A hybrid self-adjusted mean value method for reliability-based design optimization using sufficient descent condition

Due to the efficiency and simplicity, advanced mean value (AMV) method is widely used to evaluate the probabilistic constraints in reliability-based design optimization (RBDO) problems. However, it may produce unstable results as periodic and chaos solutions for highly nonlinear performance functions. In this paper, the AMV is modified based on a self-adaptive step size, named as the self-adjusted mean value (SMV) method, where the step size for reliability analysis is adjusted based on a power function dynamically. Then, a hybrid self-adjusted mean value (HSMV) method is developed to enhance the robustness and efficiency of iterative scheme in the reliability loop, where the AMV is combined with the SMV on the basis of sufficient descent condition. Finally, the proposed methods (i.e. SMV and HSMV) are compared with other existing performance measure approaches through several nonlinear mathematical/structural examples. Results show that the SMV and HSMV are more efficient with enhanced robustness for both convex and concave performance functions.