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Phase space warping: nonlinear time-series analysis for slowly drifting systems.
1Department of Mechanical Engineering & Applied Mechanics, University of Rhode Island, Kingston, RI 02881, USA. chelidze@egr.uri.edu
Summary
This study introduces a novel dynamical systems approach for analyzing non-stationary data by tracking slow variable drifts. The method accurately predicts failure time in experiments, demonstrating its effectiveness in real-time damage assessment.
Area of Science:
- Dynamical Systems
- Data Analysis
- Non-stationarity
Background:
- Tracking slowly evolving variables is crucial for understanding non-stationarity in complex systems.
- Existing methods may struggle with real-time analysis of dynamic changes.
Purpose of the Study:
- To present a general dynamical systems approach for analyzing non-stationarity.
- To develop a method for tracking slow variables in fast subsystems.
- To apply the method for real-time damage assessment and failure prediction.
Main Methods:
- Phase space warping to detect distortions caused by slow drifts.
- Short-time reference model prediction error as a key measurement.
- Vector-tracking using smooth orthogonal decomposition analysis.
Main Results:
- Demonstrated tracking of damage evolution in a nonlinear vibrating beam.
- Identified damage evolution as a scalar process.
- Provided real-time damage state estimates and accurate time-to-failure predictions.
Conclusions:
- The presented dynamical systems approach effectively tracks non-stationarity.
- The method enables accurate real-time damage assessment and advanced failure prediction.
- Phase space warping offers a powerful tool for analyzing dynamic systems.