## 3 Prediction Dataset and Boosting Process  
The NASA N-CMAPSS dataset offers simulated degradation trajectories of a fleet of turbofan engines, which are designed to mimic run-to-failure scenarios under real flight conditions. The baseline health status of these engines are unknown. The dataset comprises eight distinct sets of simulated data collected from a total of 128 individual engines. These units are subject to five distinct failure modes, all of which have the potential to impact the flow and efficiency of the rotating sub-components. Table 1 presents a comprehensive summary of flight classes and their corresponding failure modes, as shown by the available datasets [28]. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multirow{2}{*}{**Engine**} & \multirow{2}{*}{**Flight**} & \multirow{2}{*}{**Failure**} & \multicolumn{2}{c}{**Fan**} & \multicolumn{2}{c}{**LPC**} & \multicolumn{2}{c}{**HPC**} & \multicolumn{2}{c}{**HPT**} & \multicolumn{2}{c}{**LPT**} \\ \cline{3-14}  & & & **Class** & & **Quantity** & **E** & **F** & **E** & **F** & **E** & **F** & **E** & **F** \\ \hline D801 & 10 & 1,2,3 & 1 & & & & & & & & Y & & & \\ D802 & 9 & 1,2,3 & 2 & & & & & & & & Y & & Y & \\ D803 & 15 & 1,2,3 & 1 & & & & & & & Y & & Y & \\ D804 & 10 & 2,3 & 1 & Y & Y & & & & Y & & & & \\ D805 & 10 & 1,2,3 & 1 & & & & Y & Y & Y & & & & \\ D806 & 10 & 1,2,3 & 1 & & & Y & Y & Y & Y & & & & \\ D807 & 10 & 1,2,3 & 1 & & & & Y & Y & Y & Y & Y & Y & Y & Y \\ D808 & 54 & 1,2,3 & 1 & Y & Y & Y & Y & Y & Y & Y & Y & Y & Y \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overview of the aircraft turbine dataset. Figure 3 depicts the intricate connections between various important operating factors, such as altitude (alt), throttle-resolver angle (TRA), flight cycles, total temperature, and the relative temperature decrease at the fan inlet (T2). This figure illustrates the interplay and impact of these variables, presenting data obtained from a dataset comprising six aircraft engines operating under different flight conditions. This representation emphasises the complex and interconnected aspects of our analysis and the detailed relationships that our model takes into account during the predictive process. The dataset used for this research is referred to as DS01 and DS02, which depict simulated examples of typical flight cycles, as evidenced by the traces of the scenario-descriptor variables. Each simulated flight cycle consists of recordings of varying durations that record the climb, cruise, and descent phases of flight when the aircraft's altitude reaches 10,000 feet. These recordings correspond to the numerous flight paths undertaken by the aircraft. The flight trajectories of the remaining units of the fleet exhibit similarities. Both the training dataset and the validation dataset are contained within each data file. The dataset comprises six distinct types of variables: the operative conditions \(\omega\), the measured signals \(x_{s}\), the virtual sensors \(x_{v}\), the engine health parameters \(\theta\), the RUL label, and the auxiliary data such as unit number \(u\), flight class number \(Fc\), flight cycle number \(c\), and the binary health state. Additionally, the parameters \(\omega\), \(x_{s}\), \(x_{v}\), and \(\theta\) contain specified variable names. A summary of numerous variables can be found in [28]. The bootstrap forest encompasses the concepts of in-bag (IB) and out-of-bag (OOB) observations. The training set observations used to form a tree are referred to as IB  
Figure 3: Interconnected relationships between scenario descriptors such as Mach number, throttle resolver angle (TRA), altitude (alt), and operative parameters such as fight cycles, HPT efficiency, total temperature, and its relative temperature drop. (**a**) Cycle versus HPT efficiency. (**b**) Cycle versus relative temperature drop. (**c**) Throttle resolver angel time series variations. (**d**) Engine Mach number variations. (**e**) Flight altitude changes.