A hybrid self-adjusted single-loop approach for reliability-based design optimization

Single-loop approach (SLA) exhibits higher efficiency than both double-loop and decoupled approaches for solving reliability-based design optimization (RBDO) problems. However, SLA sometimes suffers from the non-convergence difficulty during the most probable point (MPP) search process. In this paper, a hybrid self-adjusted single-loop approach (HS-SLA) with high stability and efficiency is proposed. Firstly, a new oscillating judgment criterion is firstly proposed to precisely detect the oscillation of iterative points in standard normal space. Then, a self-adjusted updating strategy is established to dynamically adjust the control factor of modified chaos control (MCC) method during the iterative process. Moreover, an adaptive modified chaos control (AMCC) method is developed to search for MPP efficiently by selecting MCC or advanced mean value method automatically based on the proposed oscillating judgment criterion. Finally, through integrating the developed AMCC into SLA, the hybrid self-adjusted single-loop approach is proposed to achieve stable convergence and enhance the computational efficiency of SLA for complex RBDO problems. The high efficiency of AMCC is demonstrated by five nonlinear performance functions for MPP search. Additionally, five representative RBDO examples indicate that the proposed HS-SLA can improve the efficiency, stability, and accuracy of SLA.