Efficient reliability analysis using prediction-oriented active sparse polynomial chaos expansion. (December 2022)

• Record Type: Journal Article
• Authors: Zhang, Jian; Gong, Weijie; Yue, Xinxin; Shi, Maolin; Chen, Lei
• Is Part Of: Reliability engineering & system safety. Volume 228(2022)
• Publication Date: 2022-12
• Subjects: Reliability analysis -- Polynomial chaos expansion -- Active learning -- Surrogate model -- Adaptive sampling -- Greedy coordinate descent; PCE polynomial chaos expansion -- GCD greedy coordinate descent; Reliability (Engineering) -- Periodicals; System safety -- Periodicals; Industrial safety -- Periodicals; Fiabilité -- Périodiques; Sécurité des systèmes -- Périodiques; Sécurité du travail -- Périodiques; 620.00452
• DOI: 10.1016/j.ress.2022.108749
• Languages: English
• ISSNs: 0951-8320

Abstract

Highlights: An adaptive sparse polynomial chaos expansion is proposed for reliability analysis. Greedy coordinate descent is fused with a local variance based optimality criterion. An active learning strategy adaptively shifts training focus to important regions. Examples of varying complexity and input dimensionality are used for comparison. This method provides accurate estimates of event probabilities with high efficiency. Abstract: In this paper, a prediction-oriented active sparse polynomial chaos expansion (PAS-PCE) is proposed for reliability analysis. Instead of leveraging on additional techniques to reduce the problem dimensionality and/or to obtain the local error estimates, which has been done in the majority of existing PCE-based methods, this study first makes use of the Bregman-iterative greedy coordinate descent in effectively solving the least absolute shrinkage and selection operator based regression for sparse PCE approximation with a small set of initial samples. Then, the local variance distribution of the performance function is predicted using the approximated PCE. By maximizing an optimality measure that balances the exploration of design space and exploitation of the PCE characteristics, a recently proposed learning function is subsequently adopted for selecting the optimal samples one by one from a candidate pool to cover the limit state surface regions proportionally to the predicted local variance. The performance of the proposed PAS-PCE is assessed on four numerical examples of varying complexity and input dimensionality through comparison with several state-of-the-art active learning methods based on a variety of surrogate models. Results show that the proposed method is superior to the benchmark algorithms in terms of both accuracy and efficiency for reliability analysis.