Sparse Time-Frequency Analysis Based on Instantaneous Frequency Estimation and Fault Diagnosis Application

Time-frequency (TF) analysis (TFA) is widely used to deal with nonstationary signals in fault diagnosis. However, traditional TFA methods fail to obtain a satisfactory TF result when processing oscillatory signals with fast time-varying instantaneous frequency (IF). Therefore, a sparse TF representation (TFR) with an adaptive weight based on IF estimation is proposed in this study, which can improve the TF energy concentration and TF accuracy. First, a sparse TF model with weighted
${l}_{1}$
-norm regularization is established. Then, the formula of a high-order IF estimator is derived and utilized as the weight operator to measure the ridge with much higher precision. Finally, fast iterative shrinkage thresholding algorithm is adopted to acquire a sparse TFR. The validity of the proposed method is illustrated through a multicomponent simulated signal and a rub-impact experimental signal. The results confirm that the proposed method can achieve the TFRs with high TF energy concentration and accuracy and it can be applied to the rub-impact fault diagnosis.