## 4 Experimental Validation and Analysis  
### Validation Data Set  
The validation data are based on the CMAPSS dataset provided by the NASA Ames Failure Prediction Research Center. It simulates the health of each output component during the degradation of a real commercial turbofan engine in different operating environments [19]. The dataset consists of four training and test sets, FD001 to FD004, which were simulated under various operating conditions and failure modes [20]. The training dataset comprises the full life cycle data from the start of the aircraft's in-service operation until failure, whereas the test set records the partial life cycle data of the aircraft from its initial state until failure [21,22]. The dataset was subjected to a degree of engine wear during the simulation due to interference from artificial noise. The size of the dataset is presented in Table 1:  
Table 2 presents the specific meaning of each monitoring parameter in the dataset. We note that, within the dataset, Setting_1, Setting_2 and TRA correspond to three different sets of operating environment conditions.  
The maximum cycle sample length distribution of all engines in datasets FD001-FD004 is shown in Figure 5. The sample lengths of the four datasets vary. FD001 and FD003 datasets were collected under a single operating condition, with sample lengths mainly  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **FD001** & **FD002** & **FD003** & **FD004** \\ \hline Number of Training Samples & 100 & 260 & 100 & 249 \\ Number of Test Samples & 100 & 259 & 100 & 248 \\ Total Length of Training Set & 20,630 & 53,758 & 24,719 & 61,248 \\ Total Length of Test Set & 13,095 & 33,990 & 16,595 & 41,213 \\ Operating Conditions & 1 & 6 & 1 & 6 \\ Fault Mode & 1 & 1 & 2 & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 1: C-MAPSS dataset.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **Parameters** & **Unit** \\ \hline
1 & Altitude (Setting\_1) & – \\
2 & Mach number (Setting\_2) & – \\
3 & Throttle resolver angle (TRA) & – \\
4 & Total temperature at fan inlet (T2) & \({}^{\circ}\)R \\
5 & LPC outlet temperature (T24) & \({}^{\circ}\)R \\
6 & HPC outlet temperature (T30) & \({}^{\circ}\)R \\
7 & LPT outlet temperature (T50) & \({}^{\circ}\)R \\
8 & Fan inlet pressure (P2) & psia \\
9 & Bypass duct pressure (P15) & psia \\
10 & HPC outlet pressure (P30) & psia \\
11 & Physical fan speed (Nf) & r/min \\
12 & Physical core speed (Nc) & r/min \\
13 & Engine pressure ratio P50/P2 (Epr) & – \\
14 & HPC outlet static pressure (Ps30) & psia \\
15 & Ratio of fuel flow to Ps30 (Phi) & pps/psia \\
16 & Corrected fan speed (Nrf) & r/min \\
17 & Corrected core speed (Nrc) & r/min \\
18 & Corrected core speed (BPR) & – \\
19 & Burner fuel–air ratio (FarB) & – \\
20 & Bleed enthalpy (htleed) & – \\
21 & Required fan speed (Nrf\_dmd) & r/min \\
22 & Required fan conversion speed (PCNrf\_dmd) & r/min \\
23 & High-pressure turbines cool air flow (W31) & lbm/s \\
24 & Low-pressure turbines cool air flow (W32) & lbm/s \\ \hline \hline \end{tabular}
\end{table}
Table 2: Description of Monitoring Parameters.  
distributed between [150 and 250], whereas datasets FD002 and FD004 were collected under six operating conditions and two fault modes, with sample lengths mainly distributed between [150 and 300]. This indicates that the engine's life cycle is shorter under a single operating condition, resulting in a large amount of degradation trajectory information that cannot be utilized.