Improved Damage Localization and Quantification Using Subset Selection
Publication: Journal of Engineering Mechanics
Volume 135, Issue 6
Abstract
Because a structure’s modal parameters (natural frequencies and mode shapes) are affected by structural damage, finite- element model updating techniques are often applied to locate and quantify structural damage. However, the dynamic behavior of a structure can only be observed in a narrow knowledge space, which usually causes nonuniqueness and ill-posedness in the damage detection problem formulation. Thus, advanced optimization techniques are a necessary tool for solving such a complex inverse problem. Furthermore, a preselection process of the most significant damage parameters is helpful to improve the efficiency of the damage detection procedure. A new approach, which combines a parameter subset selection process with the application of damage functions is proposed herein to accomplish this task. Starting with a simple 1D beam, this paper first demonstrates several essential concepts related to the proposed model updating approach. A more advanced example considering a 2D model is then considered. To determine the capabilities of this approach for more complex structures, a trust region-based optimization method is adopted to solve the corresponding nonlinear minimization problem. The objective is to provide an improved robust solution to this challenging problem.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writers are grateful to the National Science Foundation for financing this research work through Grant Nos NSF0625640 and NSF0245402.
References
ABAQUS 6.6. (2006). Analysis user’s manual and ABAQUS scripting user’s manual, ABAQUS, Inc., Hibbitt, Karlsson, Sorensen, Providence, R.I.
Aktan, A. E., Lee, K. L., Chuntavan, C., and Aksel, T. (1994). “Modal testing for structural identification and condition assessment of constructed facilities.” Proc., 12th Int. Modal Analysis Conf., 462–468.
Allemang, R. J., and Brown, D. L. (1982). “A correlation coefficient for modal vector analysis.” Proc., 1st Int. Modal Analysis Conf., 110–116.
Bernal, D. (2000). “Extracting flexibility matrices from state-space realizations.” Proc., COST F3 Conf. on System Identification and Structural Health Monitoring, 127–135.
Bernal, D., and Beck, J. L. (2004). “Special section: Phase I of the IASC-ASCE structural health monitoring benchmark.” J. Eng. Mech., 130(1), 1–127.
Cawley, P., and Adams, R. D. (1979). “The locations of defects in structures from measurements of natural frequencies.” J. Strain Anal. Eng. Des., 14(2), 49–57.
Cornwell, P., Doebling, S. W., and Farrar, C. R. (1997). “Application of the strain energy damage detection method to plate like structures.” Proc., 15th Int. Modal Analysis Conf., 1312–1318.
Dennis, J. E., and Schnabel, R. B. (1996). Numerical methods for unconstrained optimization and nonlinear equations, SIAM Publications, Philadelphia.
Doebling, S. W., Farrar, C. R., and Prime, M. B. (1998). “A summary review of vibration-based damage identification methods.” Shock Vib. Dig., 30(2), 91–105.
Draper, N. R., Guttman, I., and Kanemasu, H. (1971). “The distribution of certain regression statistics.” Biometrika, 58, 295–298.
Efroymson, M. A. (1960). “Multiple regression analysis.” Mathematical methods for digital computers, Vol. 1, A. Ralston and H. S. Wilf, eds., Wiley, New York, 191–203.
Farrar, C. R., Sohn, H., Hemez, F. M., Anderson, M. C., Bement, M. T., Cornwell, P. J., Doebling, S. W., Lieven, N., Roberson, A. N., and Schultze, J. F. (2003). “Damage prognosis: Current status and future needs.” Rep. No. LA-14051-MS, Los Alamos National Labs.
Fox, J. (1997). Applied regression analysis, linear models, and related methods, Sage Publications Inc., Thousand Oaks, Calif.
Fox, R. L., and Kapoor, M. P. (1968). “Rate of change of eigenvalues and eigenvectors.” AIAA J., 12(6), 2426–2429.
Friswell, M. I., and Mottershead, J. E. (1995). Finite-element model updating in structural dynamics, Kluwer, Norwell, Mass.
Friswell, M. I., Penny, J. E. T., and Garvey, S. D. (1997). “Parameter subset selection in damage location.” Inverse Probl. Eng., 5(3), 189–215.
Guyan, R. J. (1965). “Reduction of stiffness and mass matrices.” AIAA J., 3, 380–380.
Jaishi, B., and Ren, W.-X. (2006). “Damage detection by finite-element model updating using modal flexibility residual.” J. Sound Vib., 290, 369–387.
