Joint input-state estimation of structures subjected to complex loads via augmented Kalman Filter with physics informed latent force models

Joint input-state estimation algorithms such as the Augmented Kalman Filter (AKF) rely on the assumption that the distribution of the input loads follows simple spatial patterns, which are either spatially distributed or sparse. However, in many real situations the spatial distribution of the loads is complex and time-varying, which poses a significant challenge. To tackle this issue, this paper introduces a novel method named the Augmented Kalman Filter with Physics Informed Latent Force Models (AKF-PILFM), which incorporates knowledge about the physics underlying the dynamics of the input loads in the estimation based on training data. In the paper, the general formulation of the AKF-PILFM is described, followed by its tailored application to structures subjected to loads with a complex spatiotemporal behavior such as wave loads. The dominant characteristics of the wave loads are identified from training data via the Dynamic Mode Decomposition, enabling the development of a state space model of the loads that can be integrated with the AKF-PILFM. To demonstrate the effectiveness of the proposed methodology, a numerical example is provided consisting of a 3D steel jacket structure subjected to nonlinear irregular waves. The AKF-PILFM shows accurate estimation results and, in the example, outperforms an existing method based on the Gaussian Process Latent Force Models and equivalent modal loads, signifying that the load's spatiotemporal behavior substantially influences the structural response.