A novel adaptive approach based on over-distance interval searching and precise step size determining for first-order structural reliability analysis

Abstract

The first-order second-moment reliability method (FORM) is a prevalent method in the reliability analyzing community owing to its accuracy and efficiency. However, it may encounter unstable solutions such as periodic oscillation and non-convergence when a high-dimensional problem with complex performance functions is involved. In this study, a novel adaptive approach based on over-distance interval searching and precise step size determining is presented to work out a solution for the above issues. First, the relationship between the state of the iterative rotation angle and the ideal step size was noticed. Therefore, a rotation control condition is proposed to dictate the selection of step size for the algorithm. After that, the determination of the step size of the proposed method here can be realized in two stages: In the first stage, an over-distance step size interval searching approach is established to define an initial exploration interval of step size with a length of 1. In the second stage, a determination approach of adaptive precise step size is then proposed to modify the fixed step sizes to make it adaptable to changes, therefore, get the final step sizes for the proposed method. Together, an over-distance adaptive precise searching approach of step size that can generate self-adaptive step sizes both greater and less than 1 is performed by interplaying the above two stages, thus preventing an excessive amount of redundant workload and speeding up the convergence while reducing the risk of oscillations. Besides, an iterative direction modification approach is given to orient the first iteration more accurately. In addition to that, the proposed method is tested on a offshore jacket platform and other seven examples to verify its performance. The results demonstrate that the proposed method provides excellent robustness and efficiency for both low and high-nonlinearity problems, showing significant merits.