Configuring a sensor network for fault detection in distributed parameter systems

Maciej Patan; Dariusz Uciński

International Journal of Applied Mathematics and Computer Science (2008)

  • Volume: 18, Issue: 4, page 513-524
  • ISSN: 1641-876X

Abstract

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The problem of fault detection in distributed parameter systems (DPSs) is formulated as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A computational scheme is provided for the design of a network of observation locations in a spatial domain that are supposed to be used while detecting changes in the underlying parameters of a distributed parameter system. The setting considered relates to a situation where from among a finite set of potential sensor locations only a subset can be selected because of the cost constraints. As a suitable performance measure, the Ds-optimality criterion defined on the Fisher information matrix for the estimated parameters is applied. Then, the solution of a resulting combinatorial problem is determined based on the branch-and-bound method. As its essential part, a relaxed problem is discussed in which the sensor locations are given a priori and the aim is to determine the associated weights, which quantify the contributions of individual gauged sites. The concavity and differentiability properties of the criterion are established and a gradient projection algorithm is proposed to perform the search for the optimal solution. The delineated approach is illustrated by a numerical example on a sensor network design for a two-dimensional convective diffusion process.

How to cite

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Maciej Patan, and Dariusz Uciński. "Configuring a sensor network for fault detection in distributed parameter systems." International Journal of Applied Mathematics and Computer Science 18.4 (2008): 513-524. <http://eudml.org/doc/207904>.

@article{MaciejPatan2008,
abstract = {The problem of fault detection in distributed parameter systems (DPSs) is formulated as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A computational scheme is provided for the design of a network of observation locations in a spatial domain that are supposed to be used while detecting changes in the underlying parameters of a distributed parameter system. The setting considered relates to a situation where from among a finite set of potential sensor locations only a subset can be selected because of the cost constraints. As a suitable performance measure, the Ds-optimality criterion defined on the Fisher information matrix for the estimated parameters is applied. Then, the solution of a resulting combinatorial problem is determined based on the branch-and-bound method. As its essential part, a relaxed problem is discussed in which the sensor locations are given a priori and the aim is to determine the associated weights, which quantify the contributions of individual gauged sites. The concavity and differentiability properties of the criterion are established and a gradient projection algorithm is proposed to perform the search for the optimal solution. The delineated approach is illustrated by a numerical example on a sensor network design for a two-dimensional convective diffusion process.},
author = {Maciej Patan, Dariusz Uciński},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {branch-and-bound; constrained experimental design; distributed parameter systems; fault detection; parameter estimation; sensor location},
language = {eng},
number = {4},
pages = {513-524},
title = {Configuring a sensor network for fault detection in distributed parameter systems},
url = {http://eudml.org/doc/207904},
volume = {18},
year = {2008},
}

TY - JOUR
AU - Maciej Patan
AU - Dariusz Uciński
TI - Configuring a sensor network for fault detection in distributed parameter systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2008
VL - 18
IS - 4
SP - 513
EP - 524
AB - The problem of fault detection in distributed parameter systems (DPSs) is formulated as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A computational scheme is provided for the design of a network of observation locations in a spatial domain that are supposed to be used while detecting changes in the underlying parameters of a distributed parameter system. The setting considered relates to a situation where from among a finite set of potential sensor locations only a subset can be selected because of the cost constraints. As a suitable performance measure, the Ds-optimality criterion defined on the Fisher information matrix for the estimated parameters is applied. Then, the solution of a resulting combinatorial problem is determined based on the branch-and-bound method. As its essential part, a relaxed problem is discussed in which the sensor locations are given a priori and the aim is to determine the associated weights, which quantify the contributions of individual gauged sites. The concavity and differentiability properties of the criterion are established and a gradient projection algorithm is proposed to perform the search for the optimal solution. The delineated approach is illustrated by a numerical example on a sensor network design for a two-dimensional convective diffusion process.
LA - eng
KW - branch-and-bound; constrained experimental design; distributed parameter systems; fault detection; parameter estimation; sensor location
UR - http://eudml.org/doc/207904
ER -

