# Intelligent Fault Diagnosis of Rolling Element Bearings Based on Modified AlexNet +
## 3 Experimental Verification Based on Vibration Signals
### Experimental Outcome
#### 3.2.1 The Proposed System's Performance  
The proposed system was trained on 1024 vibration images and tested on 400 vibration images. Five BN layers were added, and the FC layer was replaced with the GAP layer to AlexNet. Table 5 shows the comparison between the FC layer, and GAP of five trials. It can be observed by comparing Table 5, that as a result of using FC, due to overfitting, the testing accuracy decreased from the training accuracy. In contrast, by using GAP instead of FC, overfitting was reduced. However, the accuracy was slightly reduced. Five BN layers were added to improve accuracy. The final proposed system's training and testing accuracy is shown in Table 6. It can be observed by comparing Table 6 that the performance of the improved AlexNet model was much better than the performance of the traditional FC AlexNet model. The full connection layer is removed in the modified AlexNet model, which has a significant impact on the model's ability to be used for online, quick fault diagnosis. This also had a big effect on the number of model parameters there are and the duration of the training required. The modified AlexNet model achieved an accuracy of 98.30%, whereas the traditional AlexNet model was 94.40% accurate [32]. The proposed modified AlexNet model's overfitting problems are not present in our proposed method. This section presents the hybrid model concept. Additionally, to achieve the best classification performance, the features obtained from the last layer of the modified AlexNet are applied as the input to various machine learning models, including Softmax, kNN, and SVM. Furthermore, the classification abilities of the models are investigated individually. Figure 11 shows the performance of the classifier on the CWRU dataset and the MFPT dataset. The accuracy of the CWRU dataset is shown in red, whereas the accuracy of the MFPT dataset is represented in blue. It can be observed by comparing Table 5 that the performance of the modified AlexNet-SVM hybrid model is much better than the performance of the modified AlexNet-Softmax, and modified AlexNet-kNN hybrid models on both the CWRU dataset, and the MFPT dataset. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method**} & **Training Accuracy (\%)** & **Testing Accuracy (\%)** & **Training Time(s)** & **Testing Time (s)** \\ \hline AlexNet & 97.50 & 94.40 & 148.92 & 0.295 \\ \hline Modified AlexNet & 98.74 & 98.30 & 112.48 & 0.157 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of results between the traditional AlexNet and modified AlexNet. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**AlexNet**} & \multicolumn{2}{c}{**Using Fully Connection Layer (FC)**} & \multicolumn{2}{c}{**Using Global Average Pooling (GAP)**} \\ \cline{2-5}  & **Training Accuracy (\%)** & **Testing Accuracy (\%)** & **Training Accuracy (\%)** & **Testing Accuracy (\%)** \\ \hline Trial 1 & 97.50 & 94.40 & 95.80 & 95.20 \\ \hline Trial 2 & 97.30 & 94.30 & 95.50 & 95.10 \\ \hline Trial 3 & 98.10 & 95.20 & 96.60 & 96.00 \\ \hline Trial 4 & 96.88 & 94.00 & 95.20 & 94.85 \\ \hline Trial 5 & 97.78 & 94.50 & 96.20 & 95.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Impact on global average pooling (GAP). This section compares the results of using DWT vs. without DWT in a noisy environment. Figure 12 shows how DWT impacted classification results. In Figure 12 the red line on the graph represents performance with DWT, while the blue dot line represents performance without DWT on the CWRU dataset and the green color line on the graph represents performance with DWT, while the yellow dot line represents performance without DWT on MFPT dataset. The noisy situation on the CWRU dataset is shown, and it is clear from the graph that using DWT is more effective than not using DWT in a noisy environment. On the MFPT dataset, the performance under noisy conditions with DWT is shown by the green color line, and the performance without DWT is shown by the yellow dot line.