Relationship Analysis Between Helicopter Gearbox Bearing Condition Indicators and Oil Temperature Through Dynamic ARDL and Wavelet Coherence Techniques

This study investigates the dynamic relationship between bearing gearbox condition indicators (BGCIs) and the lubrication oil temperature within the framework of health and usage monitoring system (HUMS) applications. Using the dynamic autoregressive distributed lag (DARDL) simulation model, we quantified both the short- and long-term responses of condition indicators to shocks in oil temperature, offering a robust framework for a counterfactual analysis. To complement the time-domain perspective, we applied a wavelet coherence analysis (WCA) to explore time–frequency co-movements and phase relationships between the condition indicators under varying operational regimes. The DARDL results revealed that the ball energy, cage energy, and inner and outer race indicators significantly increased in response to the oil temperature in the long run. The WCA results further confirmed the positive association between oil temperature and the condition indicators under examination, aligning with the DARDL estimations. The DARDL model revealed that the ball energy and the inner race energy have statistically significant long-term effects on the oil temperature, with p-values < 0.01. The adjusted R2 of 0.785 and the root mean square error (MSE) of 0.008 confirm the model’s robustness. The wavelet coherence analysis showed strong time–frequency correlations, especially in the 8–16 scale range, while the frequency-domain causality (FDC) tests confirmed a bidirectional influence between the oil temperature and several condition indicators. The FDC analysis showed that the oil temperature significantly affected the BGCIs, with evidence of feedback effects, suggesting a mutual dependency. These findings contribute to the advancement of predictive maintenance frameworks in HUMSs by providing practical insights for enhancing system reliability and optimizing maintenance schedules. The integration of dynamic econometric approaches demonstrates a robust methodology for monitoring critical mechanical components and encourages further research in broader aerospace and industrial contexts.