# On infinite horizon active fault diagnosis for a class of non-linear non-Gaussian systems

Ivo Punčochář; Miroslav Šimandl

International Journal of Applied Mathematics and Computer Science (2014)

- Volume: 24, Issue: 4, page 795-807
- ISSN: 1641-876X

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topIvo Punčochář, and Miroslav Šimandl. "On infinite horizon active fault diagnosis for a class of non-linear non-Gaussian systems." International Journal of Applied Mathematics and Computer Science 24.4 (2014): 795-807. <http://eudml.org/doc/271900>.

@article{IvoPunčochář2014,

abstract = {The paper considers the problem of active fault diagnosis for discrete-time stochastic systems over an infinite time horizon. It is assumed that the switching between a fault-free and finitely many faulty conditions can be modelled by a finite-state Markov chain and the continuous dynamics of the observed system can be described for the fault-free and each faulty condition by non-linear non-Gaussian models with a fully observed continuous state. The design of an optimal active fault detector that generates decisions and inputs improving the quality of detection is formulated as a dynamic optimization problem. As the optimal solution obtained by dynamic programming requires solving the Bellman functional equation, approximate techniques are employed to obtain a suboptimal active fault detector.},

author = {Ivo Punčochář, Miroslav Šimandl},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {active fault detection; non-linear stochastic systems; optimal input design; dynamic programming; nonlinear stochastic systems},

language = {eng},

number = {4},

pages = {795-807},

title = {On infinite horizon active fault diagnosis for a class of non-linear non-Gaussian systems},

url = {http://eudml.org/doc/271900},

volume = {24},

year = {2014},

}

TY - JOUR

AU - Ivo Punčochář

AU - Miroslav Šimandl

TI - On infinite horizon active fault diagnosis for a class of non-linear non-Gaussian systems

JO - International Journal of Applied Mathematics and Computer Science

PY - 2014

VL - 24

IS - 4

SP - 795

EP - 807

AB - The paper considers the problem of active fault diagnosis for discrete-time stochastic systems over an infinite time horizon. It is assumed that the switching between a fault-free and finitely many faulty conditions can be modelled by a finite-state Markov chain and the continuous dynamics of the observed system can be described for the fault-free and each faulty condition by non-linear non-Gaussian models with a fully observed continuous state. The design of an optimal active fault detector that generates decisions and inputs improving the quality of detection is formulated as a dynamic optimization problem. As the optimal solution obtained by dynamic programming requires solving the Bellman functional equation, approximate techniques are employed to obtain a suboptimal active fault detector.

LA - eng

KW - active fault detection; non-linear stochastic systems; optimal input design; dynamic programming; nonlinear stochastic systems

