# A Hybrid Degradation Modeling and Prognostic Method for the Multi-Modal System
## 4 Conclusions  
In this paper, a hybrid degradation modeling and prognostic method is proposed for a multi-modal system. Firstly, the cumulative dynamic differential feature is constructed to describe the physical characteristics with the existence of mode switching. The constructed health indicator is based on the three properties, including monotonicity, threshold similarity, and trend similarity. Based on the cumulative dynamic differential health indicator, the long-term cumulative degradation assessment model is constructed by gated recurrent unit. Then, the time window is used to extract energy and statistical features to obtain local features. The latest degradation effect is predicted based on light gradient boosting machine. Finally, the model is averaged to construct a decision-level fusion model. In the experimental analysis section, the theoretical experiment uses synthetic data to study the sensitivity of the proposed method to different types of input data. Most of systems show a slow aging trend in the early stage and a fast aging trend in the later stage. The synthetic data with exponential functional form are constructed according to based on exponential functional and Gaussian random variable. The experimental result shows the proposed method has good performances on samples with different trends. In addition, experimental analysis on the C-MAPSS turbofan aero-engine dataset, which includes four different working environment sub-datasets, demonstrates the effectiveness and generality of the proposed method. Compared with other popular methods, the proposed model has shown very promising prognostic performance. In the future, the proposed method will be extended in the following ways: (1) How can one reconstruct data samples while working with different mode switchings from historic data samples? The accuracy of prediction depends on the completeness of the dataset. An effective reconstruction sample model could supplement the dataset to improve the accuracy of prediction. (2) How can one construct the health indicators which have better prediction performance? This paper constructed a health indicator based on three properties, including monotonicity, threshold similarity and trend similarity. Exploring more properties of the health indicators and studying optimization solution of complex multi-objective programming are the challenges. (3) A complex system may have different kinds of failures during useful life. The type and number of failures have an impact on the aging process of the system. Thus, how to construct a prediction model considering the impact of both the type and number of failures on remaining useful life is a significant issue. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Methods** & **Metric** & **FD001** & **FD002** & **FD003** & **FD004** \\ \hline SVR & RMSE & 0.147 & 0.241 & 0.205 & 0.272 \\  & Score & 1.139 & 3.874 & 1.757 & 4.461 \\ CNN & RMSE & 0.132 & 0.234 & 0.193 & 0.243 \\  & Score & 1.304 & 2.893 & 1.418 & 3.36 \\ LSTM & RMSE & 0.149 & 0.223 & 0.215 & 0.231 \\  & Score & 1.256 & 3.312 & 1.862 & 3.975 \\ SAEs & RMSE & 0.145 & 0.259 & 0.233 & 0.294 \\  & Score & 1.672 & 4.023 & 2.047 & 4.351 \\ GBDT & RMSE & 0.124 & 0.213 & 0.218 & 0.302 \\  & Score & 1.562 & 2.421 & 1.592 & 3.461 \\ Proposed & RMSE & **0.119** & **0.172** & **0.184** & **0.217** \\ model & Score & **1.042** & **2.213** & **1.387** & **2.84** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The evaluation metrics values of each dataset based on different models. **Author Contributions:** Conceptualization, J.P. and S.W. ; methodology, S.W. and Y.C. ; software, S.W. ; validation, S.W. ; formal analysis, W.Y. ; investigation, X.Z. ; resources, D.G. ; data curation, B.C. ; writing--original draft preparation, S.W. ; writing--review and editing, Y.C. ; visualization, Y.Y. ; supervision, Z.H. ; project administration, J.P.; funding acquisition, J.P. and S.W. All authors have read and agreed to the published version of the manuscript.