Joint parameter estimation and abrupt change quantification with uncertainty quantification in high degree of freedom dynamical systems via an optimized adaptive unscented Kalman filter

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.