## 4 Experimental Results on Surface Roughness Prediction
### Performance of the Three Applied Models
(**a**) The distribution of Self-Prediction; (**b**) The error of Self-Prediction; (**c**) The distribution of Self-Prediction; (**d**) The error of Self-Prediction. Figure 15: FFT-LSTM model training results. (**a**) The distribution of Self-Prediction; (**b**) The error of Self-Prediction; (**c**) The distribution of Self-Prediction; (**d**) The error of Self-Prediction. Error analysis in training and prediction are used to explore the performance of each model in the present study. The self-predictive model after training performs effectively at lower and approximately mean Ra value, but suffers from poor learning prediction problems for higher Ra values. In practice, higher Ra values correspond to violent vibration signals. The 1-D CNN model, which essentially extracts abundant feature data with sufficient datasets, served as a superior predictive model. In the case of the lack of datasets in this study, under-fitting results appear at higher Ra values in the training process. FFT-LSTM and FFT-DNN could be well-trained over a range of Ra values using a weak feature extractor for few datasets. To compare FFT-LSTM and FFT-DNN with the same FFT extractor, the training results are displayed in Figure 14a,b for the FFT-DNN, and Figure 15a,b for the FFT-LSTM, respectively; FFT-LSTM, with the same training datasets, shows that FFT-DNN presents higher deviations over all training datasets. FFT-LSTM outperforms the training effectiveness of the 1-D CNN model in the training process. Finally, cross-validation for testing is performed to evaluate the predictive performance of the surface roughness via vibration signal datasets after training datasets. Using the afore-described methods for choosing the test dataset numbers, dataset numbers (3, 13, 23, 33, 43), (4, 14, 24, 34, 44), (5, 15, 25, 35, 45), (6, 16, 26, 36, 46), and (7, 17, 27, 37, 47) are chosen for testing the datasets to account for cross-validation in the testing process. The mean error results of the dataset cross-validation is provided to evaluate the predictive accuracy of the trained model. The criteria of prediction performance presented in [40] declare that MAPE ranges from less 10%, 10%-20%, 20%-50%, and greater 50% response correspond to highly accurate, accurate, reasonable, and not accurate predictions, respectively. An overview of the results of the three predictive models is shown in Figure 17a to Figure 17c. FFT-LSTM achieves the best predictive performance over Ra values in the studied Ra range. Moreover, the three models have poor predictive capability for lower Ra range and higher Ra range. Overall, the FFT-DNN with 48.75% MAPE at lower Ra range falls into the not accurate predictive level. Excluding the lower and higher Ra ranges, the three models are at the accurate  
Figure 16: 1-D CNN model training results. (**a**) The distribution of Self-Prediction; (**b**) The error of Self-Prediction; (**c**) The distribution of Self-Prediction; (**d**) The error of Self-Prediction. predictive level. Moreover, the predictive performance of 1-D CNN obtained a highly accurate level in the medium Ra range, 9.95%, and 8.92% MAPE, as shown in Figure 17a. The higher Ra range prediction of FFT-LSTM exhibits preferred results in comparison with the three models. These findings reveal that FFT-LSTM takes advantage of temporal modeling to present forecasting in the high Ra range. At lower Ra ranges, 1-D CNN achieves the best predictive ability because this model can extract insensitive feature information; this ability is helpful for prediction in high-precision milling processes.