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 引用本文: 杨迪雄. 结构可靠度分析FORM迭代算法的混沌控制[J]. 力学学报, 2007, 23(5): 647-654.
Chaos control of form iterative algorithm in structural reliability analysis[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(5): 647-654.
 Citation: Chaos control of form iterative algorithm in structural reliability analysis[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(5): 647-654.

## Chaos control of form iterative algorithm in structural reliability analysis

• 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.

Abstract: The HL-RF algorithm of First Order ReliabilityMethod (FORM) in structural reliability analysis is an iterativealgorithm for reliability index with a wide application. However, itsometimes suffers from convergent failure such as periodic oscillation,bifurcation and chaosfor some nonlinear limit state functions. The convergent failure of FORM iscontrolled by using chaos control principle in the present paper. Theinherent relationship of various kinds of methods for global and local chaosfeedback control is clarified. It is shown that the stability transformationmethod and adaptive adjustment method are global chaos feedbackcontrol method, and the adaptive adjustment method can be viewed as aspecial case of the stability transformation method. The parameter adjustmenthybrid method is only a different form of the relaxed Newton method, bothof which are local chaos feedback control methods. Thecorresponding relationship between the formulations of chaos feedbackcontrol and iterative schemes for convergence control in engineeringmechanics is explored. Furthermore, the effectiveness and limitations ofthese measures for convergence control of iterative algorithms arediscussed.An effective, simple and general chaos feedback control methodcombining the stability transformation and relaxed Newton method isproposed, which is applied to control the periodic oscillation, bifurcationand chaos of FORM iterative algorithm for reliability analysis.

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