Ferry quays experience rapid deterioration due to their exposure to harsh maritime environments and ferry impacts. Vibration-based structural health monitoring offers a valuable approach to assessing structural integrity and understanding the structural implications of these impacts. However, practical limitations often restrict sensor placement at critical locations. Consequently, virtual sensing techniques become essential for establishing a Digital Twin and estimating the structural response. This study investigates the application of the Gaussian Process Latent Force Model (GPLFM) for virtual sensing on the Magerholm ferry quay, combining in-operation experimental data collected during a ferry impact with a detailed physics-based model. The proposed Physics-Encoded Machine Learning model integrates a reduced-order structural model with a data-driven GPLFM representing the unknown impact forces via their modal contributions. Significant challenges are addressed for the development of the Digital Twin of the ferry quay, including unknown impact characteristics (location, direction, intensity), time-varying boundary conditions, and sparse sensor configurations. Results show that the GPLFM provides accurate acceleration response estimates at most locations, even under simplifying modeling assumptions such as linear time-invariant behavior during the impact phase. Lower accuracy was observed at locations in the impact zone. A numerical study was conducted to explore an optimal real-world sensor placement strategy using a Backward Sequential Sensor Placement approach. Sensitivity analyses were conducted to examine the influence of sensor types, sampling frequencies, and incorrectly assumed damping ratios. The results suggest that the GP latent forces can help accommodate modeling and measurement uncertainties, maintaining acceptable estimation accuracy across scenarios.

The problem of combined state and input estimation of linear structural systems based on measured responses and a priori knowledge of structural model is considered. A novel methodology using Gaussian process latent force models is proposed to tackle the problem in a stochastic setting. Gaussian process latent force models (GPLFMs) are hybrid models that combine differential equations representing a physical system with data-driven non-parametric Gaussian process models. In this work, the unknown input forces acting on a structure are modelled as Gaussian processes with some chosen covariance functions which are combined with the mechanistic differential equation representing the structure to construct a GPLFM. The GPLFM is then conveniently formulated as an augmented stochastic state-space model with additional states representing the latent force components, and the joint input and state inference of the resulting model is implemented using Kalman filter. The augmented state-space model of GPLFM is shown as a generalization of the class of input-augmented state-space models, is proven observable, and is robust compared to conventional augmented formulations in terms of numerical stability. The hyperparameters governing the covariance functions are estimated using maximum likelihood optimization based on the observed data, thus overcoming the need for manual tuning of the hyperparameters by trial-and-error. To assess the performance of the proposed GPLFM method, several cases of state and input estimation are demonstrated using numerical simulations on a 10-dof shear building and a 76-storey ASCE benchmark office tower. Results obtained indicate the superior performance of the proposed approach over conventional Kalman filter based approaches.