Advancements in machine learning and an abundance of structural monitoring data have inspired the integration of mechanical models with probabilistic models to identify a structure's state and quantify the uncertainty of its physical parameters and response. In this paper, we propose an inference methodology for classical Kirchhoff-Love plates via physics-informed Gaussian Processes (GP). A probabilistic model is formulated as a multi-output GP by placing a GP prior on the deflection and deriving the covariance function using the linear differential operators of the plate governing equations. The posteriors of the flexural rigidity, hyperparameters, and plate response are inferred in a Bayesian manner using Markov chain Monte Carlo (MCMC) sampling from noisy measurements. We demonstrate the applicability with two examples: a simply supported plate subjected to a sinusoidal load and a fixed plate subjected to a uniform load. The results illustrate how the proposed methodology can be employed to perform stochastic inference for plate rigidity and physical quantities by integrating measurements from various sensor types and qualities. Potential applications of the presented methodology are in structural health monitoring and uncertainty quantification of plate-like structures.

翻译：机器学习技术的进步以及大量结构监测数据的涌现，推动了力学模型与概率模型的融合，以识别结构状态并量化其物理参数与响应的不确定性。本文提出了一种基于物理信息高斯过程的经典Kirchhoff-Love板推断方法。该概率模型通过将高斯过程先验置于挠度上，并利用板控制方程的线性微分算子推导协方差函数，构建为多输出高斯过程。采用马尔可夫链蒙特卡洛采样方法，基于含噪声的测量数据以贝叶斯方式推断抗弯刚度、超参数及板响应的后验分布。通过两个实例验证了方法的适用性：正弦荷载作用下的简支板与均布荷载作用下的固定板。结果表明，所提方法能够整合多种传感器类型与质量的测量数据，实现对板刚度及物理量的随机推断。该方法在板状结构的结构健康监测及不确定性量化中具有潜在应用价值。