Joint parameter estimation and abrupt change quantification with uncertainty quantification in high degree of freedom
Esmaeil Ghorbani1,2, Quentin Dollon3, Frederick P Gosselin2
1Department of Civil and Environmental Engineering, Princeton University, 54 Olden Street, Princeton, NJ 08544 USA.
Abstract:
The Unscented Kalman Filter (UKF) represents a robust method for estimating latent states and parameters within specified nonlinear equations of dynamic systems under noisy sensor data. Nonetheless, adjusting the filter's hyperparameters (HP)s is essential for effective performance and poses difficulties, especially in systems with many parameters and states to identify, or when it is necessary for the filter to both detect and measure anomaly levels in parameters. Building on the authors previous research on introducing a physics-aware objective function to tune the UKF, this study advances the capabilities of the objective function to tune different adaptive variants of the UKF which facilitates virtual sensing, joint state-parameter estimation, damage quantification and uncertainty quantification under partial observation for systems with many degrees of freedom (DoF) as an open-ended question in structural health monitoring field. To validate the framework, a three DoF damped mass-spring system experiencing a sudden change in physical characteristics is used. Subsequently, the filter's precision in estimating parameters and states is evaluated using a ten DoF system with 40 states and unknown parameters, featuring sparsely placed sensors. Furthermore, the Lorenz attractor under partial observation is used as another case study to highlight why and how the physics-aware objective outperforms other commonly used data-driven objective functions. These results demonstrate the potential of the proposed framework for addressing challenging identification problems in dynamical systems such as tracking sudden changes and evaluating the uncertainties linked to both modeling and measurement, particularly those with limited and noisy sensor data.
Related Concept Videos
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation
On...
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Propagation of Uncertainty from Systematic Error
Modeling with Differential Equations
One-Degree-of-Freedom System
A one-degree-of-freedom system is defined by an independent variable that determines its state and behavior. One example of a one-degree-of-freedom system is a simple harmonic oscillator, such as a...
