Application of Structured Low Rank Approximation Method for Noise Elimination from Measured Impulsive Response Functions

Abstract:

This paper develops a structured low rank approximation (SLRA) method for noise elimination from a noisy impulsive response function (IRF). Cadzow’s algorithm is implemented for the SLRA on the Hankel matrix constructed by measured IRF in order to obtain a filtered IRF. Using the proposed noise elimination scheme, some important factors, such as the size of a Hankel matrix and the quantification of the noise reduction performance are evaluated. Synthesized IRFs are applied to demonstrate the performance, and illustrate the procedure as well, of the proposed scheme in the numerical study. The results indicate that this method can eliminate noise from measured IRFs efficiently.

• Periodical: Applied Mechanics and Materials (Volumes 48-49)
• Pages: 261-264
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.48-49.261
• Online since: February 2011
• Authors: Cui Lin Li, Xing Xian Bao
• Keywords: Cadzow’s Algorithm, Impulsive Response Function, Noise Elimination, Structured Low Rank Approximation

References

[1] Pickrel C.R., in: Estimating the rank of measured response data using SVD and principal response functions [C]. Proceedings of the Second International Conference on Structural Dynamics Modeling, Test Analysis and Correlation DTA/NAFEMS, 1996: 89-100.

[2] Juang J.N. and Pappa R.S., in: Effects of noise on modal parameters identified by the eigensystem realization algorithm [J]. Journal of Guidance, Control and Dynamics, 1986, 9: 294–303.

DOI: 10.2514/3.20106

[3] Allemang R.J. and Brown D.L., in: A unified matrix polynomial approach to modal identification [J]. Journal of Sound and Vibration, 1998, 211: 301–322.

DOI: 10.1006/jsvi.1997.1321

[4] Liu K., in: Application of SVD in optimization of structural modal test [J]. Computers & Structures, 1997, 63: 51–99.

DOI: 10.1016/s0045-7949(96)00329-x

[5] Cadzow J.A., in: Spectral estimation: an overdetermined rational approach [C]. Proceedings of the IEEE, 1982, 70: 907–939.

DOI: 10.1109/proc.1982.12424

[6] Braun S.G. and Ram Y.M., in: Determination of structural modes via the prony method: system order and noise induced poles [J]. Journal of the Acoustical Society of America, 1987, 81: 1447–1459.

DOI: 10.1121/1.394497

[7] De Moor B., in: Structured total least squares and L2 approximation problems [J]. Linear Algebra and its Applications, 1993: 188-189: 163–207.

DOI: 10.1016/0024-3795(93)90468-4

[8] Markovsky I. and Huffel S.V., in: Overview of total least squares methods [J]. Signal Processing, 2007, 87: 2283–2302.

DOI: 10.1016/j.sigpro.2007.04.004

[9] Markovsky I., in: Structured low-rank approximation and its applications [J]. Automatica, 2008, 44: 891–909.

DOI: 10.1016/j.automatica.2007.09.011

[10] Cadzow J.A., in: Signal enhancement—A composite property mapping algorithm [J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1988, 36: 49–62.

DOI: 10.1109/29.1488

[11] Hu S-L.J., Bao X.X. and Li H.J., in: Model order determination and noise removal for modal parameter estimation[J]. Mechanical Systems and Signal Processing, 2010, 24: 1605-1620.

DOI: 10.1016/j.ymssp.2010.01.005

[12] Tufts D. and Shah A., in: Estimation of a signal waveform from noisy data using low-rank approximation to a data matrix [J]. IEEE Transactions on Signal Processing, 1993, 41: 1716–1721.

DOI: 10.1109/78.212753

[13] Johnson L.W. and Riess R.D., in: Numerical Analysis [M]. 2nd Edition, Addison-Wesley Press, Reading, Massachusetts, (1982).