Dynamical accelerated performance measure approach for efficient reliability-based design optimization with highly nonlinear probabilistic constraints

For satisfactory performance of reliability-based design optimization (RBDO) tools, stable and efficient estimation of the nonlinear probabilistic constraints is of utter importance. Unfortunately, popular methods for reliability analysis, such as hybrid chaos control, self-adaptive chaos control and adaptive chaos control, have several drawbacks which include unstable results and slow rate of convergence. To address this issue, a dynamical accelerated chaos control (DCC) -based beta-circle search direction algorithm is proposed. In order to compute the chaos control factor within DCC, a novel merit function is also proposed in this work. The efficiency and robustness of the proposed DCC method have been illustrated with four nonlinear reliability problems and four RBDO examples. Compared to available state-of-the-art methods, the proposed approach is found to be efficient and accurate. This certifies its possible application to realistic RBDO problems.