## 4 The Accurate and Stable MDTF Fault Identification Framework and Its Experimental Evaluation
### Dcna Construction  
In this study, the contents of the enriched visualized feature pool, which are called WVIs are obtained from the CWT of low-noise optimized vibration sub-bands, are provided as an input to DCNA. The WVI contains fault-related information in the form of edges, lines, curves, spots, or pixels with various intensities (which are represented by the R, G, and B channels of the RGB image). The DCNA is used primarily to recognize images. Figure 9 demonstrates the architecture of the proposed DCNA used in this study. The proposed DCNA has fifteen layers, including five convolutional layers (Cv), three pooling layers (Pm), two drop-out layers (Do), three fully connected layers (Fc), one input layer, and one terminal output layer (Os). The DCNA makes a start with an input layer of size 224 \(\times\) 224 \(\times\) 3, according to the size of RGB images (224 \(\times\) 224 indicates the values of length and width, and 3 denotes three R, G, B channels of the input image). Next, the features are extracted from fault-related images by the first convolutional layer with 96 kernels of size 11 \(\times\) 11 \(\times\) 3 and the stride of 4. The results of the first convolutional calculation are feature spaces of size 54 \(\times\) 54 \(\times\) 96. After the first convolution layer (Cv1), the max-pooling layer (Pm1) is applied for down-sampling. Moreover, the drop-out layer (Do1) is located in series to extenuate the over-fitting issue [50]. The second convolutional layer has 256 filters of size 5 \(\times\) 5 \(\times\) 48, and it is followed by pooling and dropout processing layers. The Cv3 and Cv4 layers consist of 384 filters with a size of 3 \(\times\) 3 \(\times\) 256 and 384 kernels with a size of 3 \(\times\) 3 \(\times\) 384, respectively. Next, Cv5 is down-sampled by the third max-pooling layer (Pm3), composed of 256 of 3 \(\times\) 3 \(\times\) 384 kernels. All of the max-pooling layers employ 3 \(\times\) 3 filters with a stride of 2. The output of the third max-pooling is used as an input to the fully connected layers (Fc1, Fc2, Fc3). Fc1 tries to implement a flattening process to convert all feature matrices (6 \(\times\) 6 \(\times\) 256) from the output of layer Pm3 to the feature vectors (1 \(\times\) 1 \(\times\) 4096) through its operation as a weighted sum with bias terms. These output feature vectors then are passed through the activation function ReLU and input to the next layer (Fc2). The second fully connected layer, which is the penultimate layer, includes 1000 neurons and functions, similarly to Fc1, to output feature vectors of size 1 \(\times\) 1 \(\times\) 1000. The last flattened layer, Fc3, including 7 neurons, which are the SoftMax activation functions, is the classification layer. It operates at a terminal spot of the DCNA for estimation of the probabilities of the categories.  
In this paper, the fifteen-layer DCNA has been conducted based on the original AlexNet architecture [54], with some modifications for this specific application. The AlexNet model has already achieved better feasibility than other models for recognizing images. This model has implemented training for 1.2 million high-resolution pictures of ImageNet for classification of up to 1000 differential species targets in the contest of LSVRC-2010 by training of 650 thousand neurons and 60 million parameters, with many optimizing processes in the network architecture. In our research, we have replaced two normalization layers with two drop-out layers in order to improve the capability of over-fitting avoidance [50; 55]. Moreover, the last fully connected layers (Fc3), which include 1000 neurons from the original AlexNet, are replaced by the same fully connected layers with a reduced number of neurons (7), for suitable application in our research with seven classifying categories. The detailed description of the proposed DCNA is shown in Table 3.