A hybrid relaxed first-order reliability method for efficient structural reliability analysis

The Hasofer-Lind and Rakwitz-Fiessler (HL-RF) algorithm is widely used for structural reliability analysis in first-order moment method (FORM). However, it meets non-convergence problem including generating periodic and chaotic solutions for highly nonlinear limit state function. In this paper, relaxed HL-RF (RHL-RF) is developed based on a relaxed factor, which is dynamically computed by the second-order interpolation between zero and one. A hybrid relaxed HL-RF (HRHL-RF) method is proposed, in which the HL-RF and RHL-RF are adaptively implemented by using an angle criterion to improve the robustness and efficiency of FORM formula. The angle condition is simply calculated based on the results from the new and previous points. Finally, the performances in terms of robustness and efficiency of the HRHL-RF are compared with several existing FORM methods through five mathematical and structural examples. The results indicate that HRHL-RF method is more robust than the HL-RF and more efficient than other existing methods.