# A Deep-Learning-Based Bearing Fault Diagnosis Using Defect Signature Wavelet Image Visualization
## 3 Fault Diagnosis Methodology Using the Defect Signature Wavelet Image
### Deep Convolution Neural Network Structure Specification
In addition, the initial layers of CNNs learn the fastest, so a short training period is adequate to achieve convergence. A lot of variations of the proposed DCNN were examined by varying the number of convolutional blocks and fully connected layers, and the number of nodes in each layer. Applying to this particular case with the fault in bearing, an extremely deep version of the network model does not give better results but does increase the time for training. The structure which is applied in this research leverages the capacity of the DCNN for exploiting the spatial structure in the DSWI data to sufficiently capture the properties of the AE signals. After the convolutionallayer, batch normalization follows to improve the convergence process by regularizing the model to avoid overfitting. Then the output from the batch normalization is fed to the nonlinear activation function. The proposed DCNN has a structure including several convolution blocks. Each block indicates one feature learning step with a specific level that includes convolution, batch-normalization, and activation function. Figure 5 depicts the designed architecture for each convolution block of the DCNN model, which consists of six blocks of convolution with filters 3-8, 8-16, 16-16, 16-16, 16-8, 8-8, and 8-1. The input image has a size of \(128\times 128\) pixels with three channels. At the output after the six blocks, the feature maps are flattened and fed to the fully connected layers. There are two fully connected layers and a soft-max layer which has the role of the classifier. The most regularly applied non-linear activation functions are the sigmoid, hyperbolic tangent, and rectified linear units (ReLU). Among them the ReLU function has been demonstrated to be more powerful than the others. However, during the training phase, ReLU units can die, and this problem can happen when great values of gradient flow across the ReLU function. This inspires the weights to be updated, and later the ReLU neuron fails to activate ever again on any data point. The leaky-ReLU function is an improved version that attempts to address this issue. The leaky-ReLU is used to introduce non-linearity into each stage, permitting the DCNN to learn complex models. Normally, the pooling layer is employed to decrease the resolution of the feature maps via the subsampling step to reduce the number of parameters and quicken the computation. In this study, instead of using pooling to reduce the size of spatial representation, the authors proposed using the convolution layer with a large kernel size and strike. This approach shows better performance when extracting the features of the image in a deep network. Figure 5: The proposed deep convolution neural network architecture diagram for the \(128\times 128\) size images. The training phase of the DCNN model relates the learning of all the weights and biases, and it is essential to obtain the optimized parameters for a successful feature learning. During the training phase of the network's parameters, it is also necessary for the DCNN to optimize the hyperparameters, which include the learning rate and dropout. The dropout holds an important characteristic of DCNN, which considerably helps to prevent the overfitting phenomenon by generalizing the model. In the designed model, dropout with a proportion of 0.5 is employed for better regularization of the DCNN. The adapted moment estimation (Adam), which is defined as a back-propagation strategy, is utilized to control the learning rate and other hyperparameters. The Adam optimization calculates the learning rate scale for different layers and avoids manual assignment to choose a suitable learning rate. Several configurations of the deep network, including LeNet-5 [29] and AlexNet [30], were tested to compare the results with the proposed. The DCNN model was trained with minibatch gradient descent and in each minibatch 100 training examples were used.