Frequency-domain generalized total least-squares identification for modal analysis

• Published in: Journal of sound and vibration 2004-11, Vol.278 (1), p.21-38
• Main Authors: Verboven, P., Guillaume, P., Cauberghe, B., Parloo, E., Vanlanduit, S.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Measurement and testing methods; Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2003.09.058

This contribution focuses on the area of modal analysis and studies the applicability of total least-squares (TLS) algorithms for the estimation of modal parameters in the frequency-domain from input–output Fourier data. These algorithms can be preferable to classical frequency response function based curve-fitting methods. This is certainly the case when periodic excitation is applied and an errors-in-variables noise model can be determined. The proposed generalized total least-squares (GTLS) algorithm provides an accurate modal parameter estimation by the integration of this noise model in the parametric identification process. Modal-based design and comfort improvement, damage assessment and structural health monitoring, and finite element model updating are important applications that strongly rely on a high accuracy of the modal model. In this paper it is shown how frequency-domain TLS and GTLS estimators can be numerically optimized to handle large amounts of modal data. In order to use an errors-in-variables noise model, a linear approximation is necessary in order to obtain a fast implementation of the GTLS algorithm. The validity of this approximation is a function of the signal-to-noise ratio of the input Fourier data and is evaluated by means of Monte Carlo simulations and experimental data.