Uncertainty-aware damage identification in short-span bridges via physics-informed variational autoencoder

2026-07-06

AI Summary

This study addresses the ill-posed inverse problem in vibration-based damage identification for short-span bridges, which is exacerbated by measurement noise, sparse sensor deployment, and environmental variability, as well as the lack of reliable uncertainty quantification and physical consistency in existing methods. To overcome these limitations, the authors propose a physics-informed Gaussian Copula variational autoencoder (PI-GCVAE). This approach innovatively integrates a differentiable eigenvalue solver into the VAE architecture and employs a Gaussian Copula to model the physical dependencies among latent variables, thereby relaxing the conventional independence assumption and enhancing both physical consistency and generalization capability. Experiments on noisy synthetic data demonstrate that the method accurately recovers the posterior damage distribution, achieving a coverage rate of 77.2%, offering a reliable and scalable solution for early-stage bridge damage diagnosis.

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.

Problem

• damage identification
• uncertainty quantification
• structural health monitoring
• ill-posed inverse problem
• vibration-based

Innovation

• physics-informed variational autoencoder
• Gaussian copula
• uncertainty quantification
• structural health monitoring
• scientific machine learning