## 4 The Accurate and Stable MDTF Fault Identification Framework and Its Experimental Evaluation
### The Experimental Classification for an MDTF Gearbox under Variable Speed Conditions  
The DCNA performs a fault-classifying process based on the input WVI imaging data for the MDTF gearbox under varying speed conditions. To verify the performance of the proposed DCNA for identifying seven MDTF fault types under varying speed conditions, we conducted an experimental setup of two scenarios, as shown in Table 4. In Scenario 1, all vibration data for four speeds were observed for classification. While in Scenario 2, four experiments were performed based on varying speed-related data. The configuration of the testing and training datasets for both of the scenarios is given in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Layers**} & **Operating** & **Number of** & \multirow{2}{*}{**Kernel Size**} & **Stride** & **Padding** \\  & **Parameters** & **Kernels** & & & \\ \hline Input layer & 224 \(\times\) 224 \(\times\) 3 & & & & \\ \hline
1 st Convolutional (Cv1) & \(55\times 55\) \(\times\) 96 & 96 & \(11\times 11\) & 4 & 0 \\ \hline
1 st Max Pooling (Pm1) & 27 \(\times\) 27 \(\times\) 96 & 96 & \(3\times 3\) & 2 & 0 \\ \hline
1 st Dropout (Do1) & 27 \(\times\) 27 \(\times\) 96 & & & & \\ \hline
2 nd Convolutional (Cv2) & 27 \(\times\) 256 & 256 & \(5\times 5\) & 1 & 2 \\ \hline
2 nd Max Pooling (Pm2) & 13 \(\times\) 13 \(\times\) 256 & 256 & \(3\times 3\) & 2 & 0 \\ \hline
2 nd Dropout (Do2) & 13 \(\times\) 13 \(\times\) 256 & & & & \\ \hline
3 rd Convolutional (Cv3) & 13 \(\times\) 13 \(\times\) 384 & 384 & \(3\times 3\) & 1 & 1 \\ \hline
4 th Convolutional (Cv4) & 13 \(\times\) 13 \(\times\) 384 & 384 & \(3\times 3\) & 1 & 1 \\ \hline
5 th Convolutional (Cv5) & 13 \(\times\) 13 \(\times\) 256 & 256 & \(3\times 3\) & 1 & 1 \\ \hline
3 rd Max Pooling (Pm3) & 6 \(\times\) 6 \(\times\) 256 & 256 & \(3\times 3\) & 2 & \\ \hline
1 st Fully Connected (Fc1) & 1 \(\times\) 1 \(\times\) 4096 & & & & \\ \hline
2 nd Fully Connected (Fc2) & 1 \(\times\) 1 \(\times\) 4096 & & & & \\ \hline
3 rd Fully Connected (Fc3) & 1 \(\times\) 1 \(\times\) 7 & & & & \\ \hline Output & SoftMax Nodes & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: The structural elements of the proposed DCNA.  
Figure 9: The applied DCNA model for implementing the fault-type identification in this study.  
For each speed (a total of four speeds: 300 RPM, 600 RPM, 900 RPM, and 1200 RPM), there were a total of 1400 one-second samples for all gear fault types (there were seven defect types or seven categories, PC, DT1, DT2, DT3, DT4, DT5, DT6, and each of them was acquired by sampling for one second, repeated 200 times, to achieve 200 one-second samples). All these samples were first preprocessed using LADT. Next, the output optimized sub-bands obtained from LADT were converted by the CWT method to attain the enriched feature scalogram images. That speed-related image subset was used as input data for the DCNA. For each experiment, we used two speed-related datasets (2800 samples) to train the proposed DCNA several times with multitudinous epochs, targeted to optimize the network parameters based on minimizing orientation of the loss function (Equation (9)), and the dataset of another speed (1400 samples) was used as the testing dataset of the constructed model. These processes were circularly acted based on four speed-related datasets to conduct all four experiments.