Cross-Entropy Based Importance Sampling for Stochastic Simulation Models

TL;DR

This paper introduces an automatic, cross-entropy based importance sampling method for stochastic simulation models that avoids complex metamodel building, improving efficiency in reliability evaluation tasks.

Contribution

It proposes a novel, automatic importance sampling approach using cross-entropy and EM algorithm, eliminating the need for domain-specific metamodels.

Findings

Method effectively approximates optimal importance sampling density.

Demonstrates improved efficiency in reliability estimation.

Validated through extensive numerical studies and a wind turbine case study.

Abstract

To efficiently evaluate system reliability based on Monte Carlo simulation, importance sampling is used widely. The optimal importance sampling density was derived in 1950s for the deterministic simulation model, which maps an input to an output deterministically, and is approximated in practice using various methods. For the stochastic simulation model whose output is random given an input, the optimal importance sampling density was derived only recently. In the existing literature, metamodel-based approaches have been used to approximate this optimal density. However, building a satisfactory metamodel is often difficult or time-consuming in practice. This paper proposes a cross-entropy based method, which is automatic and does not require specific domain knowledge. The proposed method uses an expectation-maximization algorithm to guide the choice of a mixture distribution model for approximating the optimal density. The method iteratively updates the approximated density to minimize its estimated discrepancy, measured by estimated cross-entropy, from the optimal density. The mixture model's complexity is controlled using the cross-entropy information criterion. The method is empirically validated using extensive numerical studies and applied to a case study of evaluating the reliability of wind turbine using a stochastic simulation model.