UR - http://eudml.org/doc/271900

ER -

## References

top- Andjelkovic, I., Sweetingham, K. and Campbell, S.L. (2008). Active fault detection in nonlinear systems using auxiliary signals, Proceedings of the 2008 American Control Conference, Seattle, WA, USA, pp. 2142-2147.
- Ashari, A.E., Nikoukhah, R. and Campbell, S.L. (2012a). Active robust fault detection in closed-loop systems: Quadratic optimization approach, IEEE Transactions on Automatic Control 57(10): 2532-2544.
- Ashari, A.E., Nikoukhah, R. and Campbell, S.L. (2012b). Effects of feedback on active fault detection, Automatica 48(5): 866-872. Zbl1246.93053
- Åström, K.J. (1965). Optimal control of Markov processes with incomplete state information, Journal of Mathematical Analysis and Applications 10(1): 174-205. Zbl0137.35803
- Atkinson, A.C. and Donev, A.N. (1992). Optimum Experimental Designs, Oxford University Press, New York, NY. Zbl0829.62070
- Bar-Shalom, Y. (1981). Stochastic dynamic programming: Caution and probing, IEEE Transactions on Automatic Control 26(5): 1184-1194. Zbl0472.93071
- Basseville, M. and Nikiforov, I.V. (1993). Detection of Abrupt Changes-Theory and Application, Prentice Hall, Englewood Cliffs, NJ.
- Bertsekas, D.P. (1995). Dynamic Programming and Optimal Control, Volume I, Athena Scientific, Belmont, MA. Zbl0904.90170
- Blackmore, L., Rajamanoharan, S. and Williams, B.C. (2008). Active estimation for jump Markov linear systems, IEEE Transactions on Automatic Control 53(10): 2223-2236.
- Buşoniu, L., Babuška, R., Schutter, B.D. and Ernst, D. (2010). Reinforcement Learning and Dynamic Programming Using Function Approximators, CRC Press, Boca Raton, FL. Zbl1191.49027
- Campbell, S.L. and Nikoukhah, R. (2004). Auxiliary Signal Design for Failure Detection, Princeton University Press, Princeton, NJ. Zbl1055.94036
- Denardo, E.V. (2003). Dynamic Programming: Models and Applications, Dover Publications, Mineola, NY. Zbl1029.90075
- Efron, B. and Tibshirani, R.J. (1994). An Introduction to the Bootstrap, Chapman and Hall, New York, NY. Zbl0835.62038
- Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011). Statistical Distributions, 4th Edn., John Wiley & Sons, Inc., Hoboken, NJ. Zbl1258.62012
- Garces, F., Becerra, V.M., Kambhampati, C. and Warwick, K. (2003). Strategies for Feedback Linearisation-A Dynamic Neural Network Approach, Springer-Verlag, London.
- Goodwin, G.C. and Payne, R.L. (1977). Dynamic System Identification: Experiment Design and Data Analysis, Academic Press, New York, NY. Zbl0578.93060
- Isermann, R. (2006). Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance, Springer, Berlin.
- Julier, S.J. and Uhlmann, J.K. (1997). New extension of the Kalman filter to nonlinear systems, Proceedings of the 1997 SPIE Conference on Signal Processing, Sensor Fusion, and Target Recognition, Orlando, FL, USA, pp. 182-193.
- Kerestecioğlu, F. (1993). Change Detection and Input Design in Dynamical Systems, Research Studies Press, Taunton. Zbl0842.93004
- Kiefer, J.C. (1959). Optimum experimental designs, Journal of the Royal Statistical Society (Series B) 21(2): 272-319. Zbl0108.15303
- Lee, J.M., Kaisare, N.S. and Lee, J.H. (2006). Choice of approximator and design of penalty function for an approximate dynamic programming based control approach, Journal of Process Control 16(2): 135-156.
- Mehra, R.K. (1974). Optimal input signals for parameter estimation in dynamic systems-Survey and new results, IEEE Transactions on Automatic Control 19(6): 753-768. Zbl0291.93054
- Nett, C.N. (1986). Algebraic aspects of linear control system stability, IEEE Transactions on Automatic Control 31(10): 941-949. Zbl0604.93051
- Niemann, H.H. (2006). A setup for active fault diagnosis, IEEE Transactions on Automatic Control 51(9): 1572-1578.
- Niemann, H.H. (2012). A model-based approach to fault-tolerant control, International Journal of Applied Mathematics and Computer Science 22(1): 67-86, DOI: 10.2478/v10006-012-0005-x. Zbl1273.93053
- Poulsen, N.K. and Niemann, H. (2008). Active fault diagnosis based on stochastic tests, International Journal of Applied Mathematics and Computer Science 18(4): 487-496, DOI: 10.2478/v10006-008-0043-6. Zbl1155.93427
- Powell, W.B. (2007). Approximate Dynamic Programming: Solving the Curses of Dimensionality, Wiley-Interscience, Hoboken, NJ. Zbl1156.90021
- Puig, V. (2010). Fault diagnosis and fault tolerant control using set-membership approaches: Application to real case studies, International Journal of Applied Mathematics and Computer Science 20(4): 619-635, DOI: 10.2478/v10006-010-0046-y. Zbl1214.93061
- Puterman, M.L. (2005). Markov Decision Processes-Discrete Stochastic Dynamic Programming, John Wiley & Sons, Hoboken, NJ. Zbl1184.90170
- Scola, H.R., Nikoukhah, R. and Delebecque, F. (2003). Test signal design for failure detection: A linear programming approach, International Journal of Applied Mathematics and Computer Science 13(4): 515-526. Zbl1049.93032
- Scott, J.K., Findeisen, R., Braatz, R.D. and Raimondo, D.M. (2013). Design of active inputs for set-based fault diagnosis, Proceedings of the 2013 American Control Conference, Washington, DC, USA, pp. 3561-3566.
- Šimandl, M., Královec, J. and Söderström, T. (2006). Advanced point-mass method for nonlinear state estimation, Automatica 42(7): 1133-1145. Zbl1118.93052
- Šimandl, M. and Punčochář, I. (2009). Active fault detection and control: Unified formulation and optimal design, Automatica 45(9): 2052-2059. Zbl1175.93237
- Šimandl, M., Punčochář, I. and Královec, J. (2005). Rolling horizon for active fault detection, Proceedings of the 44th IEEE Conference on Decision and Control/European Control Conference 2005, Seville, Spain, pp. 3789-3794.
- Široký, J., Šimandl, M., Axehill, D. and Punčochář, I. (2011). An optimization approach to resolve the competing aims of active fault detection and control, Proceedings of the 50th IEEE Conference on Decision and Control/European Control Conference, Orlando, FL, USA, pp. 3712-3717.
- Zhang, X.J. (1989). Auxiliary Signal Design in Fault Detection and Diagnosis, Springer-Verlag, Berlin. Zbl0679.68207

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