# Detection and Monitoring of Fitting Progression on Gear Tooth Flank Using Deep Learning
## 4 Validation  
For the validation of the model and the whole approach to detecting and monitoring pitting damage, three images of one tooth (tooth no. 7) that has three-level pitting damage were used. The first level (Figure 3) is the damage with \"smaller pitting\", which is seeded in two places--\"Pitting 1\" on the left and \"Pitting 2\" on the right side of tooth 7. The second level (Figure 4) of the damage is \"middle-size damage\", in which pitting damage (Pitting 1 and 2) is extended on the left side. The third level (Figure 5) of the damage is \"bigger-size damage\", in which pitting damage is further developed (Pitting 1 and 2) on the left side. The prediction confidence for Pitts 1 and 2, on the one hand, and for tooth 7, on the other hand, shows that the prediction confidence for the tooth is a little bit smaller. Figures 3-5 show the prediction confidence for other teeth, such as tooth 6 or 8, and it can be seen that the prediction confidence for these teeth is between 97 and 99%, while pitting damage prediction confidence is between 99.5 and 99.9%. Table 1 provides the results concerning the output images with start and end coordinates of the bounding boxes. Rectangular bounding boxes are defined with two diagonally distant points. Table 1 also lists diagonal coordinates for Pitts 1 and Pitts 2 for all three levels of pitting damage. Additionally, Table 1 gives the output data for tooth 7 as they are important for further analysis. The size of pitting or tooth in pixels was obtained by subtraction of end and start coordinates. Figure 4: Output image of the gear with middle pitting damage. Figure 3: Output image of the gear with smaller pitting damage. The sizes of pitting damage in the \(x\) and \(y\) direction were calculated according to the data from Table 1. For further calculation the gear width was set to 50 mm, which corresponds to the \(y\) direction on the image, and through a simple ratio of pixels for the pitting area and the tooth, the \(x\) and \(y\) direction sizes are obtained in millimeters. Table 2 lists the physically measured and calculated results with a difference that is given in percentages. The difference between the measured and the calculated results show that the calculated results are almost always bigger than the measured results. The average difference for all the cases is 7.04%, while it is 6.07% for the cases in the x direction and 8.01% for the \(y\) direction. Figure 6 shows the results for Fitting 1 and 2 in the \(y\) direction. It can be observed that pitting is stagnating or has a very small increase, which corresponds to the progression of pitting given in Figures 3-5. Figure 7 shows the results for Fitting 1 and 2 in the \(x\) direction. It can be observed that pitting increases at all levels, which corresponds to the progression of pitting given in Figures 3-5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Coordinates of Boxes (Start)**} & \multicolumn{2}{c}{**Coordinates of Boxes (End)**} & \multicolumn{2}{c}{**Prediction Confidence**} \\  & & **(Pixel)** & **(Pixel)** & **(\%)** \\ \hline \multirow{3}{*}{Pitting 1} & 1 st level & 3637.1069; 1157.3285 & 3948.2188; 1461.5745 & 99.86 \\  & 2 nd level & 2357.3508; 1171.1965 & 2741.0522; 1418.6853 & 99.94 \\  & 3 rd level & 2561.0249; 959.416 & 3165.9492; 1308.5024 & 99.91 \\ \hline \multirow{3}{*}{Pitting 2} & 1 st level & 2555.4255; 1114.2948 & 2839.6267; 1399.51 & 99.8 \\  & 2 nd level & 3289.771; 1180.4796 & 3832.9392; 1448.9137 & 99.91 \\  & 3 rd level & 3396.7253; 1029.2837 & 4248.0825; 1308.5024 & 99.91 \\ \hline \multirow{3}{*}{Tooth 7} & 1 st level & 1803.7611; 1096.854 & 4927.0244; 1528.479 & 97.5 \\  & 2 nd level & 1698.1724; 1136.9203 & 4797.167; 1581.1718 & 97.78 \\ \cline{1-1}  & 3 rd level & 2155.6003; 978.2216 & 5201.3003; 1474.3358 & 98.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of output images for Fitting 1 and 2, and Tooth 7. Figure 5: Output image of the gear with greater pitting damage.