Chaotic dynamics analysis and control of iterative algorithms in structural optimization and reliability analysis
2015年04月06日 16:47 点击：
The property of numerous structural and mechanical systems is nonlinear, and the iterative computation is a kind of general method for engineering system analysis. However, for some nonlinear problems the iterative method does not obtain convergent solution, but the oscillating periodic solution and even disordered chaotic solution. We introduce the theory of chaotic dynamics and chaos control to implement the mechanism analysis and cntrol of nonconvergence of iterative algorithms in the numerical analysis of engineering mechanics, such as the structural optimization, reliability analysis, capacity spectrum method and so on. Firstly, the nonlinear map of iterative algorithms is established and the dynamical system with equivalent topology is reconstructed. The stability and convergence of iterative solution of system is identified via the bifurcation plot and Lyapunov exponent. Then, the applicability, efficiency and inherent relationship of several kinds of effective methods of chaos feedback control, including the stability transformation, relaxed Newton method and self-locating method etc., is investigated comparatively. The chaos feedback control method based on the model without prior knowledge is proposed. Moreover, the feedback control method with better performance is selected to apply to the oscillation and chaos control of dynamical system of iterative algorithms, and the expected fixed points of system are captured. This project will generate a series of original methods of mechanism analysis and control on the basis of chaotic dynamics for solving the nonconvergence problem of iterative schemes of engineering system. It is helpful for deepening and updating the understanding and comprehension of iterative algorithms of engineering mechanics.
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