A sample-based stochastic finite element method for structural reliability analysis

TL;DR

This paper introduces a novel sample-based stochastic finite element method that efficiently computes structural reliability and failure probabilities across all spatial points simultaneously, effectively addressing high-dimensional challenges.

Contribution

The paper develops a new sample-based SFEM that decouples stochastic responses, enabling efficient high-dimensional reliability analysis without the curse of dimensionality.

Findings

Accurately computes failure probabilities for all spatial points.

Reduces computational costs compared to Monte Carlo simulation.

Effective for large-scale, high-dimensional problems.

Abstract

This paper presents a new methodology for structural reliability analysis via stochastic finite element method (SFEM). A novel sample-based SFEM is firstly used to compute structural stochastic responses of all spatial points at the same time, which decouples the stochastic response into a combination of a series of deterministic responses with random variable coefficients, and solves corresponding stochastic finite element equation through an iterative algorithm. Based on the stochastic response obtained by the SFEM, the limit state function described by the stochastic response and the multidimensional integral encountered in reliability analysis can be computed without any difficulties, and failure probabilities of all spatial points are calculated once time. The proposed method can be applied to high-dimensional stochastic problems, and one of the most challenging issues encountered in high-dimensional reliability analysis, known as Curse of Dimensionality, can be circumvented without expensive computational costs. Three practical examples, including large-scale and high-dimensional reliability analysis, are given to demonstrate the accuracy and efficiency of the proposed method in comparison to the Monte Carlo simulation.