A Method for Sensor Placement Taking into Account Diagnosability Criteria

Yassine, Abed; Ploix, Stéphane; Flaus, Jean-Marie

doi:10.2478/v10006-008-0044-5

Abstract

This paper presents a new approach to sensor placement based on diagnosability criteria. It is based on the study of structural matrices. Properties of structural matrices regarding detectability, discriminability and diagnosability are established in order to be used by sensor placement methods. The proposed approach manages any number of constraints modelled by linear or nonlinear equations and it does not require the design of analytical redundancy relations. Assuming that a constraint models a component and that the cost of the measurement of each variable is defined, a method determining sensor placements satisfying diagnosability specifications, where all the diagnosable, discriminable and detectable constraint sets are specified, is proposed. An application example dealing with a dynamical linear system is presented.

References

Apt K. (2003). Principles of Constraint Programming, Cambridge University Press, Amsterdam, The Netherlands.10.1017/CBO9780511615320
Search in Google Scholar
Blanke M., Kinnaert M., Lunze J. and Staroswiecki M. (2006). Diagnosis and Fault-tolerant Control, Springer-Verlag, Berlin/Heidelberg.
Search in Google Scholar
Bollobás B. (1998). Modern Graph Theory, Springer, New York, NY.10.1007/978-1-4612-0619-4
Search in Google Scholar
Chittaro L. and Ranon R. (2004). Hierarchical model-based diagnosis based on structural abstraction, Artificial Intelligence 155(1-2): 147-182.10.1016/j.artint.2003.06.003
Search in Google Scholar
Commault C., Dion J.-M. and Yacoub Agha S. (2006). Structural analysis for the sensor location problem in fault detection and isolation, Proceedings of the IFAC Symposium SAFEPROCESS' 2006 Beijing, China, CD-ROM.10.1016/B978-008044485-7/50151-2
Search in Google Scholar
Console L., Picardi C. and Ribando M. (2000). Diagnosis and diagnosability analysis using process algebra, Proceedings of the 11th International Workshop on Principles of Diagnosis DX'2000, Morelia, Mexico.
Search in Google Scholar
Cordier M.-O., Dague P., Lévy F., Dumas M., Montmain J., Staroswiecki M. and Travé-Massuyès L. (2000). A comparative analysis of AI and control theory approaches to model-based diagnosis, Proceedings of the IFAC Symposium SAFEPROCESS 2000, Budapest, Hungary, pp. 329-334.
Search in Google Scholar
Dalton T., Klotzek P. and Frank P. (1999). Application of sensitivity theory to fuzzy logic based FDI, International Journal of Applied Mathematics and Computer Science 9(3): 619-636.
Search in Google Scholar
de Kleer J. and Williams B. C. (1992). Diagnosis with behavioral modes, in (W. Hamscher, L. Console and J. de Kleer, Eds.), Readings in Model-Based Diagnosis, Morgan Kaufmann Publishers Inc., San Francisco, CA, pp. 124-130.
Search in Google Scholar
Dulmage A. L. and Mendelsohn N. S. (1959). A structure theory of bi-partite graphs of finite exterior extension, Transactions of the Royal Society of Canada 53(III): 1-13.
Search in Google Scholar
Frisk E. and Krysander M. (2007). Sensor placement for maximum fault isolability, Proceedings of the 18th International Workshop on Principles of Diagnosis (DX-07), Nashville, TN, USA.
Search in Google Scholar
Hamscher W., Console L. and De Kleer J. (1992). Readings in Model-Based Diagnosis, Morgan Kaufmann Publishers Inc., San Francisco, CA.
Search in Google Scholar
Korbicz J., Patan K. and Obuchowicz A. (1999). Dynamic neural networks for process modelling in fault detection and isolation, International Journal of Applied Mathematics and Computer Science 9(3): 519-546.
Search in Google Scholar
Koscielny J., Syfert M. and Bartys M. (1999). Fuzzy logic faut diagnosis of industrial process actuators, International Journal of Applied Mathematics and Computer Science 9(3): 653-666.
Search in Google Scholar
Krysander M., Aslund J. and Nyberg M. (2008). An efficient algorithm for finding minimal overconstrained subsystems for model-based diagnosis, IEEE Transactions on Systems, Man and Cybernetics, Part A 38(1): 197-206.10.1109/TSMCA.2007.909555
Search in Google Scholar
Lopez-Toribio C., Patton R. and Uppal F. (1999). Artificial intelligence approaches to fault diagnosis for dynamic systems, International Journal of Applied Mathematics and Computer Science 9(3): 471-518.
Search in Google Scholar
Madron F. and Veverka V. (1992). Optimal selection of measuring points in complex plants by linear models, AIChE Journal 38(2): 227-236.10.1002/aic.690380208
Search in Google Scholar
Maquin D., Luong M. and Ragot J. (1997). Fault detection and isolation and sensor network design, European Journal of Automation 31(2): 393-406.
Search in Google Scholar
Nyberg M. and Krysander M. (2003). Combining AI, FDI, and statistical hypothesis-testing in a framework for diagnosis, Proceedings of the IFAC Symposium SAFEPROCESS'03, Washington, DC, USA, pp. 813-818.
Search in Google Scholar
Ploix S., Désinde M. and Touaf S. (2005). Automatic design of detection tests in complex dynamic systems, Proceedings of the 16th IFAC World Congress, Prague, Czech Republic.10.3182/20050703-6-CZ-1902.01882
Search in Google Scholar
Ploix S., Touaf S. and Flaus J. M. (2003). A logical framework for isolation in fault diagnosis, Proceedings of the IFAC Symposium SAFEPROCESS'2003, Washington, DC, USA.10.1016/S1474-6670(17)36592-8
Search in Google Scholar
Pothen A. and Chin-Ju F. (1990). Computing the block triangular form of a sparse matrix, ACM Transactions on Mathematical Software 16(4): 303-324.10.1145/98267.98287
Search in Google Scholar
Pulido B. and Alonso C. (2002). Possible conflicts, arrs, and conflicts, Proceedings of the 13th International Workshop on Principles of Diagnosis (DX02), Semmering, Austria, pp. 122-128.
Search in Google Scholar
Shumsky A. (2007). Redundancy relations for fault diagnosis in nonlinear uncertain systems, International Journal of Applied Mathematics and Computer Science 17(4): 477-489.10.2478/v10006-007-0040-1
Search in Google Scholar
Struss P. (1992). What's in SD? Towards a theory of modeling for diagnosis, in (W. Hamscher, L. Console and J. de Kleer, Eds.), Readings in model-based diagnosis, Morgan Kaufmann Publishers Inc., San Francisco, CA, pp. 419-449.
Search in Google Scholar
Struss P., Rehfus B., Brignolo R., Cascio F., Console L., Dague P., Dubois P., Dressler O. and Millet D. (2002). Modelbased tools for the integration of design and diagnosis into a common process — A project report, Proceedings of the International Workshop on Principles of Diagnosis DX'02, Semmering, Austria, pp. 25-32.
Search in Google Scholar
Travé-Massuyès L., Escobet T. and Milne R. (2001). Model-based diagnosability and sensor placement application to a frame 6 gas turbine subsystem, Proceedings of the 12th International Workshop on Principles of Diagnosis, Sansicario, Via Lattea, Italy, pp. 205-212.
Search in Google Scholar
Witczak M. (2006). Advances in model-based fault diagnosis with evolutionary algorithms and neural networks, International Journal of Applied Mathematics and Computer Science 16(1): 85-99.
Search in Google Scholar

A Method for Sensor Placement Taking into Account Diagnosability Criteria

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