# Multi-Sensor GA-BP Algorithm Based Gearbox Fault Diagnosis
## 4 Experiments
### Experimental Data Acquisition
The data from the training set is first fed into the diagnostic model, and then the remaining 14 sets are fed into the diagnostic model as a test set for fault testing. The test results of the two algorithms are shown in Tables 6 and 7. The speed of the two algorithms is shown in Figures 14 and 15, and the accuracy is shown in Figure 16.  
Figure 12: Gears with different degrees of pitting. (**a**) Normal condition, (**b**) single pitting condition, (**c**) double pitting condition, (**d**) triple pitting condition. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & \multicolumn{3}{c}{**Test Data**} & **Fault** \\ \hline
1 & 1.000506 & 0.033438 & \(-0.03357\) & \(-0.00037\) & 1 \\
2 & 1.009513 & 2.120288 & \(-2.13004\) & \(0.000242\) & 1 \\ \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\
14 & 0.999489 & 0.016411 & \(-0.01581\) & \(-8.5\times 10^{-5}\) & 1 \\
1 & \(-0.00104\) & 1.303728 & \(-0.30177\) & \(-0.00092\) & 2 \\
2 & 0.00067 & 0.856819 & 0.142685 & \(-0.00017\) & 2 \\ \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\
14 & 0.011091 & 1.862498 & \(-0.87288\) & \(-0.0007\) & 2 \\
1 & 0.000317 & 0.652486 & 0.347745 & \(-0.00055\) & 3 \\
2 & \(-0.00145\) & 1.01321 & \(-0.01084\) & \(-0.00092\) & 3 \\ \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\
14 & \(-0.00106\) & 0.30225 & 0.700755 & \(-0.00194\) & 3 \\
1 & \(7.07\times 10^{-5}\) & \(-0.00017\) & 0.000117 & 0.999984 & 4 \\
2 & \(7.16\times 10^{-5}\) & \(-0.00048\) & 0.000427 & 0.999984 & 4 \\ \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\
14 & \(6.84\times 10^{-5}\) & \(-0.00027\) & 0.000219 & 0.999984 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: BP algorithm experimental test data. Figure 13: Vibration signals for 4 types of gear health monitoring. (**a**) Normal condition, (**b**) single pitting condition, (**c**) double pitting condition, (**d**) triple pitting condition. Figure 14: The number of iterations of the BP algorithm. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & \multicolumn{2}{c}{**Test Data**} & \multicolumn{1}{c}{**Fault**} \\ \hline
1 & 1.002133 & 0.001423 & 0.004012 & 0.002554 & 1 \\
2 & 1.000103 & 0.005562 & 0.007136 & 0.003179 & 1 \\ \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) \\
14 & 1.000276 & 0.006608 & 0.008686 & 0.004462 & 1 \\
1 & 0.0055 & 1.00047 & 0.008853 & 0.009767 & 2 \\
2 & 0.005802 & 1.000651 & 0.006563 & 0.007881 & 2 \\ \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) \\
14 & 0.007025 & 1.000013 & 0.002331 & 0.009472 & 2 \\
1 & 0.009201 & 0.009637 & 1.002577 & 0.009345 & 3 \\
2 & 0.007863 & 0.007472 & 1.000319 & 0.009347 & 3 \\ \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) \\
14 & 0.00661 & \(-0.00853\) & 1.00067 & 0.00025 & 3 \\
1 & 0.001398 & 0.006349 & 0.007977 & 1.000525 & 4 \\ \hline
2 & 0.000851 & 0.007368 & 0.006932 & 1.001214 & 4 \\ \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) \\
14 & 0.008507 & 0.005294 & 0.001008 & 1.00231 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: GA-BP algorithm experimental test data. Figure 15: The number of iterations of the GA-BP algorithm. As shown in Figures 14 and 15, the number of iterations tested using the BP algorithm was 2193 epochs (around 3 s). While the number of iterations using the genetic algorithm was 648 epochs (around 0.886 s), which 2.38 times faster convergence during testing. From the Figure 16, we can also see that the GA-BP algorithm has a higher accuracy than the BP algorithm. According to Figure 16, above the three algorithms, the BP algorithm is the most volatile and the GABP algorithm is the most stable.