A hybrid chaos control approach of the performance measure functions for reliability-based design optimization

• Convergence improving mechanisms of different MPTP search methods are analyzed.
• A modified chaos control (MCC) of performance measure function is proposed.
• The hybrid chaos control (HCC) method is proposed based on function type criterion.
• The HCC method is applied for different RBDO approaches.

Performance measure approach (PMA) is an effective tool of the reliability-based design optimization (RBDO). And the advanced mean value (AMV) method is widely used for the evaluation of probabilistic constraint due to its simplicity and efficiency. However, the AMV method shows instability and inefficiency when applied to the concave performance measure functions, so do other existing iterative methods. In this paper, to overcome the difficulties, a modified chaos control (MCC) is applied to the AMV iterative procedure through modifying the iterative step of the chaotic dynamics analysis. Since the MCC method is inefficient for convex performance measure functions, a hybrid chaos control (HCC) method is also proposed by employing the AMV method or the MCC method adaptively during the RBDO process. Moreover, we equip PMA and sequential optimization and reliability assessment (SORA) with the HCC method for solving RBDO problems. Numerical examples are presented to demonstrate the simplicity, efficiency and robustness of the HCC method.