A combined reliability analysis approach with dimension reduction method and maximum entropy method

Gang Li, Kai Zhang

Research output: Contribution to journalArticlepeer-review

99 Scopus citations

Abstract

This paper presents a combined reliability analysis approach which is composed of Dimension Reduction Method (DRM) and Maximum Entropy Method (MEM). DRM has emerged as a new approach in this field with the advantages of its sensitivity-free nature and efficiency instead of searching for the most probable point (MPP). However, in some recent implementations, the Moment Based Quadrature Rule (MBQR) in the DRM was found to be numerically instable when solving a system of linear equations for the integration points. In this study, a normalized Moment Based Quadrature Rule (NMBQR) is proposed to solve this problem, which can reduce the condition number of the coefficient matrix of the linear equations considerably and improve the robustness and stableness. Based on the statistical moments obtained by DRM+NMBQR, the MEM is applied to construct the probability density function (PDF) of the response. A number of numerical examples are calculated and compared to the Monte Carlo simulation (MCS), the First Order Reliability Method (FORM), the Extended Generalized Lambda Distribution (EGLD) and Saddlepoint Approximation (SA). The results show the accuracy and efficiency of the proposed method, especially for the multimodal PDF problem and multiple design point problem.

Original languageEnglish
Pages (from-to)121-134
Number of pages14
JournalStructural and Multidisciplinary Optimization
Volume43
Issue number1
DOIs
StatePublished - Jan 2011
Externally publishedYes

Keywords

  • Dimension Reduction Method (DRM)
  • Maximum Entropy Method (MEM)
  • Moment Based Quadrature Rule (MBQR)
  • Reliability analysis

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