A Novel Spatial Sampling Strategy Combining the Kriging Model and Maximin Design for Structural Reliability Analysis

The Kriging model has been widely explored in structural reliability analysis. Multiple sampling strategies combining the Kriging model are researched to alleviate the computational burden, especially in finite element analysis. In this paper, a novel sampling strategy is proposed to update the Design of Experiments (DoE) by combining Kriging and Maximin design. Maximin design is an experimental design to acquire a spatial distribution matrix. Benefiting from the characteristic of Maximin design, the spatial distance of the selected sample point is taken into account when updating the DoE. The selected sample points are evenly distributed in the sample space, which avoids excessive fitting of the Kriging model. Consequently, the proposed strategy requires relatively few points when constructing the Kriging model, to improve the efficiency of calculation while ensuring accuracy. An explicit example verifys the efficiency and accuracy of the sampling strategy, and a truss structure verifies the outperformance of the proposed method in calculating implicit performance functions.

I. Introduction

To make the structure complete the specified task in its service period safely and reliably, reliability analysis has been a key part of structure design. A variety of reliability analysis methods have been explored, intended for calculating the failure probability. The Monte Carol Simulation (MCS) [1], [2] is a direct method to reach the failure probability. However, it requires the entire population to be calculated to obtain the failure probability, which is computationally expensive. To reduce the computational expense, surrogate models were introduced to approximate the calculations, including the classic polynomial response surface [3], the support vector machine [4], [5], the neural networks [6] and Kriging [7], [8].