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

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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.

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Acknowledgements

The supports of the National Natural Science Foundation of China (No.90815023 and No.10721062), the National Basic Research Program of China (973 Program, 2006CB705403) are much appreciated.

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis of Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116023, China

    Gang Li & Kai Zhang

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  1. Gang Li
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  2. Kai Zhang
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Correspondence to Gang Li.

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Li, G., Zhang, K. A combined reliability analysis approach with dimension reduction method and maximum entropy method. Struct Multidisc Optim 43, 121–134 (2011). https://doi.org/10.1007/s00158-010-0546-2

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