结构可靠度分析FORM迭代算法的混沌控制  

CHAOS CONTROL OF FORM ITERATIVE ALGORITHM IN STRUCTURAL RELIABILITY ANALYSIS

作　　者：杨迪雄[1] 

机构地区：[1]大连理工大学工程力学系工业装备结构分析国家重点实验室,大连116023

出　　处：《力学学报》2007年第5期647-654,共8页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(10672030);973国家重点基础研究发展计划(2006CB601205)资助项目.

摘　　要：利用混沌控制原理对FORM收敛失败进行控制.理清了全局性和局部性两类混沌反馈控制各种方法的内在联系,说明稳定转换法和自适应调节法属于全局混沌反馈控制方法,自适应调节法可视为稳定转换法的特例.参数调节混合法不过是松弛牛顿法的另一种表达形式,它们都属于局部混沌反馈控制方法.阐明了混沌反馈控制表达式与工程力学收敛控制迭代算法的对应关系.也揭示了这些迭代算法收敛控制措施的功效和局限性.提出了一个以稳定转换法为主联合松弛牛顿法的混沌反馈控制方法,对可靠度分析FORM迭代算法实现了周期振荡、分岔和混沌控制.　The HL-RF algorithm of First Order Reliabihty Method（FORM）in structural reliability analysis is an iterative algorithm for reliability index with a wide application.However,it sometimes suffers from convergent failure such as periodic oscillation,bifurcation and chaos for some nonlinear limit state functions.The convergent failure of FORM is controlled by using chaos control principle in the present paper.The inherent relationship of various kinds of methods for global and local chaos feedback control is clarified.It is shown that the stability transformation method and adaptive adjustment method are global chaos feedback control method,and the adaptive adjustment method can be viewed as a special case of the stability transformation method.The parameter adjustment hybrid method is only a different form of the relaxed Newton method,both of which are local chaos feedback control methods.The corresponding relationship between the formulations of chaos feedback control and iterative schemes for convergence control in engineering mechanics is explored. Furthermore,the effectiveness and limitations of these measures for convergence control of iterative algorithms are discussed.An effective,simple and general chaos feedback control method combining the stability transformation and relaxed Newton method is proposed,which is applied to control the periodic oscillation,bifurcation and chaos of FORM iterative algorithm for reliability analysis.

关 键 词：可靠度分析 FORM迭代算法 混沌动力学 收敛失败 混沌反馈控制 

分 类 号：O213.2[理学—概率论与数理统计] TU311.2[理学—数学]