A novel chaos control method based on conjugate direction and adaptive step size

Abstract

The Hasofer-Lind-Rackwitz-Fiessler method (HL-RF method) with the negative gradient direction as the iteration direction often oscillates or even does not converge during the iteration process due to the unreasonable control of the negative gradient direction. This greatly reduces the convergence and robustness of the HL-RF method. Chaos control method (CC method) is also a method with negative gradient direction as the iterative direction. However, in order to alleviate the oscillation problem caused by unreasonable control of negative gradient direction, it introduces a smaller iterative step size in the iterative process. Because its iterative step size is a fixed small value, the iterative efficiency of the CC method is not high. In view of the above problems, in order to reduce the iterative oscillation phenomenon and increase the iterative efficiency at the same time, it proposes a novel chaos control method based on conjugate direction and adaptive step size (CDCC method). Firstly, it uses the conjugate direction instead of the negative gradient direction, so as to fundamentally avoid the problem that the negative gradient direction is easy to cause oscillation. It effectively increases the convergence and robustness of the method. Secondly, it uses iteration information to adaptively control the iteration step size, increasing the computational efficiency of the method effectively. In addition, it also discusses the optimal value of the modification coefficient in the adaptive step size control. Finally, eight examples are given to show that the proposed method has obvious advantages in computational efficiency, convergence and robustness.