Abstract
The establishment of a non-parametric system description in terms of a Frequency Response Function matrix is an essential step in many structural and vibro-acoustic analysis approaches such as Modal Analysis, Load Identification, Transfer Path Analysis and Substructuring. A crucial step in many of these applications is the inversion of a matrix of this FRF matrix. Several studies have been reported on the influence of stochastic FRF errors on this matrix inversion, leading to the use of a pseudo-inverse approach, SVD truncation, regularization etc. but little is known about the effect of systematic errors, such as amplitude or frequency shifts and inter-FRF inconsistencies on the matrix inversion result. The present paper investigates the effect of selected systematic FRF measurement errors on applications involving matrix inversion, with emphasis on the Transfer Path Analysis method. The subject is reviewed through analytical considerations and through simulations on a reference numerical model (the Garteur model). In particular, the sensitivity of two Transfer Path Analysis methods with respect to the studied systematic errors is analyzed and considerations on increasing the robustness of these methods are derived.
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
G. Desanghere, “Identification of external forces based on frequency response measurements”, in Proc. 8-th International Seminar on Modal Analysis, Leuven, Belgium, 1983.
M. Ohlrich and A. Crone: An equivalent force description of gear-box sources applied in prediction of structural vibrational in wind turbines. In Pro.Inter-Noise 88, the International Conference on Noise Control Engineering, Avignon, France, 1988, pp. 479-484.
H. Van der Auweraer, P. Mas, S. Dom, A. Vecchio, K. Janssens and P. Van de Ponseele, “Transfer Path Analysis in the critical path of vehicle refinement: the role of fast, hybrid and operational path analysis”, in Proc. SAE Noise and Vibration Conf., May 14-17, 2007, SAE paper no. 2007-01-2352.
K. Janssens, P. Gajdatsy, L. Gielen, P. Mas, L. Britte, W. Desmet and H. Van der Auweraer, “OPAX: a new transfer path analysis method based on parametric load models”, Accepted for publication in Mechanical Systems and Signal Processing, 2010
P. Gajdatsy, K. Janssens, W. Desmet and H. Van der Auweraer, “Application of the transmissibility concept in transfer path analysis”, Mechanical Systems and Signal Processing, vol. 24, no. 7, pp. 1963-1976, Oct. 2010.
D. de Klerk and A. Osipov, “operational transfer path analysis: theory, guidelines and tire noise applications”, Mechanical Systems and Signal Processing, vol. 24, no. 7, pp. 1950-1962, Oct. 2010.
J.M. Starkey and G.L. Merrill, "On the ill-conditioned nature of indirect force-measurement techniques," Journal of Modal Analysis, vol. 4, no. 3, pp. 103-108, July 1989.
H. R. Tschudi, "Le methdode des voies de transmission des forces - une alternative interessante par rapport aux essais de demontage," in Unikeller Conference, 1991.
P. Mas, P. Sas, and K Wyckaert, "Indirect force identification based upon impedace matrix inversion: a study on statistical and deterministical accuracy," in ISMA 19, Leuven, Belgium, September, 1994.
M. Blau, "Force spectra identification by FRF matrix inversion: A sensor placement criterion," Journal of the Acoustical Society of America, vol. 105, no. 2, p. 970, 1999.
M. Blau, "Inverse force synthesis: state of the art and future research," in InterNoise 2000, Nice, France, 27-30 August 2000.
M. Blau, "Indirect Measurement of Multiple Excitation Force Spectra by FRF Matrix Inversion: Influence of Errors in Statistical Estimates of FRFs and Response Spectra," Acta Acustica united with Acustica, vol. 85, no. 4, pp. 464-479, July/August 1999.
A.N. Thite and Thompson D.J., "Selection of response measurement locations to improve inverse force determination," Applied Acoustics, vol. 67, no. 8, pp. 797-818, August 2006.
A.N. Thite and D.J. Thompson, "The quantification of structure-borne transmission paths by inverse methods. Part 1: Improved singular value rejection methods," Journal of Sound and Vibration, vol. 264, no. 2, pp. 411-431, July 2003.
A.N. Thite and D.J. Thompson, "The quantification of structure-borne transmissionpaths by inverse methods. Part 2: Use of regularization techniques," Journal of Sound and Vibration, vol. 264, no. 2, pp. 433-451, July 2003.
H. Van der Auweraer, S. Donders and B. Peeters, ”Importance of Uncertainty in Identifying and Using Modal Models”, in Proc. Managing Uncertainty in Noise Measurement and Prediction Symposium, 27-29 June 2005, Le Mans, France
H.K. Tönshoff and D. Ahlborn, "Sensor orientation errors in frequency response function measurements," The Int. Journal of Analytical and Experimental Modal Analysis, vol. 8, no. 3, pp. 219-227, July 1993.
W Hendrickx, "Accurate vehicle FRF measurements for indirect force determination based upon matrix inversion," in Proc. ISMA 19, Leuven, Belgium, 1994, pp. 1037-1048.
O. Dossing, "Prediction of transducer mass-loading effects and identification of dynamic mass," in Proc. of 9th IMAC, Firenze, Italy, Apr. 15-18, 1991, pp. 306-311.
K.G. McConnel, "Interaction of force transducers with their test environment," in Proc. 10th IMAC, San Diego, CA, USA, Feb 3-7, 1992, pp. 1309-1316.
H. Van der Auweraer, W. Leurs, P. Mas, and Hermans L., "On the problem of obtaining consistent estimates from multi-patch modal tests," in Proc. ISMA 25, Leuven, Belgium, Sept. 13-15, 2000
B. Cauberghe, P. Guillaume, B. Dierckx, and Verboven P., "Identification of modal parameters from inconsistent data," in Proc. 20th IMAC, Los Angeles, CA, USA, 4-7 February, 2002.
E. Dascotte, "The Use of FE Model Updating and Probabilistic Analysis for Dealing with Uncertainty in Structural Dynamics Simulation," in Proc. JMAC, Tokyo, Japan, Sept. 10-13, 2003.
M. Degener and M. Hermes, "Round vibration test and finite element analysis of the Garteur SM-AG19 testbed," DLR - German Aerospace Research Establishment, Institute for Aeroelasticity, Technical Report IB 232-96 J 08 October 1996.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this paper
Cite this paper
Gajdatsy, P., Sas, P., Desmet, W., Janssens, K., Van der Auweraer, H. (2011). Effect of systematic FRF errors on matrix inversion based vibro-acoustic analysis methods. In: Proulx, T. (eds) Sensors, Instrumentation and Special Topics, Volume 6. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9507-0_20
Download citation
DOI: https://doi.org/10.1007/978-1-4419-9507-0_20
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-9506-3
Online ISBN: 978-1-4419-9507-0
eBook Packages: EngineeringEngineering (R0)