An efficient approach for high-dimensional structural reliability analysis

Abstract

Abstract This paper presents a new method to address the challenge of high-dimensional reliability analysis based on a small number of samples. The method is established based on the maximum entropy method (MEM) with the low-order fractional moments as constraints. A coordinate transformation is first implemented since a positive random variable is required for fractional operations. Then, an estimator-corrector scheme is employed to obtain the probability density function (PDF) of the performance function. This scheme first promptly provides an estimated fractional orders and Lagrange multipliers by solving a linear system of equations as initial values, and then searches the more accurate solutions around the initial values to recover the PDF. Besides, the local optimum can be avoided by using the estimator-corrector scheme. The centered L2 (CL2) discrepancy oriented sequential Latin-hyper cube simulation is proposed to evaluate the low-order fractional moments involved in MEM, which is of critical importance to the efficiency and accuracy for high-dimensional reliability analysis. Typical numerical examples are investigated to validate the proposed method. The results show that the proposed method is of efficacy for high-dimensional reliability problems, even with very low failure probabilities.