Active incipient fault detection in continuous time systems with multiple simultaneous faults

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2011, 1(2): 211-224. doi: 10.3934/naco.2011.1.211

Active incipient fault detection in continuous time systems with multiple simultaneous faults

Martene L. Fair ^1, and Stephen L. Campbell ^2,

1.	Department of Physics and Mathematics, Tennessee State University, Nashville, Tennessee, United States
2.	Department of Mathematics, North Carolina State University, Raleigh, North Carolina, United States

Received October 2010 Revised January 2011 Published June 2011

Abstract
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The problem of detecting small parameter variations in linear uncertain systems due to incipient faults, with the possibility of injecting an input signal to enhance detection, is considered. Most studies assume that there is only one fault developing. Recently an active approach for two or more simultaneous faults has been introduced for the discrete time case. In this paper we extend this approach to the continuous time case. A computational method for the construction of an input signal for achieving guaranteed detection with specified precision is presented. The method is an extension of a multi-model approach used for the construction of auxiliary signals for failure detection, however, new technical issues must be addressed.

Keywords: numerical methods., Fault detection.

Mathematics Subject Classification: Primary: 34H05; Secondary: 49N9.

Citation: Martene L. Fair, Stephen L. Campbell. Active incipient fault detection in continuous time systems with multiple simultaneous faults. Numerical Algebra, Control and Optimization, 2011, 1 (2) : 211-224. doi: 10.3934/naco.2011.1.211

References:

