Latent variable models for simultaneous EOV identification and removal in population-based SHM
Authors: M. D. Champneys, M. R. Jones, A. J. Hughes, T. J. Rogers, E. J. Cross, K. Worden
Organizations: Dynamics Research Group, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK · Centre for Machine Intelligence, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK
Abstract
The robust treatment of environmental and operational variability (EOV) is an open challenge in population-based structural health monitoring (PBSHM). The difficulty is compounded in the case that the EOV signals are unmeasured. A common approach in conventional SHM is to apply \emph{projection-based} methods that discard subspaces of healthy feature data, reasoning that the EOV signal dominates the variance of the measured features. However, a common pitfall of projection-based approaches is that when damage acts close to the same variance-dominant direction, damage sensitivity is removed along with the EOV. An alternative identifying assumption for the removal of particular unmeasured EOVs is slowness; the latent EOV process is characterised by its long temporal correlation. In this paper, the latent EOV is cast as a state-space Gaussian process, enabling tractable O(T) inference via a Kalman filter. A robust hierarchical Bayesian identification framework is developed that enables population-level identification of latent EOVs and EOV-free residual features, using a Laplace approximation. The approach is first validated on a single laboratory-scale benchmark structure from the literature, subject to thermal EOVs, demonstrating robust damage detection and EOV recovery. The method is then applied to a simulated nine-turbine offshore wind farm with staggered deployment and damage, where it delivers a substantial true-positive uplift over projection and cointegration-based baselines at matched false-positive rates.
Damage identification is a core task in structural health monitoring. In practice, however, its reliability is often compromised by confounding non-damage effects, such as variations in excitation and environmental conditions, which can induce changes comparable to or larger than those caused by structural damage. To address this challenge, this study proposes a self-supervised label-free disentangled representation learning framework for robust vibration-based structural damage identification. The proposed framework employs an autoencoder with two latent representations to learn directly from raw vibration acceleration signals. A self-supervised invariance regularization, implemented via Variance-Invariance-Covariance Regularization (VICReg), is imposed on one latent representation using baseline data where structural damage is assumed constant but operational and environmental conditions vary. In addition, a frequency-domain constraint is introduced to enforce agreement between the power spectral density reconstructed from the latent representation and that computed from the corresponding input time series. Together, these mechanisms promote disentanglement, enabling the learned representation to be sensitive to damage-related characteristics while remaining invariant to nuisance variability. The framework is trained in a fully end-to-end and label-free manner, requiring no prior information on damage, excitation, or environmental conditions, making it well-suited for real-world applications. Its effectiveness is validated on two distinct real-world vibration datasets, including a bridge and a gearbox. The results demonstrate robustness to operational variability, strong generalization capability, and good performance in both damage detection and quantification.
Xudong Jian, Charikleia Stoura, Simon Scandella +1
Vibration-based damage identification in civil infrastructure is a challenging, ill-posed inverse problem due to measurement noise, sparse sensor arrays, and environmental variability. While deep learning is powerful for system identification, deterministic approaches lack reliable uncertainty quantification and can yield physically inconsistent results. This work proposes a robust probabilistic Scientific Machine Learning (SciML) framework: a physics-informed Gaussian copula variational autoencoder (PI-GCVAE) for structural health monitoring (SHM). First, we eliminate the need for data-driven surrogates by embedding a differentiable numerical eigenvalue solver directly into the VAE architecture. This ensures that latent space samples satisfy the governing equations of structural dynamics, reducing the trainable parameter space and improving generalization. Second, we replace the conventional independence assumption of latent variables with a Gaussian copula. This model captures complex, physics-dependent spatial cross-correlations between adjacent structural elements, defining feasible solutions while accounting for inherent system variability and measurement errors. Third, compared with alternatives such as Gaussian mixtures, our copula-based VAE provides an efficient distributional model for high-dimensional, strongly correlated latent spaces. We validate the approach using a synthetic dataset of a simply supported bridge subjected to various damage scenarios and corrupted with stochastic Gaussian noise. Synthetic data enables exhaustive validation against ground-truth stiffness values unavailable in practice. Results demonstrate that the PI-GCVAE accurately recovers the true posterior distribution, achieving 77.2% coverage. The proposed framework provides a reliable, scalable tool for early-stage damage diagnosis in operating bridges.
Ana Fernandez-Navamuel, A. Javier Omella, Diego Zamora-Sanchez +1
Identifying latent state representations and dynamics is essential when direct modeling in observation space is infeasible, particularly under partial and high-dimensional observations. In such settings, representation learning and physics-aware modeling are inherently coupled. We study this problem for latent port-Hamiltonian systems, a structured class encompassing both conservative and dissipative dynamics. We propose a two-stage identify-then-project framework. First, a contrastive teacher learns continuous-time latent dynamics from partial observations. Then, a student projects the identified teacher representation and dynamics onto a port-Hamiltonian submanifold via a learned affine chart, yielding a physically consistent realization. As a conceptual counterfactual, we also consider a single-stage variant that jointly learns latent identification and port-Hamiltonian structure, but find it to be less reliable, motivating the proposed two-stage teacher-student framework. We show theoretically that affine projection is the natural bridge between the affine gauge of contrastive latent identification and the port-Hamiltonian systems. Empirically, we demonstrate that the proposed two-stage approach preserves the teacher's dynamics while enforcing physical structure, and performs more reliably than the single-stage alternative, particularly in dissipative regimes and high-dimensional visual settings.