# A Fault-Signal-Based Generalizing Remaining Useful Life Prognostics Method for Wheel Hub Bearings
## 5 Conclusions  
The RUL prognostics method designed in this study only utilizes the information of the fault signal. This method successfully avoids the problem of directly obtaining parameters of fracture mechanics in complex and mutative environments during the working process. The RUL can be dynamically prognosticated in real time with respect to time change for inaccurate fault signal with fatigue damage types in the actual working environment. This method also has the ability to obtain better accuracy for prognostics results, especially in the wheel hub bearing's initial running stage. The proposed method gained good accuracies for RUL prognostics for the amplitude, energy, and kurtosis features with fatigue damage types. The proposed method can process inaccurate fault signals with different kinds of noises in an actual working environment. The proposed RUL prognostics method has better long term prognostics ability than existing methods. As such, the proposed RUL prognostics method has good generalization.  
The current method is only the simplified solution of the generalizing RUL prognostics method in Equation (18), combined with the fault signal model in Equation (16). To further improve the accuracy of RUL prognostics results, (a) a relatively complete solution, as in Equations (16) and (18), should be studied in future work, and (b) the fault signals should be decomposed from the synthesis signal with fault signals, environmental noise signals, and system noise signals in future work.  
**Author Contributions:** [PERSON] and [PERSON] conceived the idea and formulated the mathematical methods behind the provided method. [PERSON] was responsible for all parameter tuning, data processing, figures, and calculations. [PERSON] was responsible for the experimental setup. [PERSON] and [PERSON] were responsible for research idea generation, the introduction, abstract, conclusions, and for the final editing and reviewing of the provided method.  
**Funding:** The work was funded by the National Science Foundation of China [51875266, 61379064, 61603326, 61772448]; the Industry-Academia Prospect Research Foundation of Jiangsu [BY2016066-06, BY2015058-01]; the Research Innovation Program for College Graduates of Jiangsu [KYLX16_0880].  
**Conflicts of Interest:** The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Accuracy** & _Original Data (25\%)_ & _Original Data (50\%)_ & _Original Data (75\%)_ & _Original Data (100\%)_ \\ \hline GM & 0.6429 & 0.5571 & 0.5642 & 0.6214 \\ GA & 0.4405 & 0.6905 & 0.8810 & 0.9988 \\ GG & 0.6113 & 0.8708 & 0.9804 & 0.9997 \\ \hline \end{tabular}
\end{table}
Table 1: The accuracy of RUL prognostics with the amplitude feature.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Accuracy** & _Original Data (25\%)_ & _Original Data (50\%)_ & _Original Data (75\%)_ & _Original Data (100\%)_ \\ \hline GM & 0.6648 & 0.5215 & 0.5279 & 0.6759 \\ GA & 0.4357 & 0.7040 & 0.8910 & 0.9998 \\ GG & 0.6160 & 0.8788 & 0.9880 & 0.9993 \\ \hline \end{tabular}
\end{table}
Table 2: The accuracy of RUL prognostics with the energy feature.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Accuracy** & _Original Data (25\%)_ & _Original Data (50\%)_ & _Original Data (75\%)_ & _Original Data (100\%)_ \\ \hline GM & 0.5026 & 0.3511 & 0.6586 & 0.7264 \\ GA & 0.4280 & 0.6924 & 0.8762 & 0.9909 \\ GG & 0.6050 & 0.8817 & 0.9976 & 0.9996 \\ \hline \end{tabular}
\end{table}
Table 3: The accuracy of RUL prognostics with the kurtosis feature.