  Recent advancements in data-driven aeroelasticity have been driven by the
wealth of data available in the wind engineering practice, especially in
modeling aerodynamic forces. Despite progress, challenges persist in addressing
free-stream turbulence and incorporating physics knowledge into data-driven
aerodynamic force models. This paper presents a hybrid Gaussian Process (GPs)
methodology for non-linear modeling of aerodynamic forces induced by gusts and
motion on bluff bodies. Building on a recently developed GP model of the
motion-induced forces, we formulate a hybrid GP aerodynamic force model that
incorporates both gust- and motion-induced angles of attack as exogenous
inputs, alongside a semi-analytical quasi-steady (QS) model as a physics-based
prior knowledge. In this manner, the GP model incorporates the absent physics
of the QS model, and the non-dimensional hybrid formulation enhances its appeal
from an aerodynamic perspective. We devise a training procedure that leverages
simultaneous input signals of gust angles, based on random free-stream
turbulence, and motion angles, based on random broadband signals. We verify the
methodology through analytical linear aerodynamics of a flat plate and
non-linear aerodynamics of a bridge deck using Computational Fluid Dynamics
(CFD). The standout feature of the presented methodology is its applicability
for aeroelastic buffeting analyses, showcasing robustness when handling
broadband excitation. Importantly, the non-linear hybrid model preserves its
capability to capture higher-order harmonics in the motion-induced forces and
remains applicable for flutter analysis, while incorporating both motion and
gust angles as input. Applications of the methodology are anticipated in the
aeroelastic analysis and monitoring of slender line-like structures.
