## 1 Introduction
### Related Work  
[PERSON] et al. proposed a method for multi-component fault diagnosis in hydraulic systems. The method first uses Pearson correlation coefficients and Neighborhood Component Analysis (NCA) for data channel selection and feature dimensionality reduction, to reduce data redundancy and improve computational efficiency. Two different types of Deep Neural Networks (DNNs) are then constructed as base learners: Stacked Sparse Autoencoder and Deep Hierarchical Extreme Learning Machine (D-ELM). A bagging voting ensemble strategy is used to combine these DNN base learners to enhance the robustness and accuracy of the diagnostic system. This paper utilizes the original bagging voting ensemble strategy, where multiple learners vote for a sample, and the class with the most votes is assigned as the predicted class for the sample [9]. [PERSON] et al. introduced a trainable combiner to optimize the ensemble results, training an XGBoost model as a meta-classifier to learn how to generate the final prediction based on the outputs of base learners. However, this meta-classifier is prediction-oriented and lacks interpretability in terms of the weight distribution of each base learner [10]. [PERSON] and [PERSON] proposed a heterogeneous ensemble-based model (HBSE) for credit card fraud detection, training a logistic regression model as a Level-1 meta-learner, using the outputs of Level-0 base learners as input, and producing the final prediction. Similar to the previous paper, this approach also lacks interpretability in the weight distribution of each base learner [11]. [PERSON] et al. provided a detailed discussion of various variants of the stacking method, which was first proposed by [PERSON] in 1992 [7]. For instance, [PERSON] introduced the use of instance-based learning classifiers as Level-0 classifiers (base learners). In this variant, base learners are no longer traditional machine learning models, but instead classify by storing a few prototypes for each class [12]. [PERSON] et al. proposed a method to evaluate the overall accuracy of a stacking ensemble model using conflict-based accuracy estimates, employing two tree-based classifiers and one rule-based classifier as base learners. For the Level-1 meta-learner, they used a non-pruned decision tree instead of a traditional decision tree [13]. [PERSON] proposed another variant of stacking, called Stacking with Correspondence Analysis and Nearest Neighbor (SCANN). In this approach, correspondence analysis is used to detect correlations between base learners, effectively removing redundant information. After removing the dependency between base learners, a nearest neighbor method is used as the meta-learner in the new feature space. SCANN improves model diversity and handles heterogeneous base learners effectively [14]. [PERSON] and [PERSON] proposed several important innovations, including using class probabilities rather than single class predictions as the output of Level-0 classifiers and using Multi-response Linear Regression (MLR) as the Level-1 classifier. While class probabilities were used as inputs to Level-1, the output was still the final prediction, which remained result-oriented and lacked interpretability in the weight distribution of base learners [15]. [PERSON] et al. addressed the class imbalance problem in classification tasks, proposing a solution using heterogeneous ensembles. In binary classification, class imbalance typically refers to situations where one class has far more samples than the other, leading to poor performance on the minority class. The paper mentions that ensemble classifiers can alleviate this issue by using different sampling methods, especially by applying different balanced datasets to each member of the ensemble, with the datasets generated via random undersampling or oversampling [16]. [PERSON] et al. explored classifier ensemble methods in incremental learning, proposing a new bagging-based incremental learning method called Bagging++.