# Intelligent Multi-Fault Diagnosis for a Simplified Aircraft Fuel System
## 3 Methodology
### Selected Machine Learning Algorithms
The nth layer consists of leaf nodes that indicate the classification results. A decision tree prioritises features for splitting based on information gain, favouring those that maximise this criterion. Several common decision tree algorithms include ID3 ([26]), C4.5 ([27]), and CART ([28]). Unlike ID3 and C4.5, CART (classification and regression trees) limits each node to two branches and is applicable to both classification and regression tasks. CART often demonstrates better classification performance than other DT algorithms, though it can be limited by its reliance on local optimal choices, potentially impacting overall accuracy. In addition to binary classification, CART can handle multiclass classification, where leaf nodes correspond to distinct classes. Decision trees have been used effectively for fault detection and isolation in various contexts, including fuel systems [29], turbofan engines [30], and auxiliary power units [31]. Support Vector Machines (SVMs) are binary classification algorithms that classify data by constructing hyperplanes, maximising the margin between classes for improved separation. Given a dataset with \(m\) features, SVMs often apply a kernel function to map data into an \((m+n)\)-dimensional space, allowing for linear separability in cases where the original data are not linearly separable. The dimension \(n\) depends on data complexity; if the data are inherently linearly separable, \(n=0\). The hyperplane for classification in this new space is defined by the closest data points, known as support vectors. To handle multiclass classification (e.g., with \(k\) classes), SVMs typically employ two strategies: one-vs-all and one-vs-one. In the one-vs-all approach, k binary classifiers are trained, each distinguishing one class from all others. Each classifier outputs a score, and the class with the highest score is selected to avoid ambiguous classifications. The one-vs-one approach, on the other hand, creates an SVM model for each pair of classes,  
Figure 6: Examples of binary and multiclass classification: (**a**) binary class classification; (**b**) multiclass classification. resulting in \(k(k-1)/2\) models, with predictions determined by a majority vote among them. Although more computationally intensive, one-vs-one generally outperforms one-vs-all by better managing data imbalances in sub-classifiers. The studies in [6; 32; 33; 34] highlight SVMs' effectiveness in fault detection for fuel systems. Artificial neural networks (ANNs) with one hidden layer, or shallow networks, are composed of an input layer, a hidden layer, and an output layer, each containing neurons (or nodes) that connect fully with the adjacent layers. These connections carry weights that the ANN adjusts during training to fit the data. Since weights and biases (extra inputs to neurons) alone form linear operations, nonlinear activation functions are applied to the hidden and output layers to enable more complex, adaptable prediction capabilities. Common activation functions in the output layer include the sigmoid for binary classification or regression and the SoftMax function for multiclass classification. While shallow ANNs are simpler than deep networks, they still exhibit black-box characteristics due to the hundreds of weighted connections they generate to learn patterns across features and classes, such as the 11 features and 32 fault classes in this study's AFS case. Weighted connections represent the network's assessment of the importance of relationships between neurons, which can aid in analysing simple neural networks. However, for a network aiming to fit 11 features and 32 classes, the large number of weighted connections reduces the efficiency and reliability of such analyses. Additionally, nonlinear activations further complicate the network's internal decision logic, making it challenging to interpret its classification processes. Nevertheless, shallow ANNs have shown promise in diagnosing mechanical faults, as demonstrated in prior studies [35; 36; 37; 38].