Optimal bounded control for maximizing reliability of Duhem hysteretic systems

doi:10.1007/s10483-015-1986-9

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (10): 1337-1346.doi: https://doi.org/10.1007/s10483-015-1986-9

Optimal bounded control for maximizing reliability of Duhem hysteretic systems

Ming XU¹, Xiaoling JIN², Yong WANG², Zhilong HUANG²

1. College of Metrology and Measurement Engineering, China Jiliang University, Hangzhou 310018, China;
2. Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China

收稿日期:2014-09-28 修回日期:2015-02-13 出版日期:2015-10-01 发布日期:2015-10-01
通讯作者: Yong WANG E-mail:yongpi.wang@gmail.com
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11202181 and 11402258) and the Special Fund for the Doctoral Program of Higher Education of China (No. 20120101120171)

Optimal bounded control for maximizing reliability of Duhem hysteretic systems

Ming XU¹, Xiaoling JIN², Yong WANG², Zhilong HUANG²

1. College of Metrology and Measurement Engineering, China Jiliang University, Hangzhou 310018, China;
2. Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China

Received:2014-09-28 Revised:2015-02-13 Online:2015-10-01 Published:2015-10-01
Contact: Yong WANG E-mail:yongpi.wang@gmail.com
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11202181 and 11402258) and the Special Fund for the Doctoral Program of Higher Education of China (No. 20120101120171)

摘要/Abstract

摘要： The optimal bounded control of stochastic-excited systems with Duhem hysteretic components for maximizing system reliability is investigated. The Duhem hysteretic force is transformed to energy-depending damping and stiffness by the energy dissipation balance technique. The controlled system is transformed to the equivalent nonhysteretic system. Stochastic averaging is then implemented to obtain the Itô stochastic equation associated with the total energy of the vibrating system, appropriate for evaluating system responses. Dynamical programming equations for maximizing system reliability are formulated by the dynamical programming principle. The optimal bounded control is derived from the maximization condition in the dynamical programming equation. Finally, the conditional reliability function and mean time of first-passage failure of the optimal Duhem systems are numerically solved from the Kolmogorov equations. The proposed procedure is illustrated with a representative example.

关键词: stochastic dynamical programming principle, reliability, Duhem hysteretic system, optimal bounded control

Abstract: The optimal bounded control of stochastic-excited systems with Duhem hysteretic components for maximizing system reliability is investigated. The Duhem hysteretic force is transformed to energy-depending damping and stiffness by the energy dissipation balance technique. The controlled system is transformed to the equivalent nonhysteretic system. Stochastic averaging is then implemented to obtain the Itô stochastic equation associated with the total energy of the vibrating system, appropriate for evaluating system responses. Dynamical programming equations for maximizing system reliability are formulated by the dynamical programming principle. The optimal bounded control is derived from the maximization condition in the dynamical programming equation. Finally, the conditional reliability function and mean time of first-passage failure of the optimal Duhem systems are numerically solved from the Kolmogorov equations. The proposed procedure is illustrated with a representative example.

Key words: reliability, Duhem hysteretic system, optimal bounded control, stochastic dynamical programming principle

中图分类号:

O327

Ming XU, Xiaoling JIN, Yong WANG, Zhilong HUANG. Optimal bounded control for maximizing reliability of Duhem hysteretic systems[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(10): 1337-1346.

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Optimal bounded control for maximizing reliability of Duhem hysteretic systems

Optimal bounded control for maximizing reliability of Duhem hysteretic systems

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