## 5 Comparison of the Proposed Method with the Existing Method
Obtain the normalized range of the harmonic frequency multiplication of various faults, see Table 5.  
Step 7. Combine the amplitude values in Table 5 with the harmonic frequency multiplication signal to construct fuzzy signal set \(F(U)\), as shown in Equation (20). \[F(U)=\left[ \begin{array}{cc}\langle 0.31,0.41\rangle\langle 0.70,0.78\rangle \langle 0.83,0.95\rangle\\ \langle 0.10,0.30\rangle\langle 0.40,0.60\rangle\langle 0.70,0.90\rangle \end{array} \right] \tag{20}\]  
Through the above steps, a diagnostic model of fault data fusion can be obtained. After that, the fault diagnosis can be performed, and the diagnosis result is the fault type \begin{table}
\begin{tabular}{c c} \hline \hline
**Fault Type** & **Ambiguous Range of Impulse Indicator** \\ \hline Minor fault & 0.31–0.41 \\ Moderate fault & 0.70–0.78 \\ Serious fault & 0.83–0.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Impulse indicators of various types of faults. Figure 13: Power spectrum of individual example data. \begin{table}
\begin{tabular}{c c} \hline \hline
**Fault Type** & **Ambiguous Range of Harmonic Frequency Multiplication** \\ \hline Minor fault & 0.10–0.30 \\ Moderate fault & 0.40–0.60 \\ Serious fault & 0.70–0.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Harmonic frequency multiplication range of various faults. set \(D=\{\)Minor fault, Moderate fault, Serious fault\(\}\), as shown in Formula (21). Where \(T\) is the target to be detected. \[D=N(T,F(U)) \tag{21}\]  
After the system is calibrated and stabilized, take any four sets of data from T150 for fault diagnosis. \(T_{1}=[\langle 0.24,0.36\rangle\ \langle 0.1,0.30\rangle]\), \(T_{2}=[\langle 0.74,0.86\rangle\ \langle 0.40,0.60\rangle]\), \(T_{3}=[\langle 0.66,0.76\rangle\ \langle 0.70,0.90\rangle]\), \(T_{4}=[\langle 0.78,0.92\rangle\ \langle 0.70,0.90\rangle]\). Then, \(D_{1}=[\langle 0.59,0.69\rangle\ \langle 0.30,0.30\rangle\ \langle 0.17,0.30\rangle]\). According to the maximum method, it is considered that \(T_{1}\) has a minor fault. The fault diagnosis results of the four groups of data are shown in Table 6.  
Use this system to diagnose faults on the T150 data set, and the visualized results are shown in Figure 14.  
The fuzzy signal fault diagnosis method proposed in this paper can determine the fault type through a simple set operation. Compared with other fault diagnosis methods, this process does not require a large amount of data as a basis. It calculates the fault attribute of the thing itself as the data and quickly identifies the fault without other complicated steps, making it easier and more efficient. The LSTM network can extract more extensive feature signals, can effectively suppress the high-frequency noise in the vibration signal, and is often used in the fault diagnosis of rolling bearings. Choose an LSTM network with two layers and 128 neurons in each layer for comparison experiments. The A150, B150, and C150 data sets are used as training data, and \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Detection Target** & **Impulse Indicator** & **Frequency Multiplication** & **Fault Type** \\ \hline T\({}_{1}\) & 0.24–0.36 & 0.10–0.30 & Minor fault \\ T\({}_{2}\) & 0.74–0.86 & 0.40–0.60 & Serious fault \\ T\({}_{3}\) & 0.66–0.76 & 0.40–0.60 & Moderate fault \\ T\({}_{4}\) & 0.78–0.92 & 0.70–0.90 & Serious fault \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Fault diagnosis results. Figure 14: Visualized results of fault diagnosis of T150 data set by this system. T150 is used as test data. Suppose the number of correct recognition is \(n\) and the total number of test samples is \(N\), then the correct identification rate \(\eta_{\text{g}}\) is as shown in Formula (22). \[\eta_{g}=\frac{n}{N}\times 100\% \tag{22}\]  
With the T150 test data set, 500 experiments were performed, respectively. Similarly, the proposed method is compared with the latest neural network methods.