Mobile sensor routing for parameter estimation of distributed systems using the parallel tunneling method

Tomasz Zięba ; Dariusz Uciński

International Journal of Applied Mathematics and Computer Science, Tome 18 (2008), p. 307-318 / Harvested from The Polish Digital Mathematics Library

Résumé

The paper deals with the problem of optimal path planning for a sensor network with mutliple mobile nodes, whose measurements are supposed to be primarily used to estimate unknown parameters of a system modelled by a partial differential equation. The adopted framework permits to consider two- or three-dimensional spatial domains and correlated observations. Since the aim is to maximize the accuracy of the estimates, a general functional defined on the relevant Fisher information matrix is used as the design criterion. Central to the approach is the parameterization of the sensor trajectories based on cubic B-splines. The resulting finite-dimensional global optimization problem is then solved using a parallel version of the tunneling algorithm. A numerical example is included to clearly demonstrate the idea presented in the paper.

Détail

Publié le : 2008-01-01

Zbl 1176.93004

EUDML-ID : urn:eudml:doc:207887

Bibliographie

[000] Atkinson A. C., Donev A. N. and Tobias R. D. (2007). Optimum Experimental Designs, with SAS, Oxford University Press, Oxford. | Zbl 1183.62129

[001] Banks H. T., Smith R. C. and Wang Y. (1996). Smart Material Structures: Modeling, Estimation and Control, Masson, Paris. | Zbl 0882.93001

[002] Bertsekas D. P. (1999). Nonlinear Programming, 2nd Edn., Athena Scientific, Belmont, MA. | Zbl 1015.90077

[003] Cassandras C. G. and Li, W. (2005). Sensor networks and cooperative control, European Journal of Control 11(4-5): 436-463. | Zbl 1293.93069

[004] Christofides P. D. (2001). Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes, Birkhäuser, Boston, MA. | Zbl 1018.93001

[005] Cressie N. A. C. (1993). Statistics for Spatial Data, Revised Edn., John Wiley & Sons, New York, NY.

[006] Daescu D. N. and Navon I. M. (2004). Adaptive observations in the context of 4D-Var data assimilation, Meteorology and Atmospheric Physics 85(4): 205-226.

[007] Demetriou M. A. (2006a). Detection and containment policy of moving source in 2D diffusion processes using sensor/actuator network, Proceedings of the European Control Conference 2007, Kos, Greece. Published on CD-ROM.

[008] Demetriou M. A. (2006b). Power management of sensor networks for detection of a moving source in 2-D spatial domains, Proceedings of the 2006 American Control Conference, Minneapolis, MN, USA. Published on CD-ROM.

[009] Demetriou M. A. (2007). Process estimation and moving source detection in 2-D diffusion processes by scheduling of sensor networks, Proceedings of the 2007 American Control Conference, New York, NY, USA. Published on CD-ROM.

[010] Fedorov V. V. and Hackl P. (1997). Model-Oriented Design of Experiments, Lecture Notes in Statistics, Springer-Verlag, New York, NY. | Zbl 0878.62052

[011] Gómez S., del Castillo N., Castellanos L. and Solano J. (2003). The parallel tunneling method, Parallel Computing 29(4): 523-533.

[012] Hussein I. I. and Demetriou M. A. (2007). Estimation of distributed processes using mobile spatially distributed sensors, Proceedings of the 2007 American Control Conference, New York, NY, USA. Published on CD-ROM. | Zbl 1182.93111

[013] 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.

[014] Jeremić A. and Nehorai A. (2000). Landmine detection and localization using chemical sensor array processing, IEEE Transactions on Signal Processing 48(5): 1295-1305.

[015] Kubrusly C. S. and Malebranche H. (1985). Sensors and controllers location in distributed systems - A survey, Automatica 21(2): 117-128. | Zbl 0555.93035

[016] Le N. D. and Zidek J. V. (2006). Statistical Analysis of Environmental Space-Time Processes, Springer-Verlag, New York, NY. | Zbl 1102.62126

[017] Levy A. V. and Montalvo A. (1985). The tunneling algorithm for the global minimization of functions, SIAM Journal on Scientific and Statistical Computing 6(1): 15-29. | Zbl 0601.65050

[018] Müller W. G. (2007). Collecting Spatial Data. Optimum Design of Experiments for Random Fields, 3rd Revised and Extended Edn., Physica-Verlag, Heidelberg. | Zbl 1266.62048

[019] Navon I. M. (1997). Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography, Dynamics of Atmospheres and Oceans 27(1): 55-79.

