Reliability-Based Design Optimization Combining the Reliability Index Approach and Performance Measure Approach

In order to provide a good cost-effective design between cost and safety, the reliability-based design optimization (RBDO) is proposed considering the uncertainties in structural design. So far, a lot of RBDO strategies have been developed to improve computational efficiency, convergence and robustness, such as the two-level RBDO approaches, the single loop RBDO approaches and the decoupled RBDO approaches. However, the performance of these RBDO approaches, such as accuracy, efficiency and robustness, still are affected by the initial points, the target reliability index, the limit state function and the random distribution. In this study, an effective combined method is proposed to enhance performance of algorithm by selecting a better search space of probabilistic constraints during iterations, which solves RBDO problem by combining the reliability index approach (RIA) and the performance measure approach (PMA) to evaluate the reliability constraints according to the value of reliability index at the current design point under the single loop strategy. During iterations, the reliability index constraints are selected as probabilistic constraints for the violated probabilistic constraints, while the performance measure constraints are selected for the inactive probabilistic constraints. Through comparative studies of mathematical and engineering problems, it is shown that the proposed approach has a good performance of accuracy, efficiency and robustness.