Entropy-Based Optimal Sensor Location for Structural Model Updating

Abstract

A statistical methodology is presented for optimally locating the sensors in a structure for the purpose of extracting from the measured data the most information about the parameters of the model used to represent structural behavior. The methodology can be used in model updating and in damage detection and localization applications. It properly handles the unavoidable uncertainties in the measured data as well as the model uncertainties. The optimality criterion for the sensor locations is based on information entropy, which is a unique measure of the uncertainty in the model parameters. The uncertainty in these parameters is computed by a Bayesian statistical methodology, and then the entropy measure is minimized over the set of possible sensor configurations using a genetic algorithm. The information entropy measure is also extended to handle large uncertainties expected in the pretest nominal model of a structure. In experimental design, the proposed entropy-based measure of uncertainty is also well-suited for making quantitative evaluations and comparisons of the quality of the parameter estimates that can be achieved using sensor configurations with different numbers of sensors in each configuration. Simplified models for a shear building and a truss structure are used to illustrate the methodology.

Keywords

System identification information entropy sensors model updating structural health monitoring

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References

Beck, J.L. , 1989, "Statistical system identification of structures ," in Proceedings of the 5th International Conference on Structural Safety and Reliability, ASCE, San Francisco, CA, pp. 1395-1402.

Beck, J.L. and Katafygiotis, L.S. , 1998, "Updating models and their uncertainties - Bayesian statistical framework," Journal of Engineering Mechanics 124(4), 455-461.

Beck, J.L. , Vanik, M.W. , and Katafygiotis, L.S. , 1994, "Determination of stiffness changes from modal parameter changes for structural health monitoring," in Proceedings of the First World Conference on Structural Control, Pasadena, CA, pp. 13-22.

Chan, E. , 1997, "Optimal design of building structures using genetic algorithms ," EERL Report 97-06, California Institute of Technology , Pasadena, CA.

Goldberg, D.E. , 1989, Genetic Algorithms in Search. Optimization and Machine Learning, Addison Wesley, Reading, MA.

Heredia-Zavoni, E. and Esteva, L. , 1998, "Optimal instrumentation of uncertain structural systems subject to earthquake ground motions," Earthquake Engineering and Structural Dynamics 27, 343-362.

Jaynes, E.T. , 1978, "Where do we stand on maximum entropy?" in The Maximum Entropy Formalism, ed. R. D. Levine and M. Tribus , MIT Press, Cambridge, MA.

Kammer, D. , 1991, "Sensor placements for on orbit modal identification and correlation of large space structures," Journal of Guidance, Control and Dynamics 14, 251-259.

Kammer, D. , 1992, "Effects of modal error on sensor placement for on orbit modal identification and correlation of large space structures," Journal of Guidance, Control and Dynamics 14, 334-341.

10.

Katafygiotis, L.S. and Beck, J.L. , 1998, "Updating models and their uncertainties - model identifiability ," Journal of Engineering Mechanics 124(4), 463-467.

11.

Katafygiotis, L.S. and Lam, H.F. , 1997, "A probabilistic approach to structural health monitoring ," in Proceedings of the International Workshop on Structural Health Monitoring, Stanford, CA , pp. 152-163.

12.

Katafygiotis, L.S. , Lam, H.F. , and Papadimitriou, C. , 1997, "Probabilistic model updating using dynamic data," in Proceedings of the Seventh International Conference on Structural Safety and Reliability, Kyoto, Japan, pp. 603-610.

13.

Katafygiotis, L.S. , Papadimitriou, C. , and Lam, H.F. , 1998, "A probabilistic approach to structural model updating ," International Journal of Soil Dynamics and Earthquake Engineering 17(7-8), 495-507.

14.

Larson, B. , Zimmerman, C. , and Marek, L. , 1994, "A comparison of modal test planning techniques: Excitation and sensor placement using the NASA 8-bay truss," in Proceedings of the Twelve International Modal Analysis Conference , Honolulu, III, pp. 205-211.

15.

Mottershead, J.E. and Friswell, M.I. , 1993, "Model updating in structural dynamics: A survey ," Journal of Sound and Vibration 167(2), 347-375.

16.

Natke, H. G. and Yao, J.T.P., eds., 1988, Structural Safety Evaluation based on System Identification Approaches, Proceedings of Workshop at Lambrecht/Pfatz, Frieder Vieweg and Son , Braunschweig, Germany. Papadimitriou, C. , Beck, J.L. , and Katafygiotis, L.S. , 1997, "Asymptotic expansions for reliability and moments of uncertain systems ," Journal of Engineering Mechanics 123(12), 1219-1229.

17.

Penny, J.E.T. , Friswell, M.I. , and Garvey, S.D. , 1994, "Automatic choice of measurement location for dynamic testing," AIAA Journal 32, 407-414.

18.

Shah, P. and Udwadia, F.E. , 1994, "A methodology for optimal sensor locations for identification of dynamic systems," Journal of Applied Mechanics 45, 188-196.

19.

Shannon, C.E. , 1949, The Mathematical Theory of Communications, University of Illinois Press, Urbana, IL .

20.

Sohn, H. and Law, K.H. , 1997, "A Bayesian probabilistic approach for structure damage detection," Earthquake Engineering and Structural Dynamics 26, 1259-1281.

21.

Udwadia, F.E. , 1994, "Methodology for optimal sensor locations for parameters identification in dynamic systems," Journal of Engineering Mechanics 120(2), 368-390.

22.

Udwadia, F.E. and Sharma, D.K. , 1978, "Some uniqueness results related to building structural identification," SIAM Journal of Applied Mathematics 34(1), 104-118.

23.

Vanik, M.W. and Beck, J.L. , 1998, "A Bayesian probabilistic approach to structural health monitoring," in Proceedings of the International Workshop on Structural Health Monitoring, Stanford, CA , pp. 140-151.