Damage Identification in a Truss Tower by Regularized Model Updating
Publication: Journal of Structural Engineering
Volume 136, Issue 3
Abstract
This paper presents a sensitivity-based damage identification of a three-dimensional truss tower tested in the laboratory. A finite-element model is updated by modal parameters obtained from ambient vibration measurements. The paper focuses on details of modeling and model updating. To get a realistic model, it was necessary to include eccentric connections, bending stiffness in truss members, and foundation flexibility. For model updating, a number of mathematical techniques are combined in a consistent way, including regularization of the nonlinear updating problem and its linearization. Considering all these details correctly, damage in the truss has been successfully identified. However, it is also demonstrated how neglecting some of these algorithmic details can lead to incorrect results. It is also shown how static condensation can lead to a model that is valid for the undamaged case but cannot adequately represent the damaged case.
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Acknowledgments
This research was supported by the ISIS Canada Network of Centres of Excellence, the Natural Sciences and Engineering Research Council of Canada, and Hydro-Québec.NSERC
References
Amin, M. S., Humar, J. L., and Soucy, Y. (2002). “Experimental verification of a vibration based damage detection technique.” Proc., Int. Modal Analysis Conf., IMAC-XX, SPIE, Bellingham, Wash.
Andrew, A. L., Chu, K. -W. E., and Lancaster, P. (1993). “Derivatives of eigenvalues and eigenvectors of matrix functions.” SIAM J. Matrix Anal. Appl., 14(4), 903–926.
ARTEMIS. (2005). ARTEMIS Extractor software, Structural Vibration Solutions, Aalborg, Denmark.
Barroso, L. R., and Rodriguez, R. (2004). “Damage detection utilizing the damage index method to a benchmark structure.” J. Eng. Mech., 130(2), 142–151.
Bernal, D., and Gunes, B. (2004). “Flexibility based approach for damage characterization: Benchmark application.” J. Eng. Mech., 130(1), 61–70.
Caicedo, J. M., Dyke, S., and Johnson, E. A. (2004). “Natural excitation technique and eigensystem realization algorithm for Phase I of the IASC-ASCE benchmark problem: Simulated data.” J. Eng. Mech., 130(1), 49–60.
Ching, J., and Beck, J. (2004). “Bayesian analysis of the Phase II IASC–ASCE structural health monitoring experimental benchmark data.” J. Eng. Mech., 130, 1233–1244.
Dennis, J. E., and Schnabel, R. B. (1996). Numerical methods for unconstrained optimization and nonlinear equations (classics in applied mathematics), SIAM, Philadelphia.
Doebling, S. W. (1996). “Minimum-rank optimal update of elemental stiffness parameters for structural damage identification.” AIAA J., 34(12), 2615–2621.
Dyke, S. J., Bernal, D., and Ventura, J. B. C. (2003). “Experimental phase II of the structural health monitoring benchmark problem.” Proc., 16th ASCE Engineering Mechanics Conf., ⟨http://www.ce.washington.edu/em2003/proceedings⟩.
Fox, R. L., and Kapoor, M. P. (1968). “Rates of change of eigenvalues and eigenvectors.” AIAA J., 6(12), 2426–2429.
Giraldo, D., Caicedo, J. M., and Dyke, S. J. (2003). “Experimental phase of the SHM benchmark studies: Damage detection using NExT and ERA.” Proc., Engineering Mechanics Conf., ⟨http://www.ce.washington.edu/em2003/proceedings⟩.
Golub, G. H., and Van Loan, C. (1996). Matrix computations, 3rd Ed., Johns Hopkins University Press, Baltimore.
Hansen, P. C. (1998). “Rank-deficient and discrete Ill-posed problems: Numerical aspect of linear inversion.” SIAM monographs on mathematical modeling and computation, SIAM, Philadelphia.
Johnson, E. A., Lam, H. F., Katafygiotis, L. S., and Beck, J. L. (2004). “Phase I IASC-ASCE structural health monitoring benchmark problem using simulated data.” J. Eng. Mech., 130(1), 3–15.
Lam, H. F., Katafygiotis, L. S., and Mickleborough, N. (2004). “Application of a statistical model updating approach on Phase I of the IASC-ASCE structural health monitoring benchmark study.” J. Eng. Mech., 130(1), 34–48.
Lim, T. W., and Kashangaki, T. A. L. (1994). “Structural damage detection of space truss structures using best achievable eigenvectors.” AIAA J., 32(5), 1049–1057.
Lus, H., Betti, R., Yu, J., and De Angelis, M. (2004). “Investigation of a system identification methodology in the context of the ASCE benchmark problem.” J. Eng. Mech., 130(1), 71–84.
Nelson, R. B. (1976). “Simplified calculation of eigenvector derivatives.” AIAA J., 14(9), 1201–1205.
Nocedal, J., and Wright, S. J. (1999). Numerical optimization, Springer, New York.
O’Sullivan, F., and Wahba, G. (1985). “A cross validated Bayesian retrieval algorithm for nonlinear remote sensing experiments.” J. Comput. Phys., 59, 441–455.
Ricles, J. M., and Kosmatka, J. B. (1992). “Damage detection in elastic structures using vibratory residual forces and weighted sensitivity.” AIAA J., 30(9), 2310–2316.
Vogel, C. R. (1987). “An overview of numerical methods for nonlinear ill-posed problems.” Inverse and ill-posed problems, H. W. Engl and C. W. Groetsch, eds., Academic, San Diego, 231–245.
Vogel, C. R. (2002). “Computational methods for inverse problems.” Frontiers in applied mathematics, SIAM, Philadelphia.
Weber, B., Paultre, P., and Proulx, J. (2007). “Structural damage detection using nonlinear parameter identification with Tikhonov regularization.” Struct. Control Health Monit., 14(3), 406–427.
Weber, B., Paultre, P., and Proulx, J. (2009). “Consistent regularization of nonlinear model updating for damage identification.” Mech. Syst. Signal Process., 23(6), 1965–1985.
Yuen, K. -V., Au, S. K., and Beck, J. (2004). “Two-stage structural health monitoring approach for Phase I benchmark studies.” J. Eng. Mech., 130(1), 16–33.
Zimmerman, D. C., and Kaouk, M. (1992). “Eigenstructure assignment approach for structural damage detection.” AIAA J., 30(7), 1848–1855.
Zimmerman, D. C., and Kaouk, M. (1994). “Structural damage detection using a minimum rank update theory.” J. Vibr. Acoust., 116(2), 222–231.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 136 • Issue 3 • March 2010
Pages: 307 - 316
Copyright
© 2010 ASCE.
History
Received: Jul 16, 2008
Accepted: Sep 4, 2009
Published online: Sep 10, 2009
Published in print: Mar 2010
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