Selective dimension reduction method (DRM) to enhance accuracy and efficiency of most probable point (MPP)–based DRM

Abstract

To perform reliability-based design optimization (RBDO) in engineering systems, reliability analysis is required to calculate probability of failure (PF) for each performance function. Most probable point (MPP)–based dimensional reduction method (DRM) has been developed to accurately estimate PF using the Gaussian quadrature integration method. However, the existing MPP-based DRM is computationally expensive for highly nonlinear and/or high dimensional problems since it needs to increase the number of integration points in all directions to guarantee accuracy. In the proposed method, three statistical model selection methods—Akaike information criterion (AIC), AIC correction (AICc), and Bayesian information criterion (BIC)—are utilized to identify characteristic of performance functions for more efficient integration point allocation. Then, genetic algorithm and simplex optimization method are used to find the best models with the smallest AIC, AICc, and BIC values. No additional function evaluations are required for the model selection process since MPP candidate points are utilized. The best models obtained through optimization show where to allocate integration points which makes it possible not to allocate unnecessary integration points. Numerical study verifies that the proposed method can guide how to allocate integration points according to characteristic of performance functions: no integration points for almost linear performance functions, minimal additional integration points for mildly nonlinear performance functions, and more integration points for highly nonlinear functions.