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

翻译：土木基础设施中构件的健康状态可根据其性能退化程度由多种离散状态描述。从可测量响应推断这些状态通常是一个病态反问题。尽管贝叶斯方法非常适合解决此类问题，但计算后验概率密度函数（PDF）仍面临挑战。由于离散状态与结构响应之间的关系不明确，似然函数无法解析表达；同时，大量构件导致的高维状态参数严重复杂化了边际似然函数的计算。为应对这些挑战，本研究提出一种基于概率图模型（PGM）的离散变量贝叶斯反演新范式。采用马尔可夫网络作为建模工具，通过数据与结构拓扑先验学习模型参数。已证明，对该PGM进行推断可产生与贝叶斯推断所得后验PDF相同的概率估计，从而有效解决上述难题。推断过程通过图神经网络（GNN）实现，并开发了一种基于图属性的GNN训练策略，使模型能够在不同图尺度下进行准确推断，从而显著降低高维问题中的计算开销。采用合成数据与实验数据共同验证所提框架的有效性。