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.

Many artificial features have been extracted and applied to the recognition of radar emitter signals. It is worth studying which features play key roles in the recognition. The traditional sparse learning-based methods can achieve feature selection by setting some of the features to zero. However, linear model-based methods cannot deal with the nonlinearity. Deep neural networks (DNNs) have a strong ability to deal with nonlinearity of input variables.. However, the sparsification of DNNs is a challenge. This paper proposes a DNN based on importance measure (DNN-IM) for feature selection. The method combines the importance of weight and gradient to gradually delete features to achieve sparsification, and finally selects the optimal feature subset through the evaluation function containing redundancy measure. This method was applied to the feature selection of expert feature sets of radar emitter signals, and the results show that our method has superior performance.