An enhanced finite step length method for structural reliability analysis and reliability-based design optimization

The finite step length (FSL) method is extensively used for structural reliability analysis due to its robustness and efficiency compared with traditional Hasofer–Lind and Rackwitz–Fiessler (HL-RF) method. However, it may generate a large computational effort when it faces some complex nonlinear limit state functions. This study explains the basic reason of inefficiency of the FSL method and proposes an enhanced finite step length (EFSL) method to improve the ability for solving complex nonlinear problems, and then apply it to reliability-based design optimization (RBDO). The tactic is to present an iterative control criterion to compensate for the deficiency of the FSL method in the oscillation amplitude criterion, which solves the problem of large computational effort caused by unchanged step length during the iterative process. Then, a comprehensive step length adjustment formula is presented, which can adaptively adjust the step length to achieve fast convergence for limit state functions with different degrees of nonlinearity. Following that, the proposed method is combined with the double loop method (DLM) to improve the efficiency and robustness for solving complex RBDO problems. The robustness and efficiency of the proposed method compared to other commonly used first-order reliability analysis methods are demonstrated by five numerical examples. In addition, four design problems are used to validate the proposed EFSL-based DLM which is effective for solving complex nonlinear RBDO problems.