A FORM based inverse reliability analysis using BFGS formula

In this research, an alternative to the existing inverse algorithm in structural reliability is proposed. The existing algorithm is named as inverse- FORM, and is based on the Hasofer-Lind-Rackwitz-Fiessler (HLRF) method. The HLRF method is a special case of sequential quadratic programming (SQP), in which the Hessian of the Lagrangian is approximated as an identity matrix. Because of this approximation, inverse-FORM is found to be computationally less efficient when applied to highly non-linear limit state functions. Alternative algorithms, based on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) formula used in SQP, are proposed. They are named as BFGS-based-inverse-FORM-1 and BFGS-based-inverse-FORM-2. They use the BFGS update formula to approximate the Hessian, instead of using an identity matrix. In this paper, comparative numerical experiments have been presented to illustrate the performance of BFGS-based-inverse-FORM-1 and BFGS-based-inverse-FORM-2, when applied to highly non-linear limit state functions. Results show that BFGSbased- inverse-FORM-1 is more efficient than inverse-FORM as it uses larger step size and hence, requires a lesser number of iterations to converge to the final solution. However, it compromises on the accuracy of the final solution. On the other hand, BFGS-based-inverse-FORM-2 achieves better efficiency than inverse- FORM without compromising the accuracy.