# An Audio-Based Motor-Fault Diagnosis System with SOM-LSTM
## 4 Case Test
### Performance Test  
In order to verify the accuracy of SOM-LSTM, this paper uses the same data to train the experimental design in Table 7 with a radial basis-function neural network (RBFNN), and conduct experimental comparisons between SOM-LSTM and SOM-RBFN. The experimental design of Exp. 1-11 is performed. According to Table 7, SOM-RBFNN, in this paper, is \(m\) = [3, 4, 5], \(\sigma\) = [0.01, 0.1, 1], and \(\gamma\) = [0.3, 0.4, 0.5]. The SOM-RBFNN of Exp. 7 has a training accuracy of 100% under the parameters of \(m\) = 5, \(\sigma\) = 0.01, and \(\gamma\) = 0.5, but the test recognition rate seems to be lower than expected, at only 54.69%, and the average accuracy rate between training and testing is 77.345%. Similarly, the SOM-LSTM in Exp. 9 has a training accuracy of 100% under the parameters \(m\) = 5, \(C_{t}\) = 150, and \(f_{t}\) = 0.5, and the test recognition rate is also 92.19%. The average accuracy rate between training and testing is 96.095%. According to the experimental analysis, the SOM-LSTM of Exp. 9 is also better than the SOM-RBFNN of Exp. 7, and the improvement in the identification rate is greater.  
This paper repeats Exp. 9 of SOM-LSTM with 100 times, and it calculates the best solution, the worst solution, and the average solution in 100 runs. The same parameters are used for each run. Identification rates for the worst, best, and average values are recorded together with the number of generations to converge and the average execution time, as shown in Table 8. The average execution time is about 1.231 s. Table 8 shows the average solution that the training sample identification rate is 98.44%, the test sample identification rate is 87.50%, and the total identification rate is 92.97%. It can be seen that the proposed algorithm is a good performer in terms of the search solution and the average execution time. The RMSE training error of the SOM-LSTM of Exp. 9 is shown in Figure 7. When the SOM-LSTM is trained to the No. 701 to No. 750 iterations, the average RMSE is 0.3248.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**1024 Hz** & **SOM** & **LSTM** & **LSTM** & **Identification Rate (\%)** \\ \hline \hline
**Exp.** & \(m\) & \(C_{t}\) & \(f_{t}\) & **Training** & **Testing** \\  & & & & **Sample** & **Sample** \\ \hline
1 & 3 & 100 & 0.4 & 79.69 & 84.38 \\ \hline
2 & 3 & 125 & 0.5 & 81.25 & 90.63 \\ \hline
3 & 3 & 150 & 0.6 & 78.13 & 84.38 \\ \hline
4 & 4 & 100 & 0.5 & 70.31 & 81.25 \\ \hline
5 & 4 & 125 & 0.6 & 81.25 & 62.50 \\ \hline
6 & 4 & 150 & 0.4 & 84.38 & 67.19 \\ \hline
7 & 5 & 100 & 0.6 & 82.81 & 79.69 \\ \hline
8 & 5 & 125 & 0.4 & 85.94 & 87.50 \\ \hline
9 & 5 & 150 & 0.5 & 75.00 & 73.44 \\ \hline Average & & & & 79.86 & 78.99 \\ \hline \end{tabular}
\end{table}
Table 6: Parameter analysis of 1024 Hz.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{3}{*}{**Exp.**} & \multicolumn{2}{c}{**SOM-LSTM**} & \multicolumn{2}{c}{**SOM-RBFNN**} \\ \cline{2-5}  & \multicolumn{2}{c}{**Identification Rate (\%)**} & \multicolumn{2}{c}{**Identification Rate (\%)**} & \multicolumn{2}{c}{**Identification Rate (\%)**} \\ \cline{2-5}  & \multicolumn{2}{c}{**Training Sample**} & \multicolumn{2}{c}{**Testing Sample**} & \multicolumn{2}{c}{**Training Sample**} & \multicolumn{2}{c}{**Testing Sample**} \\ \hline
1 & 100.00 & 78.13 & 75.00 & 46.88 \\ \hline
2 & 100.00 & 84.38 & 87.50 & 51.56 \\ \hline
3 & 100.00 & 57.81 & 76.56 & 45.31 \\ \hline
4 & 100.00 & 84.38 & 79.69 & 60.94 \\ \hline
5 & 100.00 & 57.81 & 64.06 & 45.31 \\ \hline
6 & 100.00 & 84.38 & 73.44 & 51.56 \\ \hline
7 & 100.00 & 70.31 & 100.00 & 54.69 \\ \hline
8 & 98.44 & 70.31 & 90.63 & 43.75 \\ \hline
9 & 100.00 & 92.19 & 92.19 & 43.75 \\ \hline Average & 99.83 & 75.52 & 82.12 & 49.31 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The performance test of SOM-LSTM and SOM-RBFN.  
Figure 6: The simulated curves of four fault identifications.