Structural vibrations induced by external excitations pose significant risks, including safety hazards for occupants, structural damage, and increased maintenance costs. While conventional model-based control strategies, such as Linear Quadratic Regulator (LQR), effectively mitigate vibrations, their reliance on accurate system models necessitates tedious system identification. This tedious system identification process can be avoided by using a model-free Reinforcement learning (RL) method. RL controllers derive their policies solely from observed structural behaviour, eliminating the requirement for an explicit structural model. For an RL controller to be truly model-free, its training must occur on the actual physical system rather than in simulation. However, during this training phase, the RL controller lacks prior knowledge and it exerts control force on the structure randomly, which can potentially harm the structure. To mitigate this risk, we propose guiding the RL controller using a Linear Quadratic Regulator (LQR) controller. While LQR control typically relies on an accurate structural model for optimal performance, our observations indicate that even an LQR controller based on an entirely incorrect model outperforms the uncontrolled scenario. Motivated by this finding, we introduce a hybrid control framework that integrates both LQR and RL controllers. In this approach, the LQR policy is derived from a randomly selected model and its parameters. As this LQR policy does not require knowledge of the true or an approximate structural model the overall framework remains model-free. This hybrid approach eliminates dependency on explicit system models while minimizing exploration risks inherent in naive RL implementations. As per our knowledge, this is the first study to address the critical training safety challenge of RL-based vibration control and provide a validated solution.

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.

Long-span bridges are subjected to a multitude of dynamic excitations during their lifespan. To account for their effects on the structural system, several load models are used during design to simulate the conditions the structure is likely to experience. These models are based on different simplifying assumptions and are generally guided by parameters that are stochastically identified from measurement data, making their outputs inherently uncertain. This paper presents a probabilistic physics-informed machine-learning framework based on Gaussian process regression for reconstructing dynamic forces based on measured deflections, velocities, or accelerations. The model can work with incomplete and contaminated data and offers a natural regularization approach to account for noise in the measurement system. An application of the developed framework is given by an aerodynamic analysis of the Great Belt East Bridge. The aerodynamic response is calculated numerically based on the quasi-steady model, and the underlying forces are reconstructed using sparse and noisy measurements. Results indicate a good agreement between the applied and the predicted dynamic load and can be extended to calculate global responses and the resulting internal forces. Uses of the developed framework include validation of design models and assumptions, as well as prognosis of responses to assist in damage detection and structural health monitoring.

Machine Learning (ML) has widely been used for modeling and predicting physical systems. These techniques offer high expressive power and good generalizability for interpolation within observed data sets. However, the disadvantage of black - box m odels is that they underperform under blind conditions since no physical knowledge is incorporated. Physics - based ML aims to address this problem by retaining the mathematical flexibility of ML techniques while incorporating physics. In accord, this paper proposes to embed mechanics - based models into the mean function of a Gaussian Process (GP) model and characterize potential discrepancies through kernel machines. A specific class of kernel function is promoted, which has a connection with the gradient of the physics - based model with respect to the input and parameters and shares similarity with the exact Auto - covariance function of linear dynamical systems. The spectral properties of the kernel function enable considering dominant periodic processes origin ating from physics misspecification. Nevertheless, the stationarity of the kernel function is a difficult hurdle in the sequential processing of long data sets, resolved through hierarchical Bayesian techniques. This implementation is also advantageous to mitigate computational costs, alleviating the scalability of GPs when dealing with sequential data. Using numerical and experimental examples, potential applications of the proposed method to structural dynamics inverse problems are demonstrated. Postdoctoral Fellow, Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Hong Kong, Email: osedehi@connect.ust.hk Ph.D. Student, Department of Civil and Environmental Engineering, The Hong Kong Universi ty of Science and Technology, Hong Kong, Email: akosikova@connect.ust.hk