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.

提出了一种通过物理信息引导的高斯过程将机械模型与概率模型相结合的方法，用于确定结构的状态并量化其物理参数和响应的不确定性。通过在偏转上放置高斯过程先验，并使用板块控制方程的线性微分算子推导协方差函数，构建了多输出高斯过程的概率模型。通过从噪声测量中进行马尔可夫链蒙特卡洛采样的贝叶斯推理，推断了挠曲刚度、超参数和板的响应的后验分布。通过两个例子展示了该方法的适用性：简支板受正弦载荷作用和固定板受均布载荷作用。结果说明了该方法可以通过整合不同传感器类型和质量的测量来执行板刚度和物理量的随机推断，适用于结构健康监测和板状结构的不确定性量化。