# Intelligent Multi-Fault Diagnosis for a Simplified Aircraft Fuel System
## 3 Methodology  
### Selected Machine Learning Algorithms  
While deep learning is increasingly used for fault diagnosis and maintenance in the aviation industry, traditional machine learning (ML) remains essential, particularly in scenarios with limited data, straightforward features, high interpretability needs, or restricted computational resources. ML-based fault diagnosis relies on algorithms that use mathematical models to map data to fault classes directly, enabling data-driven decisions without needing prior domain knowledge or expert input. These simpler algorithms are often more interpretable, making them especially suitable for high-value assets like aircraft, where understanding model decisions is crucial for trust and safety. Consequently, ML's interpretability advantage over deep learning makes it valuable for fault diagnosis in aviation. Given the limited sample size per class (around 200 samples) and the use of simple features with clear physical meanings, traditional ML was considered suitable for the fault diagnosis task in this study. Based on the data's characteristics, four criteria were established to guide the selection of appropriate ML algorithms:  
* Classification task: this study frames fault diagnosis as a classification problem with discrete fault classes. Thus, all selected algorithms must be suitable for classification tasks. * Supervised learning: the dataset from the simulation model is fully labelled, so only supervised learning methods were considered. * Data efficiency and interpretability: unlike deep learning methods, the algorithms should perform well on small datasets and avoid excessive opacity to support ease of understanding and trust. * Comparable predictive and interpretability performance: the chosen algorithms should balance predictive accuracy and interpretability, allowing for meaningful analysis and discussion of these key performance metrics. These requirements ensure that the selected ML methods are effective for the available data and meet the demands for interpretability in the high-stakes context of aviation fault diagnosis. Following the outlined requirements, logistic regressions, decision trees, support vector machines, and artificial neural networks were selected to evaluate diagnostic capability and interpretability in this study. Each method meets the data requirements and offers a balance between accuracy and interpretability. The following four subsections provide a concise overview of each approach. The logistic regression (LR) is a foundational machine learning algorithm for classification, typically used in binary classification tasks where only two outcomes are possible. In a binary setting, such as distinguishing between circles and squares in Figure 6a, an LR estimates the likelihood of an event occurring based on the data. It uses a linear function to fit the data, passing through a nonlinear sigmoid function that maps the results to a range between 0 and 1. By setting a threshold, an LR classifies the data into two classes. LRs can be extended to multinomial logistic regression for multiclass classification, where the data have more than two classes (e.g., circles, squares, and stars in Figure 6b). This approach applies multiple LR models to calculate the probability of each class relative to a reference class. Since the total probability across all classes must be 1, the algorithm predicts the class with the highest calculated probability. Multinomial logistic regression is, thus, well-suited for multiclass tasks. Although logistic regression has been infrequently applied to fault diagnosis for fuel systems, it was used in one study [25] to detect faults, underscoring its potential applicability. Decision trees (DTs) are machine learning algorithms that represent decisions in a tree-like structure with multiple layers of nodes. Typically, a DT has at least two layers: the first to the \((n-1)\)th layers comprises nodes where features are assessed, and branches represent decision outcomes.