# A Bearing Fault Diagnosis Method Based on Wavelet Denoising and Machine Learning
## 3 Results and Discussion
### Applications of Supervised Learning  
In order to solve the binary classification problem based on the supervised learning method, quadratic support vector machine (SVM), random forest (RF), decision tree (DT) and AdaBoost algorithm are used for binary classification.  
On the basis of the evaluation index of unsupervised learning, the evaluation index of entropy value and contour coefficient is removed, and the evaluation index AUC value and precision rate are added. The AUC value is an evaluation index dedicated to the binary classification, which is used to evaluate the quality of the binary classification classifier. Its advantage is that it can avoid converting probability predictions into categories. A classifier with a larger AUC value has a higher correct rate.  
Figure 6 shows the clustering results of the double SVM.  
Figure 5: K-means cluster analysis effect diagram.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Number of** & **Accuracy/\%** & **Recall Rate/\%** & **Time Cost/ms** & **Silhouette Coefficient** & **F Value** & **Entropy Value** \\ \hline
1 & 96 & 97.1 & 1.9 & 0.93 & 0.96 & 0.24 \\
2 & 94 & 95.7 & 1.8 & 0.91 & 0.94 & 0.26 \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\
100 & 92 & 91.6 & 1.9 & 0.92 & 0.95 & 0.27 \\ average & 94 & 94.8 & 1.87 & 0.92 & 0.95 & 0.26 \\ standard deviation & 1.63 & 2.33 & 0.05 & 0.01 & 0.01 & 0.01 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Evaluation index table of clustering results.  
Table 6 shows the results of classification evaluation metrics using various supervised machine learning algorithms.  
It can be seen from the table that the accuracy of double SVM classification is the lowest, and when the accuracy of other classification methods is the same, the time-consumption of the decision tree is the shortest and the AUC value is the highest. From this analysis, it can be concluded that for the binary classification algorithm using supervised learning, the effect of equipment fault diagnosis using decision tree classification is the most ideal.  
Using the decision tree algorithm to conduct 100 classification experiments, the following evaluation Table 7 can be obtained:  
For this result, the mean accuracy rate is 96.8%, and each item is above 95%. Therefore, the clustering result is stable, and the standard deviation of the accuracy rate is 0.330.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Classification Method** & **Accuracy/\%** & **Recall Rate/\%** & **Time Cost/ms** & **Silhouette Coefficient** & **F Value** & **Entropy Value** \\ \hline decision tree & 96.7 & 96.7 & 18 & 0.968 & 0.966 & 0.987 \\ random forest & 96.7 & 96.7 & 1040 & 0.968 & 0.966 & 0.91 \\ Adaboost & 96.7 & 96.7 & 867 & 0.968 & 0.967 & 0.986 \\ double SVM & 96 & 95.8 & 1690 & 0.96 & 0.96 & 0.987 \\ \hline \end{tabular}
\end{table}
Table 6: Evaluation index table of clustering results of different classifiers.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Number of Experiments** & **Accuracy/\%** & **Recall Rate/\%** & **Time Cost/ms** & **Silhouette Coefficient** & **F Value** & **Entropy Value** \\ \hline
1 & 96.7 & 96.7 & 18 & 0.968 & 0.966 & 0.987 \\
2 & 97.2 & 97.2 & 18 & 0.973 & 0.974 & 0.987 \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\
100 & 96.4 & 96.4 & 18 & 0.965 & 0.962 & 0.987 \\ average & 96.8 & 96.8 & 18 & 0.969 & 0.967 & 0.987 \\ standard deviation & 0.33 & 0.33 & 0 & 0.003 & 0.005 & 0 \\ \hline \end{tabular}
\end{table}
Table 7: Evaluation table for 100 classification experiments.  
Figure 6: Double SVM clustering result graph.