# A Model-Based Fault Detection and Diagnosis Scheme for Distributed Parameter Systems: A Learning Systems Approach

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 7, page 43-67
- ISSN: 1292-8119

## Access Full Article

top## Abstract

top## How to cite

topDemetriou, Michael A.. "A Model-Based Fault Detection and Diagnosis Scheme for Distributed Parameter Systems: A Learning Systems Approach." ESAIM: Control, Optimisation and Calculus of Variations 7 (2010): 43-67. <http://eudml.org/doc/90630>.

@article{Demetriou2010,

abstract = {
In this note, fault detection techniques based on finite dimensional
results are extended and applied to a class of infinite dimensional
dynamical systems. This special class of systems assumes linear
plant dynamics having an abrupt additive perturbation as the fault.
This fault is assumed to be linear in the (unknown) constant (and possibly
functional) parameters.
An observer-based model estimate is proposed which serves
to monitor the system's dynamics for unanticipated failures,
and its well posedness is summarized.
Using a Lyapunov synthesis approach extended and applied to infinite
dimensional systems, a stable adaptive fault diagnosis
(fault parameter learning) scheme is developed. The resulting parameter
adaptation rule is able to “sense” the instance of the fault occurrence.
In addition, it identifies the fault parameters using the additional
assumption of persistence of excitation. Extension of the adaptive
monitoring scheme to incipient faults (time varying faults) is summarized.
Simulations studies are used to illustrate the applicability
of the theoretical results.
},

author = {Demetriou, Michael A.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Fault detection; distributed parameter systems.; distributed parameter systems; fault detection},

language = {eng},

month = {3},

pages = {43-67},

publisher = {EDP Sciences},

title = {A Model-Based Fault Detection and Diagnosis Scheme for Distributed Parameter Systems: A Learning Systems Approach},

url = {http://eudml.org/doc/90630},

volume = {7},

year = {2010},

}

TY - JOUR

AU - Demetriou, Michael A.

TI - A Model-Based Fault Detection and Diagnosis Scheme for Distributed Parameter Systems: A Learning Systems Approach

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 7

SP - 43

EP - 67

AB -
In this note, fault detection techniques based on finite dimensional
results are extended and applied to a class of infinite dimensional
dynamical systems. This special class of systems assumes linear
plant dynamics having an abrupt additive perturbation as the fault.
This fault is assumed to be linear in the (unknown) constant (and possibly
functional) parameters.
An observer-based model estimate is proposed which serves
to monitor the system's dynamics for unanticipated failures,
and its well posedness is summarized.
Using a Lyapunov synthesis approach extended and applied to infinite
dimensional systems, a stable adaptive fault diagnosis
(fault parameter learning) scheme is developed. The resulting parameter
adaptation rule is able to “sense” the instance of the fault occurrence.
In addition, it identifies the fault parameters using the additional
assumption of persistence of excitation. Extension of the adaptive
monitoring scheme to incipient faults (time varying faults) is summarized.
Simulations studies are used to illustrate the applicability
of the theoretical results.

LA - eng

KW - Fault detection; distributed parameter systems.; distributed parameter systems; fault detection

