## 4 Vibration Signal Analysis of Rolling Bearing  
The vibration monitoring method is suitable for bearings of various types and working conditions. The vibration analysis method is widely used in the field of mechanical equipment fault diagnosis due to the advantages of easy acquisition of vibration signals and strong practicability. It is currently the most used and one of the most sensitive and effective methods for early diagnosis of small faults. It has become the main way to diagnose rolling bearing faults. Vibration signal monitoring and processing are simple, intuitive, and reliable in diagnosis. It contains the fault signal of the equipment, but the fault cannot be seen directly from the vibration signal. A series of processing and analysis of the vibration signal is required to obtain the fault characteristics. The fuzzy signal fault diagnosis system can analyze and process vibration signals. It can be seen from Figure 6 that the vibration amplitude of the rolling bearing always fluctuates within a certain range under normal working conditions. When it exceeds this range and the amplitude presents periodic changes, it can be considered that the rolling bearing has failed. Therefore, the average value of multiple sets of normal working condition data can be calculated according to Formula (16) as the upper limit of the normal amplitude range (excluding outliers). \[\overline{x}=\frac{1}{N}\sum_{i=1}^{N}\left|x_{i}\right| \tag{16}\]  
Generally, the amplitude of the vibration signal exceeding the normal amplitude range is positively related to the impact force received by the bearing, so the impulse indicators in different periods can be used to reflect the degree of fault. The impulse index is shown in formula (17). Under normal circumstances, the fault amplitude is several times the normal  
Figure 6: The optimized vibration data of the system under normal working conditions. amplitude, which is a number greater than 1. To better apply the algorithm proposed, the data should be normalized. The normalization formula is shown in Equation (18). \[I=\frac{|x_{\max}|}{\overline{x}} \tag{17}\]  
\[Q=\frac{I-I_{min}}{I_{max}-I_{min}} \tag{18}\]  
The degree of fault and the amplitude are only a positive correlation, not a strictly proportional relationship, so the degree of fault cannot be judged strictly. Therefore, relevant indicators of frequency can be integrated to accurately distinguish the degree of fault. Therefore, the physical quantity of \"harmonic\" can be fused to diagnose the degree of fault. Refer to the analysis of the power spectrum of the vibration signal of the paper machine dryer bearing fault, as shown in Figure 7. \"2 times, 3 times, 4 times\" harmonics appear in the picture. The more harmonics, the more serious the bearing fault. In addition, the fault frequency can be used to determine the outer race fault of the dryer bearing. The fast Fourier transform (FFT) can convert the time-domain signal of the original discrete vibration data into a continuous frequency domain signal. It provides convenient conditions for fault diagnosis methods based on vibration signal spectrum analysis. For the same set of data shown in Figure 6, the FFT spectrogram is shown in Figure 8, and the analysis result of the time-frequency conversion of this system is shown in Figure 9. From the results, the time-frequency conversion of this system has a more obvious noise reduction effect than the FFT method, which provides a good data source for further obtaining harmonic signals from the power spectrum. After obtaining the frequency spectrum, the fault location can be determined according to the rolling bearing fault frequency. When the bearing fails, it will produce regular vibration. Assuming that the rotation speed of the bearing is fixed, the time interval of the impact caused by the rotation inside the faulty bearing is also fixed; that is to say, the frequency of the impact is fixed. Therefore, this frequency is the fault frequency of the bearing.