References

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  1. Amouroux M. and Babary J. P. (1988). Sensor and control location problems, in M. G. Singh (Ed), Systems & Control Encyclopedia. Theory, Technology, Applications, Vol. 6, Pergamon Press, Oxford, pp. 4238-4245. 
  2. Atkinson A. C., Donev A. N. and Tobias R. (2007). Optimum Experimental Design, with SAS, Oxford University Press, Oxford. Zbl1183.62129
  3. Bernstein D. S. (2005). Matrix Mathematics. Theory, Facts, and Formulas with Application to Linear Systems Theory, Princeton University Press, Princeton, NJ. Zbl1075.15001
  4. Bertsekas D. P. (1999). Nonlinear Programming, 2nd Edn, Athena Scientific, Belmont, MA. Zbl1015.90077
  5. Boer E. P. J., Hendrix E. M. T. and Rasch D. A. M. K. (2001). Optimization of monitoring networks for estimation of the semivariance function, in A. C. Atkinson, P. Hackl and W. Müller (Eds), mODa 6, Proceedings of the 6th International Workshop on Model-Oriented Data Analysis, Puchberg/Schneeberg, Austria, Physica-Verlag, Heidelberg, pp. 21-28. 
  6. Boyd S. and Vandenberghe L. (2004). Convex Optimization, Cambridge University Press, Cambridge. Zbl1058.90049
  7. Cassandras C. G. and Li W. (2005). Sensor networks and cooperative control, European Journal of Control 11(4-5): 436-463. Zbl1293.93069
  8. Chiang L. H., Russell E. L. and Braatz R. D. (2001). Fault Detection and Diagnosis in Industrial Systems, Springer-Verlag, London. Zbl0982.93005
  9. Fedorov V. V. and Hackl P. (1997). Model-Oriented Design of Experiments, Lecture Notes in Statistics, Springer-Verlag, New York, NY. Zbl0878.62052
  10. Floudas C. A. (2001). Mixed integer nonlinear programming, MINLP, in C. A. Floudas and P. M. Pardalos (Eds), Encyclopedia of Optimization, Kluwer Academic Publishers, Dordrecht, Vol. 3, pp. 401-414. 
  11. Gerdts M. (2005). Solving mixed-integer optimal control problems by branch&bound: A case study from automobile test-driving with gear shift, Journal of Optimization Theory and Applications 26: 1-18. 
  12. Isermann R. (1997). Supervision, Fault Detection and Diagnosis of Technical Systems, Control Engineering Practice 5(5): 639-652. 
  13. Korbicz J., Kościelny J., Kowalczuk Z. and Cholewa W. (2004). Fault Diagnosis. Models, Artificial Intelligence, Applications, Springer-Verlag, Berlin. Zbl1074.93004
  14. Kubrusly C. S. and Malebranche H. (1985). Sensors and controllers location in distributed systems - A survey, Automatica 21(2): 117-128. Zbl0555.93035
  15. Maculan N., Santiago C. P., Macambira E. M. and Jardim M. H. C. (2003). An O(n) algorithm for projecting a vector on the intersection of a hyperplane and a box in Rn, Journal of Optimization Theory and Applications 117(3): 553-574. Zbl1115.90397
  16. Omatu S. and Seinfeld J. H. (1989). Distributed Parameter Systems: Theory and Applications, Oxford University Press, New York, NY. Zbl0675.93001
  17. Patan M. (2004). Optimal Observation Strategies for Parameter Estimation of Distributed Systems, Zielona Góra University Press. Accessible at http://www.zbc.zgora.pl. Zbl1104.93011
  18. Patan M. and Patan K. (2005). Optimal observation strategies for model-based fault detection in distributed systems, International Journal of Control 78(18): 1497-1510. Zbl1122.93018
  19. Patan M., Uciński D. and Baranowski P. (2005). Optimal observation strategies for fault detection in distributedparameter systems, Pomiary, Automatyka, Kontrola (9): 71-73. 
  20. Patton R. J., Frank P. M. and Clark R. (2000). Issues of Fault Diagnosis for Dynamic Systems, Springer-Verlag, Berlin. 
