## 4 Experimental Results  
In this section, the authors present and discuss the achieved results of proposed research. The capability of the proposed DNN was evaluated through experimental results predicting the bearing degradation levels in the fault conditions of BCO, BCI, and BCR, which were collected under different crack size conditions. The 5-s AE signals of each bearing defect related to variable crack sizes were acquired at the sampling frequency of 250 KHz. Consequently, three datasets of bearings were given to verify the performance of the proposed approach. The detailed description of these datasets is given in Table 1. Each dataset contained 90 samples for each bearing health condition considered in this work. With three varying crack sizes of 3, 6, and 12 mm, there were 270 samples of each bearing condition collected for evaluation of degradation levels. Firstly, the EPS signals of bearing defects were calculated using the envelope analysis technique to detect the abnormal frequencies of bearings from the obtained spectral signals. A GDM-based window method was effectively applied only to capture the fault frequencies of BPFO, BPFI, and 2 \(\times\) BSF in bearings for correct estimation of the fault severity via the HI computations. These obtained HI values for each bearing condition were the first training dataset for teaching the DNN to precisely predict the bearing degradation levels under the varying conditions used in this study. Figure 5 presents the obtained EPS signals of the bearing defects at different crack sizes and the correlated HI values representing the severity of those defects. The analysis results show that as the crack sizes generated in bearings became larger, the protrusion of periodic impulses around the harmonics at the characteristic defect frequencies became clearer, resulting in increasing HI values. The proposed DNN was designed with five layers of neural networks consisting of one input layer, three hidden layers, and one output layer. The number of nodes in the input layer was determined based on the dimension of the input signal samples, and the number of nodes in the hidden layers were 800, 200, and 100, respectively. The output layer, however, was only one single node, which gave us the degradation levels of bearing defect conditions, as displayed in Figure 4. The neural layers of the proposed DNN used a sigmoidal function for activation. The synaptic weights and biases of the DNN were optimally initialized by the Xavier initialization method. The proposed DNN was trained using the Adam optimization-based backpropagation algorithm. The number of training iterations was set to 1000. This DNN was implemented using TensorFlow framework. As mentioned above, the dataset included three primary bearing defect conditions (BCO, BCI, and BCR) which were collected under three different crack sizes (3, 6, and 12 mm) for evaluation. Furthermore, the appropriate configuration of training and testing datasets was an essential aspect for evaluating DNN performance. In this study, 100 signal samples were selected randomly for training the DNN, and the remaining 170 signal samples were used to test the performance of the DNN. The number of training samples was kept less than the number of testing samples to ensure the high reliability of the prediction performance of the proposed DNN method. Each signal sample contained 2500 data points in the envelope spectrum analysis domain. The training and testing processes were accomplished for each bearing health condition,respectively. The prediction results of the bearing degradation using the proposed DNN method are shown in Figure 6, demonstrating that the proposed approach was able to efficiently predict the degradation levels of each bearing defect under varying crack size conditions.