An improved chaos control with adaptive active set approach combined in reliability-based design optimization.

To overcome the drawbacks of the traditional chaos control method (CC), such as non-convergence, inefficiency and repeated adjustment of control factor, a new method named adaptively active set-based CC (AASCC) is presented and further extended to the reliability-based design optimization (RBDO). First, the AASCC method builds a relationship between the iterative step size and search region of the minimum performance target point (MPTP) via gradient on the MPTP. This approach can adjust the iterative step size to respond dynamically to changes while automatically scaling the search domain of MPTP to eliminate unnecessary MPTP. As a result, it minimizes the demand for frequent debugging of control factors meanwhile accelerating computational efficiency. Second, the proposed strategy is combined with the reliability index to establish a dynamic dictate condition to optimize the performance of the RBDO-based double-loop method (DLM) in efficiency and accuracy. The dynamic dictate condition is executed to refresh the active determined constraint so that it effectively relieves the excessive redundant workloads. Finally, the proposed method is tested on several authoritative examples, involving both MPTP searching cases and RBDO problems to verify its characteristics, showing notable advantages.