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**1 - 1**of**1**### Author manuscript, published in "Thirteen International Congress on Sound and Vibration, ICSV13, Vienne: Austria (2006)" Time-Frequency Segmentation for Engine Speed Monitoring

, 2009

"... This paper presents a segmentation algorithm of a Time-Frequency Representation, which automatically selects time-frequency patterns containing signal of interest. Considering a deterministic non-stationary signal embedded in a white Gaussian noise, we know that the real and imaginary parts of the S ..."

Abstract
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This paper presents a segmentation algorithm of a Time-Frequency Representation, which automatically selects time-frequency patterns containing signal of interest. Considering a deterministic non-stationary signal embedded in a white Gaussian noise, we know that the real and imaginary parts of the Short Time Fourier Transform coefficients (STFT) have a Gaussian distribution. We already proposed an unsupervised segmentation based on the spectrogram, the squared modulus of the STFT, whose coefficients have a non-central chi-square distribution. In order to keep simple Gaussian distributions and the phase information, we consider here only real and imaginary part of the STFT. We first highlight the difference existing between the variance of these real and imaginary parts. The ratio of these variances is a function of the nature and length of the analysis window. Estimated on a cell around each time-frequency location, these variances are used to determine if a time-frequency location contains deterministic signal or noise only. Given that the noise variance is unknown, an iterative algorithm is proposed. In addition of the STFTâ€™s parameters, which are the size and shape of the analysis window, the overlap between two consecutive windows, and the amount of zero padding, three different parameters control the segmentation. The most important one is the kurtosis of the distribution, calculated on time-frequency coefficients supposed to contain noise only. It is used to define a stop criterion of the segmentation and permits the monitoring of the signal pattern segmentation. The influence of the other parameters on the segmentation result is also discussed. This tool is applied to monitor a three-phase AC induction motor on the test bench GOTIX of the laboratory. Sensors measure vibration, torque and phase tensions and intensities. Segmented patterns provide information about time evolution of the spectral energy, and permit the tracking of the engine speed. F. Millioz and N. Martin