# BearingCog: A Bearing Fault Diagnosis Method under Variable Operational Conditions
## 4 Experimental Results and Discussion
### Feature Extraction Analysis
\begin{table}
\begin{tabular}{c c} \hline \hline
**Data Set** & **Different Data Feature** & **Recognition Accuracy Rate** \\ \hline \multirow{4}{*}{Experimental data} & Dimensionless time domain characteristics & 63.6\% \\  & EMD decomposition energy & 71.0\% \\  & VMD decomposition energy & 76.6\% \\  & **Multi-information fusion** & **94.1\%** \\  & Dimensionless time domain characteristics & 75.3\% \\  & EMD decomposition energy & 84.5\% \\  & VMD decomposition energy & 90.7\% \\  & **Multi-information fusion** & **96.4\%** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The average accuracy of recognition using different feature types. In addition, to further verify the effectiveness of the proposed scheme, the datasets from Case Western Reserve University (CWRU) are introduced for analysis. The details of the defective bearing dataset are listed in Table 6. Then, the proposed method is applied to the data of CWRU, and the experimental results are shown in Table 5. In Table 5, it is obvious that the accuracy of the CWRU dataset is significantly better than the data collected by our designed test bench. The reason is due to assembly and bearing fault processing and the data of CWRU are not considered in the literature. Figure 5: The confusion matrix results of the four SVM classifiers with different features. (**a**) SF-SVM, (**b**) EMDE-SVM, (**c**) VMDE-SVM, and (**d**) BearingCog-SVM. Figure 6: The accuracy of four kinds of SVM classifiers. other problems, which makes the collected data contain more background noise. However, the calculation results show that our method is superior to other methods. On the other hand, the robustness of the proposed method to noise is also demonstrated. To further investigate the performance of these four classifiers, the receiver operating characteristic (ROC) curves are imported to depict the tradeoff relationship between the true positive rate (TPR) and the false positive rate (FPR). The definition of the TPR and FPR is listed in the Equation (9). \[ \begin{array}{l}\text{FPR}=\frac{\text{FP}}{\text{TP}+\text{TN}}\\ \text{TPR}=\frac{\text{TP}}{\text{TP}+\text{FN}}\end{array}  \tag{9}\]  
Among those, the TP represents the true positive samples. The FP represents the false positive samples. The TN represents the true negative samples. The FN represents the false negative samples. During the classification, a threshold is set appropriately to determine the predicted result. By decreasing the threshold value, more positive samples are recognized, which would raise the TPR. Oppositely, a larger threshold would assign more samples into the negative class, which would raise the FPR. Then, the area of the ROC is utilized as an effective indicator to evaluate the classifier's performance. To be specific, if the area of the ROC is closer to 1, it represents the classifier's model showing better robustness. In Figure 7, the areas of the SF-SVM, EMDE-SVM, VMDE-SVM, and BearingCog model is blue, green, red, and black, respectively. Based on the definition, it verifies that the proposed BearingCog is able to recognize the different fault-level bearings effectively. In Figure 8, to better visualize the effectiveness of the classification model, some samples are trained to demonstrate the effects of the model. Meanwhile, the t-distributed stochastic neighbor embedding is utilized to map the high-dimensional features into a two- dimensional space. It is observed that the proposed BearingCog model exhibits