Sequential sampling and reliability analysis method with improved accuracy and efficiency for reliability-based design optimization

Abstract

As reliability of engineering systems under uncertainty becomes more important in various industries due to global competitive market situation, a safer and more reliable product design to satisfy consumers’ needs is required. To satisfy these requirements, there have been various attempts to accurately and efficiently compute the product reliability, which is obtained from reliability analysis and used as a probabilistic constraint of reliability-based design optimization (RBDO). Among various reliability analysis methods, analytical reliability analysis methods such as the first-order reliability method (FORM), the second-order reliability method (SORM), and the most probable point (MPP)-based dimension reduction method (DRM) are performed. All of these methods approximate a performance function to calculate reliability or probability of failure (PF), and have advantages and disadvantages in terms of computational amount and accuracy. On the other hand, since the sampling-based RBDO requires a significant amount of computation, it is common to use a surrogate model that mimics the real model with several test/analysis responses. In the past decades, both analytical and sampling-based methods have attempted to improve its accuracy and efficiency. In this thesis, accuracy and efficiency improved methods in the SORM, DRM, and the sampling-based RBDO are discussed. First, in order to improve the efficiency of the novel SORM which is the improved accuracy in the general SORM, a convolution integration approach is applied to the novel SORM is proposed. Second, to efficiently improve the accuracy of the existing univariate DRM, a selectively extending to the bivariate dimension method through a statistical model selection method is proposed. Finally, a new framework incorporating space mapping for the sequential sampling of surrogate models in sampling-based RBDO is introduced. The proposed methods are introduced in each chapter, and enhanced accuracy and efficiency of PF calculation and design optimal results are verified through several numerical examples.