Efficient Model Correction Method with Modal Measurement
Publication: Journal of Engineering Mechanics
Volume 136, Issue 1
Abstract
An efficient model correction method is proposed by using the modal measurement from a structural system. The method corrects/updates the mass and stiffness matrix without imposing any parameterization. It considers the information from both the nominal finite-element model and the measurement of modal frequencies and mode shapes. The method is computationally very efficient and it does not require computation of the complete set of eigenvalues and eigenvectors of the nominal model. Instead, only the nominal eigenvalues and eigenvectors of the modes to be corrected are needed. The Gram-Schmidt orthogonalization process is used to construct a basis that satisfies the mass orthogonality condition. This basis is used to transform the eigenvectors of the nominal model so that the corrected model is compatible with the measurement. A thousand-degree-of-freedom chainlike system and a 1,440-degree-of-freedom structural frame are used to illustrate the proposed method.
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Acknowledgments
This work was supported by the research committee of University of Macau under Research Grant Nos. UNSPECIFIEDRG074/05-06S/07R/YKV/FST and UNSPECIFIEDRG077/07-08S/YKV/FST. These grants are gratefully acknowledged.
References
Agbabian, M. S., and Masri, S. F., eds. (1988). Proc., Int. Workshop on Nondestructive Evaluation for Performance of Civil Structures, Univ. of Southern Calif., Los Angeles.
Beck, J. L. (1978). “Determining models of structures from earthquake records.” Technical Rep. No. EERL 78-01, California Institute of Technology, Earthquake Engineering Research Laboratory, Pasadena, Calif.
Beck, J. L., Au, S. K., and Vanik, M. W. (2001). “Monitoring structural health using a probabilistic measure.” Comput. Aided Civ. Infrastruct. Eng., 16, 1–11.
Beck, J. L., and Wu, Z., eds. (2006). “Special issue on structural health monitoring.” Comput. Aided Civ. Infrastruct. Eng., 21(4).
Berman, A. (1979). “Mass matrix correction using an incomplete set of measured modes.” AIAA J., 17(10), 1147–1148.
Berman, A., and Flannelly, W. G. (1971). “Theory of incomplete models of dynamics structures.” AIAA J., 9(8), 1481–1487.
Bernal, D. (2002). “Load vectors for damage localization.” J. Eng. Mech., 128(1), 7–14.
Bernal, D., and Beck, J. L., eds. (2004). “Special issue on Phase I of the IASC-ASCE structural health monitoring benchmark.” J. Eng. Mech., 130(1).
Chang, F. K., ed. (2003). Proc., 4th Int. Workshop on Structural Health Monitoring, DEStech, San Francisco.
Ching, J., and Beck, J. L. (2004). “New Bayesian model updating algorithm applied to a structural health monitoring benchmark.” Struct. Health Monit., 3, 313–332.
Clough, R. W., and Penzien, J. (1975). Dynamics of structures, McGraw-Hill, New York.
Cooper, J. E. (1989). “Comparison of some time domain system identification techniques using approximate data correlations.” Int. J. Anal. Exp. Modal Anal., 4, 51–57.
Farhat, C., and Hemez, F. M. (1993). “Updating finite element dynamics models using element-by-element sensitivity methodology.” AIAA J., 31(9), 1702–1711.
Friswell, M. I., and Mottershead, J. E. (1995). Finite element model updating in structural dynamics, Kluwer Academic, Boston.
Gersch, W., Taoka, G. T., and Liu, R. (1976). “Structural system parameter estimation by two-stage least squares method.” J. Eng. Mech., 102(5), 883–899.
Ghanem, R., and Sture, S., eds. (2000). “Special issue on structural health monitoring.” J. Eng. Mech., 126(7).
Hearn, G., and Testa, R. B. (1991). “Modal analysis for damage detection in structures.” J. Struct. Eng., 117(10), 3042–3063.
Hoshiya, M., and Saito, E. (1984). “Structural identification by extended Kalman filter.” J. Eng. Mech., 110(12), 1757–1770.
Ibrahim, S. R. (1986). “Double least squares approach for use in structural modal identification.” AIAA J., 24(3), 499–503.
