An approximate single-loop chaos control method for reliability based design optimization using conjugate gradient search directions

Single-loop methods based on the Karush-Kuhn-Tucker conditions are considered to be efficient reliability based design optimization (RBDO) methods. The probabilistic performance functions are converted to deterministic functions for reducing the computational burden of reliability analysis. However, the most probable target point (MPTP) estimated using steepest descent search directions diverges or oscillates for highly nonlinear performance functions. Therefore, an approximate single-loop chaos control method is proposed to address this challenge by estimating MPTP using conjugate gradient search directions. An oscillation criterion is also proposed to track the oscillation of MPTP in every iteration. When this criterion is satisfied, the chaos control theory is used to update the current MPTP. The proposed method is tested on six mathematical and two engineering RBDO examples from the literature. Monte Carlo simulations are performed on the obtained solutions for estimating their reliability. The results demonstrate that the proposed method generates the best reliable solution and is also computationally efficient on the chosen set of examples over seven RBDO methods from the literature.