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• The overall transmission error (OTE) is directly applied to the planet fault differential diagnosis (DD) for the tooth flank spall and the gear fillet crack. • A novel reordered SVD approach guided by the sparse index L2/L1 norm is proposed for fault-dependent residual OTE extraction. • Fault components with different scales can be accurately extracted in residual OTE. • The proposed DD framework is robust in extremely low-speed or varying-speed conditions. Owing to recent studies on the relationship between the transmission error and the localized gear fault, TE-based differential diagnosis (DD) technology has emerged as a promising approach to identifying the tooth flank spall and the gear fillet crack which have similar signatures but quite different fault mechanisms and prognoses. However, due to complex structural factors, the fault modes can hardly be identified from the calculated overall transmission error (OTE). In light of this, a novel DD framework based on encoder-measured data is proposed in this work. Specifically, the OTE signal calculated from resampled data are filtered by flexible time synchronous average. A reordered singular values decomposition (RSVD) approach guided by the sparse index L2/L1 norm is then developed for fault-dependent residual OTE extraction. Experimental results validate that the faulty events can be accurately identified by the proposed framework without prior information under different speed conditions for planet gear DD. [ABSTRACT FROM AUTHOR]

• The GARCH family models from time series analysis is introduced for the first time into machine condition monitoring. • Health indicators constructed based on GARCH and EGARCH models demonstrate the capability to detect incipient faults in bearings, verified through two experimental cases. • In accelerated degradation tests, it is established that acoustic emission signals are closely associated with damage evolution. • Acoustic emission technology can be employed for quantitative assessment of bearing damage. Recent progress in digital twin (DT) has significantly contributed to the advancement of predictive maintenance. The interaction of data between physical and virtual models is facilitated through carefully designed health indicators (HIs). Conventional condition monitoring HIs are inadequate for early-stage fault detection and lack the capacity to quantitatively assess defects. In light of this, the paper proposes HIs based on the generalised autoregressive conditional heteroskedasticity (GARCH) family time series model to characterise the evolution of bearings dynamic response, specifically the cyclostationarity of the repetitive transients. The verification of the proposed indicators is assessed using a publicly available vibration dataset and acoustic emission signals acquired from accelerated bearing degradation tests. The result shows that the GARCH oriented indicators can determine the incipient failure earlier than traditional statistical HIs and have the ability to quantify defects. Significantly, the improved Exponential GARCH model-based indicator demonstrates heightened stability throughout the monitoring process. [ABSTRACT FROM AUTHOR]