Multi-parameter identification from scalar time series generated by a Malkus-Lorenz water wheel

Area of Science:

• Dynamical Systems and Control Theory
• Nonlinear Dynamics
• Parameter Estimation

Background:

• Chaotic systems, like the Malkus water wheel, present challenges for parameter estimation due to their sensitive dependence on initial conditions.
• Accurate parameter estimation is crucial for understanding and modeling complex nonlinear systems.

Purpose of the Study:

• To compare the effectiveness of a globally convergent adaptive observer and an extended Kalman filter (EKF) for multi-parameter estimation from scalar outputs of chaotic systems.
• To investigate the ability of these estimators to distinguish between noise and model imperfections in chaotic system modeling.

Main Methods:

• Utilized the Malkus water wheel experimental system and its corresponding Lorenz-equations model for simulations.
• Implemented and compared a globally convergent adaptive observer and an extended Kalman filter (EKF) for estimating three unknown model parameters.
• Investigated model generalization and EKF uncertainty estimates to differentiate noise from model errors.

Main Results:

• Both the adaptive observer and the EKF successfully identified all three unknown parameters of the Lorenz-equations model.
• Estimated parameter values closely matched those obtained from direct experimental measurements.
• The study could exclude asymmetric inflow as a source of model discrepancy.

Conclusions:

• Globally convergent adaptive observers and EKFs are effective tools for multi-parameter estimation in chaotic systems.
• The Lorenz-equations model, while useful, does not perfectly capture the dynamics of the Malkus water wheel, indicating potential model imperfections beyond simple noise or inflow asymmetry.