ARMA MODELS FOR MODAL ANALYSIS: EFFECT OF MODEL ORDERS AND SAMPLING FREQUENCY

Modal analysis is usually conducted in the frequency domain. If frequency domain methods work very well when damping is low, noise level is low and natural frequencies are not too much closed, these methods however by requiring an averaging of the samples, are always time-consuming. On the other hand, time-series analysis are very attractive because samples with very short length are sufficient, but these time-series methods are actually not user friendly. This paper compares the accuracy of three auto-regressive moving average methods (recursive least-squares, output error and corrected covariance matrix methods) for identifying modal parameters of mechanical systems. These methods are applied to industrial structures both from numerical simulations and from experimental measurements. It is shown that these methods are very sensitive to the sampling frequency and that an optimal sampling frequency must be selected in order to have confidence in the identification. When sampling frequency chosen is too high, the order of the model must be increased which leads to a lack of accuracy. A sampling frequency selected approximately between three and ten times the maximal frequency of interest was revealed as acceptable while oversampling led to false results. The output error method was the less accurate one for the studied cases, especially for the damping rate identification. Elsewhere the corrected covariance matrix method revealed as the more accurate, the less sensitive to sampling frequency and the more stable method according to the selected order. The corrected covariance matrix method was applied to a complex industrial application with completely unknown dynamic behaviour and number of degrees of freedom. The application of the corrected covariance matrix method allowed to find the number of frequencies in a specific bandwidth and furthermore to identify the modal parameters.