## 3 The Proposed Method  
SAX-LZ can effectively recognize the fault severity of a bearing. Nevertheless, the noise in the vibration signal limits the accuracy of SAX-LZ in the fault severity recognition of bearing. However, the ACLHC can effectively highlight the mutation components caused by bearing fault in the signal and reduce the noise in the signals. Therefore, the ACLHC can be effectively used to process the vibration signal of bearings to highlight the impact components and reduce the interference of noise. The recognition accuracy of SAX-LZ can be effectively improved after processing by ACLHC. Given a signal \(X=\{x_{1},x_{2},\cdots,x_{n}\}\), the SAX-LZ of the signal processed by ACLHC is calculated as follows:  
Step 1: According to Equation (6), transform the signal amplitude to the positive value \(X^{\prime}=\{x^{\prime}{}_{1},x^{\prime}{}_{2},\cdots,x^{\prime}{}_{n}\}\):  
\[x^{\prime}{}_{i}=x_{i}-\min(X); \tag{6}\]  
Step 2: Then, the signal \(X^{\prime}=\{x^{\prime}{}_{1},x^{\prime}{}_{2},\cdots,x^{\prime}{}_{n}\}\) is divided into different segments \(SX=\{sx_{1},sx_{2},Step 5: The ACLHC C is normalized to obtain the normalized series \(NC=\{Nc_{1},Nc_{2},\cdots,Nc_{n-l+1}\}\) by the Equation (2);  
Step 6: The SAX-LZ of the normalized series \(NC\) is obtained according to the description in Section 2.2. The calculation process is illustrated in Figure 2.  
To illustrate the characteristics of the ACLHC in the description of impact, two sets of simulation signals with different SNR are constructed, as follows:  
\[X(t)=x(t)+n(t), \tag{8}\]  
where \(X(t)\) is the simulation signal with different signal-to-noise ratios (SNR), the waveform of the \(X(t)\) with SNR of 13 dB is shown in Figure 3b, while that with SNR of 3 dB is shown in Figure 4b. \(n(t)\) is the noise, \(x(t)\) is the simulation signal without noise, the \(x(t)\) is shown as follows:  
\[x(t)=\left(\sum_{k=-\infty}^{+\infty}d\cdot\delta(t-zT_{o})*e(t)\right)\cdot \sin(2\pi f_{n}), \tag{9}\]  
where \(d\) is the intensity of the impact forces, \(\delta(t)\) is the unit impact function, \(z\) is the number of the impacts, \(T_{o}=1/f_{o}\) is the interval between two impacts, \(f_{o}\) is the characteristic frequency of the bearing, \(e(t)\) is the attenuation function, \(f_{n}\) is the resonance frequency. The waveform of \(x(t)\) is shown in Figures 3a and 4a. In order to better illustrate the effect of ACLHC in noise reduction, the ACLHC was compared with other three frequency band selection methods (protrugram, sparsogram, and genetic algorithm sparsogram (GA-sparsogram)). The results of the simulation signals processed by the above four methods are shown in Figures 3 and 4. Figure 2: The calculation process of the proposed method. For the simulation signal with high SNR, as shown in Figure 3a,c, as the amplitude of the signal was more dispersed when the impact occurred, the probability of the signal was dispersed at this time. So, the ACLHC of the impact component is lower than that of other components when there are impacts in the signals. Although there are some differences between Figure 3a,c, the location of each impact can be restored by ACLHC well. However, although the approximate shape of the impact could be restored by GA-sparsogram, as shown in Figure 3f, the number of impacts was less than that of the impact signal in Figure 3a. In addition, the location and shape of the impact in Figure 3d,e were completely different from that in Figure 3a. Therefore, compared with protrugram, sparsogram, and GA-sparsogram, the ACLHC can effectively restore the location of the impact and highlight the impact components of signal. For the simulation signal with low SNR, the time-domain waveforms and frequency spectrums of the simulation signal processed by different methods are shown in Figure 4.  
Figure 3: The waveforms at the signal-to-noise ratio (SNR) of 13 dB.