Possibilistic Approach for Damage Detection in Structural Health Monitoring
Publication: Journal of Structural Engineering
Volume 133, Issue 9
Abstract
This article suggests the process of structural health monitoring (SHM) in the context of a nonstatistical damage detection paradigm. We particularly focus on applying the theory of possibility to the damage detection problem. The basic idea behind the proposed approach is that the application of possibility theory does not require probabilistic knowledge or assumptions on the damage feature and thus encompasses aleatoric and epistemic types of uncertainties. The approach is not damage feature dependent and thus is generic for use in many SHM systems. Additionally, two new damage metrics are introduced. These metrics extract information concerning damage evidence from observations performed at unknown health states of structures. Damage detection with the aid of the proposed approach is demonstrated by means of a case study.
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Acknowledgments
This research was funded by Sandia National Laboratories (SNL). The writers would like to extend their appreciation for this funding. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract No. DOEDE-AC04-94AL85000. Special thanks to Dr. K. K. Choi for his valuable discussion and review of the manuscript.
References
Altunok, E. (2006). “Fuzzy and possibility methods for damage detection in structural health monitoring.” MSc thesis, Dept. of Electrical and Computer Engineering, Univ. of New Mexico, Albuquerque, N.M.
Benferhat, S., Dubois, D., Kaci, S., and Prade, H. (2006). “Bipolar possibility theory in preference modeling: Representation, fusion, and optimal solutions.” Information Fusion, 7(1), 135–150.
Brown, L. C. (2002). “QUAL2E-UNCAS: A framework for modeling uncertainty.” Italy–US Bilateral Workshop on Mathematical Models for Water Quality in Isolated Environments, Venice, Italy.
Casas, J. R., Matos, J. C., Figueiras, J. A., Vehí, J., García, O., and Herrero, P. (2005). “Bridge monitoring and assessment under uncertainty via interval analysis.” Proc., 9th Int. Conf. On Structural Safety And Reliability–ICOSSAR 2005, 487–494.
Donald, S. (2003). “Development of empirical possibility distributions in risk analysis.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of New Mexico, Albuquerque, N.M.
Dubois, D., and Prade, H. (1994). “Possibility theory and data fusion in poorly informed environments.” Control Eng. Pract., 2(5), 811–823.
Dyke, S. J., Bernal, D., Beck, J. L., and Ventura, C. (2001). “An experimental benchmark problem in structural health monitoring.” Proc., 3rd Int. Workshop on Structural Health Monitoring.
Farrar, C. R., Duffey, T. A., Doebling, S. W., and Nix, D. A. (2000a). “A statistical pattern recognition paradigm for vibration-based structural health monitoring.” Proc., 2nd Int. Workshop on Structural Health Monitoring, Stanford, Calif., 764–773.
Farrar, C. R., Sohn, H., and Doebling, S. W. (2000b). “Structural health monitoring at Los Alamos National Laboratory.” 13th Int. Congress and Exhibition on Condition Monitoring and Diagnostic Management (COMADEM 2000), Houston.
Grabisch, M., Nguyen, H. T., and Walker, E. A. (1984). Fundamentals of uncertainty calculi with applications to fuzzy inference, Kluwer Academic, Boston.
Gupta, M. M., and Qi, J. (1991). “Theory of T-norms and fuzzy inference methods.” Fuzzy Sets Syst., 40(3), 431–450.
Hera, A., and Hou, Z. (2004). “Application of wavelet approach for ASCE structural heath monitoring benchmark studies.” J. Eng. Mech., 130(1), 96–104.
Jamison, K. D. (1998). “Modeling uncertainty using probabilistic based possibility theory with applications to optimization.” Ph.D. thesis, Dept. of Applied Mathematics, Univ. of Colorado, Denver.
Joslyn, C. (1997). “Measurement of possibilistic histograms from interval data.” Int. J. Gen. Syst., 26(1–2), 9–33.
