## 2 Fuzzy Signal Analysis on Fault Diagnosis System  
Aimed at analyzing the fault diagnosis method of rolling bearings, this paper constructs a diagnosis system based on fuzzy fault signals. A fuzzy signal refers to replacing a certain value of traditional fault data with an interval. The lower bound of the interval can be determined, while the upper bound is an uncertain value. The system consists of three parts:  
(1) Analysis and processing of rolling bearing fault signals.  
(2) Define the fault diagnosis function and give the fault diagnosis method.  
(3) Conduct training and test experiments, as well as system stability training.  
After the system has stabilized in training, it will be applied in practice. The specific working flow chart of the fuzzy signal fault diagnosis system is shown in Figure 1.  
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. The vibration analysis method is currently the most used, and it is also one of the most sensitive and effective methods for the early diagnosis of small faults and has become the method for equipment fault diagnosis [26]. Therefore, this paper uses vibration signals to diagnose faults in rolling bearings. The discrete vibration signal collected in practice contains noise interference, and the original vibration signal data without denoising is shown in Figure 1(a). Figure 1(b) illustrates the image after adding noise to the original signal. The waveform contains a large amount of useless low-amplitude noise data, which cannot highlight the high-amplitude features of the fault. Analyzing its amplitude characteristics, it can be seen that the shock pulse of the vibration signal at the time of fault increases rapidly at first and then slowly decays the oscillation in the form of an exponential. The signal is denoised and normalized. This system can reduce noise and optimize the amplitude of the fault characteristics based on the above-mentioned vibration signal fault characteristic analysis. The result is shown in Figure 3.  
Figure 1: Flow chart of fuzzy signal fault diagnosis system.  
Figure 2: Actually collected raw vibration data.  
A single signal processing technology has made it difficult to meet the increasingly complex equipment fault diagnosis requirements [27]. Therefore, the optimized vibration data can be used for time-frequency analysis using this system, and the frequency domain characteristic signal of the fault data can be extracted by using frequency spectrum analysis, as shown in Figure 4. The system can fuse different fault signal characteristics for fault diagnosis and can customize fault classification according to the different needs of different objects. The visualized diagnosis result of the fusion of the two kinds of signal is shown in Figure 5.  
After the system is completed, if the system stability requirements cannot be met, the system needs to be calibrated according to Formula (1).  
\[\omega(n)=\omega(n-1)+\eta|\omega(n)-\omega(n-1)| \tag{1}\]  
where \(\omega(n)\) is the stability amplitude of the current system, and \(\omega(n-1)\) is the stability amplitude of the system at the previous moment. When the system is stable, \(\eta\) usually  
Figure 4: Time-frequency conversion result of this system.  
Figure 3: The optimized vibration data of the system.  
needs to be less than the range of \(\sigma\in[0.005,0.007]\). The actual application can only be carried out when the stability of the system meets the requirements.