Efficient Evaluation Approaches for Probabilistic Constraints in Reliability-Based Design Optimization

This paper presents new efficient evaluation methods for probabilistic constraints in reliability-based design optimization (RBDO) to substantially improve computational efficiency when applied to large-scale applications. Two different methods are presented: efficient identification of feasible probabilistic constraints and fast reliability analysis using the condition of design closeness. Unlike deterministic design optimization, a significant computational burden is imposed on feasibility check of constraints in the RBDO process due to expensive reliability analysis. Such difficulties can be effectively resolved by using a mean value (MV) first-order method with an allowable accuracy for the purpose of feasibility identification, and by carrying out the refined reliability analysis using the hybrid mean value (HMV) first-order method for ε-active and violate constraints in the RBDO process. The fast reliability analysis method is proposed by reusing some of the information obtained at the previous RBDO iteration to efficiently evaluate probabilistic constraints at the current design iteration under the assumption of the design closeness. To demonstrate numerical efficiency of the new RBDO process, two numerical examples including a large-scale multi-crash application are employed.