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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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Cointegration Approach for Vibration-Based Misalignment Detection in Rotating Machinery Under Varying Load

Sylwester Szewczyk1,2, Roman Barczewski3, Wiesław J Staszewski1

  • 1AGH University of Krakow, Faculty of Mechanical Engineering and Robotics, Department of Robotics and Mechatronics, al. Mickiewicza 30, 30-059 Krakow, Poland.

Sensors (Basel, Switzerland)
|November 13, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a novel vibration analysis method using cointegration to reliably detect shaft misalignment in rotating machinery, even under changing loads. The technique enhances condition monitoring by identifying faults and their severity through signal stationarity and cointegration residuals.

Keywords:
Augmented Dickey–Fuller (ADF) testcointegrationcondition-based maintenancedata analysismisalignment detectionrotating machineryvarying load effectsvibration measurements

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Area of Science:

  • Mechanical Engineering
  • Condition Monitoring
  • Signal Processing

Background:

  • Shaft misalignment is a frequent issue in rotating machinery, posing challenges for traditional vibration-based diagnostic techniques, especially under variable operating loads.
  • Existing methods struggle with reliable misalignment detection when load conditions fluctuate, necessitating advanced diagnostic frameworks.

Purpose of the Study:

  • To develop and validate a new vibration-based framework for detecting shaft misalignment in rotating machinery.
  • To address the challenge of reliable misalignment detection under varying load conditions using cointegration analysis.

Main Methods:

  • A three-stage approach combining the Augmented Dickey-Fuller (ADF) test with cointegration analysis was employed.
  • The method analyzes the stationarity of raw vibration signals, performs cointegration on time series, and re-evaluates stationarity on post-cointegrated data.
  • Experimental validation was conducted on a test rig with a motor, gearbox, and hydraulic gear pump under healthy and misaligned states across various loads.

Main Results:

  • The proposed cointegration-based framework successfully detected shaft misalignment despite variations in load conditions.
  • The method demonstrated effectiveness in identifying the severity of misalignment.
  • Residuals from the cointegration process showed high sensitivity to damage, proving valuable for condition monitoring.

Conclusions:

  • The developed framework offers a robust solution for detecting shaft misalignment in rotating machinery under dynamic load conditions.
  • Cointegration analysis and its residuals provide effective features for advanced vibration-based condition monitoring and fault diagnosis.