Unsupervised damage detection using singular-vector feature maps and 2D convolutional autoencoders: Validation on a multi-state shear-frame experiment

We present an unsupervised, vibration-based damage detection framework that integrates a new cross-spectral feature with a deep convolutional autoencoder (CAE). While autoencoders have been widely explored for analyzing time-series responses, the use of spectral features—and particularly those exploiting cross-spectral structure—remains limited. We introduce a tensor-valued, damage-sensitive feature (the SMAC), constructed from the leading singular vectors of the cross-spectral density matrix. This tensor encodes the spectral spatial-correlation structure of the response into a compact, bounded, and robust representation whose computation requires only standard spectral estimation and frequency-wise singular value decomposition, facilitating automated and efficient deployment for long-term monitoring. A 2D CAE is trained exclusively on SMAC tensors from the undamaged state to learn a low-dimensional latent manifold of healthy responses. A covariance-based latent regularization scheme promotes an approximately Gaussian latent geometry, enabling simple statistical modeling. Structural novelty is quantified through two indicators—the reconstruction loss and a latent Mahalanobis distance—whose tail probabilities are fused into a scalar damage score via Fisher’s method. The framework is experimentally validated on a shear-frame structure featuring multiple floor-by-floor damage states and added-mass configurations. Results show high sensitivity to structural changes, clear separation of damaged states, and consistent response to graded mass modifications, with reversion to baseline after mass removal. Analysis of experimental data further elucidates the reconstruction–regularization trade-off and identifies Jacobian—vector-product sensitivities as effective unsupervised diagnostics for model selection. Overall, the proposed method demonstrates strong performance and a modular structure that is readily extensible toward field-oriented, condition-aware SHM systems.