An adaptive hybrid single-loop method for reliability-based design optimization using iterative control strategy

Single-loop approach (SLA) is one of the most promising methods for solving linear and weakly nonlinear reliability-based design optimization (RBDO) problems. However, since SLA locates the current approximate most probable point (MPP) by using the gradient information of the previous one to reduce the computational cost, it may lead to inaccuracy when the nonlinearity of probabilistic constraints becomes relatively high. To overcome this limitation, a new adaptive hybrid single-loop method (AH-SLM) that can automatically choose to search for the approximate MPP or accurate MPP is proposed in this paper. Moreover, to get the accurate MPP more efficiently and alleviate the oscillation in the search process, an iterative control strategy (ICS) with two iterative control criteria is developed. In each iterative step, the KKT-condition of performance measure approach (PMA) is introduced to check the validity of the approximate MPP. If the approximate MPP is infeasible, ICS will be further carried out to search for the accurate MPP. The two iterative control criteria are used to update the oscillation control step length, then ICS can converge fast for both weakly and highly nonlinear performance functions. Besides, numerical examples are presented to verify the efficiency and robustness of our proposed method.