Reliable modal identification from output-only vibration data remains a challenging problem under measurement noise, sparse sensing, and structural variability. These challenges intensify when global modal quantities and spatially distributed mode shapes must be estimated jointly from frequency-domain data. This work presents a physics-aware variational graph autoencoder, termed UResVGAE, for joint modal identification with uncertainty quantification from power spectral density (PSD) representations of truss structures. The framework represents each structure as a graph in which node attributes encode PSD and geometric information, while edges capture structural connectivity. A residual GraphSAGE-based encoder, attention-driven graph pooling, and a variational latent representation are combined to learn both graph-level and node-level modal information within a single, unified formulation. Natural frequencies and damping ratios are predicted through evidential regression, and full-field mode shapes are reconstructed through a dedicated node-level decoder that fuses global latent information with local graph features. Physical consistency is promoted via mode-shape reconstruction and orthogonality regularisation. The framework is assessed on numerically generated truss populations under varying signal-to-noise ratios and sensor availability. Results demonstrate accurate prediction of natural frequencies, damping ratios, and mode shapes, with high modal assurance criterion values and stable performance under noisy and sparse sensing conditions. Reliability analysis indicates that the predictive uncertainty is broadly consistent with empirical coverage. The proposed framework offers a coherent and physically grounded graph-based route for joint modal identification with calibrated uncertainty from frequency-domain structural response data.

翻译：仅基于输出振动数据的可靠模态识别在测量噪声、稀疏传感和结构变异性下仍具挑战性。当需从频域数据中联合估计全局模态参数和空间分布振型时，这些挑战尤为突出。本文提出一种物理感知的变分图自编码器（UResVGAE），用于基于桁架结构功率谱密度（PSD）表示的联合模态识别与不确定性量化。该框架将每个结构表示为图，其中节点属性编码PSD与几何信息，边表征结构连通性。结合基于残差图注意力采样（Residual GraphSAGE）的编码器、注意力驱动图池化及变分隐空间表示，在统一框架中同时学习图级和节点级模态信息。通过证据回归预测固有频率与阻尼比，并通过融合全局隐信息与局部图特征的专用节点级解码器重建全场振型。物理一致性通过振型重建与正交正则化促进。该框架在数值生成的桁架群体上进行了评估，考虑了不同信噪比与传感器可用性。结果表明，在噪声和稀疏传感条件下，固有频率、阻尼比和振型预测准确，模态置信准则值高且性能稳定。可靠性分析表明预测不确定性大致与经验覆盖一致。所提框架为基于频域结构响应数据的联合模态识别提供了一种一致且物理基础的图驱动路径，兼具校准的不确定性。