Step Direction Computation of the First-Order Reliability Analysis Based on Two-Step Root-Finding Methods

The iHLRF algorithm is a popular iterative algorithm for determining the failure probability in structural reliability problems. It belongs to the family of first-order reliability methods (FORM) and is known for its fast convergence and remarkable simplicity. However, in cases where the limit state function oscillates significantly near the design point, which often occurs in high nonlinear limit state functions, the iHLRF algorithm may suffer from convergence issues. To address these convergence issues, this paper proposes three two-step direction determination techniques for first-order analysis. These techniques are based on two-step root-finding methods with a higher convergence rate than existing methods. The proposed techniques aim to improve the accuracy and robustness of the iHLRF algorithm, especially in cases where the limit state function shows highly nonlinear behavior. A numerical example with high nonlinear limit state functions in standard normal space is presented to demonstrate the proposed techniques' efficiency and capability. The performance of each proposed technique is compared with other existing methods, highlighting the advantages and limitations of each approach. Overall, this paper aims to contribute to developing more accurate and reliable methods for determining the reliability index in structural reliability problems, with the potential to be applied in various engineering fields.