Limited conjugate gradient method for structural reliability analysis

A limited conjugate gradient method is proposed to improve the robustness and efficiency of the first-order reliability method (FORM). A new search direction vector is developed for structural reliability analysis using a limited scalar factor with Armijo’s rule and sufficient descent condition, namely limited Fletcher–Reeves (LFR) method. The conjugate gradient search direction is adaptively determined based on limited scalar factor and the instabilities of FORM formula are dynamically controlled by sufficient descent condition in the proposed LFR method. The LFR method is compared with the Hasofer–Lind and Rackwitz–Fiessler (HL–RF), stability transformation method (STM), finite-step size (FSS), chaotic conjugate stability transformation method (CCSTM), and directional stability transformation method (DSTM) using five mathematical and structural problems. Results of numerical examples illustrated that LFR is more efficient than the STM, FSS, CCSTM, and DSTM reliability methods and more robust than the HL–RF for highly non-linear performance functions.