## 2 Background
### Data Collection and Processing  
To produce data for this study, the SESAC code was run under four operating conditions, summarised in Table 2. Condition A represents a ground-running condition, and conditions B-D represent cruise conditions. Condition B (28k ft) corresponds to a typically low cruise altitude, and condition D (41k ft) to a typically high cruise altitude for a Boeing 737-800. All conditions and associated parameters were obtained from a dataset with the actual ECS data of a Boeing 737-800, so the parameters used represent real flight conditions. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Fault Mode**} & \multicolumn{3}{c}{**Degradation Degree**} \\ \cline{2-4}  & **Minor** & **Medium** & **Severe** \\ \hline ACM fault & 25\% & 50\% & 75\% \\ \hline PHX fault & 20\% & 50\% & 80\% \\ \hline SHX fault & 20\% & 50\% & 80\% \\ \hline RI blockage & 25\% & 50\% & 75\% \\ \hline \hline \end{tabular} \
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{TCV fault (normally 15\({}^{\circ}\)–18\({}^{\circ}\))} & Undershoot: & \multirow{2}{*}{
\begin{tabular}{c} Overshoot: \\ Fixed at 10\({}^{\circ}\) \\ \end{tabular} } \\  & & \\ \end{tabular}
\end{table} 
Table 1: Summary of all degradation levels simulated for each failure mode considered in the PACK simulation. Under each condition, the main factors that determine the operation of the PACK are listed in Table 2, which includes the temperature and pressure from the engine bleed air, ram-air temperature, target temperature, and mass flow rate settings. To incorporate real-life noise and uncertainties in the SESAC simulation results, the simulations were run with slightly perturbed parameters, in addition to runs with the original parameters. Specifically, a perturbation was imposed on the target temperature and target mass flow rate. The target temperature in each condition was set with values within a range of \(\pm\)10 K from its mean value (i.e., a maximum of roughly 4% perturbation), and the target mass flow rate was set with values within a range \(\pm\)0.02 kg s\({}^{-1}\) from its mean value (a maximum of roughly 5% perturbation). For each operating condition, 91 healthy-state cases were simulated and recorded, and 90 faulty-state cases were simulated and recorded, with 18 cases in each fault mode under various degradation severities. Among the temperature, pressure, and mass flow rate profiles, the temperature profile of the PACK was selected as the basis for developing its fault diagnosis algorithm, because it displays distinct patterns under different health states. Before inputting data to the diagnosis algorithm, only one processing stage is conducted on the simulation results, which is normalising the temperature readings against the corresponding target temperature in each case, a boundary condition input in the simulations as the commanded temperature for PACK outlet. This was to alleviate the influence on the temperature profiles owing to the different target temperatures set in each case. Figure 2 shows the normalised simulation results of PACK temperature profiles under the four different operating conditions, plotted against temperature points proceeding from inlet to exit, aligned with the stations shown in Figure 1. For example, ThiPHX is the temperature at the inlet of the PHX. The different colours relate to the different health status of each component, with the baseline healthy condition being shown in green. The TCV fault is really only one fault with two states: undershoot or overshoot, as shown in Table 1. For clarity, one representative case per class is plotted, while other cases are shown in transparent lines.