AKgram: A Robust Adaptive Framework for Bearing Fault Diagnosis Under Speed-Varying Condition

Rolling bearing fault diagnosis under speed-varying condition (SVC) presents a significant challenge due to the non-stationary nature of vibration signals. The narrowband filtering demodulation (NFD) methods, while effective under constant speeds, faces severe limitations under such non-stationary operations. Specifically, their traditional feature indicators fail to characterize the non-stationary fault impulses, leading to significant performance degradation. Furthermore, the inherent fixed frequency band segmentation strategy of these methods can also impair their diagnostic accuracy. To address these limitations, this paper proposes AKgram, a novel adaptive diagnostic method designed specifically for the SVC. First, the fluctuation trend spectrum (FTS) is derived from the signal spectrum to realize adaptive frequency band segmentation, constructing a multi-level tower-shaped boundary distribution map while preserving full spectral component integrity and overcoming fixed segmentation limitations. Then, average kurtosis (AK) is introduced as a robust indicator to quantify fault-induced impulses and extract non-stationary fault features under SVC. Finally, AK values of segmented sub-bands are visualized in the tower-shaped map to form the AKgram, with the sub-band of maximum AK identified as the optimal demodulation band for direct fault feature extraction. The effectiveness and superiority of AKgram are validated via simulation and experimental data from a variable-speed bearing test bench, outperforming the classical Kurtogram method in optimal band identification and fault feature extraction.