An augmented step size adjustment method for the performance measure approach: Toward general structural reliability-based design optimization

Abstract Heavy computational burden has been one of the largest barriers to the application of reliability-based design optimization (RBDO) in real-world structures. The key difficulty of RBDO lies in how to perform reliability analysis efficiently and robustly. In performance measure approach (PMA)-based RBDO, the reliability analysis process searches for the minimum performance target point (MPTP) with the target reliability index in standard normal space. Many methods have been proposed to improve the efficiency and robustness of the PMA. However, these methods may face the convergence problem for highly nonlinear constraint functions; or high computational cost for weakly nonlinear ones. More importantly, most existing methods are very sensitive to the selection of algorithm parameters. In this paper, an augmented step size adjustment (ASSA) method is proposed to boost the iterative process in terms of both efficiency and robustness. According to the relative positions of the direction vector and negative gradient direction and the angle between them at each iterative point, a fire-new strategy is established to identify the oscillation during the iterative process and define the iterative step size. Seven inverse reliability analysis problems and three RBDO benchmarks are used to validate the performance of the ASSA method. The results indicate that the ASSA method has wide applicability for nonlinear constraint functions and achieves efficient and robust performance. Furthermore, the results demonstrate that the ASSA method can be regarded as a reliable and effective method for addressing PMA-based RBDO problems.