# Bearing Health Monitoring Using Relief-F-Based Feature Relevance Analysis and HMM
## 4 Results and Discussion  
First, we introduce an illustrative example of the time and frequency parameters concerning the four classes problem. Figure 2 shows the time-domain waveform of some vibration segments with their corresponding frequency spectrum. As seen, the frequency spectrum varies for every bearing state. Besides, the main harmonic information is contained until 9 kHz. Now, Figure 3 shows the SFS-based feature relevance values for both \(C=4\) and \(C=10\) scenarios. Accordingly, the most relevant features are those calculated in the TF domain. Indeed, Mel-cepstrum measures exhibit the highest importance of the studied segments. Then, such parameters in TF can code both temporal and frequency information to support the identification of non-stationary bearing fault patterns. Figure 2: Exemplary of some vibration signals in T and F domains for the four class problem. The bearing fault diagnosis and evaluation results are exposed in Figure 4, which displays the learning curves obtained for the four and ten class problems. The VRA, SW, LS, DW, and the SFS-based rankings are studied using an HMM-based classification (see Section 3). Besides, Tables 4 and 5 show in the center column the best-achieved classification results and the number of features ranked by each method and in the right column the classification accuracy statistically equal to the best using fewer features. It is possible to note that the VRA method holds a classification accuracy of \(\{95.63\pm 1.07\}\%\) for \(C=4\) and \(\{99.01\pm 0.42\}\%\) for \(C=10\), but requiring 51 and 47 features, respectively. Moreover, achieved results demonstrate that unsupervised approaches, e.g., VRA, SW, and LS, cannot reveal relevant features in comparison to the supervised ones, e.g., DW and SFS. Though after 20 relevant features, the SW and LS algorithms attain an acceptable discrimination performance (a classification accuracy greater than 90%), the supervised methods accomplish such a classification threshold using less than ten features. Supervised approaches avoid the inclusion of redundant parameters as the performance curve falls after ten features, showing that the newly added features decrease the discrimination accuracy as they add unnecessary (noisy) information. In fact, the DW-based ranking exhibits classification accuracies of \(\{99.36\pm 0.39\}\%\) (\(C=4\)) and \(\{99.76\pm 0.11\}\%\) (\(C=10\)), using 13 and seven relevant features, respectively. Likewise, our SFS approach, which includes a relief-f-based feature selection, reaches \(\{99.56\pm 0.040\}\%\) and \(\{99.74\pm 0.21\}\%\) classification accuracies using nine features for \(C=4\) problem and seven parameters for \(C=10\). So, the SFS  
Figure 3: SFS-based relevance values for T, F, and TF domain features. approach converges faster than the DW technique. In a nutshell, Tables 4 and 5, present the best classification accuracies and the number of relevant features required for the \(C=4\) and the \(C=10\) problems, regarding the studied feature rankers. In turn, note that the supervised approaches' time complexity highly depends on the number of samples (see Section 2.2 for SFS analysis). Nonetheless, the training is offline, and the number of selected features is much lower than the number of input attributes, alleviating the time complexity of the testing set prediction. Figure 5 shows the confusion matrix obtained for both classification scenarios using only the relevant features computed by our SFS. As seen, the accuracy in both cases is closer to 100%. On the one hand, for the four-class problem, the B, IR, and OR classes tend to be slightly confused, while the N class is classified satisfactorily. On the other hand, for the ten class problem, the N, B1, B2, B3, and IR1 are correctly detected; however, data belonging to the IR2, IR3, OR1, OR2, and OR3 classes still tend to be slightly confused with other bearing states.