HLRF‐BFGS‐Based Algorithm for Inverse Reliability Analysis

Abstract

This study proposes an algorithm to solve inverse reliability problems with a single unknown parameter. The proposed algorithm is based on an existing algorithm, the inverse first-order reliability method (inverse-FORM), which uses the Hasofer Lind Rackwitz Fiessler (HLRF) algorithm. The initial algorithm analyzed in this study was developed by modifying the HLRF algorithm in inverse-FORM using the Broyden-Fletcher-Goldarb-Shanno (BFGS) update formula completely. Based on numerical experiments, this modification was found to be more efficient than inverse-FORM when applied to most of the limit state functions considered in this study, as it requires comparatively a smaller number of iterations to arrive at the solution. However, to achieve this higher computational efficiency, this modified algorithm sometimes compromised the accuracy of the final solution. To overcome this drawback, a hybrid method by using both the algorithms, original HLRF algorithm and the modified algorithm with BFGS update formula, is proposed. This hybrid algorithm achieves better computational efficiency, compared to inverse-FORM, without compromising the accuracy of the final solution. Comparative numerical examples are provided to demonstrate the improved performance of this hybrid algorithm over that of inverse-FORM in terms of accuracy and efficiency.

A New Approach to Symmetry Reliability: Combination of Forward and Inverse Reliability Principle and Its Application to Frame Structures and Bamboo Bridges

“…Yi and Zhu [23] conducted research on the value of the iteration step in the iterative algorithm for the inverse reliability analysis. Ramesh et al [24] proposed an inverse reliability analysis solution method based on the HLFR-BFGS algorithm. Li et al [25] proposed an inverse reliability analysis method based on improved adaptive chaos control.…”