Uncertainty-aware damage identification in short-span bridges via physics-informed variational autoencoder
2026-07-06 • Machine Learning
Machine Learning
AI summaryⓘ
The authors developed a new method to find damage in bridges by using vibrations and a special type of machine learning that respects the physics of how structures work. They combined a physics-based math solver with a smart model that understands complex connections between parts of the bridge, making it better at handling noisy and limited sensor data. Testing on simulated bridge data showed their method could reliably estimate damage levels and uncertainty. This approach aims to help detect structural problems early with more trustworthy results.
structural health monitoringvibration-based damage identificationvariational autoencoderGaussian copulaphysics-informed modelinginverse problemseigenvalue solveruncertainty quantificationsystem identificationstructural dynamics
Authors
Ana Fernandez Navamuel, A. Javier Omella, Diego Zamora-Sanchez, David Pardo
Abstract
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.