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2008 | 18 | 4 | 513-524
Tytuł artykułu

Configuring a sensor network for fault detection in distributed parameter systems

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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.
Opis fizyczny
  • Institute of Control and Computation Engineering, University of Zielona Góra, ul. Podgórna 50, 65-246 Zielona Góra, Poland
  • Institute of Control and Computation Engineering, University of Zielona Góra, ul. Podgórna 50, 65-246 Zielona Góra, Poland
  • 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.
  • Atkinson A. C., Donev A. N. and Tobias R. (2007). Optimum Experimental Design, with SAS, Oxford University Press, Oxford.
  • Bernstein D. S. (2005). Matrix Mathematics. Theory, Facts, and Formulas with Application to Linear Systems Theory, Princeton University Press, Princeton, NJ.
  • Bertsekas D. P. (1999). Nonlinear Programming, 2nd Edn, Athena Scientific, Belmont, MA.
  • 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.
  • Boyd S. and Vandenberghe L. (2004). Convex Optimization, Cambridge University Press, Cambridge.
  • Cassandras C. G. and Li W. (2005). Sensor networks and cooperative control, European Journal of Control 11(4-5): 436-463.
  • Chiang L. H., Russell E. L. and Braatz R. D. (2001). Fault Detection and Diagnosis in Industrial Systems, Springer-Verlag, London.
  • Fedorov V. V. and Hackl P. (1997). Model-Oriented Design of Experiments, Lecture Notes in Statistics, Springer-Verlag, New York, NY.
  • 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.
  • 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.
  • Isermann R. (1997). Supervision, Fault Detection and Diagnosis of Technical Systems, Control Engineering Practice 5(5): 639-652.
  • Korbicz J., Kościelny J., Kowalczuk Z. and Cholewa W. (2004). Fault Diagnosis. Models, Artificial Intelligence, Applications, Springer-Verlag, Berlin.
  • Kubrusly C. S. and Malebranche H. (1985). Sensors and controllers location in distributed systems - A survey, Automatica 21(2): 117-128.
  • 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.
  • Omatu S. and Seinfeld J. H. (1989). Distributed Parameter Systems: Theory and Applications, Oxford University Press, New York, NY.
  • Patan M. (2004). Optimal Observation Strategies for Parameter Estimation of Distributed Systems, Zielona Góra University Press. Accessible at
  • 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.
  • Patan M., Uciński D. and Baranowski P. (2005). Optimal observation strategies for fault detection in distributedparameter systems, Pomiary, Automatyka, Kontrola (9): 71-73.
  • Patton R. J., Frank P. M. and Clark R. (2000). Issues of Fault Diagnosis for Dynamic Systems, Springer-Verlag, Berlin.
  • Patton R. J. and Korbicz J. (Eds.) (1999). Advances in Computational Intelligence, International Journal of Applied Mathematics and Computer Science 9 (3).
  • Pázman A. (1986). Foundations of Optimum Experimental Design, D. Reidel Publishing Company, Dordrecht.
  • Pukelsheim F. (1993). Optimal Design of Experiments, John Wiley & Sons, New York, NY.
  • 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.
  • Rafajłowicz E. (1981). Design of experiments for eigenvalue identification in distributed-parameter systems, International Journal of Control 34(6): 1079-1094.
  • 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.
  • 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.
  • Russell S. J. and Norvig P. (2003). Artificial Intelligence: A Modern Approach, 2nd Edn, Pearson Education International, Upper Saddle River, NJ.
  • Sun N.-Z. (1994). Inverse Problems in Groundwater Modeling, Kluwer Academic Publishers, Dordrecht.
  • Uciński D. (1992). Optimal sensor location for parameter identification of distributed systems, International Journal of Applied Mathematics and Computer Science 2(1): 119-134.
  • Uciński D. (1999). Measurement Optimization for Parameter Estimation in Distributed Systems, Technical University Press, Zielona Góra. Available at
  • 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.
  • 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).
  • Uciński D. (2005). Optimal Measurement Methods for Distributed-Parameter System Identification, CRC Press, Boca Raton, FL.
  • 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.
  • van de Wal M. and de Jager B. (2001). A review of methods for input/output selection, Automatica 37(4): 487-510.
  • Walter É. and Pronzato L. (1997). Identification of Parametric Models from Experimental Data, Communications and Control Engineering, Springer-Verlag, Berlin.
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