[020] Nehorai A., Porat B. and Paldi E. (1995). Detection and localization of vapor-emitting sources, IEEE Transactions on Signal Processing 43(1): 243-253.

[021] Pacheco P. S. (1997). Programming parallel with MPI, Morgan Kaufmann, San Francisco, CA. | Zbl 0877.68013

[022] Papalambros P. Y. and Wilde D. J. (2000). Principles of Optimal Design. Modeling and Computation, 2nd Edn., Cambridge University Press, Cambridge. | Zbl 0962.90002

[023] Pázman A. (1986). Foundations of Optimum Experimental Design, D. Reidel Publishing Company, Dordrecht. | Zbl 0588.62117

[024] Porat B. and Nehorai A. (1996). Localizing vapor-emitting sources by moving sensors, IEEE Transactions on Signal Processing 44(4): 1018-1021.

[025] Press W. H., Teukolsky S. A., Vetterling W. T. and Flannery B. P. (1992). Numerical Recipes in FORTRAN. The Art of Parallel Scientific Computing, 2nd Edn., Cambridge University Press, Cambridge. | Zbl 0778.65002

[026] Pukelsheim, F. (1993). Optimal Design of Experiments, John Wiley & Sons, New York, NY. | Zbl 0834.62068

[027] Quarteroni A., Sacco R. and Saleri F. (2000). Numerical Mathematics, Springer-Verlag, New York, NY. | Zbl 0957.65001

[028] 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. | Zbl 0431.93017

[029] Rafajłowicz E. (1981). Design of experiments for eigenvalue identification in distributed-parameter systems, International Journal of Control 34(6): 1079-1094. | Zbl 0476.93071

[030] 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. | Zbl 0521.93066

[031] Rafajłowicz E. (1986). Optimum choice of moving sensor trajectories for distributed parameter system identification, International Journal of Control 43(5): 1441-1451. | Zbl 0581.93066

[032] Sacks E. W. (1998). Semi-infinite programming in control, in R. Reemtsen and J.-J. Rückmann (Eds.), Semi-Infinite Programming, Kluwer Academic Publishers, Boston, MA, pp. 389-411. | Zbl 0911.90331

[033] Scott L. R., Clark T. and Bagheri B. (2005). Scientific Parallel Computing, Princeton University Press, Princeton, NJ. | Zbl 1067.68074

[034] Sun N.-Z. (1994). Inverse Problems in Groundwater Modeling, Kluwer Academic Publishers, Dordrecht.

[035] Tricaud C., Patan M., Uciński D. and Chen Y. (2008). D-optimal trajectory design of heterogeneous mobile sensors for parameter estimation of distributed systems, Proceedings of the 2008 American Control Conference, Seattle, WA, USA. Published on CD-ROM.

[036] Uciński D. (1999). Measurement Optimization for Parameter Estimation in Distributed Systems, Technical University Press, Zielona Góra.

[037] Uciński D. (2000). Optimal sensor location for parameter estimation of distributed processes, International Journal of Control 73(13): 1235-1248. | Zbl 1004.93015

[038] Uciński D. (2005). Optimal Measurement Methods for Distributed-Parameter System Identification, CRC Press, Boca Raton, FL. | Zbl 1155.93003

[039] 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. Published on CD-ROM.

[040] Uciński D. and Chen Y. (2006). Sensor motion planning in distributed parameter systems using Turing's measure of conditioning, Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, CA, USA. Published on CD-ROM.

[041] Uciński D. and Demetriou, M. A. (2008). Resource-constrained sensor routing for optimal observation of distributed parameter systems, Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems, Blacksburg, VA, USA. Published on CD-ROM.

[042] Uciński D. and Korbicz J. (2001). Optimal sensor allocation for parameter estimation in distributed systems, Journal of Inverse and Ill-Posed Problems 9(3): 301-317. | Zbl 0994.35123

[043] 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. | Zbl 1180.90173

[044] Walter É. and Pronzato L. (1997). Identification of Parametric Models from Experimental Data, Communications and Control Engineering, Springer-Verlag, Berlin. | Zbl 0864.93014

[045] Wyrzykowski R., Meyer N. and Stroiński M. (2004). Clusterix: National cluster of linux systems, Proceedings of the 2nd European Across Grids 2004 Conference, Nicosia, Cyprus. Available at: http://grid.ucy.ac.cy/axgrids04/AxGrids.

[046] Zhao F. and Guibas L. J. (2004). Wireless Sensor Networks: An Information Processing Approach, Morgan Kaufmann Publishers, Amsterdam.