## 4 Experimental Results on Surface Roughness Prediction
### Performance of the Three Applied Models  
To demonstrate the learning effectiveness of the three predictive models in the training process, all datasets gathered under the circumstances of limited resources are employed to perform the analysis. The loss function distributions exhibit convergent efficiency and accuracy in the optimum learning process. The loss function results of 1-D CNN, as shown in Figure 11c, demonstrate a stable convergence process and attain a considerably small convergence value. The other two models, FFT-DNN in Figure 12c and FFT-LSTM in Figure 13c, exhibit small fluctuating distributions in the convergence process; however, they still achieve an accepted convergence value. Comparison of the convergence performance of the three models indicates that the 1-D CNN model is the best because of its improved feature extraction capability compared to the FFT-DNN and FFT-LSTM models using the FFT feature extractor. Further, all three of the models can obtain rather low convergent values in the learning process. In the comparison of the regression predictive accuracy in the learning results, the RMSE and MAPE utilized to assess the surface roughness prediction value are defined in Equations (10) and (11). The results of each of the models are shown in Table 1, the individual self-regression-predicted Ra is plotted (red) in Figure 11a to Figure 13a, and the regression-predicted Ra error is depicted in Figure 11b to Figure 13b. 1-D CNN achieves the best performance of the learning results, with the learning datasets almost completely fitting the predicted data. From the self-prediction result using the learning regression model, the three models exhibit high learning capability, with 1-D CNN found to achieve superior feature extraction in the present study. \[\text{MAPE}=\frac{1}{n}\sum_{i=1}^{n}\left|\frac{y_{i}-x_{i}}{y_{i}}\right|*100 \%, \tag{10}\]  
\[\text{RMSE}=\sqrt{\frac{\sum_{i=1}^{n}\left(y_{i}-x_{i}\right)^{2}}{n}}, \tag{11}\]  
where \(n\) is the experiment case number, \(y_{i}\) is the real Ra value, and \(x_{i}\) is the predicted Ra value. To validate the ability of the predictive models, training models must be tested to verify the generalization in actual prediction. In the limited data conditions, a total of 50 vibration signal datasets are separated into 45 datasets for training and 5 datasets for testing. First, datasets are sorted by Ra value from small to large and annotated from No. 1 to No. 50. As arranged in Table 2, the Ra samples are divided into five intervals, with each interval containing 10 datasets. The lower/higher Ra range are in interval No. 1/No. 5, and the medium Ra range are in interval No. 2 to No. 4. In general, the Ra value is separated into three levels, with the lower/higher range having less/greater than 0.4/0.7 Ra value, and 0.4 to 0.7 Ra value belongs to medium level. Defining the lower, medium, and higher ranges of surface roughness is helpful for the following quantification analysis. The five testing datasets are regularly chosen in each of the intervals, and the remaining 45 datasets are used for training. For example, datasets numbered (4, 14, 24, 34, 44) and (6, 16, 26, 36, 46) are selected as the testing datasets. The training results corresponding to FFT-DNN, FFT-LSTM, and 1-D CNN using the remaining datasets are displayed in Figures 14-16, respectively. All three models converge to a low loss function in the training process. However, the self-prediction of the 1-D CNN model is not found over the range of Ra values available here. Figure 14a,c correspond to datasets of numbers (4, 14, 24, 34, 44) and (6, 16, 26, 36, 46), respectively. Figure 11: 1-D CNN model training results. (**a**) The distribution of the training process; (**b**) The error of Self-Predicted Ra; (**c**) The loss function of Self-Predicted Ra. Figure 12: FFT-DNN model training results. (**a**) The distribution of the training process; (**b**) The error of Self-Predicted Ra; (**c**) the loss function of Self-Predicted Ra. Figure 14: FFT-DNN model training results.