Stochastic Inference of Plate Bending from Heterogeneous Data: Physics-informed Gaussian Processes via Kirchhoff-Love Theory

2024-05-21

Journal of engineering mechanics

AI Summary

This work addresses the stochastic inverse problem of inferring plate bending states under heterogeneous sensor data in structural health monitoring. We propose a physics-informed Bayesian modeling framework that integrates Kirchhoff–Love plate theory with multi-output Gaussian processes (GPs). Crucially, we derive the GP covariance function directly from the governing differential operator, enabling joint uncertainty quantification of flexural rigidity and bending response without assuming parametric prior forms. The method supports robust inference under heterogeneous data sources and non-uniform noise. Numerical experiments on simply supported and clamped plates demonstrate sub-3% relative error in flexural rigidity estimation and accurate characterization of posterior uncertainty for both responses and physical parameters. Results confirm the framework’s robustness and generalizability across multi-source noisy measurement scenarios.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

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.

Problem

• Infer plate bending using physics-informed Gaussian Processes
• Quantify uncertainty in plate rigidity and response
• Integrate heterogeneous sensor data for structural monitoring

Innovation

• Physics-informed Gaussian Processes for plate bending
• Bayesian inference with MCMC sampling
• Multi-output GP for structural monitoring