Identification of Localized Structural Damage from Highly Incomplete Modal Information: Theory and Experiments
Publication: Journal of Engineering Mechanics
Volume 142, Issue 2
Abstract
The paper presents a methodology for identification of localized structural damage using highly incomplete modal information, such as a subset of modal frequencies. The proposed methodology is based on linearized modal sensitivities and -norm minimization of the algebraic difference between identified frequencies in damaged and undamaged states. The method is verified using stochastic simulations and validated using a series of laboratory experiments in which the number of potentially damaged elements is significantly larger than the number of identified modal frequencies.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The author would like to acknowledge the assistance of Mr. Floyd Vilmont in constructing the experimental setup presented in this paper.
References
Adhikari, S., Friswell, M. I., Lonkar, K., and Sarkar, A. (2009). “Experimental case studies for uncertainty quantification in structural dynamics.” Probab. Eng. Mech., 24(4), 473–492.
Ahmadian, H., Mottershead, J. E., and Friswell, M. I. (1998). “Regularization methods for finite element model updating.” Mech. Syst. Sig. Process., 12(1), 47–64.
Au, S. K., and Zhang, F. L. (2011). “On assessing posterior mode shape uncertainty in ambient modal identification.” Probab. Eng. Mech., 26(3), 427–434.
Boyd, S., and Vandenberghe, L. (2004). Convex optimization, Cambridge University Press, New York.
Candes, E., and Romberg, J. (2006). “l1-magic: A collection of MATLAB routines for solving the convex optimization programs central to compressive sampling: User guide.” 〈http://statweb.stanford.edu/~candes/l1magic/#papers〉 (Oct. 1, 2006).
Cha, P. D., and Gu, W. (2000). “Model updating using an incomplete set of experimental modes.” J. Sound Vib., 233(4), 583–596.
Chartrand, R. (2004). “Exact reconstruction of sparse signals via nonconvex optimization.” IEEE Trans. Signal Process., 52(8), 2153–2164.
Chen, S. S., Donoho, D. L., and Saunders, M. A. (2001). “Atomic decomposition by basis pursuit.” SIAM Rev., 43(1), 129–159.
Doebling, S. W. (1996). “Minimum-rank optimal update of elemental stiffness parameters for structural damage identification.” AIAA J., 34(12), 2615–2621.
Doebling, S. W., Farrar, C. R., Prime, M. B., and Shevitz, D. W. (1996). “Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review.”, Los Alamos, NM.
Döhler, M., Lam, X.-B., and Mevel, L. (2013). “Uncertainty quantification for modal parameters from stochastic subspace identification on multi-setup measurements.” Mech. Syst. Sig. Process., 36(2), 562–581.
Donoho, D. L., and Elad, M. (2003). “Optimally sparse representation in general (nonorthogonal) dictionaries via l1 minimization.” Proc. Natl. Acad. Sci., 100(5), 2197–2202.
Farrar, C. R., Doebling, S. W., and Nix, D. A. (2001). “Vibration-based structural damage detection.” Phil. Trans. R. Soc., A, 359(1778), 131–149.
Hernandez, E. M. (2014). “Identification of isolated structural damage from incomplete spectrum information using -norm minimization.” Mech. Syst. Signal Process., 46(1), 59–69.
Hernandez, E. M., and Polanco, N. (2014). “Uncertainty quantification in identified modal parameters using fisher information criterion.” Proc., XXXII Int. Modal Analysis Conf., Society for Experimental Mechanics, Bethel, CT.
Kaouk, M., and Zimmerman, D. C. (1994). “Structural damage assessment using a generalized minimum rank perturbation theory.” AIAA J., 32(4), 836–842.
Michel, A. N., and Herget, C. J. (1981). Applied algebra and functional analysis, Dover Publications, New York.
Moser, P., and Moaveni, B. (2011). “Environmental effects on the identified natural frequencies of the Dowling Hall Footbridge.” Mech. Syst. Sig. Process., 25(7), 2336–2357.
Mottershead, J. E., Link, M., and Friswell, M. (2011). “The sensitivity method in finite element model updating. A tutorial.” Mech. Syst. Sig. Process., 25(7), 2275–2296.
Ray, L., and Tian, L. (1999). “Damage detection in smart structures through sensitivity-enhancing feedback control.” Proc., SPIE Smart Structures and Materials: Smart Structures and Integrated Systems, International Society for Optical Engineering, Bellingham, WA.
Salawu, O. S. (1997). “Detection of structural damage through changes in frequency: A review.” Eng. Struct., 19(9), 718–723.
Sohn, H., Farrar, C. R., Hemez, F., and Shunk, D. D. (2003). “A review of structural health monitoring literature: 1996–2001.”, Los Alamos, NM.
Tropp, J. A. (2004). “Greed is good: Algorithmic results for sparse approximation.” IEEE Trans. Inf. Theory, 50(10), 2231–2242.
Wang, X., Yang, C., Wang, L., Yang, H., and Qiu, Z. (2013). “Membership-set identification method for structural damage based on measured natural frequencies and static displacements.” Struct. Health Monit., 12(1), 23–34.
Wipf, D., and Rao, B. (2004). “Sparse Bayesian learning for basis selection.” IEEE Trans. Sig. Process., 52(8), 2153–2164.
Yuen, K.-V. (2012). “Updating large models for mechanical systems using incomplete modal measurement.” Mech. Syst. Sig. Process., 28, 297–308.
Information & Authors
Information
Published In
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Sep 8, 2014
Accepted: Jun 4, 2015
Published online: Jul 23, 2015
Discussion open until: Dec 23, 2015
Published in print: Feb 1, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.