A hybrid self-adaptive conjugate first order reliability method for robust structural reliability analysis

The traditional First Order Reliability Method (FORM) using steepest descent search direction may yield unstable solutions due to periodic nature and chaos for reliability analysis problems involving highly nonlinear performance functions. A conjugate search direction approach is attempted in the present study to overcome such problem of the FORM for Most Probable Point (MPP) search. Two iterative FORM schemes are investigated based on conjugate descent direction using self-adaptive conjugate (SAC) and hybrid self- adaptive conjugate (HSAC) search directions for estimating reliability index. The SAC is proposed using Fletcher and Reeves (FR) method and an adaptive conjugate scalar factor to improve the efficiency of the FR method for reliability analysis of highly nonlinear performance function. The HSAC is adaptively computed using FR and SAC methods to improve the robustness and efficiency of the FORM formula. The effectiveness of the proposed SAC and HSAC approaches are studied compare to the traditional FORM algorithms through several numerical examples. The proposed methods based on conjugate search direction are found to be more efficient and robust than the usual FORM algorithms.