Uncertain Bayesian decision tree: a new method for multi-class fault diagnosis with observation uncertainty

Decision trees are widely adopted for multi-class fault diagnosis due to their capability to handle both continuous and discrete data. However, the presence of epistemic and aleatoric uncertainties in observational measurements can severely degrade their predictive performance and pose significant challenges to model construction. In this work, we introduce an Uncertain Bayesian Decision Tree (UBDT) framework that explicitly models imprecise observations as uncertain variables and leverages their inverse distribution properties to generate crisp split values. A new hyperparameter is integrated in UBDT to govern the inverse uncertain function, enabling adaptive control of uncertainty ranges across feature dimensions. At each tree node, Bayesian updating of posterior uncertainty distributions dynamically incorporates new data, mitigating the effects of measurement noise and environmental variability. Experimental studies on diverse datasets demonstrate that UBDT outperforms traditional decision tree algorithms in classification accuracy and computational efficiency, offering a robust and adaptive solution for real-world fault diagnosis.