Inference of dominant modes for linear stochastic processes

Area of Science:

• Dynamical Systems and Control Theory
• Signal Processing
• Electrical Engineering

Background:

• Asymptotically stable linear systems are fundamental models in various scientific and engineering fields.
• Real-time analysis of system dynamics is crucial for monitoring and control.
• Gaussian noise is a common disturbance in observational data.

Purpose of the Study:

• To develop methods for real-time inference of dominant modes (real or complex) in noisy linear dynamical systems.
• To estimate parameters such as damping rates, frequencies, and mode shapes.
• To infer the mode covariance matrix encoding amplitudes and correlations.

Main Methods:

• Utilizes observational data from asymptotically stable linear systems subjected to Gaussian noise.
• Employs techniques for real-time estimation of system modes.
• Develops algorithms to infer damping rates, frequencies, and mode shapes for both real and complex modes.
• Focuses on estimating the mode covariance matrix.

Main Results:

• Successfully developed and validated methods for real-time dominant mode inference.
• Demonstrated the ability to distinguish and quantify parameters of real (monotone decay) and complex (oscillatory decay) modes.
• Showcased the inference of mode amplitudes and correlations via the mode covariance matrix.

Conclusions:

• The developed methods provide effective real-time estimation of dominant modes in noisy linear dynamical systems.
• These techniques are applicable to complex systems, including the detection of oscillations in AC electrical power networks.
• The approach offers potential for broader applications in system identification and analysis.