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.

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