Distribution reconstruction and reliability assessment of complex LSFs via an adaptive Non-parametric Density Estimation Method

Quanfu Yu and Jun Xu

Reliability Engineering and System Safety, 2025, vol. 254, issue PB

Abstract: Complex limit state functions (LSFs), often characterized by strong nonlinearity, non-smoothness, or discontinuity, pose challenges for structural reliability analysis in engineering practices. Conventional methods for uncertainty propagation and reliability assessment may struggle to handle these issues effectively. This paper introduces a novel approach to adaptively reconstruct the unknown distributions of complex LSFs. The Non-parametric Density Estimation Method based on Harmonic Transform (NDEM-HT) is employed as the tool for this purpose. An adaptive strategy is then proposed to determine the number of harmonic moments required in NDEM-HT for achieving high accuracy. Specifically, the Adaptive Kernel Density Estimation (AKDE) method is also adopted to provide an initial estimation of the rough distribution. Subsequently, the optimal number of harmonic moments is determined by minimizing the relative entropy between the distributions obtained by AKDE and NDEM-HT. The efficacy of the proposed method is demonstrated through five numerical examples, considering various types of complex LSFs. Comparative results are also provided employing MCS along with both conventional and state-of-the-art methods.

Keywords: Harmonic transform; Adaptive kernel density estimation; Non-parametric Density Estimation Method; Complex LSFs; Relative entropy (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:254:y:2025:i:pb:s095183202400680x

DOI: 10.1016/j.ress.2024.110609

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