## 4 Experimental Results
In this work, to validate the effectiveness of the proposed DNN methodology in predicting the degradation levels of each bearing defect, the prediction accuracy (PA) was determined by the average absolute percentage error calculation, which is one of the most popular measures for prediction models [28]. This PA is computed as follows:  
\[\text{PA}=\left(1-\frac{1}{\text{N}}\sum_{i=1}^{\text{N}}\left|\frac{\text{A} _{i}-\text{P}_{i}}{\text{A}_{i}}\right|\right)\times 100\% \tag{14}\]  
where \(\text{A}_{i}\) and \(\text{P}_{i}\) are the actual estimated and predicted values, respectively, and N is the number of data samples (i.e., \(\text{N}_{\text{train}}\) = 100, and \(\text{N}_{\text{test}}\) = 170). A comparison of the prediction performance of the proposed DNN method with state-of-the-art approaches is presented in Table 2, including the radial-basis-function-based support vector machine regression (RBF_SVM) [29] and the backpropagation-based artificial neural network (BP_ANN) [14]. The RBF_SVM employs the support vector regression (SVR) method using the RBF kernel, which is suitable for a prediction case of the degradation level of bearing conditions. This RBF_SVM trained the same datasets preprocessed by the envelope analysis technique. The obtained results are obvious that the RBF_SVM performed poorly at predicting bearing degradation compared to others methods, as illustrated in Figure 7. Similarly, the same datasets of bearing EPS signals were provided as inputs to the BP_ANN for the training process using the backpropagation algorithm. This BP_ANN had the same hierarchical architecture as the proposed DNN, in which its weights were initialized with random values and the biases of the neurons were set up to zero. Its performance was lower than the proposed method, as demonstrated in Figure 7. The aforementioned approaches were trained and tested with the same datasets to provide a fair and suitable comparison. As a result, the proposed DNN approach outperformed the existing methods in predicting the degradation level of each bearing  
Figure 5: Estimation of the bearing defect severity corresponding to a bearing crack on the outer surface (BCO), a bearing crack on the inner surface (BCI), and a bearing crack on the roller (BCR) using the Gaussian distribution model (GDM)-based HI calculation. defect collected simultaneously under different crack size conditions with a high average accuracy of 97.93% for training and 95.38% for testing. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Methodologies**} & \multicolumn{4}{c}{**Training (\%)**} & \multicolumn{4}{c}{**Testing (\%)**} \\ \cline{2-7}  & **BCO** & **BCI** & **BCR** & **BCO** & **BCI** & **BCR** \\ \hline RBF\_SVM [29] & 72.19 & 73.26 & 78.01 & 60.88 & 63.79 & 74.70 \\ BP\_ANN [14] & 93.76 & 92.53 & 93.50 & 92.08 & 90.67 & 91.45 \\ Proposed DNN & 98.14 & 97.12 & 98.54 & 96.05 & 94.17 & 95.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Accuracy of the proposed DNN approach in predicting the degradation levels of bearing defects. RBF\_SVM: radial-basis-function-based support vector machine regression; BP_ANN: backpropagation-based artificial neural network. Figure 6: The prediction results of the degradation levels for each bearing condition (BCO, BCI, and BCR) under varying crack sizes using the proposed DNN-based method: (**a**) training and (**b**) testing. Figure 7: Degradation prediction of bearing defects according to varying crack sizes using the proposed DNN approach and other methods: (**a**) training and (**b**) testing.