## 4 Results and Comparison
### Comparison with Previous Studies
#### 4.2.1 Review of Representative Solutions  
In this section, we compare the performance of our proposed IBL approach with the previous studies [35, 36, 37, 38, 39, 40, 41, 42]. Eight representative solutions are briefly reviewed as follows and summarized in Table 8. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline  & \multicolumn{2}{c}{**Prognostic Features**} & \multicolumn{1}{c}{**RUL Prediction Model/Method**} \\ \cline{2-4}  & \multicolumn{1}{c}{**Extraction**} & \multicolumn{1}{c}{**Reduction**} & \multicolumn{1}{c}{**RUL Prediction Model/Method**} \\ \hline [PERSON] et al. [35] (2012) & * Average of Peaks & & - Ratios of time durations of multiple degradation stages \\ \hline [PERSON] [36] (2012) & * Peak, RMS, Kurtosis, Energy (in sub-frequency-band signals in both original and demodulated signals) & - PCA (Hoteling’s T2) & - Average of detect-to-failure times of learning samples (as the estimated RUL) \\ \hline [PERSON] et al. [37] (2014) & * IMFs from WPD-EMD & - SOM (MQE) & - GPR method for modeling degradation process \\ \hline [PERSON] et al. [38] (2015) & * Variance & & - Two exponential degradation models for the two extracted prognostic features, respectively. - EKF \\ \hline  & * Peak-to-Peak, Mean, Root-Mean-Square, Crest Factor, Shape Factor, Impulse Factor, Effress, Kurtosis, Entropy, SD of IHC, SD of HIS & - SOM (WMQE) & - Paris-Erdogan model of degradation (WMQE) & - PF \\ \hline  & * Variance, Peak-to-Peak, Mean, Root-Mean-Square, Crest Factor, Wave Factor, Impulse Factor, Effress, Kurtosis, Entropy (in both original and sub-frequency-band signals) & - Similarity, monotonicity, and correlation metrics - RNN & - Double exponential model of degradation processes - PF \\ \hline  & * Energy of sub-frequency-bands generated by WPD & - RNN based on encoder–decoder /with attention & - Linear regression/extrapolation \\ \hline  & * Similarity based features & & \\ [PERSON] et al. [42] (2020) & * Mean, Peak-to-Peak, SD, Energy, Skewness, Kurtosis, Entropy, Energy/Entropy & - RNN & - Nonlinear regression/extrapolation \\ \hline  & & & - An IBL approach with data augmentation and similarity evaluation \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Summary of the existing solutions. Among the participants in the IEEE PHM 2012 competition, the team of [PERSON] et al. proposed the champion solution [35]. In their third solution, the RUL estimation was based on making comparisons on the durations of degradation stages between the learning and test bearing instances. Anomalies were detected by analyzing the changes of frequency signatures in the signal spectrogram. The authors attempted to create a prognostic feature by taking the average of five Peaks of the vibration signal. Their RUL estimation results achieved the best performance in the competition. As the second winner in the IEEE PHM 2012 competition, [PERSON] extracted time-domain statistical features, i.e., Peak, RMS, Kurtosis, and Energy from two demodulated envelope settings on vibration signals [36]. The PCA technique was applied to these extracted feature data to generate Hoteling's T\({}^{2}\) statistic as the representative prognostic feature. In this work, no local regression model was developed to predict RUL for test bearings. Instead, the average of the detect-to-failure times of the learning bearings were directly used to estimate RUL for the test bearings. [PERSON] et al. developed a method to evaluate the bearing degradation state and estimate the RUL for the bearing datasets [37]. For feature extraction, the EMD technique was used to generate a set of intrinsic mode functions (IMFs) based on the signal Energy and Entropy profiles from WPD. A self-organizing map (SOM) network was then trained on the IMF data obtained under normal stage of the bearing usage. To evaluate the degradation state, the trained SOM network was applied on the observed IMF data to produce the minimum quantization error (MQE), which acted as a prognostic feature, named the confidence value (CV).