Parameter extraction with reservoir computing: Nonlinear time series analysis and application to industrial...

Area of Science:

• Dynamical Systems Theory
• Machine Learning
• Signal Processing

Background:

• Accurate parameter estimation is crucial for understanding and controlling dynamical systems.
• Traditional methods can be computationally intensive or limited in handling complex, chaotic systems.
• Reservoir computing offers a novel approach for time-series analysis and system identification.

Purpose of the Study:

• To investigate the efficacy of reservoir computing techniques for parameter determination in dynamical systems.
• To compare the performance of time-domain and frequency-domain random feature models derived from reservoir activations.
• To assess the robustness and accuracy of these methods across different system types and operating conditions.

Main Methods:

• Utilized variations of reservoir computing to generate random features from time-series data.
• Analyzed reservoir activations in both the time and frequency domains to extract system parameters.
• Applied the developed models to benchmark dynamical systems (Lorenz, Rössler) and real-world vibration data from centrifugal pumps.

Main Results:

• Achieved accurate and robust parameter extraction for the Lorenz and Rössler systems across stable and chaotic regimes.
• Demonstrated significant ability to recover the operating regime from centrifugal pump vibration data.
• Observed that time-domain models excelled for numerical systems, while frequency-domain models were superior for application data.

Conclusions:

• Reservoir computing provides an effective framework for parameter estimation in dynamical systems.
• The choice between time-domain and frequency-domain models depends on the specific application context.
• This approach shows promise for both theoretical system analysis and practical engineering diagnostics.