Stochastic Inference of Plate Bending from Heterogeneous Data: Physics-informed Gaussian Processes via Kirchhoff-Love Theory
This work addresses uncertainty quantification in structural health monitoring for plate-like structures, representing an incremental improvement by combining existing physics-informed Gaussian processes with classical plate theory.
The paper tackles the problem of inferring the state and physical parameters of plate-like structures from noisy, heterogeneous sensor data by integrating Kirchhoff-Love plate theory with Gaussian processes, resulting in a Bayesian methodology that quantifies uncertainty in flexural rigidity and plate response using MCMC sampling.
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.