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2012 | 22 | 1 | 25-40
Tytuł artykułu

Sensor network scheduling for identification of spatially distributed processes

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The work treats the problem of fault detection for processes described by partial differential equations as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A simple node activation strategy is discussed for the design of a sensor network deployed in a spatial domain that is supposed to be used while detecting changes in the underlying parameters which govern the process evolution. The setting considered relates to a situation where from among a finite set of potential sensor locations only a subset of them 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. The problem is then formulated as the determination of the density of gauged sites so as to maximize the adopted design criterion, subject to inequality constraints incorporating a maximum allowable sensor density in a given spatial domain. The search for the optimal solution is performed using a simplicial decomposition algorithm. The use of the proposed approach is illustrated by a numerical example involving sensor selection for a two-dimensional diffusion process.
Rocznik
Tom
22
Numer
1
Strony
25-40
Opis fizyczny
Daty
wydano
2012
otrzymano
2011-01-27
poprawiono
2011-09-12
Twórcy
  • Institute of Control and Computation Engineering, University of Zielona Góra, ul. Podgórna 50, 65-246 Zielona Góra, Poland
Bibliografia
  • 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.
  • Armstrong, M. (1998). Basic Linear Geostatistics, Springer-Verlag, Berlin.
  • Atkinson, A.C. and Donev, A.N. (1992). Optimum Experimental Designs, Clarendon Press, Oxford.
  • Atkinson, A.C., Donev, A.N. and Tobias, R.D. (2007). Optimum Experimental Designs, with SAS, Oxford University Press, Oxford.
  • Banks, H.T., Smith, R.C. and Wang, Y. (1996). Smart Material Structures: Modeling, Estimation and Control, Research in Applied Mathematics, Masson, Paris.
  • Bauer, P.H. (2008). New challenges in dynamical systems: The networked case, International Journal of Applied Mathematics and Computer Science 18(3): 271-277, DOI: 10.2478/v10006-008-0025-8.
  • Bernstein, D.S. (2005). Matrix Mathematics. Theory, Facts, and Formulas with Application to Linear Systems Theory, Princeton University Press, Princeton, NJ.
  • Botkin, N.D. and Stoer, J. (2005). Minimization of convex functions on the convex hull of a point set, Mathematical Methods of Operations Research 62(2): 167-18.
  • Caselton, W.F., Kan, L. and Zidek, J.V. (1992). Quality data networks that minimize entropy, in A. Walden and P. Guttorp (Eds.), Statistics in the Environmental and Earth Sciences, Halsted Press, New York, NY, Chapter 2, pp. 10-38.
  • Caselton, W.F. and Zidek, J.V. (1984). Optimal monitoring network design, Statistics & Probability Letters 2: 223-227.
  • 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.
  • Chong, C.-Y. and Kumar, S.P. (2003). Sensor networks: Evolution, opportunities, and challenges, Proceedings of the IEEE 91(8): 1247-1256.
  • Christofides, P.D. (2001). Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes, Systems & Control: Foundations & Applications, Birkhäuser, Boston, MA.
  • COMSOL AB (1995). Partial Differential Equation Toolbox for Use with Matlab. User's Guide, The MathWorks, Inc., Natick, MA.
  • Cressie, N.A.C. (1993). Statistics for Spatial Data, Revised Edn., John Wiley & Sons, New York, NY.
  • Daescu, D.N. and Navon, I.M. (2004). Adaptive observations in the context of 4D-Var data assimilation, Meteorology and Atmospheric Physics 85: 205-226.
  • Demetriou, M.A. (2009). Natural consensus filters for second order infinite dimensional systems, Systems & Control Letters 58(12): 826-833.
  • Demetriou, M.A. (2010). Guidance of mobile actuator-plussensor networks for improved control and estimation of distributed parameter systems, IEEE Transactions on Automatic Control 55(7): 1570-1584.
  • Demetriou, M.A. and Hussein, I.I. (2009). Estimation of spatially distributed processes using mobile spatially distributed sensor network, SIAM Journal on Control and Optimization 48(1): 266-291.
  • Demetriou, M.A., Ito, K. and Smith, R.C. (2007). Adaptive monitoring and accommodation of nonlinear actuator faults in positive real infinite dimensional systems, IEEE Transactions on Automatic Control 52(12): 2332-2338.
  • El Jai, A. and Hamzaoui, H. (2009). Regional observation and sensors, International Journal of Applied Mathematics and Computer Science 19(1): 5-14, DOI: 10.2478/v10006009-0001-y.
  • Fedorov, V.V. (1989). Optimal design with bounded density: Optimization algorithms of the exchange type, Journal of Statistical Planning and Inference 22: 1-13.
  • Fedorov, V.V. and Hackl, P. (1997). Model-Oriented Design of Experiments, Lecture Notes in Statistics, Springer-Verlag, New York, NY.
  • Gevers, M. (2005). Identification for control: From the early achievements to the revival of experiment design, European Journal of Control 11(4-5): 335-352.
  • Goodwin, G. C. and Payne, R. L. (1977). Dynamic System Identification. Experiment Design and Data Analysis, Mathematics in Science and Engineering, Academic Press, New York, NY.