[1]	S. L. Campbell and C. D. Meyer Jr., "Generalized Inverses of Linear Transformations," SIAM Publishers, Philadelphia, PA, 2008.
[2]	S. L. Campbell and R. Nikoukhah, "Auxiliary signal design for failure detection," Princeton University Press, Princeton, 2004.
[3]	D. Choe, S. L Campbell and R. Nikoukhah, A comparison of optimal and suboptimal auxiliary signal design approaches for robust failure detection, IEEE Conference on Control Applications, Toronto, 2005.
[4]	S. L. Campbell, J. P. Chanclier and R. Nikoukhah, "Modeling and Simulation in Scilab/Scicos with ScicosLab 4.4," Second Edition, Springer, New York, 2010. doi: 10.1007/978-1-4419-5527-2.
[5]	D. Choe, S. L. Campbell and R. Nikoukhah, Optimal piecewise-constant signal design for active fault detection, International Journal of Control, 82 (2009), 130-146. doi: 10.1080/00207170801993587.
[6]	K. J. Drake, S. L. Campbell, I. Andjelkovic and K. Sweetingham, Active incipient failure detection: a nonlinear case study, Proc 4th International Conference on Computing, Communications and Control Technologies: CCCT '06, Orlando, 2006.
[7]	M. Y. Chow., "Methodologies of Using Neural Network and Fuzzy Logic Technologies for Motor Incipient Fault Detection," World Scientific Publishing Company, 1997. doi: 10.1142/9789812819383.
[8]	M. A. Demetriou and M. M. Polycarpou, Incipient fault diagnosis of dynamical systems using on-line approximators, IEEE Trans. Automatic Control, 43 (1998), 1612-1617. doi: 10.1109/9.728881.
[9]	M. Fair and S. L. Campbell, Active incipient fault detection with two simultaneous faults, Proc. 7th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes (Safeprocess 2009), Barcelona.
[10]	M. Fair and S. L. Campbell, Active incipient fault detection with more than two simultaneous faults, Proc. IEEE International Conference on Systems, Man, and Cybernetics, San Antonio, 2009.
[11]	P. V. Goode and M. Y. Chow, Using a neural/fuzzy system to extract knowledge of incipient fault in induction motors part I - methodology, IEEE Trans. Industrial Electronics, 42 (1995), 131-138. doi: 10.1109/41.370378.
[12]	P. V. Goode and M. Y. Chow, Using a neural/fuzzy system to extract knowledge of incipient fault in induction motors part II - application, IEEE Trans. Industrial Electronics, 42 (1995), 139-146. doi: 10.1109/41.370379.
[13]	R. Isermann, "Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance," Springer, Berlin, 2006.
[14]	B. Jiang, M. Staroswiecki and V. Cocquempot, Active fault tolerant control for a class of nonlinear systems, Proc. Safeprocess 2003, Washington, DC, 127-132.
[15]	F. Kerestecioglu and M. B. Zarrop, Input design for detection of abrupt changes in dynamical systems, International Journal of Control, 59 (1994), 1063-1084. doi: 10.1080/00207179408923118.
[16]	F. L. Lewis and V. L. Syrmos, "Optimal Control, Second Edition," Wiley, New York, 1995.
[17]	H. H. Niemann, A setup for active fault diagnosis, IEEE Transactions on Automatic Control, 51 (2006), 1572-1578. doi: 10.1109/TAC.2006.878724.
[18]	H. H. Niemann, Active fault diagnosis in closed-loop uncertain systems, 6th IFAC Symposium on Fault Detection Supervision and Safety for Technical Processes, SAFEPROCESS'2006, Beijing, China, 2006.
[19]	R. Nikoukhah and S. L. Campbell, Robust detection of incipient faults: an active approach, Proc. IEEE Med. Conf. Control and Automation, 2006.
[20]	R. Nikoukhah and S. L. Campbell, Auxiliary signal design for active failure detection in uncertain linear systems with a priori information, Automatica, 42 (2006), 219-228. doi: 10.1016/j.automatica.2005.09.011.
[21]	R. Nikoukhah and S. L. Campbell, On the detection of small parameter variations in linear uncertain systems, European J. Control, 14 (2008), 158-171. doi: 10.3166/ejc.14.158-171.
[22]	R. Nikoukhah, S. L. Campbell and K. J. Drake, An active approach for detection of incipient faults, International Journal Systems Science, 41 (2010), 241-257. doi: 10.1080/00207720903045817.
[23]	I. R. Petersen and D. C. McFarlane, A methodology for process fault detection, Proc. IEEE Conference Decision and Control, Phoenix, AZ, (1999), 4984-4989.
[24]	A. V. Savkin and I. R. Petersen, A new approach to model validation and fault diagnosis, J. Optimization Theory and Application, 94 (1997), 241-250. doi: 10.1023/A:1022676106903.
[25]	M. Simandl, I. Puncochar and J. Kralovec, Rolling horizon for active fault detection, Proc. of IEEE Conf. on Decision and Control and European Control Conf., Seville, Spain, 2005, 3789-3794. doi: 10.1109/CDC.2005.1582752.
[26]	M. Simandl and I. Puncochar, Unified solution of optimal active fault detection and optimal control, Proc. 2007 American Control Conference, New York, USA, 3222-3227. doi: 10.1109/ACC.2007.4282446.

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References:

