Set‐membership parity space approach for fault detection in linear uncertain dynamic systems

In this paper, a set-membership parity space approach for linear uncertain dynamic systems is proposed. First, a set of parity relations derived from the parity space approach is obtained by means of a transformation derived from the system characteristic polynomial. As a result of this transformation, parity relations can be expressed in regressor form. On the one hand, this facilitates the parameter estimation of those relations using a zonotopic set-membership algorithm. On the other hand, fault detection is then based on checking, at every sample time, the non-existence of a parameter value in the parameter uncertainty set such that the model is consistent with all the system measurements. The proposed approach is applied to two examples: a first illustrative case study based on a two-tank system and a more realistic case study based on the wind turbine fault detection and isolation benchmark in order to evaluate its effectiveness. Copyright © 2014 John Wiley & Sons, Ltd.

[1]  Peter Fogh Odgaard,et al.  Fault-Tolerant Control of Wind Turbines: A Benchmark Model , 2009, IEEE Transactions on Control Systems Technology.

[2]  Pierre Apkarian,et al.  Robust pole placement in LMI regions , 1999, IEEE Trans. Autom. Control..

[3]  Dan T. Horak.  Failure detection in dynamic systems with modeling errors , 1988 .

[4]  Vicenç Puig,et al.  Observer Gain Effect in Linear Interval Observer-Based Fault Detection , 2007 .

[5]  Mogens Blanke,et al.  SATOOL - A SOFTWARE TOOL FOR STRUCTURAL ANALYSIS OF COMPLEX AUTOMATION SYSTEMS 1,2 , 2006 .

[6]  A. Vicino,et al.  Sequential approximation of feasible parameter sets for identification with set membership uncertainty , 1996, IEEE Trans. Autom. Control..

[7]  J. Norton,et al.  Bounding Approaches to System Identification , 1996 .

[8]  Jordi Saludes,et al.  Robust fault detection using polytope-based set-membership consistency test , 2009, 2010 Conference on Control and Fault-Tolerant Systems (SysTol).

[9]  Fault diagnosis of wind turbines using a set-membership approach , 2011 .

[10]  Vicenç Puig,et al.  Fault diagnosis and fault tolerant control using set-membership approaches: Application to real case studies , 2010, Int. J. Appl. Math. Comput. Sci..

[11]  Jie Chen,et al.  Robust Model-Based Fault Diagnosis for Dynamic Systems , 1998, The International Series on Asian Studies in Computer and Information Science.

[12]  P. Gahinet,et al.  H∞ design with pole placement constraints: an LMI approach , 1996, IEEE Trans. Autom. Control..

[13]  Vicenç Puig,et al.  Passive Robust Fault Detection of Dynamic Processes Using Interval Models , 2008, IEEE Transactions on Control Systems Technology.

[14]  Vicenç Puig,et al.  Identification for passive robust fault detection using zonotope‐based set‐membership approaches , 2011 .

[15]  Eduardo F. Camacho,et al.  Bounded error identification of systems with time-varying parameters , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[16]  Vicenç Puig,et al.  Worst-Case Simulation of Discrete Linear Time-Invariant Interval Dynamic Systems , 2003, Reliab. Comput..

[17]  Steven X. Ding,et al.  Model-based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools , 2008 .

[18]  Luc Jaulin,et al.  Applied Interval Analysis , 2001, Springer London.

[19]  Vicenç Puig,et al.  Robust Fault Diagnosis of Nonlinear Systems Using Interval Constraint Satisfaction and Analytical Redundancy Relations , 2014, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[20]  M. V. Iordache,et al.  Diagnosis and Fault-Tolerant Control , 2007, IEEE Transactions on Automatic Control.

[21]  Janos Gertler,et al.  Fault detection and diagnosis in engineering systems , 1998 .

[22]  A. Willsky,et al.  Analytical redundancy and the design of robust failure detection systems , 1984 .

[23]  Peter Fogh Odgaard,et al.  Fault Detection of Wind Turbines with Uncertain Parameters: A Set-Membership Approach , 2012 .

[24]  Vicenç Puig,et al.  Observer gain effect in linear interval observer-based fault detection , 2010, 2007 46th IEEE Conference on Decision and Control.

[25]  Seyedmojtaba Tabatabaeipour.  Active fault detection and isolation of discrete-time linear time-varying systems: a set-membership approach , 2015, Int. J. Syst. Sci..

[26]  Michèle Basseville,et al.  Detection of abrupt changes: theory and application , 1993 .

[27]  Damiano Rotondo,et al.  FDI and FTC of wind turbines using the interval observer approach and virtual actuators/sensors , 2014 .

[28]  J. Quevedo,et al.  Observers for Interval Systems using Set and Trajectory-based Approaches , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[29]  Stéphane Ploix,et al.  Parity relations for linear uncertain dynamic systems , 2006, Autom..

[30]  Vicenç Puig,et al.  ROBUST FAULT DETECTION USING INVERSE IMAGES OF INTERVAL FUNCTIONS , 2006 .