## 5 Result and Discussion  
In the first phase model training, values for time delay (\(\tau\) = 10) and embedding dimension (\(m\) = 4) are obtained using the autocorrelation function method and false nearest neighbor method [27; 28]. These are chosen as inputs for the SSA decomposition, and one non-stationary source and three stationary sources signals are extracted. There are two reasons for setting one non-stationary source signal: (1) non-stationary source contains more fault feature information to distinguish different fault classes than stationary source; (2) one source signal is convenient to calculate time- and frequency-domain indexes for follow-up process in the proposed approach. SSA training data for three damage classes are shown in Figures 5-7. Ten dimensionless time-frequency parameters were chosen from the non-stationary source of each class, and these were used as the input data for LS-SVM. The Gaussian RBF kernel (\(K(x_{p},x_{q})=\exp{(-\frac{\left\lVert x_{p}-x_{q}\right\rVert^{2}}{2\sigma ^{2}})}\)) was selected, and the kernel parameter \(\sigma\) is optimized using fast leave-one-out cross validation optimization proposed in [32]. Figure 5: SSA results of normal tool sample. Figure 6: SSA results of mild wear tool sample. The classification results of the proposed SSA + LS-SVM method are shown in Tables 2 and 3. Table 2 presents the classification results with training set, all normal tools can be correctly identified; however, the accuracy of the mild wear and severe wear tools is 87.5% and 92.5%, respectively. Five mild wear tools were identified wrongly as severe wear tools, and three severe wear tool were identified as mild wear tools. Table 3 shows the classification results with testing set, all normal tools can be correctly identified; however, the accuracy of the mild wear and severe wear tools is 80% and 85%, respectively. Four mild wear tools were identified as severe wear tools, and three severe wear tool were identified as mild wear tools. Fortunately, as shown in Tables 2 and 3, the proposed method can significantly distinguish between normal tools and wear tools (included mild and severe wears) both in training sets and testing sets. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multirow{2}{*}{**Training Classes**} & \multicolumn{4}{c}{**Training Result**} & \multirow{2}{*}{**Classification**} \\ \cline{3-4} \cline{6-6}  & & **Normal Tool** & & **Mild Wear Tool** & **Severe Wear Tool** & **Accuracy** \\ \hline SSA + LS-SVM & normal tool & 40 & 0 & 0 & 100\% \\ proposed & mild wear tool & 0 & 35 & 5 & 87.5\% \\  & severe wear tool & 0 & 3 & 37 & 92.5\% \\ \hline Original & normal tool & 37 & 3 & 0 & 92.5\% \\ LS-SVM & mild wear tool & 4 & 29 & 7 & 72.5\% \\  & severe wear tool & 0 & 8 & 32 & 80\% \\ \hline PCA + LS-SVM & normal tool & 38 & 2 & 0 & 95\% \\  & mild wear tool & 5 & 30 & 5 & 75\% \\  & severe wear tool & 2 & 6 & 32 & 80\% \\ \hline \multirow{2}{*}{SSA + LDA} & normal tool & 31 & 9 & 0 & 77.5\% \\  & mild wear tool & 6 & 26 & 8 & 65\% \\ \cline{1-1}  & severe wear tool & 0 & 11 & 29 & 72.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Result of stationary subspace analysis (SSA) + least squares support vector machine (LS-SVM), original LS-SVM, Principal Component Analysis (PCA) + LS-SVM and SSA + linear discriminant analysis (LDA) with training set. Figure 7: SSA results of severe wear tool sample. The proposed SSA + LS-SVM method was compared with the original LS-SVM, PCA (Principal Component Analysis) + LS-SVM, and with SSA + LDA (linear discriminant analysis). The original LS-SVM method means that the original vibration signals measured in experiment are the input of LS-SVM, in which do not extract signals by SSA and PSR. Its algorithm calculates 10 dimensionless time-frequency indexes (described in Table 1) from the original vibration signals and be used as inputs for training the LS-SVM classifier model. The PCA + LS-SVM method substitute SSA for PCA in Algorithm 3, that is to say, PCA is used to feature extraction.