Lallement, G., and Piranda, J. (1990). “Localisation methods for parameter updating of finite-element models in elastodynamics.” Proc., 8th Int. Modal Analysis Conf., 579–585.
Lieven, N. A. J., and Ewins, D. J. (1988). “Spatial correlation of mode shapes, the coordinate modal assurance criterion (COMAC).” Proc., 6th Int. Modal Analysis Conf., 690–695.
MATLAB optimization toolbox. (2006). MathWorks, Inc.
Millar, A. J. (2002). Subset selection in regression, 2nd Ed., Chapman and Hall/CRC, Boca Raton, Fla.
Moré, J. (1983). “Recent developments in algorithms and software for trust region methods.” Mathematical programming, the state of the art, A. Bachem, M. Grotschel, and G. Korte, eds., Springer, New York, 256–287.
Mottershead, J. E., and Friswell, M. I. (1993). “Model updating in structural dynamics: A survey.” J. Sound Vib., 167(2), 347–375.
Nocedal, J. (1992). “Theory of algorithms for unconstrained optimization.” Acta Numerica, 1, 199–242.
O’Callahan, J. C. (1989). “A new procedure for an improved reduced system (IRS) model.” Proc., 7th Int. Modal Analysis Conf., 17–21.
O’Callahan, J. C., Avitabile, P., and Riemer, R. (1989). “System equivalent reduction expansion process (SEREP).” Proc., 7th Int. Modal Analysis Conf., 29–37.
Pandey, A. K., and Biswas, M. (1994). “Damage detection in structures using changes in flexibility.” J. Sound Vib., 169(1), 3–17.
Pandey, A. K., and Biswas, M. (1995). “Damage diagnosis of truss structures by estimation of flexibility change.” Int. J. Anal. Exp. Modal Anal., 10(2), 104–117.
Pandey, A. K., Biswas, M., and Samman, M. M. (1991). “Damage detection from changes in curvature mode shapes.” J. Sound Vib., 145(2), 321–332.
Paz, M. (1984). “Dynamic condensation.” AIAA J., 22(5), 724–727.
Pope, P. T., and Webster, J. T. (1972). “The use of an F-statistic in stepwise regression procedures.” Technometrics, 14, 327–340.
Powell, M. J. D. (1975). “Convergence properties of a class of minimization algorithms.” Nonlinear programming 2, O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds., Academic, San Diego, 1–27.
Salawu, O. S. (1997). “Detection of structural damage through changes in frequency: A review.” Eng. Struct., 19(9), 718–723.
Sohn, S., Dzonczyk, M., Straser, E. G., Kiremidjian, A. S., Law, K. H., and Meng, T. (1999). “An experimental study of temperature effect on modal parameters of the Alamosa Canyon Bridge.” Earthquake Eng. Struct. Dyn., 28, 879–897.
Song, W., and Dyke, S. (2006). “Ambient vibration based modal identification of the Emerson Bridge considering temperature effects.” Proc., 4th World Conf. on Structural Control and Monitoring, Univ. of California, San Diego.
Teughels, A., and De Roeck, G. (2004). “Structural damage identification of the highway bridge Z24 by FE model updating.” J. Sound Vib., 278, 589–610.
Teughels, A., Maeck, J., and De Roeck, G. (2002). “Damage assessment by FE model updating using damage functions.” Comput. Struct., 80(25), 1869–1879.
Titurus, B., Friswell, M. I., and Starek, L. (2003). “Damage detection using generic elements. Part II: Damage detection.” Comput. Struct., 81, 2287–2299.
Toksoy, T., and Aktan, A. E. (1994). “Bridge-condition assessment by modal flexibility.” Exp. Mech., 34, 271–278.
Wolff, T., and Richardson, M. (1989). “Fault detection in structures from changes in their modal parameters.” Proc., 7th Int. Modal Analysis Conf., 87–94.
Wu, Z., and Abe, M., eds., (2003). Proc., Int. Conf. on Structural Health Monitoring and Intelligent Infrastructure, Swets and Zeitlinger, Lisse, The Netherlands.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 135 • Issue 6 • June 2009
Pages: 548 - 560
Copyright
© 2009 ASCE.
History
Received: Feb 8, 2008
Accepted: Oct 16, 2008
Published online: Mar 3, 2009
Published in print: Jun 2009
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.