| 结构可靠度分析FORM迭代算法的混沌控制 |
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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,2007,39(5):647-654. |
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| 作者姓名： | 杨迪雄 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金，国家重点基础研究发展计划(973计划) |
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| 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.
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| 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 |
| 文章编号： | 0459-1879（2007）05-0647-08 |
| 收稿时间： | 2006-10-13 |
| 修稿时间： | 2006-10-13 |
CHAOS CONTROL OF FORM ITERATIVE ALGORITHM IN STRUCTURAL RELIABILITY ANALYSIS |
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| Yang Dixiong.CHAOS CONTROL OF FORM ITERATIVE ALGORITHM IN STRUCTURAL RELIABILITY ANALYSIS[J].chinese journal of theoretical and applied mechanics,2007,39(5):647-654. |
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| Authors: | Yang Dixiong |
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| Affiliation: | Department of Engineering Mechanics,Dalian University of Technology State Key Laboratory for Structural Analysis of Industrial Equipment,Dalian 116023,China |
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| Abstract: | The HL-RF algorithm of First Order Reliability
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. |
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| Keywords: | reliability analysis FORM iterative algorithm chaotic dynamics convergent failure chaos feedback control |
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