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Entropy 2013, 15(1), 32-52; doi:10.3390/e15010032
Article

Function Based Fault Detection for Uncertain Multivariate Nonlinear Non-Gaussian Stochastic Systems Using Entropy Optimization Principle

1,2,*  and 1
1 School of Information and Control, Nanjing University of Information Science & Technology, Ninglu Road No. 219, Pukou District, Nanjing, 210044, China 2 School of Automation Science and Electrical Engineering, Beijing University of Aeronautics & Astronautics, Xueyuan Road No. 37, Haidian District, Beijing, 100191, China
* Author to whom correspondence should be addressed.
Received: 26 June 2012 / Revised: 16 December 2012 / Accepted: 18 December 2012 / Published: 21 December 2012
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Abstract

In this paper, the fault detection in uncertain multivariate nonlinear non-Gaussian stochastic systems is further investigated. Entropy is introduced to characterize the stochastic behavior of the detection errors, and the entropy optimization principle is established for the fault detection problem. The principle is to maximize the entropies of the stochastic detection errors in the presence of faults and to minimize the entropies of the detection errors in the presence of disturbances. In order to calculate the entropies, the formulations of the joint probability density functions (JPDFs) of the stochastic errors are presented in terms of the known JPDFs of both the disturbances and the faults. By using the novel performance indexes and the formulations for the entropies of the detection errors, new fault detection design methods are provided for the considered multivariate nonlinear non-Gaussian plants. Finally, a simulation example is given to illustrate the efficiency of the proposed fault detection algorithm.
Keywords: fault detection; multivariate stochastic systems; uncertain; entropy optimization; non-Gaussian system fault detection; multivariate stochastic systems; uncertain; entropy optimization; non-Gaussian system
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Yin, L.; Zhou, L. Function Based Fault Detection for Uncertain Multivariate Nonlinear Non-Gaussian Stochastic Systems Using Entropy Optimization Principle. Entropy 2013, 15, 32-52.

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