Probabilistic Graphical Model using Graph Neural Networks for Bayesian Inversion of Discrete Structural Component States

TL;DR

This paper introduces a novel Bayesian inversion framework using Probabilistic Graphical Models and Graph Neural Networks to infer discrete structural component states efficiently, addressing high-dimensional and ill-posed challenges.

Contribution

It proposes a new GNN-based Bayesian inversion method with a graph property-based training strategy, improving computational efficiency for high-dimensional problems.

Findings

The method accurately infers component states from synthetic and experimental data.

The GNN training strategy enables scalable inference across different graph sizes.

The approach effectively addresses the ill-posed nature of inverse problems in structural health monitoring.

Abstract

The health condition of components in civil infrastructures can be described by various discrete states according to their performance degradation. Inferring these states from measurable responses is typically an ill-posed inverse problem. Although Bayesian methods are well-suited to tackle such problems, computing the posterior probability density function (PDF) presents challenges. The likelihood function cannot be analytically formulated due to the unclear relationship between discrete states and structural responses, and the high-dimensional state parameters resulting from numerous components severely complicates the computation of the marginal likelihood function. To address these challenges, this study proposes a novel Bayesian inversion paradigm for discrete variables based on Probabilistic Graphical Models (PGMs). The Markov networks are employed as modeling tools, with model parameters learned from data and structural topology prior. It has been proved that inferring this PGM produces the same probabilistic estimation as the posterior PDF derived from Bayesian inference, which effectively solves the above challenges. The inference is accomplished by Graph Neural Networks (GNNs), and a graph property-based GNN training strategy is developed to enable accurate inference across varying graph scales, thereby significantly reducing the computational overhead in high-dimensional problems. Both synthetic and experimental data are used to validate the proposed framework