Combining model‑based and data‑driven paradigms yields a fault‑diagnosis framework that blends the interpretability of analytical redundancy relations (ARR) with the adaptability of learning techniques. ARR are input‑output equations used as diagnosis indicators in model‑based methods, while data‑driven methods can capture complex system behavior.
DT4X is a recent diagnosis algorithm that employs symbolic regression to produce multivariate expressions, which are then used as split functions in a decision tree. By leveraging some properties of ARR, the generated expressions retain a degree of interpretability. However, DT4X optimizes the separation of only two selected classes at each node, often fragmenting the remaining classes and degrading overall interpretability and diagnostic performance.
To address these shortcomings, we introduce DT4X+. The enhancement modifies the construction of training sets so that target and non‑target classes remain coherent within each node, and it augments the symbolic‑regression loss with a term that preserves the internal consistency of non‑target classes while still maximizing the separation of the target classes.
As a result, the derived expressions fully satisfy ARR properties, provide more informative splits, improve the robustness of the decision tree, and achieve superior performance on dynamic‑system datasets. Experiments on several benchmark systems demonstrate that DT4X+ outperforms the original DT4X in accuracy, robustness, and interpretability.
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