A point mapping strategy-based sparse grid integration method for statistical moments estimation and structural reliability analysis

Abstract

The high-order moment-based method is an attractive non-intrusive approach for structural reliability analysis, while it remains a challenge to strike a balance between accuracy, efficiency, and versatility in estimating statistical moments of performance functions. In this paper, a point mapping strategy-based sparse grid integration (SGI) method is proposed for statistical moment estimation and structural reliability analysis, with improved efficiency while ensuring the accuracy. Firstly, a point mapping strategy (PMS) is developed based on the adaptive high dimensional model representation (HDMR), by which the traditional SGI is reconstructed as a sum of multiple integrations over the sparse grid point sets with different effective dimensions. With this new form of SGI, the estimation of statistical moments only requires the evaluation of the performance function at a small number of necessary reference points, once the effects of some interaction terms are negligible. The validity and feasibility of the proposed PMS-based SGI method for statistical moments estimation are verified by several numerical examples. Then, the proposed method is applied to structural reliability analysis with the aid of an improved maximum entropy method. Two engineering examples are investigated, including the strength failure problem of tubular tower K-shape connection joints and the fatigue failure problem of a marine riser resulting from the vortex-induced vibration (VIV). The results indicate that the proposed method provides a better trade-off between accuracy and efficiency in evaluating the first four order statistical moments and structural failure probability compared to conventional methods.