An efficient-robust structural reliability method by adaptive finite-step length based on Armijo line search

The robustness of iterative formula as well as its computational efficiency is the essential characteristic of interest for effective reliability analysis of structures by first order reliability method (FORM). A robust and efficient iterative algorithm termed as finite-based Armijo search direction (FAL) method is proposed in the present study for FORM-based structural reliability analysis. A finite-step size is proposed using the Armijo rule and sufficient descent condition to achieve the stabilization of the FORM algorithm. The FAL is adaptively adjusted based on the information obtained from the iterative algorithm at each iteration and Armijo rule. The robustness and efficiency of the proposed FAL method is elucidated using several problems. The results obtained by the proposed method are compared with various existing reliability methods based on steepest descent search direction. The results of the numerical study indicate that the FAL approach is more robust and efficient than the other existing FORM schemes and improves the robustness of FORM formula. Thus, the FAL can be successfully implemented as a robust FORM-based iterative reliability analysis procedure.