# Surface Roughness Prediction of Bearing Ring Precision Grinding Based on Feature Extraction
## 5 Experimental Results and Discussion
In order to validate the effectiveness and performance of the established feature extraction-based surface roughness prediction method for precision grinding of bearing outer rings, different feature sets and different regression models were compared in two dimensions. In order to quantitatively assess performance of the proposed prediction method, \(R^{2}\), \(MAE\), \(RMSE\), and \(MAPE\) are selected as the criteria for evaluation. (1) Comparison of feature sets  
In order to verify the effectiveness of the signal multi-transform domain feature fusion scheme and the combination of signal features and grinding parameters to predict the surface roughness of the bearing collar outer ring grinding, three different feature combinations, \(T\&F\) (Figure 6a), \(T\&F\&E\) (Figure 6b), and \(T\&F\&E\&P\) (Figure 6c), are compared, respectively, with \(T\&F\) indicating the combination of the signal time-domain and frequency-domain features, \(T\&F\&E\) indicating the combination of the signal-time, frequency, and entropy-domain multi-transform domain features, and \(T\&F\&E\&P\) indicating the combination of the signal multi-transform domain features and grinding parameters proposed in this research. The signal features of the three different feature combinations are fused via PCA, then the final feature vectors are input into the SVR for surface roughness fitting. The SVR model parameters are set up via grid search and 5-fold cross-validation, and the fitting results are shown in Table 8 and Figure 6.  
The vibration and acoustic emission signals collected during the grinding experiments captured subtle changes in the grinding process, which contained information about the changes in the surface roughness of the workpiece during the grinding process of the bearing collar. After using the entropy feature as an input to the model, the \(R^{2}\) is improved from 0.9706 to 0.9838, which represents a significant improvement in the fitting degree of the model, and the model is more capable of interpreting the surface roughness and can more accurately characterize the changes in the surface roughness. the _MAE_, _RMSE_, and _MAPE_ are reduced from 0.0041, 0.0125, and 0.0361, respectively, to 0.0034, 0.0093, and 0.0311 respectively, which demonstrates that the average error, variance, and average percentage error of the model prediction have been reduced. The absolute error of the model can also be seen in the figure, which indicates that the model's prediction results are more accurate, and the prediction accuracy is more balanced and reliable. After again using the processing parameters as one of the model inputs, the \(R^{2}\) is further improved to 0.9953, and the _MAE_, _RMSE_, and _MAPE_ are further decreased to 0.0020, 0.0050, and 0.0187. The absolute error of the model is also further reduced, which represents a further improvement in the degree of fit, prediction accuracy, precision, and reliability of the model. In summary, using the signal entropy feature as one of the inputs to the model can better capture the complexity and dynamic changes in the data during the grinding process, while the processing parameters have an important influence on predicting the surface roughness, which can provide additional information that can help the model to more accurately capture the changes in the working conditions during the grinding process, thus improving the accuracy and reliability of the prediction. (2) Model comparison  
In order to verify the advantages of the SVR model (Figure 7b) in processing small sample data, the BP neural network model (Figure 7a) is used as a comparison to analyze the prediction effect. The _T&F&E&P_ dataset is taken as the input sample, and the same partition ratio and random seed are given when dividing the training set and test set samples to ensure that the training set and test set are the same each time, to eliminate random errors, and to debug and optimize the parameters of the two algorithms, respectively.