## 3 Experimental Study
### Experimental Setup
#### 3.1.2 Data Preprocessing and Feature Selection  
Each training and test dataset of turbofan engines contained outputs from 21 sensors. The characteristics of sensors, such as prognosability, monotonicity, trendability, and robustness, along with detailed analyses, can be found in [33; 56; 57; 58].  
Some sensor measurements did not provide degradation information for RUL prediction since they had constant values throughout the engine's lifetime [8; 56]. To choose a subset of informative sensors from the FD001 dataset, the sensors that exhibited trending and constant values as time progressed are categorized in Table 3. As a result, sensors with constant values were discarded and only 14 of them were selected for further analysis as in [8; 9; 17].  
\begin{table}
\begin{tabular}{c c} \hline \hline
**FD001** & \\ \hline Train Trajectories & 100 \\ Test Trajectories & 100 \\ Operating Conditions & 1 \\ Fault Modes & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Details of the FD001 sub-dataset of the C-MAPSS dataset.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Sensor Number** & **Sensor Description** & **Units** \\ \hline
1 & Fan inlet temperature & \({}^{\circ}\)R \\
2 & LPC outlet temperature & \({}^{\circ}\)R \\
3 & HPC outlet temperature & \({}^{\circ}\)R \\
4 & LPT outlet temperature & \({}^{\circ}\)R \\
5 & Fan inlet pressure & psia \\
6 & Bypass duct pressure & psia \\
7 & HPC outlet pressure & psia \\
8 & Physical fan speed & rpm \\
9 & Physical core speed & rpm \\
10 & Engine pressure ratio P50/P2 & - \\
11 & HPC outlet static pressure & psia \\
12 & Ratio of fuel flow to Ps30 & pps/psia \\
13 & Corrected fan speed & rpm \\
14 & Corrected core speed & rpm \\
15 & Bypass ratio & - \\
16 & Burner fuel–air ratio & - \\
17 & Bleed enthalpy & - \\
18 & Required fan speed & rpm \\
19 & Required fan conversion speed & rpm \\
20 & High-pressure turbines cool airflow & lb/s \\
21 & Low-pressure turbines cool airflow & lb/s \\ \hline \hline \end{tabular}
\end{table}
Table 2: Description of 21 sensors in the C-MAPSS dataset.  
In the C-MAPSS dataset, measurements from different sensors varied in magnitudes and units. In order to suppress the different effects of low and high magnitudes in the model, the sensor data needed to be normalized. The sensor measurements were normalized to the [0, 1] range using the min-max normalization Formula (12), as outlined in Section 2.5, which represents the feature scaling step in the feature engineering process. As an example, the normalized life-cycle data of 14 sensors of engine #1 is illustrated in Figure 5.  
As mentioned, the simulated sensor signals were mixed with noise, which could be removed using a low-pass filter to smooth the sensor data. A low-pass filter passes signals with lower frequencies and attenuates signals with higher frequencies, thereby preserving long-term trends while removing small fluctuations and outliers [59]. The sampling frequency of data recordings was 1 Hz. The designed low-pass filter was a first-order filter with a 0.08 Hz critical frequency. The signal of a randomly selected engine sensor from the FD001 sub-dataset is shown in Figure 6 with and without filtering.  
Figure 5: Normalized time series data of 14 sensors of engine #1 in the training set.  
Figure 6: Filtering dataset: (**a**) before filtering: (**b**) after filtering.  
\begin{table}
\begin{tabular}{c c} \hline
**Trend** & **Sensors** \\ \hline Ascending & 2, 3, 4, 8, 9, 11, 13, 15, 17 \\ Descending & 7, 12, 14, 20, 21 \\ Constant & 1, 5, 6, 10, 16, 18, 19 \\ \hline \end{tabular}
\end{table}
Table 3: Trends of the sensor data in FD001 [17].