Self-adaptive conjugate method for a robust and efficient performance measure approach for reliability-based design optimization

The advanced mean value and hybrid mean value methods are commonly used to evaluate the probabilistic constraint of reliability-based design optimization (RBDO) problems. These iterative methods can yield unstable solutions to highly nonlinear performance functions. The conjugate gradient analysis (CGA) and modified chaos control (MCC) algorithms have recently been employed to achieve the stabilization of reliability analysis in RBDO problems. However, the CGA and the MCC methods can be inefficient for convex performance functions. In this paper, a self-adaptive conjugate gradient (SCG) method is proposed to improve the efficiency of the minimum performance target point (MPTP) search based on an adaptive conjugate scalar factor for highly nonlinear concave and convex problems. With this aim, the conjugate search direction is adaptively computed using the mean value of the previous performance function with a limited conjugate scalar factor. The efficiency and robustness of the proposed SCG algorithm are compared with those of different reliability methods using five nonlinear concave/convex reliability problems and two mathematical/structural RBDO examples. The results indicate that the SCG method accurately converges after less iterations compared to other existing reliability methods. The SCG method is a robust iterative formula for inverse reliability analysis and RBDO.