Damage Identification through Regularization Method. I: Theory
Publication: Journal of Engineering Mechanics
Volume 124, Issue 1
Abstract
This paper presents a solution procedure for damage identification through measured structural response. The cost functional employed is based on the regulation method for inverse problems. An optimization procedure using the Euler-Lagrange equation is developed to reduce the minimization problem to a two-point boundary value problem (TPBVP) with jump discontinuities. Compared to existing techniques in solving the minimization problem, this approach does not resolve to more advanced mathematical tools and is thus more easily accepted in the engineering application field. Numerical studies of 2-DOF and 10-DOF shear beam-type structures and experimental correlation with a three-story model structure demonstrate the feasibility and accuracy of the proposed approach and are reported in a companion paper.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ahmadi, A. K., and Torkamani, A. M.(1988). “Stiffness identification of frames using simulated ground excitation.”J. Engrg. Mech., ASCE, 114(5), 753–776.
2.
Alekseev, A. M., Tikhomirov, V. M., and Fomin, S. V. (1987). Optimal Control. Consultants Bureau, New York, N.Y.
3.
Athans, M., and Falb, P. (1966). Optimal control. McGraw-Hill Inc., New York, N.Y.
4.
Beck. J. L., and Jennings(1988). “Structural identification using linear models and earthquake records.”Earthquake Engrg. and Struct. Dynamics, 8, 145–160.
5.
Beck, J. L., Vanik, M. W., and Katafygiotis, L. S. (1994). “Determination of stiffness changes from modal parameter changes for structural health monitoring.”Proc., 1st World Conf. on Struct. Control, Los Angeles, Calif, TA3-13–TA3-22.
6.
Billings, S. A. (1980). “Identification of nonlinear systems—a survey.”IEEE Proc., 127(D6), 272–284.
7.
Bryson, A. E., and Ho, Y. C. (1975). Applied optimal control. John Wiley & Sons, Inc., New York, N.Y.
8.
Casas, J. R., and Aparicio, A. C. (1994). “Structural damage identification from dynamic-test data.”J. Struct. Engrg., ASCE 120(8), 2437–2450.
9.
Chen, H. L., Spyrakos, C. C., and Venkatesh, G.(1995). “Evaluating structural deterioration by dynamic response.”J. Struct. Engrg., ASCE, 121(8), 1197–1204.
10.
Geering, H. P. (1976). “Continuous time optimal control theory for cost functionals including discrete state penalty terms.”IEEE Trans. Automatic Control, AC-21, 863–869.
11.
Ghanem, R. G., Gavin, H., and Shinozuka, M. (1991). “Experimental verification of a number of structural system identification algorithms.”Tech. Rep. NCEER 91-0024, Nat. Ctr. for Earthquake Engrg. Res., Buffalo, N.Y.
12.
Koh, C. G., See, L. M., and Balenra, T.(1995). “Damage detection of buildings: Numerical and experimental studies.”J. Struct. Engrg., ASCE, 121(8), 1155–1160.
13.
Kondo, I., and Hamamoto, T. (1996). “Seismic damage detection of multi-story buildings using vibration monitoring,”llth World Conf. on Earthquake Engrg., Acapulco, Mexico.
14.
Lessons from Northridge: Property Risk is higher than previously known. (1995). EQE International, San Francisco, Calif.
15.
Lin, C. C., Soong, T. T., and Natke, H. G.(1990). “Real-time system identification of degrading structures.”J. Engrg. Mech., ASCE, 116(10), 2258–2274.
16.
Liu, P. L.(1995). “Identification and damage detection of trusses using modal data.”J. Struct. Engrg., ASCE, 121(4), 599–608.
17.
Mook, D. J., and Junkins, J. L.(1987). “Minimum model error estimation for poorly modeled dynamic systems.”J. Guidance, 11(3), 256–261.
18.
Morozov, V. A. (1984). Methods for solving incorrectly posed problems. Springer-Verlag New York, Inc., New York, N.Y.
19.
Natke, H. G., Juang, J. N., and Gawronski, (1988). “A brief review of the identification of nonlinear mechanical systems.”Proc., 6th IMAC, Orlando, Fla, 1569–1574.
20.
Natke, H. G., and Yao, J. T. P. (1986). “System identification approach in structural damage evaluation,”CE-STR-86-21, Purdue Univ., Lafayette, Ind.
21.
Osborne, M. R.(1969). “On shooting methods for boundary value problems.”J. Mathematical Analysis and Applications, 27, 417–433.
22.
Peng, C. Y., and Iwan, W. D. (1988). “Identification of hysteretic structural behavior from strong motion accelerograms.”Structural safety evaluation based in system identification, Natke and Yao, eds., Vieweg Verlag.
23.
Press, W. H., et al. (1992). Numerical recipes in Fortran, the art of scientific computing. University Press, Cambridge, Mass.
24.
Saito, Y., and Hoshiya, M. (1996). “Identification of M, C and K of a multiple degree of freedom system.”Proc., 11th World Conf. on Earthquake Engrg., Acapulco, Mexico.
25.
Seidman, T. I., and Vogel, C. R.(1989). “Well posedness and convergence of some regularization methods for non-linear ill-posed problems.”Inverse Problem, 5, 227–238.
26.
Shi, T., Jones, N. P., and Ellis, J. H. (1995). “System identification using output measurement.”Proc., 10th Conf. on Engrg. Mech., ASCE Press, New York, 305–308.
27.
Stubbs, N., and Topole, K. G. (1993). “A damage localization algorithm for nonlinear structures.”Safety evaluation based on identification approaches, Natke/Tomlinson/Yao, eds., Lambrecht, Germany.
28.
Tikhonov, A. N., and Arsenin, V. Y. (1977). Solutions of ill-posed problems. John Wiley & Sons, Inc., New York, N.Y.
29.
Udwadia, F. E., and Shah, P. C.(1976). “Identification of structures through records obtained during strong ground shaking.”J. Engrg. for Industry, ASME, 98(4), 1347–1362.
30.
Yun, C. B., and Shinozuka, M. (1980) “Identification of nonlinear structural dynamic systems.”J. Struct. Mech., ASCE, 8(2), 187–203.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 124 • Issue 1 • January 1998
Pages: 103 - 108
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Jan 1, 1998
Published in print: Jan 1998
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.