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.

翻译：本文提出了一种基于物理信息的多输出高斯过程机器学习模型，该模型利用欧拉-伯努利梁方程构建。在给定适当数据集的情况下，该模型可用于回归结构弯曲刚度的解析值、插值响应，并对潜在物理量进行概率推断。所开发的模型应用于数值模拟的悬臂梁，评估了回归得到的弯曲刚度，并研究了测量噪声对预测质量的影响。进一步地，将回归得到的概率刚度分布用于结构健康监测，采用马氏距离推断结构系统中损伤的可能位置与程度。为验证该框架，开展了实验，并利用实测异质数据集对假定的解析结构模型进行了更新。