Klir, G. J. (2006). Uncertainty and information, Wiley, Hoboken, N.J.
Klir, G. J., and Yuan, B. (1995). Fuzzy sets and fuzzy logic, Prentice-Hall, Upper Saddle River, N.J.
Link, T., Lew, J.-S., Garcia, E., and Keel, L. H. (1996). “Interval model identification and robustness analysis for uncertain flexible structures.” IEEE Trans. Control Syst. Technol., 4(3), 411–418.
Mas, M., Mayor, G., and Torrens, J. (1999). “t-Operators.” Int. J. Uncertainty, 7(1), 31–50.
McCuskey, M. C., Reda Taha, M. M., Horton, S. R., and Baca, T. J. (2006). “Identifying damage in the ASCE benchmark structure using a neural wavelet module.” Proc., 6th Int. Workshop on Structural Health Monitoring, Granada, Spain, Giiemes et al., eds., 421–428.
Mezic, I., and Runolfsson, T. (2004). “Uncertainty analysis of complex dynamical systems.” 2004 American Control Conf., Boston.
Möller, B., Beer, M., Graf, W., and Hoffmann, A. (1998). “Possibility theory based safety assessment.” Microcomputers in civil engineering, Blackwell, Cambridge, Oxford, U.K., Special Issue: Fuzzy Logic, S. 81–91.
Möller, B., Graf, W., and Beer, M. (2000). “Fuzzy structural analysis using -level optimization.” Comput. Mech., 26(6), 547–565.
Nair, K. K., Kiremidjian, A. S., and Law, K. H. (2006). “Time series-based damage detection and localization algorithm with application to the ASCE benchmark structure.” J. Sound Vib., 291, 349–368.
Oberkampf, W. L., Helton, J. C., Joslyn, C. A., Wojtkiewicz, S. F., and Ferson, S. (2004). “Challenge problems: Uncertainty in system response given uncertain parameters.” Reliab. Eng. Syst. Saf., 85, 11–19.
Oussalah, M., Maaref, H., and Barret, C. (2003). “Application of a possibilistic-based approach to mobile robotics.” J. Intell. Robotic Syst., 38(2), 175–195.
Reda Taha, M. M., and Lucero, J. (2005). “Damage identification for structural health monitoring using fuzzy pattern recognition.” Eng. Struct., 27(12), 1774–1783.
Ross, T. J. (2004). Fuzzy logic with engineering applications, Wiley, Chichester, U.K.
Sohn, H., Allen, D. W., Worden, K., and Farrar, C. R. (2005). “Structural damage classification using extreme value statistics.” ASME J. Dyn. Syst., Meas., Control, 127(1), 125–132.
Sohn, H., Fugate, M., and Farrar, C. R. (2000). “Damage diagnosis using statistical process control.” Conf. on Recent Advances in Structural Dynamics, Southampton, U.K.
Soundappan, P., Nikolaidis, E., Haftka, R. T., Grandhi, R. V., and Canfield, R. A. (2004). “Comparison of evidence theory and bayesian theory for uncertainty modeling.” Reliab. Eng. Syst. Saf., 85, 295–311.
Yager, R. R. (1998). “A general approach to the fusion of imprecision information.” Int. J. Intell. Syst., 12(1), 1–29.
Youn, B. D., Choi, K. K., Du, L., and Gorsich, D. (2005). “Integration of possibility-based optimization to robust design for epistemic uncertainty.” 6th World Congresses of Structural and Multidisciplinary Optimization, Rio de Janeiro, Brazil.
Zadeh, L. (1978). “Fuzzy sets as a basis for a theory of possibility.” Fuzzy Sets Syst., 1, 3–28.
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© 2007 ASCE.
History
Received: Sep 8, 2006
Accepted: Dec 14, 2006
Published online: Sep 1, 2007
Published in print: Sep 2007
Notes
Note. Associate Editor: Shahram Sarkani
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