Articles

Optimal bounded control for maximizing reliability of Duhem hysteretic systems

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

Received date: 2014-09-28

  Revised date: 2015-02-13

  Online published: 2015-10-01

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)

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.

Cite this article

Ming XU, Xiaoling JIN, Yong WANG, Zhilong HUANG . Optimal bounded control for maximizing reliability of Duhem hysteretic systems[J]. Applied Mathematics and Mechanics, 2015 , 36(10) : 1337 -1346 . DOI: 10.1007/s10483-015-1986-9

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