A new reliability analysis method based on the conjugate gradient direction

Reliability-based design optimization (RBDO) is an important area in structural optimization. A principal step of the RBDO process is to solve a reliability analysis problem. This problem has been considered in inner loop of double-loop RBDO approaches. Although many algorithms have been developed for solving this problem, there are still some challenges. Existing algorithms do not have good convergence rates and often diverge. There is a need to develop more efficient and stable algorithms that can be used for evaluating all performance functions sufficiently. In this paper, a new method, called “Conjugate Gradient Analysis (CGA) Method”, is proposed to apply in the reliability analysis problems. This method is based on the conjugate gradient method. Some mathematical problems are provided in order to demonstrate the advantages of the proposed method compared with the existing methods.