A physics-informed machine learning model, in the form of a multi-output Gaussian process, is formulated using the Euler-Bernoulli beam equation. Given appropriate datasets, the model can be used to regress the analytical value of the structure's bending stiffness, interpolate responses, and make probabilistic inferences on latent physical quantities. The developed model is applied on a numerically simulated cantilever beam, where the regressed bending stiffness is evaluated and the influence measurement noise on the prediction quality is investigated. Further, the regressed probabilistic stiffness distribution is used in a structural health monitoring context, where the Mahalanobis distance is employed to reason about the possible location and extent of damage in the structural system. To validate the developed framework, an experiment is conducted and measured heterogeneous datasets are used to update the assumed analytical structural model.

利用物理信息的机器学习模型，以多输出高斯过程的形式，利用欧拉-伯努利梁方程制定，可用于回归结构的弯曲刚度的解析值、插值响应以及对潜在物理量进行概率推断。该模型应用于数值模拟悬臂梁上，评估回归的弯曲刚度并研究预测质量中测量噪声的影响。进一步，使用回归的概率刚度分布在结构健康监测中，利用马氏距离推理结构系统中损伤的可能位置和范围。为验证开发的框架，进行了实验并使用测量的异构数据集更新了假设的解析结构模型。

基于物理信息的高斯过程模型用于Euler-Bernoulli梁元