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

2026-07-09 · Source: cs.LG updates on arXiv.org · Field: Science & Research — Engineering & Applied Sciences, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

A novel Scientific Machine Learning (SciML) framework, the physics-informed Gaussian copula variational autoencoder (PI-GCVAE), is proposed for uncertainty-aware damage identification in short-span bridges. This framework addresses the ill-posed inverse problem of vibration-based structural health monitoring, which is complicated by measurement noise, sparse sensor arrays, and environmental variability. The PI-GCVAE introduces three key innovations: it directly embeds a differentiable numerical eigenvalue solver into the VAE, eliminating data-driven surrogates and ensuring physical consistency. It replaces the conventional independence assumption of latent variables with a Gaussian copula, capturing complex, physics-dependent spatial cross-correlations between structural elements. This copula-based VAE also offers an efficient distributional model for high-dimensional, strongly correlated latent spaces. Validated on a synthetic dataset of a simply supported bridge with 2.5% frequency and 5% mode shape noise, the PI-GCVAE accurately recovered the true posterior distribution, achieving 77.2% coverage, demonstrating its reliability for early-stage bridge damage diagnosis.

Key takeaway

For Structural Health Monitoring (SHM) engineers developing bridge damage identification systems, traditional deterministic deep learning methods often lack reliable uncertainty quantification. You should consider adopting physics-informed probabilistic models like the PI-GCVAE to ensure physically consistent results and robustly quantify damage uncertainty. This approach, validated with 77.2% coverage, provides a scalable tool for early-stage diagnosis, enhancing the reliability of your infrastructure assessments.

Key insights

A physics-informed Gaussian copula VAE robustly identifies bridge damage by quantifying uncertainty and ensuring physical consistency.

Principles

• Embed physics solvers directly into ML for consistency.
• Model latent variable cross-correlations for physical accuracy.
• Quantify uncertainty in ill-posed inverse problems.

Method

The PI-GCVAE encodes modal properties to Gaussian copula PDF parameters, samples stiffness reduction factors, then uses a differentiable eigenvalue solver to update stiffness and solve the generalized eigenvalue problem.

In practice

• Diagnose early-stage damage in bridges.
• Monitor structural health with sparse sensor data.
• Quantify stiffness reduction in civil infrastructure.

Topics

• Scientific Machine Learning
• Uncertainty Quantification
• Variational Autoencoders
• Structural Health Monitoring
• Bridge Damage Identification
• Gaussian Copulas

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.LG updates on arXiv.org.