New efficient and robust method for structural reliability analysis and its application in reliability-based design optimization

Due to its advantages of simplicity and high efficiency, Hasofer–Lind and Rackwitz–Fiessler (HL–RF) method is widely used in structural reliability analysis. However, it may encounter difficulties in convergence, such as periodic oscillation, bifurcation and chaos when complex performance functions are involved. In this study, a new efficient and robust method is proposed to deal with the convergence problem and is applied to reliability-based design optimization (RBDO). The strategy is to modify the search direction of HL–RF to make it adaptable to changes, thereby reducing the risk of periodic oscillations. A step size adjustment formula is then established to adaptively adjust the finite-step size to prevent bifurcation or chaos. In addition, the proposed method is integrated into double loop method (DLM) to strengthen the robustness and efficiency of DLM for complex RBDO problems. The efficiency and robustness of the proposed method are demonstrated by comparison with other existing first order reliability methods (FORMs) through five numerical examples and two structural examples. Two complex RBDO problems also show that DLM based on the proposed method has the ability to solve complex RBDO problems. •A new efficient and robust structural reliability method is proposed.•The search direction of HL–RF method is modified.•A new adaptive step size adjustment formula is established.•The proposed method improves the efficiency and robustness of FORM method.•The proposed method is applied to solve complex RBDO problems.