An adaptive high‐dimensional model representation method for reliability analysis of geotechnical engineering problems

Abstract

SummaryIn this study, a new reliability analysis method was developed based on the adaptive high‐dimensional model representation (HDMR) and applied to geotechnical engineering problems. For practical problems requiring finite element (FE) analysis or other numerical methods to evaluate system responses such as stresses and deformations, an efficient and accurate metamodeling technique is needed because it is not efficient or straightforward to directly adopt the conventional sampling‐based or gradient‐based reliability analysis approaches. In this work, an adaptive metamodeling approach was created and studied based on the HDMR framework and augmented radial basis functions (ARBFs). In this adaptive ARBF‐HDMR technique, a simple and inexpensive first‐order ARBF‐HDMR metamodel was first constructed to explicitly express a performance function, and an alternate first‐order reliability method (FORM) was applied to locate the design point and compute the reliability index. A local window was then defined such that additional sample points were generated and a higher‐order HDMR component function was created using ARBF and added to the existing ARBF‐HDMR metamodel. The accuracy of the ARBF‐HDMR metamodel was improved through this adaptive process, especially in the region surrounding the design point. One mathematical and four geotechnical engineering problems were studied and solved using the proposed adaptive ARBF‐HDMR approach. The proposed method was found to be capable of obtaining accurate reliability indices within a few iterations in all test problems.