## 5 Experimental Results and Discussion
### Experiment 1
#### 5.1.1 Description of Experimental Data  
The CWRU dataset [41] represents a standard dataset for bearing fault diagnosis. The bearing test rig which, was used as an experimental device, mainly consisted of a 2 hp motor, a power meter, a torque sensor, and an electronic control device, as shown in Figure 3. The bearing model was SKF6205, the roller diameter was 7.5 mm, the diameter of the section was 39 mm, the number of rollers was 9, and the contact angle was 0 degrees. The bearing had been machined by the Electric Discharge Machining (EDM) with three kinds of defect positions, namely rolling element damage, outer race  
Figure 2: The flowchart of the validation method for the MDI-CNN model. Accuracy 1 and Accuracy 2 represent the classification accuracy obtained by entering normal test samples and test sample containing the noise into the trained MDI-CNN, respectively, and Accuracy 3 indicates the classification accuracy of the model after the incremental training on the noisy test samples. MDI-CNN, Multi-Dimension Input convolutional neural network; FFT, Fourier transformation; ESA, envelope spectrum analysis.  
damage, and inner race damage. The size of the damage diameter was 0.007 inches, 0.014 inches, and 0.021 inches, and three were a total of nine damage states.  
In Experiment 1, the data of the bearing at the driving end was selected as the test data when the load was 1 hp, and the sampling frequency of the system was 12 kHz. In order to optimize the network training process, each signal was normalized. As shown in Figure 4, the data augment algorithm was used to carry out the overlapping sampling of samples to increase training samples, and, thus, enhance the generalization ability of the deep neural network.  
Table 2 shows the composition of the test dataset, which had a total of 10 different fault types, 2000 samples for each fault type, and a total of 20,000 samples. A training set of 1750 samples was randomly selected from each fault type sample set, and the remaining 250 samples constituted the test set.  
The determination of proper CNN structure and network parameters depends to a large extent on experience. According to the previous research results, the fault diagnosis model of rolling bearing based on the MDI-CNN had a three-input-layer structure, and the input data of the three layers was respectively the original signal data, the fast Fourier transform data, and the envelope spectrum analysis data. The number of network layers in the model was equal to two, and the number of neurons  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Damage Position** & **None** & \multicolumn{3}{c}{**Scroll Body**} & \multicolumn{3}{c}{**Inner Ring**} & \multicolumn{3}{c}{**Outer Ring**} \\ \hline
**Label** & **0** & **1** & **2** & **3** & **4** & 5 & 6 & 7 & 8 & 9 \\ Damage diameter/inch & 0 & 0.007 & 0.014 & 0.021 & 0.007 & 0.014 & 0.021 & 0.007 & 0.014 & 0.021 \\ Training set & 1750 & 1750 & 1750 & 1750 & 1750 & 1750 & 1750 & 1750 & 1750 \\ Test set & 250 & 250 & 250 & 250 & 250 & 250 & 250 & 250 & 250 & 250 \\ \hline \end{tabular}
\end{table}
Table 2: The experimental data.  
Figure 4: The method of data augment.  
Figure 3: Image of the bearing test rig.  
per layer was six and twelve, respectively. Each layer contained a convolution layer and a pooling layer. The final model parameters after many comparison tests are shown in Table 3.