  • Hearn, D.W., Lawphongpanich, S. and Ventura, J.A. (1985). Finiteness in restricted simplicial decomposition, Operations Research Letters 4(3): 125-130.
  • Hirsch, M.J., Pardalos, P.M., Murphey, R. and Grundel, D. (Eds.) (2008). Advances in Cooperative Control and Optimization. Proceedings of the 7th International Conference on Cooperative Control and Optimization, Springer-Verlag, Berlin.
  • Hjalmarsson, H. (2005). From experiment design to closed-loop control, Automatica 41: 393-438.
  • Isermann, R. (1997). Supervision, Fault Detection and Diagnosis of Technical Systems, Control Engineering Practice 5(5), Special section.
  • Jain, N. and Agrawal, D.P. (2005). Current trends in wireless sensor network design, International Journal of Distributed Sensor Networks 1: 101-122.
  • Jeremić, A. and Nehorai, A. (1998). Design of chemical sensor arrays for monitoring disposal sites on the ocean floor, IEEE Transactions on Oceanic Engineering 23(4): 334-343.
  • Jeremić, A. and Nehorai, A. (2000). Landmine detection and localization using chemical sensor array processing, IEEE Transactions on Signal Processing 48(5): 1295-1305.
  • Kammer, D.C. (1990). Sensor placement for on-orbit modal identification and correlation of large space structures, Proceedings of the American Control Conference, San Diego, CA, USA, Vol. 3, pp. 2984-2990.
  • Kammer, D.C. (1992). Effects of noise on sensor placement for on-orbit modal identification of large space structures, Transactions of the ASME 114: 436-443.
  • Khapalov, A.Y. (2010). Source localization and sensor placement in environmental monitoring, International Journal of Applied Mathematics and Computer Science 20(3): 445-458, DOI: 10.2478/v10006-010-0033-3.
  • Kincaid, R.K. and Padula, S.L. (2002). D-optimal designs for sensor and actuator locations, Computers & Operations Research 29: 701-713.
  • Korbicz, J., Kościelny, J., Kowalczuk, Z. and Cholewa, W. (2004). Fault Diagnosis. Models, Artificial Intelligence, Applications, Springer-Verlag, Berlin/Heidelberg.
  • Kubrusly, C.S. and Malebranche, H. (1985). Sensors and controllers location in distributed systems-A survey, Automatica 21(2): 117-128.
  • Ljung, L. (1999). System Identification: Theory for the User, 2nd Edn., Prentice Hall, Upper Saddle River, NJ.
  • Martínez, S. and Bullo, F. (2006). Optimal sensor placement and motion coordination for target tracking, Automatica 42: 661-668.
  • Müller, W.G. (2001). Collecting Spatial Data. Optimum Design of Experiments for Random Fields, 2nd Revised Edn., Contributions to Statistics, Physica-Verlag, Heidelberg.
  • Munack, A. (1984). Optimal sensor allocation for identification of unknown parameters in a bubble-column loop bioreactor, in A.V. Balakrishnan and M. Thoma (Eds.), Analysis and Optimization of Systems, Part 2, Lecture Notes in Control and Information Sciences, Vol. 63, Springer-Verlag, Berlin, pp. 415-433.
  • Navon, I.M. (1997). Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography, Dynamics of Atmospheres and Oceans 27: 55-79.
  • Nehorai, A., Porat, B. and Paldi, E. (1995). Detection and localization of vapor-emitting sources, IEEE Transactions on Signal Processing 43(1): 243-253.
  • Nychka, D., Piegorsch, W.W. and Cox, L.H. (Eds.) (1998). Case Studies in Environmental Statistics, Lecture Notes in Statistics, Vol. 132, Springer-Verlag, New York, NY.
  • Nychka, D. and Saltzman, N. (1998). Design of air-quality monitoring networks, in D. Nychka, W.W. Piegorsch and L.H. Cox (Eds.), Case Studies in Environmental Statistics, Lecture Notes in Statistics, Vol. 132, Springer-Verlag, New York, NY, pp. 51-76.
  • Ögren, P., Fiorelli, E. and Leonard, N.E. (2004). Cooperative control of mobile sensor networks: Adaptive gradient climbing in a distributed environment, IEEE Transactions on Automatic Control 49(8): 1292-1302.
  • Omatu, S. and Seinfeld, J.H. (1989). Distributed Parameter Systems: Theory and Applications, Oxford Mathematical Monographs, Oxford University Press, New York, NY.
  • 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. and Uciński, D. (2008). Configuring a sensor network for fault detection in distributed parameter systems, International Journal of Applied Mathematics and Computer Science 18(4): 513-524, DOI: 10.2478/v10006-0080045-4.
  • Patriksson, M. (2001). Simplicial decomposition algorithms, in C.A. Floudas and P.M. Pardalos (Eds.), Encyclopedia of Optimization, Vol. 5, Kluwer Academic Publishers, Dordrecht, pp. 205-212.
  • 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), Special issue.
  • Pázman, A. (1986). Foundations of Optimum Experimental Design, Mathematics and Its Applications, D. Reidel Publishing Company, Dordrecht.
