Abstract
The rational fraction polynomial algorithm is the entry-level model of the high-order, frequency-domain modal parameter estimation methods. However, it has some well-known issues with numerical ill-conditioning for a high model order and a wide frequency range. Among the alternatives that have been proposed over the years to address this shortcoming is a change of basis functions from power polynomials to orthogonal polynomials. While this approach does cure the numerical ill-conditioning issues, this algorithm has not yet achieved mainstream acceptance, with the reasons for this reluctance typically cited being additional complication or increased computation time. This paper introduces an improved implementation of the orthogonal polynomial algorithm that uses the orthogonal complement, coupled with QR decomposition, to greatly reduce the time of the accumulation phase. The neat trick performed by the orthogonal complement is to get all of the overdetermination possible without having to do all of the work.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Richardson PM,Please provide location for all the proceedings. Formenti DL (1982) Parameter estimation from frequency response measurements using rational fraction polynomials. In: Proceedings, international modal analysis conference, pp 167–182
Van der Auweraer H, Leuridan J (1987) Multiple input orthogonal polynomial parameter estimation. Mech Syst Signal Process 1(3):259–272
Shih CY, Tsuei YG, Allemang RJ, Brown DL (1988) A frequency domain global parameter estimation method for multiple reference frequency response measurements. Mech Syst Signal Process 2(4):349–365
Shih CY (1989) Investigation of numerical conditioning in the frequency domain modal parameter estimation methods. Doctoral dissertation, University of Cincinnati, p 127
Vold H (1990) Numerically robust frequency domain modal parameter estimation. Sound and Vibration, Jan 1990, p 3
Vold H (1990) Statistics of the characteristic polynomial in modal analysis. In: Proceedings, international seminar on modal analysis, pp 53–57
Rolain Y, Pintelon R, Xu KQ, Vold H (1995) Best conditioned parametric identification of transfer function models in the frequency domain. IEEE Trans Autom Control 40(11):1954–1960
Vold H, Richardson M, Napolitano K, Hensley D (2008) Aliasing in modal parameter estimation – a historical look and new innovations. In: Proceedings, international modal analysis conference, p 15
Orthogonal Complement. Wikipedia. 26 June 2014. http://en.wikipedia.org/wiki/. Accessed 2 Oct 2014. Orthogonal_complement
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 The Society for Experimental Mechanics, Inc.
About this paper
Cite this paper
Fladung, W., Vold, H. (2015). An Improved Implementation of the Orthogonal Polynomial Modal Parameter Estimation Algorithm Using the Orthogonal Complement. In: Mains, M. (eds) Topics in Modal Analysis, Volume 10. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-15251-6_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-15251-6_16
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-15250-9
Online ISBN: 978-3-319-15251-6
eBook Packages: EngineeringEngineering (R0)