  21. Patton R. J. and Korbicz J. (Eds.) (1999). Advances in Computational Intelligence, International Journal of Applied Mathematics and Computer Science 9 (3). Zbl0932.00017
  22. Pázman A. (1986). Foundations of Optimum Experimental Design, D. Reidel Publishing Company, Dordrecht. Zbl0588.62117
  23. Pukelsheim F. (1993). Optimal Design of Experiments, John Wiley & Sons, New York, NY. Zbl0834.62068
  24. Quereshi Z. H., Ng T. S. and Goodwin G. C. (1980). Optimum experimental design for identification of distributed parameter systems, International Journal of Control 31(1): 21-29. Zbl0431.93017
  25. Rafajłowicz E. (1981). Design of experiments for eigenvalue identification in distributed-parameter systems, International Journal of Control 34(6): 1079-1094. Zbl0476.93071
  26. Rafajłowicz E. (1983). Optimal experiment design for identification of linear distributed-parameter systems: Frequency domain approach, IEEE Transactions on Automatic Control 28(7): 806-808. Zbl0521.93066
  27. Reinefeld A. (2001). Heuristic search, in C. A. Floudas and P. M. Pardalos (Eds), Encyclopedia of Optimization, Kluwer Academic Publishers, Dordrecht, Vol. 2, pp. 409-411. 
  28. Russell S. J. and Norvig P. (2003). Artificial Intelligence: A Modern Approach, 2nd Edn, Pearson Education International, Upper Saddle River, NJ. Zbl0835.68093
  29. Sun N.-Z. (1994). Inverse Problems in Groundwater Modeling, Kluwer Academic Publishers, Dordrecht. 
  30. Uciński D. (1992). Optimal sensor location for parameter identification of distributed systems, International Journal of Applied Mathematics and Computer Science 2(1): 119-134. Zbl0762.93022
  31. Uciński D. (1999). Measurement Optimization for Parameter Estimation in Distributed Systems, Technical University Press, Zielona Góra. Available at http://www.zbc.zgora.pl. 
  32. Uciński D. (2000). Optimal selection of measurement locations for parameter estimation in distributed processes, International Journal of Applied Mathematics and Computer Science 10(2): 357-379. Zbl0965.93041
  33. Uciński D. (2003). On optimum experimental design for technical diagnostics of processes, in Z. Kowalczuk (Ed), Proceedings of 6-th National Conference on Diagnostics of Industrial Processes, Władysławowo, Poland, Technical University Press, Gdańsk, pp. 207-212, (in Polish). 
  34. Uciński D. (2005). Optimal Measurement Methods for Distributed-Parameter System Identification, CRC Press, Boca Raton, FL. Zbl1155.93003
  35. Uciński D. and Patan M. (2007). D-optimal design of a monitoring network for parameter estimation of distributed systems, Journal of Global Optimization 39(2): 291-322. Zbl1180.90173
  36. van de Wal M. and de Jager B. (2001). A review of methods for input/output selection, Automatica 37(4): 487-510. Zbl0995.93002
  37. Walter É. and Pronzato L. (1997). Identification of Parametric Models from Experimental Data, Communications and Control Engineering, Springer-Verlag, Berlin. Zbl0864.93014

Citations in EuDML Documents

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  1. Jean-Philippe Georges, Didier Theilliol, Vincent Cocquempot, Jean-Christophe Ponsart, Christophe Aubrun, Fault tolerance in networked control systems under intermittent observations
  2. Dariusz Uciński, Maciej Patan, Sensor network design for the estimation of spatially distributed processes
  3. Maciej Patan, Distributed scheduling of sensor networks for identification of spatio-temporal processes
  4. Dariusz Uciński, Sensor network scheduling for identification of spatially distributed processes

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