Intelligent time–frequency feature embedding and reshaping for bearing fault diagnosis in motion control applications

Accurate diagnosis of bearing faults under nonstationary operating conditions presents significant challenges, particularly in independent cart systems where variable speeds, coupled translational-rotational motion, and transient dynamics substantially influence vibration signals. In such contexts, traditional time-frequency representations and unsupervised learning methods often yield inadequate class separation and unreliable anomaly detection results. This study presents a fully unsupervised diagnostic framework that overcomes existing limitations through two complementary innovations. First, an intelligent strategy automatically selects the lengths of the spectrogram windows using Theil index-based inequality measures. Second, a technique for reshaping distributions transforms the extracted features into compact, uniformly distributed representations without the need for class labels. Experimental validation using the MOIRA-UNIMORE bearing dataset demonstrated significant enhancements in terms of feature compactness and class separability. Further robustness and cross-dataset validation on the Case Western Reserve University and Politecnico di Torino bearing datasets corroborated the stability and generalizability of the proposed framework. These findings suggest that integrating adaptive time-frequency analysis with principled distribution reshaping provides an effective, computationally efficient solution for unsupervised bearing-fault diagnosis in nonstationary industrial environments.