A novel nonlinear feature extractor based on transition fuzzy slope entropy for fault diagnosis of mechanical rotating components

Slope entropy (SlE) is a recently proposed effective metric for quantifying the complexity of nonlinear signals. However, its representation of fine-grained features and dynamic information remains incomplete, primarily due to rigid hard-threshold slope symbolic segmentation and inadequate characterization of the state transition information in symbol patterns. To address these issues, transition fuzzy slope entropy (TFuSlE) is proposed, which for the first time integrates fuzzy sign partitioning of the slopes derived from two consecutive data samples with the dynamic transition probabilities of the resulting symbol mode sequences into the SlE framework. This integration enables TFuSlE to capture more detailed dynamic information from nonlinear signals, thereby yielding more accurate and comprehensive entropy estimates. Through experiments on simulated data, the optimal parameter configuration for TFuSlE is first determined, and the superiority of its multiple performance metrics in accurately characterizing signal complexity is validated. Finally, TFuSlE is evaluated on two real-world datasets related to mechanical components. The experimental results demonstrate that the health-state features extracted from vibration signals using TFuSlE exhibit well-separated visual distributions and achieve superior classification accuracy and noise robustness compared to other entropy methods.