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.

翻译：大跨度桥梁在其服役期内会受到多种动态激励作用。为考虑这些作用对结构系统的影响，设计阶段采用多种载荷模型模拟结构可能经历的条件。这些模型基于不同的简化假设，其参数通常由测量数据随机识别确定，导致输出结果具有固有不确定性。本文提出一种基于高斯过程回归的概率物理信息机器学习框架，用于根据测量得到的挠度、速度或加速度重构动态力。该模型能够处理不完整且受污染的测量数据，并提供一种天然的正则化方法处理测量系统中的噪声。通过对大贝尔特东桥的气动分析给出了该框架的应用实例。基于准稳态模型数值计算气动响应，并利用稀疏且含噪声的测量数据重构底层作用力。结果表明，预测动态载荷与实际载荷具有良好一致性，该方法可推广至计算整体响应及由此产生的内力。所提出框架的应用场景包括验证设计模型与假设，以及用于辅助损伤检测与结构健康监测的响应预测。