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Mathematical Problems in Engineering
Volume 2017, Article ID 4317670, 15 pages
Research Article

HLRF-BFGS-Based Algorithm for Inverse Reliability Analysis

School of Computing Engineering and Mathematics, Western Sydney University, Penrith, NSW 2747, Australia

Correspondence should be addressed to Won-Hee Kang; ua.ude.yendysnretsew@gnaK.W

Received 10 March 2017; Accepted 7 June 2017; Published 17 July 2017

Academic Editor: Roman Lewandowski

Copyright © 2017 Rakul Bharatwaj Ramesh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.