Hybrid high dimensional model representation for failure probability estimation

Abstract

This work presents a new probabilistic method based on Hybrid High Dimensional Model Representation (HHDMR) for predicting the failure probability of randomly parametered structural/mechanical system. High Dimensional Model Representation (HDMR) is a general set of quantitative model assessment and analysis tools for capturing the high-dimensional relationships between sets of input and output model variables. It is a very efficient formulation of the system response, if higher order variable cooperative effects are weak and if the response function is dominantly of additive nature, allowing the physical model to be captured by the first few lower order terms. But, if multiplicative nature of the response function is dominant then Factorized HDMR (FHDMR) must be used, to get a desired accuracy with least number of numerical calculations. But in most cases the nature of the limit state/performance function has neither additive nor multiplicative nature. Rather it has an intermediate nature. This paper presents a new HHDMR based approximation of an implicit limit state/performance function has neither additive nor multiplicative nature but rather an intermediate nature. The proposed approximation of an implicit limit state/performance function includes both HDMR and FHDMR expansions through a hybridity parameter. Results of six numerical examples involving elementary mathematical functions and structural/solid-mechanics problems indicate that the failure probability obtained using HHDMR approximation of an implicit limit state/performance function provides significant accuracy when compared with the conventional Monte Carlo method, while requiring fewer original model simulations.