, Vicenzo Nava (codir. tes.)
, Francisco Javier Gutierrez García (tut. tes.) 
This dissertation tackles the structural health monitoring (SHM) of floating offshore wind turbine (FOWT) mooring lines, mathematically framed as an inverse problem. Reliably detecting degradation is a key challenge for the viability of FOWTs, as sensor data is often limited or noisy. This leads to an ill-posed and potentially non-unique inverse problem. The main mathematical contributions include developing and applying deep learning models tailored to the problem at hand. Deterministic neural networks were initially used, introducing an autoencoder with a two-step training strategy to ensure physically plausible estimations of damage by optimizing measurement reconstruction loss. Aleatoric uncertainty in structural and environmental parameters was addressed by incorporating Gaussian noise layers and performing variance-based sensitivity analysis (Sobol indices) to identify critical parameters. A probabilistic variational autoencoder employing a Gaussian mixture model in the latent space was developed to handle the non-uniqueness and quantify predictive uncertainty, especially under limited data. This approach employs variational inference principles and optimizes the Evidence Lower Bound (ELBO), balancing data misfit and distributional (KL divergence) loss terms. This enables robust damage identification even with faulty instrumentation. Statistical analysis from simulated time and frequency domain responses was crucial for feature extraction efforts, enabling dimensionality reduction and physical interpretability.
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