# Gearbox Fault Diagnosis Based on Multi-Sensor and Multi-Channel Decision-Level Fusion Based on SDP
## 4 Multi-Channel Fault Fusion Diagnosis  
### Multi-Channel Fault Diagnosis  
The data that were collected from three-directions of each sensor were used simultaneously, and the data from the three channels of the sensor were converted into SDP image arms based on SDP technology in order to form a multi-channel mix SDP image arm. By taking the multi-channel of sensor one as an example (its SDP image is shown in Figure 14), a gear fault diagnosis method based on multi-channel fusion was proposed, given that the multi-channel can collect the gear health status more comprehensively. The framework is shown in Figure 15.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Before Fusion** & \multicolumn{3}{c}{**After Fusion**} \\ \hline
**Single Sensor** & **Accuracy** & **Fusion Method** & **Accuracy** \\ \hline Sensor 1 & 88.32\% & Sensors 1 and 2 & 99.77\% \\ \hline Sensor 2 & 82.39\% & Sensors 1 and 3 & 99.98\% \\ \hline Sensor 3 & 88.36\% & Sensors 2 and 3 & 99.46\% \\ \hline \multicolumn{3}{c}{All sensors} & 99.99\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Accuracy comparison before and after single-channel fusion.  
The time-domain vibration signals were converted into SDP image hysteresis, the parameters that could change more significantly in the pitting state were initially determined, and 10 sets of comparison experiments were performed, respectively. The time hysteresis coefficient \(l\) rose from 0 to 10 in steps of one, and the angular gain factor \(\xi\) rose from 0 to 40 in steps of five. In addition, it was found that the fault states of \(l=10\), \(\xi=35^{\circ}\) in the case of \(\theta=120^{\circ}\), were most clearly distinguished. Table 4 shows the parameter settings of the three sensors with multiple channels.  
Figure 14: Transformation from multiple-channel signals to SDP image.  
Figure 15: Fault diagnosis framework based on multi-channel gear pitting level.  
Figure 16-18 show the different pitting levels of the three channels of the sensors, respectively, for the clustering templates of the three datasets of the three pitting levels.  
Figure 16: Clustering templates of sensor 1 in the three pitting level. (**a**) Normal; (**b**) Single pitting; (**c**) Double pitting.  
Figure 17: Clustering templates of sensor 2 in the three pitting level. (**a**) Normal; (**b**) Single pitting; (**c**) Double pitting.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{2}{c}{**Value**} \\ \cline{2-3}  & \(l\) & \(\xi(^{\circ})\) \\ \hline Sensor 1 & 10 & 35 \\ \hline Sensor 2 & 6 & 25 \\ \hline Sensor 3 & 6 & 30 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Optimal SDP parameters for different datasets.  
Figure 18: Clustering templates of sensor 3 in the three pitting level. (**a**) Normal; (**b**) Single pitting; (**c**) Double pitting.  
According to Figures 16-18, most of the image features are different for each sensor dataset, mainly in arm thickness, concentration, and curvature, and from these feature indicators, the differences of the SDP image arms in the different states can be found. Figures 16, 17 and 18c show the degree of pitting of the SDP image from the normal state to the double pitting state. In Figure 18b the image arm was thicker when single pitting was present. Based on these discrepancies, it was possible to analyze the differences in the gears at the different pitting levels and to make an accurate diagnosis.  
After generating the state templates for each dataset, the moderate model was trained in the VGG16 network. The accuracy and the loss of each multi-channel sensor are shown in Figure 19 in order to measure the stability metrics of the model.  
Figure 19: _Cont._  
According to Figure 19, sensor one had 99.92% accuracy and 0.0037 loss in the fault diagnosis model of VGG16; sensor two had 99.96% accuracy and 0.0021 loss; sensor three had 99.91% accuracy and 0.00475 loss.