Autoregressive Order Selection for Rotating Machinery

This paper provides a practical rule for determining the minimum model order for Autoregressive (AR) based spectrum analysis of data from rotating machinery. The use of parametric methods for spectral estimation, though having superior frequency resolution than Fast Fourier Transform (FFT) based methods, has remained less favoured mainly because of the difficulties in estimating the model order. The minimum model order pmin required is the ratio of the sampling rate and the rotating speed of the machine. This is the number of samples in one shaft revolution. Traditional model order selection criteria, Akaike Information Criterion (AIC), Finite Information Criterion (FPE), Minimum Description Length (MDL), Criterion Autoregressive Transfer-function (CAT), and Finite Information Criterion (FIC) are used to estimate the optimal order. These asymptotic criteria for model order estimation are functions of the prediction error and the optimal order of an AR model is chosen as the minimum of this function. Experimental results, using vibration data taken from a dry vacuum pump at different sampling rates and rotating speeds, show that at there is a pmin marked reduction in the prediction error. For low speed rotating machinery, the optimal order is pmin. As the speed of the rotating machine increases, there is some advantage in using twice or thrice pmin, to produce more accurate frequency estimates. The Box- Jenkins method of order determination using autocorrelation and partial autocorrelations plots are also used for justification of the selection of this minimal order.