概率约束评估的功能度量法的混沌控制

功能度量法是基于可靠度的结构优化设计中评估概率约束的一种方法,其改进均值(AMV)迭代格式具有简洁、高效的优点,但对一些非线性功能函数搜索最小功能目标点时可能陷入周期振荡或混沌解,本文利用混沌反馈控制的稳定转换法对功能度量法的AMV迭代格式实施收敛控制.首先展示一些功能函数应用功能度量法AMV格式迭代计算产生了周期解和混沌解现象,并对迭代算法进行了混沌动力学分析.然后利用稳定转换法对功能度量法迭代失败的参数区间进行混沌控制,使嵌入周期和混沌轨道的不稳定不动点稳定化,获得了稳定收敛解,实现了迭代解的周期振荡、分岔和混沌控制.

Chaos control of performance measure approach for evaluation of probabilistic constraints

Performance measure approach(PMA) is a recently proposed method for evaluation of probabilistic constraints in reliability based design optimization.The advanced mean-value(AMV) method is well suitable for PMA due to its simplicity and efficiency.However,when the AMV iterative scheme is applied to search for the minimum performance target point for some nonlinear performance functions,the iterative sequences could fall into the periodic oscillation and even chaotic state.The convergence control of AMV procedure of PMA is implemented by the stability transformation method of chaos feedback control in the present paper.Firstly,it is illustrated that using the AMV iterative scheme the iterative solution generates the phenomenon of periodic oscillation and chaos for some performance functions.And the chaotic dynamics analysis on this iterative procedure is performed.Then,the stability transformation method is employed for the chaos control of solution in the parameter interval in which the iterative scheme of AMV fails.The numerical results demonstrate that the control of periodic oscillation,bifurcation and chaos for AMV iterative procedure is achieved,and the expected stable convergent solutions are obtained.