Juang, J. N., and Suzuki, H. (1988). “An eigen-system realization algorithm in frequency domain for modal parameter identification.” Journal of Vibration, Acoustics, Stress, and Reliability in Design, 110(1), 24–29.
Kabe, A. M. (1985). “Stiffness matrix adjustment using mode data.” AIAA J., 23(9), 1431–1436.
Lam, H. F., Ko, J. M., and Wong, C. W. (1998). “Localization of damaged structural connections based on experimental modal and sensitivity analysis.” J. Sound Vib., 210(1), 91–115.
Lam, H. F., Yuen, K. -V., and Beck, J. L. (2006). “Structural health monitoring via measured ritz vectors utilizing artificial neural networks.” Comput. Aided Civ. Infrastruct. Eng., 21(4), 232–241.
Lin, R. M., Lim, M. K., and Du, H. (1995). “Improved inverse eigensensitivity method for structural analytical model updating.” J. Vibr. Acoust., 117(2), 192–198.
Natke, H. G., and Yao, J. T. P. (1988) Proc., Workshop on Structural Safety Evaluation Based on System Identification Approaches, Vieweg and Sohn, Wiesbaden, Germany.
Naylor, A. W., and Sell, G. R. (1982). Linear operator theory in engineering and science, Springer, New York.
Pandey, A. K., and Biswas, M. (1995). “Experimental verification of flexibility difference method for locating damage in structures.” J. Sound Vib., 184, 311–328.
Quek, S. T., Wang, W. P., and Koh, C. G. (1999). “System identification of linearMDOF structures under ambient excitation.” Earthquake Eng. Struct. Dyn., 28, 61–77.
Sanayei, M., McClain, J. A. S., Wadia-Fascetti, S., and Santini, E. M. (1999). “Parameter estimation incorporating modal data and boundary conditions.” J. Struct. Eng., 125(9), 1048–1055.
Smyth, A. W., Masri, S. F., Caughey, T. K., and Hunter, N. F. (2000). “Surveillance of intricate mechanical systems on the basis of vibration signature analysis.” J. Appl. Mech., 67(3), 540–551.
Topole, K. G., and Stubbs, N. (1995). “Non-destructive damage evaluation in complex structures from a minimum of modal parameters.” Int. J. Anal. Exp. Modal Anal., 10(2), 95–103.
Vanik, M. W., Beck, J. L., and Au, S. K. (2000). “Bayesian probabilistic approach to structural health monitoring.” J. Eng. Mech., 126(7), 738–745.
Wei, F. S. (1990). “Analytic dynamic model improvement using vibration test data.” AIAA J., 28(1), 175–177.
Yao, J. T. P., ed. (2001). “Special issue on structural health monitoring.” Comput. Aided Civ. Infrastruct. Eng., 16(1).
Yuen, K. -V., Au, S. K., and Beck, J. L. (2004). “Two-stage structural health monitoring methodology and results for Phase I benchmark studies.” J. Eng. Mech., 130(1), 16–33.
Yuen, K. -V., Beck, J. L., and Katafygiotis, L. S. (2006). “Efficient model updating and monitoring methodology using incomplete modal data without mode matching.” Struct. Control Health Monit., 13(1), 91–107.
Yuen, K. -V., and Katafygiotis, L. S. (2001). “Bayesian time-domain approach for modal updating using ambient data.” Probab. Eng. Mech., 16(3), 219–231.
Yuen, K. -V., and Katafygiotis, L. S. (2002). “Bayesian modal updating using complete input and incomplete response noisy measurements.” J. Eng. Mech., 128(3), 340–350.
Yuen, K. -V., and Katafygiotis, L. S. (2006). “Substructure identification and health monitoring using response measurement only.” Comput. Aided Civ. Infrastruct. Eng., 21(4), 280–291.
Yuen, K. -V., and Lam, H. F. (2006). “On the complexity of artificial neural networks for smart structures monitoring.” Eng. Struct., 28(7), 977–984.
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Information
Published In
Journal of Engineering Mechanics
Volume 136 • Issue 1 • January 2010
Pages: 91 - 99
Copyright
© 2010 ASCE.
History
Received: Mar 31, 2008
Accepted: Jun 19, 2009
Published online: Jun 22, 2009
Published in print: Jan 2010
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