## 2 Background
### AdaBoost with Weak Classifiers for Fault Severity Prediction  
The proposed method utilizes a boosting algorithm known as AdaBoost, which combines multiple weak classifiers to improve predictive accuracy [34]. In this context, the algorithm utilizes three time-frequency features extracted from the motor current signal as machine health indicators, denoted as \(f_{1}\), \(f_{2}\), and \(f_{3}\). AdaBoost works by iteratively training weak classifiers on a weighted dataset, where each weak classifier focuses on specific aspects of the input features. These weak classifiers are combined in a weighted manner to form the ensemble classifier. Let \(h_{t}(x)\) represent the prediction of the \(t\)-th weak classifier for the input feature vector \(x\) and \(\alpha_{t}\) represent its corresponding weight. The final prediction model, denoted as \(H(x)\), is a function of the input feature vector \(x\). It is computed by combining the predictions of all weak classifiers, weighted by their respective performances, as given in Equation (17):  
\[H(x)=\sum_{t=1}^{T}\alpha_{t}\cdot h_{t}(x) \tag{17}\]  
where \(T\) is the total number of weak classifiers. AdaBoost with weak classifiers improves prediction by leveraging the strengths of multiple models that work well together. This makes it suitable for predicting the severity of faults in machine health monitoring. Weak classifiers with AdaBoost emerge as a superior technique for fault severity prediction due to several key advantages over alternative methods [34]. While Hidden Semi-Markov Models (HSMMs) offer flexibility in modeling variable-duration states, they may struggle with complex data patterns and require extensive parameter tuning [36]. Deep Learning Neural Networks, renowned for capturing intricate patterns, demand substantial computational resources and extensive data for effective training, limiting their practical applicability in resource-constrained environments [37]. Ensemble Learning Methods, including Random Forests and Gradient Boosting Machines, provide robustness against overfitting and enhance generalization by combining multiple models. However, they may suffer from increased computational complexity and a lack of interpretability [38]. Fuzzy Logic Systems offer a framework for handling uncertainty but may struggle with capturing complex nonlinear relationships in data [39]. In contrast, AdaBoost with weak classifiers achieves high predictive accuracy while maintaining computational efficiency [40]. By iteratively training weak learners on weighted subsets of data, AdaBoost focuses on misclassified samples, gradually improving performance. This approach effectively addresses the challenges of noisy data and complex data patterns, making it particularly suitable for fault severity prediction tasks in industrial settings [40]. Additionally, the simplicity of weak classifiers enhances model interpretability, facilitating insights into the underlying factors contributing to fault severity. It turns out that AdaBoost with weak classifiers is a strong and effective way to accurately predict the severity of a fault, which can be used in a number of real-world situations [40].