Abstract
Principal Component Analysis (PCA) methods have been variously developed and applied within the experimental modal community for some time based upon the underlying linear/superposition nature of structural dynamics. While historically the use of these techniques has been restricted to the areas of model order determination (Complex Mode Indicator Function [CMIF]), enhanced frequency response function estimation, and parameter identification, increasingly they are being applied to the areas of test/model validation, experimental model correlation/repeatability and experimental/structural model comparison. With the increasing volume of data being collected today, techniques which provide effective extraction of the significant data features for quick, easy comparison are essential. This paper explores the general development and application of PCA to experimental modal analysis and its ability to provide the analyst with an effective global trend visualization tool. As examples, the results from a laboratory test structure (circular plate), a civil infrastructure (bridge), and a comparative study (automotive) are presented.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Wilkinson, J.H., The Algebraic Eigenvalue Problem, Oxford University Press, Oxford, U.K., 1965, pp. 12–13.
Strang, G., Linear Algebra and Its Applications, Third Edition, Harcourt Brace Jovanovich Publishers, San Diego, CA, 1988, 505 pp.
Lawson, C.L., Hanson, R.J., Solving Least Squares Problems, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1974, 340 pp.
Jolliffe, I.T., Principal Component Analysis Springer-Verlag New York, Inc., New York, NY, 1986, 271 pp.
Ljung, Lennar t, System Identification: Theory for the User, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1987, 519 pp.
Deprettere, E.F.A., SVD and Signal Processing: Algorithms, Applications and Architectures, Elsevier Science Publishing Company, Inc., New York, NY, 1988, 477 pp.
Hyvarinen, A., Karhunen, J, Oja, E., Independent Component Analysis, John Wiley & Sons, Inc., New York, NY, 2001, 481 pp.
Jackson, Edward J., A User’s Guide to Principal Components, John Wiley & Sons,Inc., Hoboken, NJ, 2003, 569 pp.
Allemang, R.J., Rost, R.W., Brown, D.L., "Multiple Input Estimation of Frequency Response Functions: Excitation Considerations", ASME Paper Number 83-DET-73, 1983, 11 pp.
Allemang, R.J., Brown, D.L., Rost, R.W., "Multiple Input Estimation of Frequency Response Functions for Experimental Modal Analysis", U.S. Air Force Report Number AFATL-TR-84-15, 1984, 185 pp.
Allemang, R.J., Brown, D.L., Rost, R.W., "Measurement Techniques for Experimental Modal Analysis", Experimental Modal Analysis and Dynamic Component Synthesis, USAF Technical Report, Contract Number F33615-83-C-3218, AFWAL-TR-87-3069, Volume 2, 1987.
"Complex Mode Indication Function and Its Application to Spatial Domain Parameter Estimation", Shih, C.Y., Tsuei, Y.G., Allemang, R.J., Brown, D.L., Journal of Mechanical Systems and Signal Processing, Academic Press Limited, Volume 2, Number 4, pp. 367–372, 1988.
"Complex Mode Indicator Function and its Application to Spatial Domain Parameter Estimation", Shih, C.Y., Tsuei, Y.G., Allemang, R.J., Brown, D.L., Proceedings, 13th International Seminar on Modal Analysis, Katholieke Universiteit Leuven, Belgium, 15 pp., 1988.
"Complex Mode Indication Function and its Application to Spatial Domain Parameter Estimation", Shih, C.Y., Tsuei, Y.G., Allemang, R., Brown, D.L., Proceedings, Inter national Modal Analysis Conference, pp. 533–540, 1989.
"A Complete Review of the Complex Mode Indicator Function (CMIF) with Applications", Allemang, R.J., Brown, D.L., Proceedings, International Conference on Noise and Vibration Engineering (ISMA), Katholieke Universiteit Leuven, Belgium, 38 pp., 2006.
"Estimating the Rank of Measured Response Data Using SVD and Principal Response Functions", Pickrel, C.R., Proceedings of the Second International Conference on Structural Dynamics Modeling, Test Analysis and Correlation DTA/NAFEMS, pp. 89–100, 1996.
"Numerical Assessment of Test Data Using SVD", Pickrel, C.R., Proceedings, International Modal Analysis Conference, pp. 1577, 1997.
"Numerical Assessment of Test Data Using SVD", Pickrel, C.R., Proceedings of SPIE, the International Society for Optical Engineering, Vol. 3089 (2), pp. 1577–1587, 1997.
"Squeak and Rattle Detection : A Comparative Experimental Data Analysis", Mantrala, Ravi, MS Thesis, University of Cincinnati, 134 pp., 2007.
"Using Group Transmissibility Concepts to Compare Dissimilar Vehicle Platforms", Yee, Abbey, MS Thesis, University of Cincinnati, 59 pp., 2009.
"FRAC: A Consistent way of Compar ing Frequency Response Functions", Heylen, W., Lammens, S., Proceedings, International Conference on Identification in Engineering, Swansea, pp. 48–57, 1996.
"The Modal Assurance Criter ion (MAC): Twenty Years of Use and Abuse", Allemang, R.J., Proceedings, International Modal Analysis Conference, pp. 397–405, 2002. Sound and Vibration Magazine, Vol. 37, No. 8, pp. 14–23, August, 2003.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Businees Media, LLC
About this paper
Cite this paper
Allemang, R.J., Phillips, A.W., Allemang, M.R. (2011). Application of Principal Component Analysis Methods to Experimental Structural Dynamics. In: Proulx, T. (eds) Structural Dynamics, Volume 3. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9834-7_45
Download citation
DOI: https://doi.org/10.1007/978-1-4419-9834-7_45
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-9833-0
Online ISBN: 978-1-4419-9834-7
eBook Packages: EngineeringEngineering (R0)