this distribution model with standard iCE, the probability assigned to a certain category often converges to 0 due to lack of occurrence of samples from this category during the adaptive sampling process, resulting in a poor IS estima tor with a strong negative bias. To circumvent this issue, we propose an algorithm termed Bayesian improved cross entropy method (BiCE). Thereby, the posterior predictive distribution is employed to update the parametric model instead of the weighted maximum likelihood estimation approach employed in the original iCE method. A set of numerical examples illustrate the efficiency and accuracy of the proposed method.