# Surface Roughness Prediction of Bearing Ring Precision Grinding Based on Feature Extraction
## 5 Experimental Results and Discussion
\(\mathbf{T}\), \(\mathbf{F}\), and \(\mathbf{E}\) form the multi-transform domain feature vector \(\mathbf{I}\) of a single signal, where \(\mathbf{I}\) is a 224-dimensional vector, as follows:  
\[\mathbf{I}=\left[T\,F\,E\right] \tag{42}\]  
For each grinding acquisition of three channels of vibration signals and two channels of acoustic emission signals--a total of five channels of signals--the multi-transform domain feature vector of the five channels of signals will be combined together to obtain the initial signal feature vector, a 1120-dimensional vector, as follows:  
\[\mathbf{Feature}=\left[I_{AE1}\,I_{AF2}\,I_{V\times X}\,I_{V\times Z}\right] \tag{43}\]  
Figure 5: Top eight IMFs components retained. where \(I_{AE1}\) denotes the narrow-frequency acoustic emission signal; \(I_{AE2}\) denotes the wide-range acoustic emission signal; \(I_{V\text{-}X}\) denotes the X-axis vibration signal; \(I_{V\text{-}Y}\) denotes the Y-axis vibration signal; and \(I_{V\text{-}Z}\) denotes the Z-axis vibration signal. In order to reduce the correlated features and the dimensionality of the dataset, the initial signal feature vectors are fused using principal component analysis (PAC), and a total of 54 principal components are obtained. These have a cumulative contribution value of 98.065%, which is able to retain most of the useful information in the original signal feature vectors. The results are shown in Table 6.  
The score coefficients of the raw features indicate the importance or weight of the feature in each principal component. These score coefficients represent the magnitude of the role that each raw feature plays in composing the principal components, with larger score coefficients indicating a higher influence in the corresponding principal component and smaller coefficients indicating a lower influence. By looking at the score coefficients, it is possible to understand which raw features play an important role in composing the principal components to better understand the structure of the data and the relationship between the features. The score coefficients for some of the raw features are shown in Table 7.  
After the initial signal feature vectors \(\boldsymbol{Feature}\) are fused by the principal component analysis, 54-dimensional signal feature vectors \(\boldsymbol{Feature_{signal}}\) are obtained, which are connected with the grinding parameters in Table 5 to form the final set of feature vectors \(\boldsymbol{Feature_{total}}\) as shown below:  
\[\boldsymbol{Feature_{total}}=[\boldsymbol{Feature_{signal}}\,\boldsymbol{ Feature_{argument}}] \tag{44}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Principal** \\ **Component** \\ \end{tabular} } & \multirow{2}{*}{**Eigenvalue**} & \multicolumn{2}{c}{**Variance**} & \multicolumn{1}{c}{**Cumulative**} \\  & & **Contribution** & **Contribution** \\  & & **Rate/\%** & **Rate/\%** \\ \hline
1 & 330.850 & 29.171 & 29.171 \\
2 & 177.041 & 15.610 & 44.781 \\
3 & 88.175 & 7.774 & 52.555 \\
4 & 57.692 & 5.087 & 57.642 \\ � & � & � & � \\
51 & 1.796 & 0.158 & 97.622 \\
52 & 1.709 & 0.151 & 97.773 \\
53 & 1.684 & 0.148 & 97.921 \\
54 & 1.625 & 0.143 & 98.065 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Partial PCA solution results. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Principal Component** \\ \end{tabular}  } & \multirow{2}{*}{**Primary Feature**} & \multirow{2}{*}{**1**} & \multirow{2}{*}{**2**} & \multirow{2}{*}{**53**} & \multirow{2}{*}{**54**} \\ \hline \(I_{AE1}(x_{1}^{1})\) & \(-\)0.035 & 0.014 & & 0.007 & 0.008 \\ \(I_{AE1}(x_{1}^{2})\) & \(-\)0.020 & 0.020 & & 0.003 & 0.023 \\ \(I_{AE  
The obtained 57-dimensional total feature vector \(\boldsymbol{Feature_{total}}\) was used as the input of the support vector regression (SVR) model to obtain the final predicted grinding surface roughness.