  • Point, N., Vande Wouwer, A. and Remy, M. (1996). Practical issues in distributed parameter estimation: Gradient computation and optimal experiment design, Control Engineering Practice 4(11): 1553-1562.
  • Porat, B. and Nehorai, A. (1996). Localizing vapor-emitting sources by moving sensors, IEEE Transactions on Signal Processing 44(4): 1018-1021.
  • Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B. P. (2007). Numerical Recipes. The Art of Scientific Computing, 3rd Edn., Cambridge University Press, Cambridge.
  • Pukelsheim, F. (1993). Optimal Design of Experiments, Probability and Mathematical Statistics, 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.
  • Rafajłowicz, E. (1986). Optimum choice of moving sensor trajectories for distributed parameter system identification, International Journal of Control 43(5): 1441-1451.
  • Rao, M.M. (1987). Measure Theory and Integration, John Wiley & Sons, New York, NY.
  • Sastry, S. and Iyengar, S.S. (2005). Real-time sensor-actuator networks, International Journal of Distributed Sensor Networks 1: 17-34.
  • Sinopoli, B., Sharp, C., Schenato, L., Schaffert, S. and Sastry, S.S. (2003). Distributed control applications within sensor networks, Proceedings of the IEEE 91(8): 1235-1246.
  • Song, Z., Chen, Y., Sastry, C.R. and Tas, N.C. (2009). Optimal Observation for Cyber-physical Systems: A Fisherinformation-matrix-based Approach, Springer-Verlag, London.
  • Sun, N.-Z. (1994). Inverse Problems in Groundwater Modeling, Theory and Applications of Transport in Porous Media, Kluwer Academic Publishers, Dordrecht.
  • Titterington, D.M. (1980). Aspects of optimal design in dynamic systems, Technometrics 22(3): 287-299.
  • Uciński, D. (1999). Measurement Optimization for Parameter Estimation in Distributed Systems, Technical University Press, Zielona Góra.
  • Uciński, D. (2000). Optimal sensor location for parameter estimation of distributed processes, International Journal of Control 73(13): 1235-1248.
  • Uciński, D. (2005). Optimal Measurement Methods for Distributed-Parameter System Identification, CRC Press, Boca Raton, FL.
  • Uciński, D. (2010). Sensor network design for spatio-temporal prediction of distributed parameter systems, in M. Kuczma and K. Wilmanski (Eds.), Computer Methods in Mechanics: Lectures of the CMM 2009, Springer-Verlag, Berlin, pp. 193-210.
  • Uciński, D. and Atkinson, A. C. (2004). Experimental design for time-dependent models with correlated observations, Studies in Nonlinear Dynamics & Econometrics 8(2), Article No. 13.
  • Uciński, D. and Bogacka, B. (2005). T-optimum designs for discrimination between two multivariate dynamic models, Journal of the Royal Statistical Society: Series B (Statistical Methodology) 67: 3-18.
  • Uciński, D. and Chen, Y. (2005). Time-optimal path planning of moving sensors for parameter estimation of distributed systems, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, Seville, Spain, (on CD-ROM).
  • Uciński, D. and Patan, M. (2007). D-optimal design of a monitoring network for parameter estimation of distributed systems, Journal of Global Optimization 39: 291-322.
  • Uciński, D. and Patan, M. (2010). Sensor network design for the estimation of spatially distributed processes, International Journal of Applied Mathematics and Computer Science 20(3): 459-481, DOI: 10.2478/v10006-010-0034-2.
  • Uspenskii, A.B. and Fedorov, V.V. (1975). Computational Aspects of the Least-Squares Method in the Analysis and Design of Regression Experiments, Moscow University Press, Moscow, (in Russian).
  • van de Wal, M. and de Jager, B. (2001). A review of methods for input/output selection, Automatica 37: 487-510.
  • Vande Wouwer, A., Point, N., Porteman, S. and Remy, M. (1999). On a practical criterion for optimal sensor configuration-Application to a fixed-bed reactor, Proceedings of the 14th IFAC World Congress, Beijing, China, Vol. I: Modeling, Identification, Signal Processing II, Adaptive Control, pp. 37-42.
  • von Hohenbalken, B. (1977). Simplicial decomposition in nonlinear programming algorithms, Mathematical Programming 13: 49-68.
  • Walter, É. and Pronzato, L. (1997). Identification of Parametric Models from Experimental Data, Communications and Control Engineering, Springer-Verlag, Berlin.
  • Zhao, F. and Guibas, L. J. (2004). Wireless Sensor Networks: An Information Processing Approach, Morgan Kaufmann Publishers, Amsterdam.
  • Zhao, T. and Nehorai, A. (2006). Detecting and estimating biochemical dispersion of a moving source in a semiinfinite medium, IEEE Transactions on Signal Processing 54(6): 2213-2225.
  • Zięba, T. and Uciński, D. (2008). Mobile sensor routing for parameter estimation of distributed systems using the parallel tunneling method, International Journal of Applied Mathematics and Computer Science 18(3): 307-318, DOI: 10.2478/v10006-008-0028-5.
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