Filter‐based fault detection and diagnosis using output PDFs for stochastic systems with time delays

In this paper, a fault detection and diagnosis (FDD) scheme is studied for general stochastic dynamic systems subjected to state time delays. Different from the formulation of classical FDD problems, it is supposed that the measured information for the FDD is the probability density function (PDF) of the system output rather than its actual value. A B-spline expansion technique is applied so that the output PDF can be formulated in terms of the dynamic weights of the B-spline expansion, by which a time delay model can be established between the input and the weights with non-linearities and modelling errors. As a result, the concerned FDD problem can be transformed into a classic FDD problem subject to an uncertain non-linear system with time delays. Feasible criteria to detect the system fault are obtained and a fault diagnosis method is further presented to estimate the fault. Simple simulations are given to demonstrate the efficiency of the proposed approach. Copyright © 2006 John Wiley & Sons, Ltd.

[1]  Lei Guo,et al.  Generalized discrete-time PI control of output PDFs using square root B-spline expansion , 2005, Autom..

[2]  Hong Wang,et al.  Applying observer based FDI techniques to detect faults in dynamic and bounded stochastic distributions , 2000 .

[3]  Rolf Isermann,et al.  Trends in the Application of Model Based Fault Detection and Diagnosis of Technical Processes , 1996 .

[4]  James Lam,et al.  Iterative LMI approach for robust fault detection observer design , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[5]  Youmin Zhang,et al.  Stochastic stability analysis of fault-tolerant control systems in the presence of noise , 2001, IEEE Trans. Autom. Control..

[6]  Ivan Nagy,et al.  Mixed‐data multi‐modelling for fault detection and isolation , 2002 .

[7]  Mehrdad Saif,et al.  Fault detection and accommodation in nonlinear time-delay systems , 2003, Proceedings of the 2003 American Control Conference, 2003..

[8]  Marios M. Polycarpou,et al.  A robust detection and isolation scheme for abrupt and incipient faults in nonlinear systems , 2002, IEEE Trans. Autom. Control..

[9]  Hong Wang,et al.  Bounded Dynamic Stochastic Systems , 2012 .

[10]  P. Frank,et al.  Survey of robust residual generation and evaluation methods in observer-based fault detection systems , 1997 .

[11]  Dominique Sauter,et al.  Optimal thresholding for robust fault detection of uncertain systems , 2000 .

[12]  Marcel Staroswiecki,et al.  Duality of Analytical Redundancy and Statistical Approach in Fault Diagnosis , 1996 .

[13]  Steven X. Ding,et al.  Fault detection filter design for LTI system with time delays , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[14]  Jason L. Speyer,et al.  Optimal stochastic fault detection filter , 2003, Autom..

[15]  Qinghua Zhang.  A new residual generation and evaluation method for detection and isolation of faults in non‐linear systems , 2000 .

[16]  Ali Saberi,et al.  Optimal fault signal estimation , 2002 .

[17]  Jian Liu,et al.  Reliable guaranteed variance filtering against sensor failures , 2003, IEEE Trans. Signal Process..

[18]  Hong Wang,et al.  Bounded Dynamic Stochastic Systems: Modelling and Control , 2000 .