Bayesian model updating provides a rigorous probabilistic framework for calibrating finite element (FE) models with quantified uncertainties, thereby enhancing damage assessment, response prediction, and performance evaluation of engineering structures. Recent advances in hierarchical Bayesian model updating (HBMU) enable robust parameter estimation under ill-posed/ill-conditioned settings and in the presence of inherent variability in structural parameters due to environmental and operational conditions. However, most HBMU approaches overlook multimodality in structural parameters that often arises when a structure experiences multiple damage states over its service life. This paper presents an HBMU framework that employs a Dirichlet process (DP) mixture prior on structural parameters (DP-HBMU). DP mixtures are nonparametric Bayesian models that perform clustering without pre-specifying the number of clusters, incorporating damage state classification into FE model updating. We formulate the DP-HBMU framework and devise a Metropolis-within-Gibbs sampler that draws samples from the posterior by embedding Metropolis updates for intractable conditionals due to the FE simulator. The applicability of DP-HBMU to damage localization is demonstrated through both numerical and experimental examples. We consider moment-resisting frame structures with beam-end fractures and apply the method to datasets spanning multiple damage states, from an intact state to moderate or severe damage state. The clusters inferred by DP-HBMU align closely with the assumed or observed damage states. The posterior distributions of stiffness parameters agree with ground truth values or observed fractures while exhibiting substantially reduced uncertainty relative to a non-hierarchical baseline. These results demonstrate the effectiveness of the proposed method in damage localization.

翻译：层次贝叶斯模型更新为有限元模型校准提供了严谨的概率框架，可量化不确定性，从而增强工程结构的损伤评估、响应预测和性能评价。近期层次贝叶斯模型更新的进展使得在病态/欠定条件下以及因环境与运行工况导致结构参数固有变异性存在时，仍能实现稳健的参数估计。然而，大多数层次贝叶斯模型更新方法忽略了结构参数的多峰性，而这种多峰性常源于结构在其服役期内经历的多种损伤状态。本文提出一种采用狄利克雷过程混合先验作用于结构参数的层次贝叶斯模型更新框架。狄利克雷过程混合是非参数贝叶斯模型，无需预先指定聚类数量即可执行聚类，从而将损伤状态分类融入有限元模型更新。我们构建了该框架，并设计了一种吉布斯内嵌梅特罗波利斯采样器，通过嵌入针对有限元模拟器导致的不可处理条件分布的梅特罗波利斯更新，从后验分布中抽取样本。通过数值和实验算例验证了该方法在损伤定位中的适用性。我们考虑具有梁端断裂的抗弯框架结构，并将该方法应用于涵盖完整状态、中度或严重损伤状态等多个损伤状态的数据集。方法推断的聚类结果与假设或观测的损伤状态高度吻合。刚度参数的后验分布与真实值或观测断裂情况一致，且相较于非层次基线模型，不确定性显著降低。这些结果证明了所提方法在损伤定位中的有效性。