## 5 Conclusions  
Since the IEEE PHM 2012 Prognostic Challenge published the PRONOSTIA bearing datasets, the RUL prediction problem has attracted much interest from researchers. Unlike the existing approaches in the literature, we propose an alternative solution to address the limitations on the number of run-to-fail examples in RUL estimation. The proposed IBL approach is summarized as follows:  
* An efficient feature extraction method is employed for extracting the prognostic feature sequences. In this method, based on the spectrograms of vibration signals, the PCA technique is utilized to extract prognostic feature sequences for the bearing instance. For a pair of the learning and test instances to be compared, the data projection base (i.e., set of PCs) is derived from the spectrogram of the learning instance.
* Inspired by the data augmentation strategy adopted in the machine learning for image classification applications, the segment scaling method is proposed to generate a set of synthetic prognostic feature sequences by modifying the observed prognostic feature sequence of the learning instance.
* An ensemble method is used to aggregate the multiple RUL estimates obtained from similar prognostic feature sequences identified via the similarity evaluation. In the averaging function of the ensemble method, each RUL estimate is weighted by its corresponding similarity measure (i.e., RMS difference measure).  
As a result, the performance comparison of our proposed approach with the eight representative solutions can become a valuable reference for researchers who attempt to achieve higher accuracy RUL estimations on the PRONOSTIA datasets in the future. For  
\begin{table}
\begin{tabular}{p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt}} \hline  & **[PERSON]** & **[PERSON] [36]** & **[PERSON] et al. [37]** & **[PERSON]** & **[PERSON] et al. [38]** & **[PERSON] et al. [39]** & **[PERSON] et al. [41]** & **[PERSON] et al. [42]** \\ \hline Proposed Approach & 0.417 & 0.011 & 0.5 & 0.5 & 0.5 & 0.417 & 0.2 & 0.5 \\ \hline \end{tabular}
\end{table}
Table 11: The \(p\)-values from significant difference test of the proposed approach with the previous solution.  
further development, our proposed IBL approach can be implemented as a generic scheme to incorporate with different data augmentation strategies, such as translating signal in time domain, shifting signal in frequency domain, and scaling signal in time domain, for different prognostic applications. It can be expected that the proposed IBL approach can be applied to different types of components and industrial systems such as wind turbines and aircraft engines, which may consist of a large number of components and have complicated degradation process modes.  
Conceptualization, J.S. and Q.S.; methodology/investigation/analysis, J.S.; validation/resources, J.S. and Q.S.; writing--original draft preparation, J.S.; writing--review and editing, Q.S.; supervision, Q.S.; project administration, Q.S.; funding acquisition, Q.S. Both authors have read and agreed to the published version of the manuscript.  
This research was funded in part by the Natural Sciences and Engineering Research Council of Canada, through the NSERC Discovery Programme, grant number RGPIN-2017-04143.  
Not applicable.  
The open-access bearing datasets PRONOSTIA were produced by FEMTO-ST Institute and originally published for IEEE PHM 2012 Prognostic Challenge.  
We acknowledge the support of the National Sciences and Engineering Research Council of Canada, NSERC Discovery Grant RGPIN-2017-04143.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.