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

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.