# Prognostics of Electromechanical Actuator with Partial Time Scaling Invariant Temporal Alignment
## 9 Conclusions  
In conclusion, our research presents a novel and robust method for time series alignment-based prognostics, which is applicable to compressed or dilated time series, incomplete time series, or even series-independent segments, making it well suited for industrial applications. We have proposed a two-part method called Partial Time Scaling Invariant Temporal Alignment (PARTITA) that can align new data to the ones in our training data set without requiring the selection of a sliding window or any hyperparameters in advance.  
The first part of our method involves an alignment algorithm that differs from the state-of-the-art methods in that it does not require the selection of an interval on which to align the time series and can align time series with different sampling frequencies. The second part involves the selection of the time index of every last point of each feature and assigning a density estimation for every one of them. Fusing every density by solving an optimal transport problem gives us the RUL of the studied system with an uncertainty measurement.  
Our proposed method can potentially be applied to the diagnosis and prognosis of electromechanical actuators and any system's behavior characterized by univariate time series in an industrial context. We believe that our approach offers a significant contribution to the field of prognostics and can be further extended to other applications as well.  
Conceptualization, A.E. and G.C.; methodology, A.E. and G.C.; software, A.E.; validation, A.E.; formal analysis, A.E.; investigation, A.E.; resources, B.M.; data curation, A.E.; writing--original draft preparation, A.E. and G.C.; writing--review and editing, A.E. and G.C.; visualization, A.E.; supervision, G.C. and B.M.; project administration, G.C. and B.M.; funding acquisition, B.M. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the French agency for research and technology (ANRT) through the CIFRE grant 2018/0649, by Safran Electronics & Defense (Safran Group) and by Laboratory Ampere CNRS--UMR5005, own funds.  
Restrictions apply to the availability of these data. Data were obtained from Safran Electronics & Defense and are not publicly available. Data sharing not applicable.  
Authors [PERSON] and [PERSON] were employed by the company Safran Electronics & Defense (Safran Group). The remaining authors declare that the research was conducted without any commercial or financial relationships that could be construed as a potential conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l}
**BGA** & Ball Grid Array \\
**CMAPSS** & Commercial Modular Aero-Propulsion System Simulation \\
**DTW** & Dynamic Time Warping \\
**LLA** & Lower Left Actuator \\
**LRA** & Lower Right Actuator \\
**PARTITA** & Partial Time Scaling Invariant Temporal Alignment \\
**PHM** & Prognostics and Health Management \\
**RMS** & Root Mean Square \\
**RUL** & Remaining Useful Life \\
**SBRLP** & Similarity-Based Residual Life Prediction \\
**SOH** & State of Health \\
**SPOT** & Sliced Partial Optimal Transport \\
**TBSP** & Trajectory Similarity-Based Prediction \\
**ULA** & Upper Left Actuator \\
**URA** & Upper Right Actuator \\ \end{tabular}