# Intelligent Multi-Fault Diagnosis for a Simplified Aircraft Fuel System
## 3 Methodology
### Interpretability of the Trained Diagnostic Algorithms
For continuous features (e.g., pressure and flow rate), the decisions are based on split points (fifth column). The decisions indicate specific feature values for discrete features (e.g., pump speed). Figure 13: The interpretability of multinomial logistic regression. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No.** & **Parent Node** & **Predictor** & **Type** & **Judge** & **Criteria** & **Unit** \\ \hline
1 & 1 & p7 & Continuous & Less than & 1.3837 & bar \\
2 & 2 & f3 & Continuous & Less than & 0.6596 & L/min \\
3 & 4 & p4 & Continuous & Less than & 2.1767 & bar \\
4 & 8 & f3 & Continuous & Less than & 0.5706 & L/min \\
5 & 16 & p7 & Continuous & Less than & 1.2293 & bar \\
6 & 22 & p5 & Continuous & Less than & 1.6392 & bar \\
7 & 34 & f3 & Continuous & Less than & 0.466 & L/min \\
8 & 56 & f3 & Continuous & Equal or larger than & 0.3643 & L/min \\
9 & 77 & Pump & Categorical & 300 & NaN & RPM \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Example rule extracted from the trained DT. The trained DT contained 939 rules (leaf nodes), with rule counts varying across different target classes. Table 10 shows the number of rules associated with specific classes at given pump speeds. Notably, the DT generally required more rules for classifications at lower pump speeds (e.g., 200 rpm) than at higher pump speeds. A comparison between the features associated with DT rules and the engineering insights (Table 3) is illustrated in Figure 14. This figure shows the alignment between the DT's rules and engineering perspectives (blue bars) alongside the F-1 score on the validation dataset (grey bars) at 300 and 600 rpm pump speeds. The interpretability of the DT is summarised in the tables below each graph. At the lowest pump speed of 300 rpm (Figure 14a), there were some discrepancies between the DT's interpretations and engineering understanding. However, the interpretability at 300 rpm was notably higher than that of the logistic regression, as indicated by the table statistics. At the highest pump speed of 600 rpm (Figure 14b), both the interpretability and predictive performance of the DT improved, resulting in an average interpretability of 82% across all five pump speeds. Figure 14: The interpretability of the decision tree under different pump speeds: **(a)** RPM = 300; **(b)** RPM = 600. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**No.** & **Parent Node** & **Predictor** & **Type** & **Judge** & **Criteria** & **Unit** \\ \hline
10 & 102 & p6 & Continuous & Less than & 1.3799 & bar \\
11 & 142 & p3 & Continuous & Equal or larger than & 1.4321 & bar \\
12 & 209 & p6 & Continuous & Equal or larger than & 1.334 & bar \\
13 & 305 & p1 & Continuous & Equal or larger than & 0.9944 & bar \\
14 & 429 & p3 & Continuous & Less than & 1.4559 & bar \\
15 & 596 & f1 & Continuous & Equal or larger than & 0.3938 & L/min \\
16 & 809 & f3 & Continuous & Equal or larger than & 0.3707 & L/min \\
17 & 1027 & p5 & Continuous & Less than & 1.4101 & bar \\
18 & 1204 & f1 & Continuous & Less than & 0.4035 & L/min \\
19 & 1392 & p3 & Continuous & Equal or larger than & 1.4343 & bar \\
20 & 1577 & p1 & Continuous & Less than & 0.9952 & bar \\
21 & 1732 & p3 & Continuous & Less than & 1.4433 & bar \\
22 & 1826 & p3 & Continuous & Less than & 1.4397 & bar \\
23 & 1876 & f1 & Continuous & Less than & 0.4001 & L/min \\ \hline \end{tabular}
\end{table} 
Table 9: _Cont._  
SVM and ANN (black-box algorithms). ** The LIME and SHAP techniques were applied to identify the four features most influential for each prediction and to calculate the degree of overlap (expressed as a percentage) between the XAI outputs and the critical features recommended by engineering insights (Table 4). For instance, a 100% overlap indicates that all features identified by XAI match those suggested by engineering insights, while a 50% overlap signifies that only two features align. The results are visualised in Figure 15, categorised by different classes.