Improved Moving Least Square-Based Multiple Dimension Decomposition (MDD) Technique for Structural Reliability Analysis

Abstract

This paper presents the state-of-the-art on different moving least square (MLS)-based dimension decomposition schemes for reliability analysis and demonstrates a modified version for high fidelity applications. The aim is to improve the performance of MLS-based dimension decomposition in terms of accuracy, number of function evaluations and computational time for large-dimensional problems. With this in view, multiple finite difference high dimension model representation (HDMR) scheme is developed. This anchored decomposition is implemented starting from an initial reference point and progressively evolving in successive iterations. Most probable point (MPP) of failure is identified in every iteration and is used as the reference point for the next decomposition until it converges. Hermite polynomials in MLS framework are used between the support points for efficient interpolation. The support points are generated sequentially using multiple sparse grids based on the Clenshaw–Curtis scheme. Once the global response surface is constructed using the support points generated in each iteration, importance sampling is employed for reliability analysis. Six different benchmark problems are solved to show its performance vis-à-vis other methods. Finally, reliability-based design of a composite plate is demonstrated, clearly showing the advantage and superiority of the proposed improvements in MLS-based multiple dimension decomposition (MDD).