# An Audio-Based Motor-Fault Diagnosis System with SOM-LSTM
## 4 Case Test
### Taguchi Parameter Design  
The parameter combination for the three levels and three factors of OED is shown in Table 2.  
This paper uses the 128, 256, 512, and 1024 Hz frequencies of the audio data. It also adopts the Taguchi orthogonal array for the experimental design and uses the data of the SOM cluster feature analysis as the input layer of the LSTM. The simulation results are shown in Tables 3-6, which show the parameter analysis of 128 Hz, 256 Hz, 512 Hz, and 1024 Hz, respectively. The identification rate (%) is the operating-status decision value of the SOM-LSTM output value. Table 3 shows the best identification rate of SOM-LSTM (128 Hz), which is 79.69% for EXP. 8. The best parameters are \(m\) = 5, \(C_{t}\) = 125, and \(f_{t}\) = 0.5. Table 4 shows the best identification rate for SOM-LSTM (128 Hz), which is 85.94% for EXP. 9. The best parameters are \(m\) = 5, \(C_{t}\) = 125, and \(f_{t}\) = 0.5. Table 5 shows the best identification rate for SOM-LSTM (128 Hz), which is 90.63% for EXP. 8. The best parameters are \(m\) = 5, \(C_{t}\) = 125, and \(f_{t}\) = 0.5. Table 5 shows the best identification rate for SOM-LSTM (128 Hz), which is 85.94% for EXP. 9. The best parameters are \(m\) = 5, \(C_{t}\) = 125, and \(f_{t}\) = 0.5. Table 5 shows the best identification rate for SOM-LSTM (128 Hz), which is 86.72% for EXP. 8. The best parameters are \(m\) = 5, \(C_{t}\) = 125, and \(f_{t}\) = 0.4. The experimental parameters and optimal identification rate are shown in Tables 2-5, Exp. 8 has the best identification rate. Therefore, this paper chooses the Exp. 8 experimental design of the Taguchi method. The dimension parameter \(m\) = 5 of the SOM and the two parameters \(C_{t}\) = 125 and \(f_{t}\) = 0.4 of the LSTM are the optimal parameter values, and they are used as the optimal parameters of SOM-LSTM. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Exp.**} & **SOM** & **LSTM** & **LSTM** \\  & \(m\) & \(C_{t}\) & \(f_{t}\) \\ \hline
1 & 3 & 100 & 0.4 \\ \hline
2 & 3 & 125 & 0.5 \\ \hline
3 & 3 & 150 & 0.6 \\ \hline
4 & 4 & 100 & 0.5 \\ \hline
5 & 4 & 125 & 0.6 \\ \hline
6 & 4 & 150 & 0.4 \\ \hline
7 & 5 & 100 & 0.6 \\ \hline
8 & 5 & 125 & 0.4 \\ \hline
9 & 5 & 150 & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The parameter combination for three levels and three factors of OED. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**128 Hz** & **SOM** & **LSTM** & **LSTM** & **Identification Rate (\%)** \\ \hline \multirow{2}{*}{**Exp.**} & \multirow{2}{*}{\(m\)} & \multirow{2}{*}{\(C_{t}\)} & \multirow{2}{*}{\(f_{t}\)} & **Training** & **Testing** \\  & & & & **Sample** & **Sample** \\ \hline
1 & 3 & 100 & 0.4 & 87.50 & 46.88 \\ \hline
2 & 3 & 125 & 0.5 & 82.81 & 64.06 \\ \hline
3 & 3 & 150 & 0.6 & 82.81 & 59.38 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameter analysis at 128 Hz. \begin{table}
\begin{tabular}{c c c c c c} \hline
**256 Hz** & **SOM** & **LSTM** & **LSTM** & **Identification Rate (\%)** \\ \hline
**Exp.** & \(m\) & \(C_{t}\) & \(f_{t}\) & \
\begin{tabular}{c} **Training** \\ **Sample** \\ \end{tabular} &
\begin{tabular}{c} **Testing** \\ **Sample** \\ \end{tabular} \\ \hline
1 & 3 & 100 & 0.4 & 81.25 & 54.69 \\ \hline
2 & 3 & 125 & 0.5 & 81.25 & 71.88 \\ \hline
3 & 3 & 150 & 0.6 & 82.81 & 81.25 \\ \hline
4 & 4 & 100 & 0.5 & 64.06 & 62.50 \\ \hline
5 & 4 & 125 & 0.6 & 81.25 & 81.25 \\ \hline
6 & 4 & 150 & 0.4 & 67.19 & 31.25 \\ \hline
7 & 5 & 100 & 0.6 & 71.88 & 73.44 \\ \hline
8 & 5 & 125 & 0.4 & 82.81 & 62.50 \\ \hline
9 & 5 & 150 & 0.5 & 87.50 & 84.38 \\ \hline Average & & & & 77.78 & 67.01 \\ \hline \end{tabular}
\end{table} 
Table 4: Parameter analysis of 256 Hz.