# Time-Frequency Modeling and Detection of random non-stationary signals for Monitoring Purposes

Abstract : This paper deals with the modelization and detection of non-stationary random signals in the time-frequency space. A time-frequency random model of signal is derived from a given temporal model. The time model we are interested in consists in a deterministic signal embedded in an additive centered Gaussian perturbation. This Gaussian model is characterized by two parameters, which are the mean and covariance matrix of the process. The corresponding time-frequency model depends on the time-frequency transform applied to the signal. For the spectrogram, the determinant parameters are the nature and length of the analysis window and the zero-padding. We show that for a Gaussian signal, spectrogram coefficients distribution can be approximated by a $chi^2$ law defined by three parameters. A time-frequency signal detection task inspired from a Neyman-Pearson strategy is performed on the basis of this probabilistic time-frequency model. The detector determines the time-frequency regions where signal energy is present. It thus provides a time-frequency signature of the signal. This information is used for structural health monitoring techniques. Extraction of the fundamental meshing frequency and harmonics of a gearbox under varying load conditions is presented.
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Conference papers
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Cited literature [3 references]

https://hal.archives-ouvertes.fr/hal-00096279
Contributor : Julien Huillery <>
Submitted on : Tuesday, September 19, 2006 - 11:37:18 AM
Last modification on : Friday, September 6, 2019 - 3:00:06 PM
Long-term archiving on : Tuesday, April 6, 2010 - 1:02:28 AM

### Identifiers

• HAL Id : hal-00096279, version 1

### Citation

Julien Huillery, Nadine Martin. Time-Frequency Modeling and Detection of random non-stationary signals for Monitoring Purposes. 47th American Institut of Aeronautics and Astronautics (AIAA) conference., 2006, Newport, United States. ⟨hal-00096279⟩

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