A novel scheme of condition monitoring and fault recognition based on time-shift multi-scale weighted slope entropy for rolling bearings under variable speed conditions

Rolling bearings are essential components in rotating machinery and their failure can cause serious downtime and economic loss. Under variable speed conditions, rolling bearings usually exhibit non-stationary and non-linear vibration characteristics, leading to severe challenges to condition monitoring and fault recognition. To address these challenges, this study proposes a novel diagnostic scheme for accurate condition monitoring and fault recognition of rolling bearings operating at variable speed. Specifically, vibration signals are pre-processed using the Subband Averaging Kurtogram (SAK) method to obtain envelope signals, followed by constructing a Time–Frequency Distribution (TFD). The bearing work condition is assessed by analyzing the ridge information from the TFD. For fault signals, Adaptive Chirp Mode Decomposition (ACMD) is employed to estimate instantaneous frequency and extract dominant fault-related components. To quantify detailed fault signal features, an enhanced slope entropy algorithm named Time-Shift Multi-scale Weighted Slope Entropy (TSMWSIE) is proposed, integrating weighted operations and time-shifted coarse-graining strategies to measure non-linear signal dynamics. The extracted features are then analyzed for fault recognition using the Kernel Extreme Learning Machine (KELM) model optimized by Leader Harris Hawks Optimization (LHHO). The suitability of the proposed diagnostic scheme is validated through two experimental cases. The results demonstrate that the developed scheme effectively monitors bearing conditions and achieves high reliability and robustness in fault recognition under different variable speed conditions. This study provides a novel scheme to condition monitoring and fault recognition for rolling bearings, contributing to improved maintenance strategies and reduced operational risks.