An improved adaptive bivariate dimension-reduction method for efficient statistical moment and reliability evaluations

Statistical moment estimations of the performance function with the aim of balancing accuracy and efficiency still remains a challenge for moment-based structural reliability analysis. In this paper, an improved adaptive bivariate dimension-reduction method in terms of vectors (i-VBDRM) is proposed for efficient statistical moments and reliability evaluations. In the proposed method, the delineation of cross terms of two-dimensional functions involved in the bivariate dimension-reduction method (BDRM) is first imple-mented, where the random variables are classified into several sub-vectors after the non-normal to normal transformation. Then, the explicit expressions of the moments of multiple component sub-vector functions are formulated, where a novel cubature formula is proposed and the Gauss-Hermite quadrature is employed to evaluate the involved two and one-dimensional Gaussian-weighted integrals. In that regard, the first-four central moments can be calculated with accuracy and efficiency. Then, the probability density function of the performance function is rebuilt by a flexible distribution model called the shifted generalized lognormal distribution based on the first-four central moments evaluated by the proposed method. To demonstrate the efficacy of the proposed method, four numerical examples are presented, where some other forms of BDRM, univariate dimension-reduction method and the crude Monte Carlo simulation are performed for comparisons. The results show that the proposed method can keep the trade-off of precision and efficiency for both the statistical moment assessments and structural reliability analysis. (c) 2020 Elsevier Ltd. All rights reserved.

Automated summary

Balancing accuracy and efficiency in moment estimations of the performance function for structural reliability analysis remains a challenge. An improved adaptive bivariate dimension-reduction method has been proposed for efficient statistical moments and reliability evaluations, utilizing novel cubature formula and Gauss-Hermite quadrature for accurate calculations. The method demonstrates a trade-off between precision and efficiency in both statistical moment assessments and structural reliability analysis.