# Multi-Source Information Fusion Fault Diagnosis for Gearboxes Based on SDP and VGG
## 4 Experiments
### VGG Fault Diagnosis Model with SDP Feature Information Fusion  
For each sensor, the experimental data of a certain direction for the gear tooth fault state were selected as the valid data for this experiment. After the analysis of the data, it was found that the changes in the Z-direction were the most obvious for each of the three sensors. Hence, the experimental data in the Z-direction were selected for all three sensors. Using the SDP image processing method, after analyzing the three sensors of the three gear faults at different time lag coefficients, magnification angles, and other important factors, all three sensors had a more obvious fault state when the time lag coefficient \(l=7\) and angular gain factor \(\xi=25^{\circ}\). The gear's health status is shown in Table 8.  
In the VGG16 network structure, the learning rate was set to 0.005, each input sample was 32, and the number of iterations was 1000. When the number of iterations was 300, the accuracy of the experimental data collected by each sensor leveled off. Hence, only the accuracy and loss of the previous 300 sets of experimental data are shown in Figure 13.  
According to Figure 13, sensor 1 had an accuracy of 99.42% and a loss of 2.6% in the VGG16 fault diagnosis model. Sensor 2 had an accuracy of 99.36% and a loss degree of 2.38%. Sensor 3 had an accuracy of 97.94% and a loss of 5.21%. To verify the effectiveness of the VGG16 fault diagnosis model, 100 datasets were randomly generated for each fault state of the gear for detection. In DS evidence theory, the evidence body E = {E1, E2, E3}, where E1, E2, and E3 represent the data collected in the z-direction of sensors 1, 2, 3, respectively. The identification framework \(\Theta=\{\text{A},\text{B},\text{C}\}\), where A, B, and C are the normal condition, slight pitting fault, and medium pitting fault of the gear teeth, respectively. The results obtained by means of inputting 100 sets of randomly generated data into the VGG16 fault diagnosis model were used as the body of evidence \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sampling Frequency (KHz)** & **Experiment Number of Times** & **Sampling Time (s)** & **Load (N \(\cdot\) m)** & **Rotation Speed (r/min)** \\ \hline \hline \multirow{8}{*}{33.28} & \multirow{8}{*}{60} & 0 & \\  & & &... & \\  & & & 10 & 500 \\  & & &... & \\  & & 1 & 30 & \\  & & & 0 & \\  & & &... & \\  & & & 10 & 600 \\  & & & 30 & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Experimental gear work. for the DS evidence method. After that, decision-level fusion was performed. The accuracy of each sensor before and after fusion is shown in Figures 14 and 15. Figure 13: VGG16 experimental results. (**a**) Sensor 1 experimental results. (**b**) Sensor 2 experimental results. (**c**) Sensor 3 experimental results. Figure 14: Before and after the fusion of multiple sensors. (**a**) Sensor 1 and sensor 2 fusion. (**b**) Sensor 1 and sensor 3 fusion. (**c**) Sensor 2 and sensor 3 fusion. (**d**) Fusion of all three sensors. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Sensors**} & \multicolumn{2}{c}{**Healthy Condition**} \\ \cline{2-3}  & **Normal Condition** & **Normal Condition** & **Medium Pitting Fault** \\ \hline \hline \multirow{2}{*}{Sensor 1} & \multirow{2}{*}{Sensor 2} & \multirow{2}{*}{Sensor 3} \\  & & & \\ Sensor 2 & & & \\ Sensor 3 & & & \\ Sensor 1 & & &  
From Figure 15, it can be concluded that before fusion, the accuracy of the three sensors was 96.43%, 93.97%, and 93.28%, respectively. When sensor 1 and sensor 2 were fused, the accuracy reached 99.93%, which is 3.52% and 6.34% higher than the accuracies of single sensors 1 and 2, respectively. When sensor 1 and sensor 3 were fused, the accuracy reached 99.96%, demonstrating an improvement of 3.36% and 6.85% compared to single sensors 1 and 3, respectively. When sensor 2 and sensor 3 were fused, the accuracy reached 99.40%, which is 5.78% and 6.56% better than single sensors 2 and 3, respectively.