An adaptive hybrid dimension-reduction model and its application for statistical moments estimation of stochastic systems and reliability analysis of structures

Abstract

From the perspective of accuracy, efficiency and versatility, calculating statistical moments for different forms of performance functions in a unified way remains a challenge, and their accuracy also considerably affects the results of subsequent reliability analysis. In this article, a new dimension-reduction model, termed as adaptive hybrid dimension-reduction model (AH-DRM), is derived to approximate the performance functions with different characteristics relatively accurately. Based on the AH-DRM, a highly flexible point estimation method (PEM), which has good versatility for the various forms of performance function, is developed for statistical moments estimation of stochastic systems. Subsequently, to illustrate the performance of the proposed method for different performance function forms, three examples, including weakly, moderately and strongly nonlinear benchmark examples, are investigated. The results indicate that the proposed method is versatile for each example and can receive desirable accuracy for evaluating the first-four central moments of the performance functions with high efficiency. Finally, the developed PEM is applied to reconstruct the probability density function of the performance function and calculate the reliability of structures with the aid of the saddle-point approximation (SPA) method, and two practical engineering examples are used to verify the applicability of the proposed method in structural reliability analysis.