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与结构监测数据的日益丰富，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。本文提出一种基于物理信息高斯过程的经典基尔霍夫-洛夫板推断方法。该概率模型通过将挠度设为高斯过程先验，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。基于含噪声测量数据，采用马尔可夫链蒙特卡罗采样以贝叶斯方式推断弯曲刚度、超参数及板响应的后验分布。我们通过两个算例验证方法的适用性：承受正弦荷载的简支板与承受均布荷载的固支板。结果表明，所提方法能够融合不同类型与精度的传感器测量数据，实现板刚度及物理量的随机推断。该方法在板状结构的健康监测与不确定性量化领域具有潜在应用价值。