A copula-based variational autoencoder for uncertainty quantification in inverse structural dynamics: Application to damage identification in an offshore wind turbine

Abstract

Identifying damage from limited sensor data is a challenging inverse problem due to solution multiplicity, which needs a probabilistic inference approach to quantify underlying uncertainty. Variational autoencoders (VAEs) are a powerful class of inference methods that have been proven effective for structural damage identification problems. However, all VAEs used in this context rely on simple Gaussian approximations, which cannot capture complex statistical dependencies among damage features. Gaussian mixture methods do not scale to high-dimensional problems: full-covariance models become computationally prohibitive, and diagonal-covariance models ignore correlations between damage features. To overcome these limitations, this work proposes a novel copula-based VAE architecture that enables the representation of highly correlated posterior distributions by decoupling the modeling of marginal and joint effects. We apply this methodology to the structural health monitoring of floating offshore wind turbine (FOWT) mooring systems, inferring the occurrence and severity of biofouling and anchoring damage from short-term platform rotation signals. We provide a comprehensive comparison of the copula and Gaussian mixture VAE approaches. Numerical experiments conducted on high-fidelity 2D synthetic datasets demonstrate that the copula VAE provides a computationally efficient solution that scales to higher dimensions while controlling parameter growth. Indeed, the proposed technique achieves the same performance with significantly fewer parameters than the Gaussian mixture alternatives, whose parameter counts grow prohibitively with the dimensionality of the latent space. Overall, these results suggest that copula-based VAEs provide a robust framework for uncertainty-aware damage detection in FOWT mooring systems.