Classification of time-frequency representations based on two-direction 2DLDA for gear fault diagnosis

Time-frequency representations (TFR) have been intensively employed for analyzing vibration signals in mechanical faults diagnosis. However, in many applications, time-frequency representations are simply utilized as a visual aid to be used for vibration signal analysis. It is very attractive to investigate the utility of TFR for automatic classification of vibration signals. A key step for this work is to extract discriminative parameters from TFR as input feature vector for classifiers. This paper contributes to this ongoing investigation by developing a two direction two dimensional linear discriminative analysis (TD-2DLDA) technique for feature extraction from TFR. The S transform, which combines the separate strengths of the short time Fourier transform and wavelet transforms, is chosen to perform the time-frequency analysis of vibration signals. Then, a novel feature extraction technique, named TD-2DLDA, is proposed to represent the time-frequency matrix. As opposed to traditional LDA, TD-2DLDA is directly conduct on 2D matrices rather than 1D vectors, so the time-frequency matrix does not need to be transformed into a vector prior to feature extraction. Therefore, the TD-2DLDA can reduce the computation cost and preserve more structure information hiding in original 2D matrices compared to the LDA. The promise of our method is illustrated by performing our procedure on vibration signals measured from a gearbox with five operating states. Experimental results indicate that the TD-2DLDA obviously outperforms related feature extraction schemes such as LDA, 2DLDA in gear fault diagnosis.