Time-frequency representation with reweighted regularization for fault diagnosis in a sparse way

Abstract

In the field of fault diagnosis, time–frequency representation (TFR) is a very popular tool due to its good performance under time-varying condition. TFR provides both time and frequency information of fault signal, and the component related to fault characteristic frequency (FCF) can be found in the time–frequency image. To improve the time–frequency resolution of TFR, a special kind of TFR method named sparse time frequency representation (STFR) combines TFR and sparse theory, where the TFR is processed in a sparse way and the energy is more concentrated on FCF. However, the underestimation problem from the optimization process limits the efficiency of STFR. Concretely, the coefficients of the components of FCF are easy to be underestimated in the iterative process of solving coefficient, which will enhance other interference components. Especially for the weak faults from the early stage or the serious noise pollution, STFR is easy to be contaminated and is hard to reveal the components of FCF because of the underestimation problem. To solve the underestimation problem, we propose a novel STFR with reweighted regularization (RSTFR) for fault diagnosis. In the proposed method, the envelope of signal is divided into small segments, and each segment is decomposed into the Fourier basis. Naturally, the sparse coefficient represents the envelope spectrum of each segment. Meanwhile, the reweighted scheme is used to solve the underestimation problem. The components related to FCF are encouraged with low thresholds while other interference components are punished with high thresholds. At last, the envelope spectrums of all segments at different time form the TFR. The proposed method can provide a higher time–frequency resolution and diagnose the fault precisely. RSTFR is applied in the both simulation cases and experimental cases of bearing fault diagnosis, and it shows the overwhelming superiority compared to other four state-of-art TFR methods.