Instabilities control of reliability analysis using hybrid HL-RF and conjugate optimization algorithms

The first order reliability method (FORM) is an effective mathematical iterative algorithm for approximating the reliability index. In highly concave problems, the FORM algorithm shows instable solutions such as as periodic oscillation, bifurcation and chaos. In this paper, to overcome the difficulties of FORM, a hybrid method is proposed based on Hasofer-Lined and Rackwitz and Fiessler (HL-RF) and conjugate gradient optimization method to control the instability of iterative mathematical reliability scheme, which called as hybrid conjugate first order reliability method (HCFR). A dynamical conjugate search direction is established using descent condition for chaos feedback control of FORM. A dynamical control factor is proposed determined based on the results extracted from limit state function in each iteration. In this control factor, the concavity effect of performance function is considered, adaptively. Two nonlinear mathematical examples are presented to demonstrate the efficiency, accuracy, and robustness of the HCFR algorithm. Numerical results illustrate that the HCFR algorithm is more robust than the HL-RF and can control the instability solution of the FORM iterative algorithm.