Gaussian mixture autoencoder for uncertainty-aware damage identification in a floating offshore wind turbine

Abstract. This work proposes an uncertainty-aware approach to the inverse problem of damage identification in a floating offshore wind turbine (FOWT). We design an autoencoder architecture, where the latent space represents the features of the target damage condition. The inverse operator (encoder) is a deep neural network that maps the measurable response to the parameters (means, variances, and weights) of a multivariate Gaussian mixture model. The Gaussian mixture model provides a convenient distributional description that is flexible enough to accommodate complex solution spaces. The decoder receives samples from the Gaussian mixture and maps the damage condition (states) to the system's measurable response. In such a problem, and depending on the quantities being observed (sensor positioning), it is possible that multiple damage states may correspond to similar measurement records. In this context, the main contribution of this work lies in developing a method to quantify the uncertainty within the context of a possibly ill-posed damage identification problem. We employ the Gaussian mixture to express the multimodal solution space and explain the uncertainty in the damage condition estimates. We design and validate the methodology using synthetic data from a FOWT in the commonly adopted OpenFAST software and consider two damage types frequently occurring in mooring lines: biofouling and anchor displacement. The method allows for the estimation of the damage state while capturing the uncertainty in the estimations and the multimodality of the solution under the availability of a limited number of response measurements.