# Intelligent Fault Diagnosis of Rolling Element Bearings Based on Modified AlexNet +
## 2 Proposed Methods and Materials
### Feature Selection
#### 2.2.2 Modified AlexNet Model
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Type** & **Activations** & **Learnable** \\ \hline Data 227 \(\times\) 227 \(\times\) 1 images & Image input & 227 \(\times\) 227 \(\times\) 1 & - \\ \hline conv1 & Convolution & 55 \(\times\) 55 \(\times\) 96 & Weights 11 \(\times\) 11 \(\times\) 1 \(\times\) 96; Bias 1 \(\times\) 1 \(\times\) 96 \\ \hline batchnorm-1 & Batch Normalization & 55 \(\times\) 55 \(\times\) 96 & offset 1 \(\times\) 1 \(\times\) 96 scale 1 \(\times\) 1 \(\times\) 96 \\ \hline Relu-1 & ReLu & 55 \(\times\) 55 \(\times\) 96 & - \\ \hline Pool-1 & Max Pooling & 27 \(\times\) 27 \(\times\) 96 & - \\ \hline conv2 & Convolution & 27 \(\times\) 27 \(\times\) 256 & Weights 5 \(\times\) 5 \(\times\) 48 \(\times\) 128; Bias 1 \(\times\) 128 \(\times\) 2 \\ \hline batchnorm-2 & Batch Normalization & 27 \(\times\) 27 \(\times\) 256 & offset 1 \(\times\) 1 \(\times\) 256 scale 1 \(\times\) 1 \(\times\) 256 \\ \hline Relu-2 & ReLu & 27 \(\times\) 27 \(\times\) 256 & - \\ \hline Pool-2 & Max Pooling & 13 \(\times\) 13 \(\times\) 96 & - \\ \hline conv3 & Convolution & 13 \(\times\) 13 \(\times\) 384 & Weights 3 \(\times\) 3 \(\times\) 256 \(\times\) 384; Bias 1 \(\times\) 1 \(\times\) 384 \\ \hline batchnorm-3 & Batch Normalization & 13 \(\times\) 13 \(\times\) 384 & offset 1 \(\times\) 1 \(\times\) 384 scale 1 \(\times\) 1 \(\times\) 384 \\ \hline Relu-3 & ReLu & 13 \(\times\) 13 \(\times\) 384 & - \\ \hline conv4 & Convolution & 13 \(\times\) 13 \(\times\) 384 & Weights 3 \(\times\) 3 \(\times\) 192 \(\times\) 128 \(\times\) 2 \\ \hline batchnorm-4 & Batch Normalization & 13 \(\times\) 13 \(\times\) 256 & - \\ \hline Relu-4 & ReLu & 13 \(\times\) 13 \(\times\) 384 & - \\ \hline conv5 & Convolution & 13 \(\times\) 13 \(\times\) 256 &
\begin{tabular}{c} Weights 3 \(\times\) 3 \(\times\) 192 \(\times\) 128 \(\times\) 2; \\ Bias 1 \(\times\) 1 \(\times\) 128 \(\times\) 2 \\ \end{tabular} \\ \hline batchnorm-5 & Batch Normalization & 13 \(\times\) 13 \(\times\) 256 & offset 1 \(\times\) 1 \(\times\) 256 scale 1 \(\times\) 1 \(\times\) 256 \\ \hline Relu-5 & ReLu & 13 \(\times\) 13 \(\times\) 256 & - \\ \hline Pool-5 & Max Pooling & 6 \(\times\) 6 \(\times\) 256 & - \\ \hline drop 6 & Dropout & 6 \(\times\) 6 \(\times\) 256 & - \\ \hline Relu-6 & ReLu & 6 \(\times\) 6 \(\times\) 256 & - \\ \hline gapool & Global Average Pooling & 1 \(\times\) 1 \(\times\) 256 & - \\ \hline Prob Softmax & Softmax & 1 \(\times\) 1 \(\times\) 4 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Hyper-parameter descriptions. where \(W_{c}=\) No. of weights, \(B_{c}=\) No. of biases, \(P_{c}=\) No. of parameters, \(K=\) width of kernels, \(N=\) No. of kernels, and \(C=\) No. of channels. In the modified AlexNet, at the conv1 layer, \(C=\) 3, \(K=\) 11, \(N=\) 96. \[\text{So},\ B_{c}=N=96\]  
\[ \begin{array}{ll}W_{c}&=C\times N\times K^{2}\\ &=3\times 96\times 11^{2}\\ &=34848\\ \\ P_{c}&=B_{c}+W_{c}\\ &=96+34,848=34,944\\ \end{array} \]  
Similarly, the number of parameters can be calculated for conv2, conv3, conv4, and conv5, and they are 614,656, 885,120, 1,327,488, and 884,992, respectively. The total number of parameters of the modified AlexNet is summarized in Table 4. It can be seen that only 3,752,704 parameters are used in the modified AlexNet whereas 62,378,344 parameters were used in the traditional AlexNet. More than 58,625,640 (62,378,344-3,752,704) parameters were used in the traditional AlexNet, which makes the model training, and testing time longer, and occurs overfitting. In contrast, the proposed modified AlexNet effectively reduces the total number of parameters, training, and testing time, and it also avoids overfitting.