Statistical Damage Assessment of Framed Structures from Static Responses
Publication: Journal of Engineering Mechanics
Volume 126, Issue 4
Abstract
This paper presents a damage assessment algorithm for framed structures based on a system identification scheme with a regularization technique. The regularization technique is introduced to alleviate the ill-posedness of the system identification problems. A new regularization function based on the Frobenius norm of the difference between the estimated and the baseline stiffness matrix is proposed. A parameter grouping technique is adopted to locate damaged members and to overcome sparseness of measured data. A data perturbation method is employed to obtain statistical distributions of system parameters with a set of noise-polluted measured data. A statistical approach by a hypothesis test is presented to assess damage. The validity of the proposed method is demonstrated through numerical examples.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ang, A. H. S., and Tang, W. H. (1975). Probability concepts in engineering planning and design. Vol. I, Wiley, New York.
2.
Banan, M. R., Banan, M. R., and Hjelmstad, K. D. (1994a). “Parameter estimation of structure from static response. I: Computational aspect.”J. Struct. Engrg., ASCE, 120(11), 3243–3258.
3.
Banan, M. R., Banan, M. R., and Hjelmstad, K. D. (1994b). “Parameter estimation of structure from static response. II: Numerical simulation studies.”J. Struct. Engrg., ASCE, 120(11), 3259–3283.
4.
Becks, J. V., and Murio, D. A. (1984). “Combined function specification—regularization procedure for the solution of inverse heat conduction problem.” AIAA J., 24, 180–185.
5.
Benjamin, J. R., and Cornell, C. A. (1970). Probability, Statistics, and Decision for Civil Engineers. McGraw-Hill, New York.
6.
Bui, H. D. (1994). Inverse problems in the mechanics of materials: An introduction. CRC Press, Boca Raton, Fla.
7.
Golub, G. H., Heath, M., and Wahba, G. (1978). “Generalized cross-validation as a method for choosing a good ridge parameter.” Technometrics, 21, 215–223.
8.
Groetsch, C. W. (1984). The theory of Tikhonov regularization for Fredholm equations of the first kind. Pitman Advanced Publishing, Boston.
9.
Hajela, P., and Soeiro, F. J. (1990). “Structural damage detection based on static and modal analysis.” AIAA J., 28(6), 1110–1115.
10.
Hansen, P. C. (1992). “Analysis of discrete ill-posed problems by means of the L-curve.” SIAM Rev., 34(4), 561–580.
11.
Hjelmstad, K. D., and Shin, S. (1997). “Damage detection and assessment of structures from static response.”J. Engrg. Mech., ASCE, 123(6), 568–576.
12.
Hjelmstad, K. D. (1996). “On the uniqueness of modal parameter estimation.” J. Sound and Vibration, 192(2), 581–598.
13.
Lee, H. S., Kim, Y. H., Park, C. J., and Park, H. W. (1999). “A new spatial regularization scheme for the identification of geometric shapes of inclusions in finite bodies.” Inter. J. Numer. Methods in Engrg., 46, 973–992.
14.
Nam, H. ( 1997). “Detection of structural damage using system identification and binary search method,” M.S. thesis, Seoul National University, Seoul, Korea (in Korean).
15.
Neuman, S. P., and Yakowitz, S. (1979). “A statistical approach to the inverse problem of aquifer hydrology.” Water Resour. Res., 15(4), 845–860.
16.
Sanayei, M., and Onipede, O. (1991). “Damage assessment of structures using static test data.” AIAA J., 29(7), 1174–1179.
17.
Schnur, D. S., and Zabaras, N. (1990). “Finite element solution of two dimensional inverse elastic problems using spatial smoothing.” Inter. J. Numer. Methods in Engrg., 30, 57–75.
Information & Authors
Information
Published In
History
Received: Dec 31, 1998
Published online: Apr 1, 2000
Published in print: Apr 2000
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.