## 1 Introduction  
Rotating machinery plays an increasingly important role in industries such as healthcare, manufacturing, and transportation [1, 2]. Under long-term operating conditions, critical components of rotating machinery, such as bearings and gears, are prone to various types of faults. These faults not only lead to production stagnation but may also trigger safety incidents. Consequently, the introduction of intelligent diagnostic technologies is crucial for accurately diagnosing faults in rotating machinery, thereby ensuring equipment safety and enhancing production efficiency [3, 4, 5]. Traditional fault diagnosis methods for rotating machinery typically rely on experiential knowledge and physical mechanisms [6]. However, in changeable working conditions, such methods often struggle to meet the demands for real-time and efficient automated diagnosis due to their reliance on expert experience, insufficient timeliness, and high maintenance costs. [PERSON] et al. [7] highlighted the limitations of expert experience in complex fault scenarios, which can result in the overlooking of subtle faults in equipment. [PERSON] et al. [8] proposed that fault diagnosis based on physical mechanisms often fails under dynamic and nonlinear conditions, leading to suboptimal diagnostic outcomes. Furthermore, traditional fault diagnosis methods impose high requirements on the quality of input data, with noise and anomalous data significantly impacting diagnostic results. Currently,with advancements in equipment diagnostic sensor technologies, researchers can set up fault conditions in laboratory settings based on actual production scenarios to obtain more comprehensive data sources. This development has allowed data-driven intelligent fault diagnosis technologies to gradually emerge in the field of fault diagnosis [9], particularly methods based on entropy for feature extraction. Entropy is a tool for measuring uncertainty and complexity, and it is widely applied in the fault diagnosis of rotating machinery [10; 11]. By analyzing the complexity of vibration signals, fault features can be extracted. [PERSON] et al. [12] proposed a fault diagnosis method for rotating machinery based on sample entropy (SE). Through the analysis of fault signals using SE, effective differentiation between normal and fault states can be achieved. Results indicate that this method demonstrates high accuracy in identifying early faults. [PERSON] et al. [13] utilized improved composite multiscale approximate entropy to analyze fault signals from rolling bearings. It was observed that this improved entropy exhibits high sensitivity to fault types, enabling the detection of minor changes in vibration signals and significantly improving fault classification accuracy. [PERSON] et al. [14] introduced fuzzy entropy (FE) as a feature extraction method, combining it with support vector machine (SVM) for fault diagnosis, which yielded favorable results. Research has shown that FE possesses strong robustness in handling noisy signals. [PERSON] et al. [15] employed multiscale entropy methods to analyze fault signals, and the results revealed that this method significantly improves fault detection sensitivity. [PERSON] et al. [16] integrated multiscale permutation entropy (MPE) with deep learning, utilizing MPE to extract signal features and performing fault classification through a convolutional neural network (CNN). This approach exhibited high diagnosis accuracy when addressing complex faults, particularly outperforming traditional diagnostic methods in noisy environments. However, challenges still exist in fault diagnosis techniques based on entropy algorithms:  
1. Variable entropy algorithms exhibit the disadvantage of difficult hyperparameter adjustment, which undermines the generalization ability and adaptability of such algorithms [17]. Even when the tuning time for the optimization of hyperparameters is reduced, the time required for the model to implement responsive tuning strategies in response to different vibration signals remains unavoidable. 2.