[1]	S. L. Campbell and C. D. Meyer Jr., "Generalized Inverses of Linear Transformations," SIAM Publishers, Philadelphia, PA, 2008.
[2]	S. L. Campbell and R. Nikoukhah, "Auxiliary signal design for failure detection," Princeton University Press, Princeton, 2004.
[3]	D. Choe, S. L Campbell and R. Nikoukhah, A comparison of optimal and suboptimal auxiliary signal design approaches for robust failure detection, IEEE Conference on Control Applications, Toronto, 2005.
[4]	S. L. Campbell, J. P. Chanclier and R. Nikoukhah, "Modeling and Simulation in Scilab/Scicos with ScicosLab 4.4," Second Edition, Springer, New York, 2010. doi: 10.1007/978-1-4419-5527-2.
[5]	D. Choe, S. L. Campbell and R. Nikoukhah, Optimal piecewise-constant signal design for active fault detection, International Journal of Control, 82 (2009), 130-146. doi: 10.1080/00207170801993587.
[6]	K. J. Drake, S. L. Campbell, I. Andjelkovic and K. Sweetingham, Active incipient failure detection: a nonlinear case study, Proc 4th International Conference on Computing, Communications and Control Technologies: CCCT '06, Orlando, 2006.
[7]	M. Y. Chow., "Methodologies of Using Neural Network and Fuzzy Logic Technologies for Motor Incipient Fault Detection," World Scientific Publishing Company, 1997. doi: 10.1142/9789812819383.
[8]	M. A. Demetriou and M. M. Polycarpou, Incipient fault diagnosis of dynamical systems using on-line approximators, IEEE Trans. Automatic Control, 43 (1998), 1612-1617. doi: 10.1109/9.728881.
[9]	M. Fair and S. L. Campbell, Active incipient fault detection with two simultaneous faults, Proc. 7th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes (Safeprocess 2009), Barcelona.
[10]	M. Fair and S. L. Campbell, Active incipient fault detection with more than two simultaneous faults, Proc. IEEE International Conference on Systems, Man, and Cybernetics, San Antonio, 2009.
[11]	P. V. Goode and M. Y. Chow, Using a neural/fuzzy system to extract knowledge of incipient fault in induction motors part I - methodology, IEEE Trans. Industrial Electronics, 42 (1995), 131-138. doi: 10.1109/41.370378.
[12]	P. V. Goode and M. Y. Chow, Using a neural/fuzzy system to extract knowledge of incipient fault in induction motors part II - application, IEEE Trans. Industrial Electronics, 42 (1995), 139-146. doi: 10.1109/41.370379.
[13]	R. Isermann, "Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance," Springer, Berlin, 2006.
[14]	B. Jiang, M. Staroswiecki and V. Cocquempot, Active fault tolerant control for a class of nonlinear systems, Proc. Safeprocess 2003, Washington, DC, 127-132.
[15]	F. Kerestecioglu and M. B. Zarrop, Input design for detection of abrupt changes in dynamical systems, International Journal of Control, 59 (1994), 1063-1084. doi: 10.1080/00207179408923118.
[16]	F. L. Lewis and V. L. Syrmos, "Optimal Control, Second Edition," Wiley, New York, 1995.
[17]	H. H. Niemann, A setup for active fault diagnosis, IEEE Transactions on Automatic Control, 51 (2006), 1572-1578. doi: 10.1109/TAC.2006.878724.
[18]	H. H. Niemann, Active fault diagnosis in closed-loop uncertain systems, 6th IFAC Symposium on Fault Detection Supervision and Safety for Technical Processes, SAFEPROCESS'2006, Beijing, China, 2006.
[19]	R. Nikoukhah and S. L. Campbell, Robust detection of incipient faults: an active approach, Proc. IEEE Med. Conf. Control and Automation, 2006.
[20]	R. Nikoukhah and S. L. Campbell, Auxiliary signal design for active failure detection in uncertain linear systems with a priori information, Automatica, 42 (2006), 219-228. doi: 10.1016/j.automatica.2005.09.011.
[21]	R. Nikoukhah and S. L. Campbell, On the detection of small parameter variations in linear uncertain systems, European J. Control, 14 (2008), 158-171. doi: 10.3166/ejc.14.158-171.
[22]	R. Nikoukhah, S. L. Campbell and K. J. Drake, An active approach for detection of incipient faults, International Journal Systems Science, 41 (2010), 241-257. doi: 10.1080/00207720903045817.
[23]	I. R. Petersen and D. C. McFarlane, A methodology for process fault detection, Proc. IEEE Conference Decision and Control, Phoenix, AZ, (1999), 4984-4989.
[24]	A. V. Savkin and I. R. Petersen, A new approach to model validation and fault diagnosis, J. Optimization Theory and Application, 94 (1997), 241-250. doi: 10.1023/A:1022676106903.
[25]	M. Simandl, I. Puncochar and J. Kralovec, Rolling horizon for active fault detection, Proc. of IEEE Conf. on Decision and Control and European Control Conf., Seville, Spain, 2005, 3789-3794. doi: 10.1109/CDC.2005.1582752.
[26]	M. Simandl and I. Puncochar, Unified solution of optimal active fault detection and optimal control, Proc. 2007 American Control Conference, New York, USA, 3222-3227. doi: 10.1109/ACC.2007.4282446.

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