UR - http://eudml.org/doc/90630

ER -

## References

top- A. Ackleh, M.A. Demetriou and S. Reich, Detection and accommodation of second order distributed parameter systems with abrupt changes in input term: Existence and approximation, in Proc. of the 6th IEEE Mediterranean Conference on Control and Systems. Alghero, Sardinia (1998). Zbl1249.93068
- A.S. Ackleh, S. Aizicovici, M.A. Demetriou and S. Reich, Existence and uniqueness of solutions to a second order nonlinear nonlocal hyperbolic equation, in Proc. of International Workshop on Differential Equations and Optimal Control. Marcel Dekker (2001). Zbl1052.35137
- R.A. Adams, Sobolev Spaces. Academic Press, New York (1975).
- N.U. Ahmed and K.L. Teo, Optimal Control of Distributed Parameter Systems. North Holland, New York (1981). Zbl0472.49001
- A.M. Annaswamy and K.S. Narendra, Adaptive control of a first order plant with time-varying parameter, in Proc. of the 1989 American Control Conference (1989) 975-980.
- height 2pt depth -1.6pt width 23pt, Adaptive control of simple time-varying systems, in Proc. of the 28th IEEE Conference on Decision and Control. Tampa, Florida (1989) 1014-1018.
- O. Axelsson and V.A. Barker, Finite Element Solutions of Boundary Value Problems. Academic Press, Orlando, Florida (1984). Zbl0537.65072
- M.J. Balas, Finite dimensional direct adaptive control for discrete-time infinite dimensional linear systems, in Proc. of the 33rd IEEE Conference on Decision and Control. Lake Buena Vista, FL, USA (1994) 3424-3429.
- H.T. Banks and M.A. Demetriou, Adaptive parameter estimation of hyperbolic distributed parameter systems: Non-symmetric damping and slowly time varying systems. ESAIM: COCV3 (1998) 133-162. Zbl1052.93506
- H.T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems. Birkhäuser, Boston (1989). Zbl0695.93020
- H.T. Banks, R.C. Smith and Y. Wang, Smart Material Structures: Modeling, Estimation and Control. Wiley, Masson, Paris (1996). Zbl0882.93001
- M. Basseville and I. Nikiforov, Detection of abrupt changes: Theory and applications. Prentice Hall, Englewood Cliffs, New Jersey (1993).
- J. Baumeister, W. Scondo, M.A. Demetriou and I.G. Rosen, On-line parameter estimation for infinite dimensional dynamical systems. SIAM J. Control Optim.35 (1997) 678-713. Zbl0873.93026
- A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and Control of Infinite Dimensional Systems, Vols. I, II. Birkauser, Boston-Basel-Berlin (1992). Zbl0781.93002
- M. Böhm, M.A. Demetriou, I.G. Rosen and S. Reich, Model reference adaptive control of distributed parameter systems. SIAM J. Control Optim. 36 (1998). Zbl0919.93044
- S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York (1994). Zbl0804.65101
- C.D. Charalambous and J. Hibey, Conditional densities for continous-time nonlinear hybrid systems with applications to fault detection. IEEE Trans. Automat. Control44 (1999) 2164-2169. Zbl1136.93448
- R.F. Curtain and J.C. Oostveen, Riccati equations for strongly stable, bounded linear systems. Automatica34 (1998) 953-967. Zbl0979.93092
- R.F. Curtain and H.J. Zwart, An Introduction to Infinite Dimensional Linear Systems Theory. Springer-Verlag, Berlin, Texts Appl. Math. 21 (1995). Zbl0839.93001
- M.A. Demetriou, Adaptive Parameter Estimation of Abstract Parabolic and Hyperbolic Distributed Parameter Systems, Ph.D. Thesis, Department of Electrical Engineering - Systems. University of Southern California, Los Angeles, California (1993).
- height 2pt depth -1.6pt width 23pt, Model reference adaptive control of slowly time-varying parabolic distributed parameter systems, in Proc. of the 33rd Conference on Decision and Control. Lake Buena Vista, Florida (1994).
- height 2pt depth -1.6pt width 23pt, Fault diagnosis for a parabolic distributed parameter system, in Proc. of the 13th World Congress. International Federation of Automatic Control, San Francisco, California, July (1996).
- M.A. Demetriou and B.G. Fitzpatrick, On line estimation of stiffness in nonlinear beam models with piezoceramic actuators, in Proc. of the 1995 ASME Fifteenth Biennial Conference on Mechanical Vibration and Noise & 1995 ASME Design Technical Conferences. Boston, Mass (1995).
- height 2pt depth -1.6pt width 23pt, Results on the adaptive estimation of stiffness in nonlinear beam models, in Proc. of the 3rd IEEE Mediterranean Symposium on New Directions in Control and Automation. Limassol, CYPRUS (1995).
- height 2pt depth -1.6pt width 23pt, An adaptive change detection scheme for a nonlinear beam model. Kybernetika33 (1997) 103-120.
- M.A. Demetriou and M.M. Polycarpou, Fault accommodation of output-induced actuator failures for a flexible beam with collocated input and output, in Proc. of the 5th IEEE Mediterranean Conference on Control and Systems. Paphos, CYPRUS (1997).
- height 2pt depth -1.6pt width 23pt, Fault detection and diagnosis of a class of actuator failures via on-line approximators, in Proc. of the 1997 36th IEEE Conference on Decision and Control. San Diego, CA (1997).
- height 2pt depth -1.6pt width 23pt, Fault diagnosis of output-induced actuator failures for a flexible beam with collocated input and output, in Proc. of the IFAC Symposium on Fault Detection, Supervision and Safety for Processes (SAFEPROCESS). Hull, England (1997).
