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A New Wavelet Shrinkage Approach for Denoising Nonlinear Time Series and Improving Bearing Fault Diagnosis

In this paper, we present a new wavelet shrinkage operator to remove noise for non-linear time series. Like other improvements, the proposed operator is used to address the discontinuity of the hard operator as well as the large bias of the soft operator. The special of this operator is that it introduces the universal threshold to divide the details of signal and noise. Such that the operator can identify those coefficients with noise, and then shrink larger for them, otherwise, shrink small. We test the denoising performance of the new operator in the chaotic time series generated by the Lorenz system. The results show that the new method successfully reduces the noise in nonlinear time series. Also, we applied our approach to improving the classification accuracy of the bearing fault in the noisy environment. The bearing fault datasets come from the Case Western Reserve University (CWRU) bearing data center and Paderborn University respectively. Experimental results show that the proposed operator effectively reduces the error rate on both traditional classifier models and deep learning models. Comparisons with the three existing shrinkage operators demonstrate the superiority of the proposal.