Cointegration Approach for Vibration-Based Misalignment Detection in Rotating Machinery Under Varying Load Conditions

Shaft misalignment is among the most common faults in rotating machinery, and although many diagnostic methods have been proposed, reliably detecting it under varying load conditions remains a major challenge for vibration-based techniques. To address this issue, this study proposes a new vibration-based misalignment detection framework that leverages cointegration analysis. The approach examines both the stationarity of vibration signals and the residuals derived from the cointegration process. Specifically, it combines the Augmented Dickey-Fuller (ADF) test with cointegration analysis in three stages: (1) applying the ADF test to raw vibration data before cointegration, (2) performing cointegration on the vibration time series, and (3) reapplying the ADF test to the post-cointegrated data. The method was validated using experimental measurements collected from a laboratory-scale test rig comprising a motor, gearbox, and hydraulic gear pump, tested under both healthy and misaligned states with varying degrees of severity. Vibration signals were recorded across multiple load conditions. The results demonstrate that the proposed method can successfully detect misalignment despite load variations, while also providing insights into fault severity. In addition, the residuals from the cointegration process proved to be highly sensitive to damage, highlighting their value as features for vibration-based condition monitoring.