- height 2pt depth -1.6pt width 23pt, Fault detection, diagnosis and accommodation of dynamical systems with actuator failures via on-line approximators, in Proc. of the 1998 American Control Conference. Philadelphia, PA (1998).
- height 2pt depth -1.6pt width 23pt, Incipient fault diagnosis of dynamical systems using on-line approximators. IEEE Trans. Automat. Control43 (1998) 1612-1617. Zbl0957.90037
- M.A. Demetriou and I.G. Rosen, On the persistence of excitation in the adaptive identification of distributed parameter systems. IEEE Trans. Automat. Control39 (1994) 1117-1123. Zbl0825.93314
- height 2pt depth -1.6pt width 23pt, Robust adaptive estimation schemes for parabolic distributed parameter systems, in Proc. of the 36th Conference on Decision and Control. San Diego, California, USA (1997) 3448-3453.
- P.M. Frank, Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy - a survey and some new results. Automatica26 (1990) 459-474. Zbl0713.93052
- J.J. Gertler, Survey of model-based failure detection and isolation in complex plants. IEEE Control System Magazine8 (1988) 3-11.
- J.J. Gertler, Fault Detection and Diagnosis in Engineering Systems. Marcel Dekker, New York (1998).
- M. Green and D.J. Limebeer, Linear Robust Control. Prentice Hall, Englewood Cliffs, New Jersey (1995). Zbl0951.93500
- P.A. Ioannou and J. Sun, Robust Adaptive Control. Prentice Hall, Englewood Cliffs, NJ (1995). Zbl0747.93048
- R. Isermann, Process fault detection based on modeling and estimation methods: A survey. Automatica20 (1984) 387-404. Zbl0539.90037
- B.V. Keulen, ${H}_{\infty}$-Control for Distributed Parameter Systems: A State-Space Approach. Birkhäuser, Boston-Basel-Berlin (1993).
- T. Kobayashi, Global adaptive stabilization of infinite-dimensional systems. Systems Control Lett.9 (1987) 215-223. Zbl0628.93051
- height 2pt depth -1.6pt width 23pt, Finite dimensional adaptive control for infinite dimensional systems. Internat. J. Control48 (1988) 289-302.
- height 2pt depth -1.6pt width 23pt, Input-output representations of spectral systems and adaptive controls. Internat. J. Systems Sci.19 (1988) 713-732.
- M. Krstic, I. Kanellakopoulos and P. Kokotovic, Nonlinear and adaptive control design. Wiley, New York (1995). Zbl0763.93043
- J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations. Springer-Verlag, New York (1971).
- J.L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems, I. Springer-Verlag, New York (1972). Zbl0223.35039
- G.P. Liu and R.J. Patton, Eigenstructure Assignment for Control System Design. John Wiley & Sons, Chichester (1998).
- D.G. Luenberger, An introduction to observers. IEEE Trans. Automat. Control16 (1971) 596-602.
- K.S. Narendra and A.M. Annaswamy, Stable Adaptive Systems. Prentice Hall, Englewood Cliffs, NJ (1989). Zbl0758.93039
- R.J. Patton, Robust model-based fault diagnosis: The state of the art, in Proc. of the IFAC Symposium on Fault Detection, Supervision and Safety for Processes (SAFEPROCESS). Espoo, Finland (1994) 1-24.
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York (1983). Zbl0516.47023
- M.M. Polycarpou and A.J. Helmicki, Automated fault detection and accomodation: A learning systems approach. IEEE Trans. Systems Man Cybernet.25 (1995) 1447-1458.
- M.M. Polycarpou and P.A. Ioannou, Neural networks as on-line approximators of nonlinear systems, in Proc. of the 31st IEEE Conference on Decision and Control. San Antonio, Texas (1993) 7-12.
- height 2pt depth -1.6pt width 23pt, Stable nonlinear system identification using neural network models, in Neural Networks in Robotics, edited by G. Bekey and K. Goldberg. Kluwer Academic Publishers (1993) 147-164.
- M.M. Polycarpou and A.T. Vemuri, Learning methodology for failure detection and accomodation. Control Systems Magazine, special issue on Intelligent Learning Control 15 (1995) 16-24.
- V.M. Popov, Hyperstability of Control Systems. Springer-Verlag, Berlin (1973). Zbl0276.93033
- L. Praly, G. Bastin, J.B. Pomet and Z.P. Jiang, Adaptive stabilization of nonlinear systems, in Foundations of Adaptive Control, edited by P.V. Kokotovic. Springer-Verlag (1991) 347-433. Zbl0787.93083
- M.H. Schultz, Spline Analysis. Prentice-Hall, Englewood Cliffs, NJ (1973). Zbl0333.41009
- L.F. Shampine, Numerical Solution of Ordinary Differential Equations. Chapman & Hall, New York (1994). Zbl0832.65063
- R.E. Showalter, Hilbert Space Methods for Partial Differential Equations. Pitman, London (1977). Zbl0364.35001
- H. Tanabe, Equations of Evolution. Pitman, London (1979). Zbl0417.35003
- S. Townley, Simple adaptive stabilization of output feedback stabilizable distributed parameter systems. Dynam. Control5 (1995) 107-123. Zbl0820.93060
- K.S. Tsakalis and P.A. Ioannou, Time-Varying Systems: Control and Adaptation. Prentice Hall, Englewood Cliff, NJ (1993). Zbl0795.93001
- J. Wen and M. Balas, Robust adaptive control in Hilbert space. J. Math. Anal. Appl.143 (1989) 1-26. Zbl0701.93086
- J. Wloka, Partial Differential Equations. Cambridge University Press, Cambridge (1987). Zbl0623.35006

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.