Fault detection and estimation for non-Gaussian stochastic systems with time varying delay

Hu Kai, Song Aiguo, Wang Weiliang, Zhang Yingchao, Fan, Fan Zhiyong

Description

In this paper, fault detection and estimation problem is studied for non-Gaussian stochastic systems with time varying delay. A new approach based on the output probability density function (PDF) and observers technique to detect and estimate time varying faults is presented. Some slack variables and scalars are introduced to design observers’ parameters, which can provide more degrees of freedom. A particle distribution example is given to illustrate the design procedures, and the simulation results show the performance of the proposed approaches.

Sujets

• Fault detection and isolation
• Observer
• PDF

Informations

• Publié par: biomed
• Publié le: 01 janvier 2013
• Nombre de lectures: 13
• Langue: English

Extrait

Hu et al. Advances in Difference Equations 2013, 2013 :22 http://www.advancesindifferenceequations.com/content/2013/1/22 R E S E A R C H Open Access Fault detection and estimation for non-Gaussian stochastic systems with time varying delay Kai Hu 1,2 , AiGuo Song 2* , WeiLiang Wang 1 , Yingchao Zhang 1 and Zhiyong Fan 1 * Correspondence: [e-mail] Abstract 2 School of Instrument Science and In this paper, fault detec i d estimation problem is studied for non-Gaussian Engineering, Southeast University, t on an Nanjing, 210096, China stochastic systems with time varying delay. A new approach based on the output Full list of author information is probability density function (PDF) and observers technique to detect and estimate available at the end of the article time varying faults is presented Some slack variables and scalars are introduced to . design observers’ parameters, which can provide more degrees of freedom. A particle distribution example is given to illustrate the design procedures, and the simulation results show the performance of the proposed approaches. Keywords: fault detection; fault estimation; observer; PDF 1 Introduction Automatic control systems are widely applied to many industrial processes. However, un- expected faults may destroy the stability of the systems. For such reasons, fault detec- tion and estimation for dynamical systems has received much attention [ –]. In past two decades, many significant approaches have been presented and applied to practical processes successfully []. In general, the fault detection (FD) results can be classified into three types: filter- or observer-based approaches [ –]; the identification-based FD scheme [, ]; and statistic approach []. For the dynamic stochastic systems, the filter- based FD approach has been shown as an effective way where generally the variables are supposed to be Gaussian in [ ] and []. It has been shown that in systems where either the system variables or not, the noise are not Gaussian in [ , ]. Existing methods may not be sufficient to characterize the closed loop system behavior. As a result, the output PDF rather than the mean variance was proposed [ –]. Here, we firstly introduce the output PDF definition. For a dynamic stochastic system, suppose that the random process y ∈ [ a , b ] is the output of the stochastic system, its output PDFs are defined by γ ( z , u ( t )), where u ( t ) ∈ Rm is control input. In output PDFs shape control, the B-spline expansion technique has been introduced in the output PDF modeling in [ –], i.e. , the following square root B-spline expansion model has been used to approximate γ ( z , u ( t )): n  γ  z , u ( t )  =  v i ( u ) b i ( z ), () i = © 2013 Hu et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribu- tion License (http://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.