## 5 Test and Verification
### Condition Detection via the Proposed Method
The RBF kernel function is also employed, and the penalty coefficients \(C\) and kernel function parameter \(\sigma\) of the SVM are optimized by using grid search. The grid search range of \(C\) and \(\sigma\) are \(2^{-8}\)-\(2^{8}\), and \(2^{-14}\)-\(2^{14}\), respectively, and the search step is 0.1. As shown in Table 5, when the diagnosis is based on a BP neural network, the normal state diagnosis accuracy reaches 90%, the outer ring defect state fault diagnosis accuracy is 68.8%, some outer ring defect vibration data are classified incorrectly as in the normal state, the inner ring defect state fault diagnosis accuracy is only 51.7%, nearly half of inner ring defect vibration data are incorrectly classified into outer ring defect and normal states, the roller element defect state fault diagnosis accuracy reaches 88.6%, and the overall accuracy is 74.75%. When the diagnosis is performed using the ELM method, the normal state diagnosis accuracy reaches 97.2%, the outer ring defect state fault diagnosis accuracy is 79%, the outer ring defect state fault diagnosis accuracy is 66%, the roller element defect state fault diagnosis accuracy reaches 95.6%, and the overall accuracy is 85.5%. When the diagnosis is based on the multiclass SVM method, the normal state diagnosis accuracy reaches 100%, the outer ring defect state fault diagnosis accuracy reaches 88.7%, the outer ring defect state fault diagnosis accuracy reaches 77.4%, the roller element defect state fault diagnosis accuracy reaches 96.8%, and the overall accuracy is 90.73%. A comparison of the results of the above four diagnosis \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{6}{c}{**Approximate Entropy**} & \multicolumn{6}{c}{**State**} \\ \hline
**IMF1** & **IMF2** & **IMF3** & **IMF4** & **Normal** & **Outer Defect** & **Inner Defect** & **Element Defect** \\ \hline
0.72001 & 0.14866 & 0.40609 & 0.42288 & 1 & 0 & 0 & 0 \\
0.72055 & 0.14759 & 0.40633 & 0.42241 & 1 & 0 & 0 & 0 \\
0.72071 & 0.14726 & 0.40579 & 0.42055 & 1 & 0 & 0 & 0 \\ \hline
0.71503 & 0.224 & 0.84966 & 0.78457 & 0 & 1 & 0 & 0 \\
0.71519 & 0.22413 & 0.84976 & 0.78629 & 0 & 1 & 0 & 0 \\
0.69023 & 0.45486 & 0.60378 & 0.99773 & 0 & 1 & 0 & 0 \\ \hline
0.68705 & 0.46803 & 0.5576 & 1.0275 & 0 & 0 & 1 & 0 \\
0.68699 & 0.46578 & 0.55627 & 1.0291 & 0 & 0 & 1 & 0 \\
0.69023 & 0.45486 & 0.60378 & 0.99773 & 0 & 0 & 1 & 0 \\ \hline
0.68039 & 0.99442 & 1.0432 & 1.0662 & 0 & 0 & 0 & 1 \\
0.68052 & 0.995 & 1.043 & 1.0649 & 0 & 0 & 0 & 1 \\
0.68109 & 0.9989 & 1.0441 & 1.0666 & 0 & 0 & 0 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Training data for each state. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Classifier**} & \multicolumn{3}{c}{**Average Diagnostic Accuracy \%**} & \multicolumn{2}{c}{**Overall**} \\ \cline{2-5}  & **N** & **O** & **I** & **R** & **Accuracy \%** \\ \hline BPNN & 90.0 & 68.7 & 51.7 & 88.6 & 74.75 \\ ELM & 97.3 & 79.0 & 66 & 95.6 & 84.48 \\ SVM & 100 & 88.7 & 77.4 & 96.8 & 90.73 \\ PSO-KELM & 100 & 90.3 & 85.7 & 96.3 & 93.08 \\ \hline \hline BPNN: Back Propagation Neural Network; ELM: extreme learning machine; SVM: support vector machine; PSO-KELM: particle swarm optimization-kernel extreme learning machine. & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison results of different algorithm.