CSP-free adaptive Kriging surrogate model method for reliability analysis with small failure probability

TL;DR

This paper introduces a CSP-free adaptive Kriging surrogate model method that enhances reliability analysis for systems with small failure probabilities by eliminating the need for candidate sample pools and optimizing sample selection.

Contribution

The proposed method innovatively removes the reliance on candidate sample pools in AK-MCS, using optimization to select representative samples for improved accuracy and efficiency.

Findings

Outperforms traditional AK-MCS in small failure probability scenarios.

Effectively balances accuracy and computational cost through optimization.

Demonstrates superior performance in numerical examples.

Abstract

In the field of reliability engineering, the Active learning reliability method combining Kriging and Monte Carlo Simulation (AK-MCS) has been developed and demonstrated to be effective in reliability analysis. However, the performance of AK-MCS is sensitive to the size of Candidate Sample Pool (CSP), particularly for systems with small failure probabilities. To address the limitations of conventional AK-MCS that relies on CSP, this paper proposes a CSP-free AK-MCS. The proposed methodology consists of two stages: surrogate model construction and Monte Carlo simulation for estimating the failure probability. In the stage of surrogate model construction, the surrogate model is iteratively refined based on the representative samples selected by solving the optimization problem facilitated by Particle Swarm Optimization (PSO) algorithm. To achieve an optimal balance between solution accuracy and efficiency, the penalty intensity control and the density control for the experimental design points are introduced to modify the objective function in optimization. The performance of the proposed methodology is evaluated using numerical examples, and results indicate that by leveraging an optimization algorithm to select representative samples, the proposed CSP-free AK-MCS overcomes the limitations of conventional CSP-based AK-MCS and exhibits exceptional performance in addressing small failure probabilities.