## 5 Conclusions  
This paper presents a novel data-driven prognostic algorithm designed exclusively for the aviation industry, with an emphasis on monitoring and managing the health of gas turbine engines. It demonstrates a significant enhancement in predictive accuracy compared to previous methods by using the NASA N-CMAPSS dataset, which provides simulated degradation trajectories. Furthermore, this paper closely simulates the operational conditions experienced during commercial aircraft flights. The approach effectively connects the engine's deterioration process with its operational history, allowing for a detailed comprehension of the different ways it can fail.  
The investigation into the physical methodology of turbofan engines uncovers a potential for more enhancement, indicating that although our existing model achieves significant accuracy, including more precise physics-based models could lead to improvements. The proposed model represents a notable departure from conventional models that rely on  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(\mathbf{R^{2}}\) & **RMSE** & **SSE** \\ \hline NtanH(3)NBoost(20) & Training: 0.9967847 & Training: 1.2688147 & Training: 5649332.2 \\  & Validation: 0.9967703 & Validation: 1.2710539 & Validation: 2834219.7 \\
[1] & Average R\({}^{2}\): 0.994 & - & - \\
[30] & Average R\({}^{2}\): 0.995 & - & - \\
[2] & - & Average: 1.35 & - \\
[3] & - & Average: 1.45 & - \\
[6] & - & - & Average: 6,000,000 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Statistical comparison between the current model and the existing ones.  
engines with lifespans of hundreds of cycles. It incorporates a sophisticated combination of bootstrap forest and hyperbolic tangent boosted neural networks and has been developed and researched extensively.  
Overall, the NtanH(3)NBoost(20) model represents a significant advancement in the precision and dependability of data-based predictions for aircraft systems. The models demonstrated a high level of accuracy, correctly predicting observed flight cycles during validation with an accuracy rate of 95-97%. Additionally, it paves the way for future improvements and developments. The encouraging outcomes achieved prompt continuous improvement of both the model itself and the fundamental physical techniques, with the goal of developing even more accurate and hybrid prognostic models in the future. This is to strengthen predictive maintenance procedures, which will ultimately lead to safer, more efficient, and more dependable aircraft operations through ongoing improvement and adaptation.  
Conceptualisation, S.F.; methodology, S.F.; software, S.F.; validation, S.F.; formal analysis, S.F.; writing--original draft preparation, S.F.; writing--review and editing, S.F. and N.P.A.; supervision, N.P.A. All authors have read and agreed to the published version of the manuscript.  
This research has received funding from the European Commission under the Marie Sklodowska Curie program through the H2020 ETN MOIRA project (GA 955681).  
Not applicable.  
The data are publicly available from the NASA prognostics data repository and mirrored on the Prognostics Health Management Society website.  
The authors gratefully acknowledge the H2020-MSCA-ITN-2020 MOIRA project and the research team at IVHM Centre, Cranfield University, UK, for supporting this research.  
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.