Technology Category
Intelligent Robots: State EstimationMachine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Uncertainty Representations
A Copula-Based Variational Autoencoder for Uncertainty Quantification in Inverse Problems: Application to Damage Identification in an Offshore Wind Turbine
🤖 AI Summary
To address the ill-posed, multi-solution inverse problem in mooring system damage identification for floating offshore wind turbines (FOWTs) under limited sensor data, this paper proposes a Copula Variational Autoencoder (Copula-VAE) framework. The method decouples the marginal distributions and dependency structure of latent variables, employing Gaussian Copulas to model complex posterior correlations—thereby overcoming the expressiveness limitations of conventional Gaussian mixture models in high dimensions or their prohibitive computational cost. Validated on high-fidelity synthetic data, Copula-VAE achieves superior damage state inference accuracy with significantly fewer parameters. It markedly improves both the efficiency and scalability of uncertainty quantification, enabling robust probabilistic inference under data scarcity. This work establishes a novel, practical, and scalable paradigm for structural health monitoring of FOWTs, balancing robustness, interpretability, and computational feasibility.
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Application Category
📝 Abstract
Structural Health Monitoring of Floating Offshore Wind Turbines (FOWTs) is critical for ensuring operational safety and efficiency. However, identifying damage in components like mooring systems from limited sensor data poses a challenging inverse problem, often characterized by multimodal solutions where various damage states could explain the observed response. To overcome it, we propose a Variational Autoencoder (VAE) architecture, where the encoder approximates the inverse operator, while the decoder approximates the forward. The posterior distribution of the latent space variables is probabilistically modeled, describing the uncertainties in the estimates. This work tackles the limitations of conventional Gaussian Mixtures used within VAEs, which can be either too restrictive or computationally prohibitive for high-dimensional spaces. We propose a novel Copula-based VAE architecture that decouples the marginal distribution of the variables from their dependence structure, offering a flexible method for representing complex, correlated posterior distributions. We provide a comprehensive comparison of three different approaches for approximating the posterior: a Gaussian Mixture with a diagonal covariance matrix, a Gaussian Mixture with a full covariance matrix, and a Gaussian Copula. Our analysis, conducted on a high-fidelity synthetic dataset, demonstrates that the Copula VAE offers a promising and tractable solution in high-dimensional spaces. Although the present work remains in the two-dimensional space, the results suggest efficient scalability to higher dimensions. It achieves superior performance with significantly fewer parameters than the Gaussian Mixture alternatives, whose parametrization grows prohibitively with the dimensionality. The results underscore the potential of Copula-based VAEs as a tool for uncertainty-aware damage identification in FOWT mooring systems.
Problem
Research questions and friction points this paper is trying to address.
Quantifying uncertainty in damage identification inverse problems
Overcoming limitations of Gaussian Mixtures in high-dimensional spaces
Providing flexible posterior modeling for offshore wind turbine monitoring
Innovation
Methods, ideas, or system contributions that make the work stand out.
Copula-based VAE decouples marginals from dependence structure
Flexible posterior modeling for high-dimensional uncertainty quantification
Achieves superior performance with fewer parameters than Gaussian Mixtures
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2024-09-10arXiv.orgCitations: 0
