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An efficient method for statistical moments and reliability assessment of structures

Abstract

The probability density function (PDF) of a performance function can be constructed from the perspective of first four statistical moments, and the failure probability can be evaluated accordingly. Since the shifted generalized lognormal distribution (SGLD) model will be fitted to recover the PDF based on the first four statistical moments, the evaluation of statistical moments of the performance function is of critical significance for the structural reliability analysis. This paper presents a new method for statistical moments and reliability assessment of structures with efficiency and accuracy, especially when large variabilities in the input random vector and nonlinearities are considered . First, a numerical method is established based on rotating the points in the quasi-symmetric point method (Q-SPM), which is very efficient for evaluating the statistical moments. This numerical method is called the rotational quasi-symmetric point method (RQ-SPM). The optimal angles of rotation in RQ-SPM can be determined via an optimization problem, where the objective function is adopted as minimizing the differences between the marginal moments of input random variables estimated by the points after rotation and their exact values. By doing so, the information of marginal distributions and their tail distributions could be better reproduced, which is of paramount importance to the statistical moments assessment of the performance function, especially for the high-order moments. Once the statistical moments are available, the PDF of the performance function can be recovered by the SGLD model. Finally, the failure probability can be evaluated by a simple integral over the PDF of the performance function. Several numerical examples are given to demonstrate the efficacy of the proposed method. Comparisons of the new method, the original Q-SPM, the univariate dimension reduction method (UDRM) and the bivariate dimension reduction method (BDRM) are also made on the statistical moments assessment. The results manifest the accuracy and efficiency of the proposed method for both the statistical moments and reliability assessment of structures.

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Acknowledgments

The research reported in this paper is supported by the National Natural Science Foundation of China (Grant No.: 51608186), Natural Science Foundation of Hunan Province (No.2017JJ3016) and the Fundamental Research Funds for the Central Universities (No.531107040890). The support is gratefully appreciated. The reviewers are highly appreciated for their constructive comments to improve the original manuscript.

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Correspondence to Jun Xu.

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Xu, J., Kong, F. An efficient method for statistical moments and reliability assessment of structures. Struct Multidisc Optim 58, 2019–2035 (2018). https://doi.org/10.1007/s00158-018-2015-2

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  • DOI: https://doi.org/10.1007/s00158-018-2015-2

Keywords

  • Statistical moments
  • High-order moments
  • Rotational quasi-symmetric point method
  • Shifted generalized lognormal distribution
  • Marginal moments