Consistent multi-input modal parameter estimators in the frequency domain

Abstract

In this paper, consistent multiple-input frequency-domain estimators will be presented based on a right matrix-fraction description of the frequency response function. This matrix-fraction description leads to a fast algorithm in the same way as the least-squares complex frequency-domain estimator (LSCF). The use of multiple inputs simultaneously in the estimation (so-called polyreference estimation) has the advantage that it allows to separate closely spaced modes.The main drawback of the LSCF estimator is that it is theoretically inconsistent, i.e.the estimates do not converge to the true values when the number of measurements increases to infinity. However, the noise information available from most measurements can be used to construct a maximum likelihood-like weighting for the LSCF estimators, giving consistent estimates. The results are fast, polyreference, and consistent weighted generalised total-least-squares (WGTLS) estimators. The iterative quadratic maximum likelihood (IQML) estimator is practically consistent for high signal-to-noise ratios, with the additional advantage that it yields clear stabilisation charts.The performance of the presented WGTLS and IQML estimators is evaluated by means of ground vibration test data and demonstrated on flight flutter test data.