Virtual sensing of subsoil strain response in monopile-based offshore wind turbines via Gaussian process latent force models

Virtual sensing techniques have gained traction in applications to the structural health monitoring of monopile-based offshore wind turbines, as the strain response below the mudline, which is a primary indicator of fatigue damage accumulation, is impractical to measure directly with physical instrumentation. The Gaussian process latent force model (GPLFM) is a generalized Bayesian virtual sensing technique which combines a physics-driven model of the structure with a data-driven model of latent variables of the system to extrapolate unmeasured strain states. In the GPLFM, unknown sources of excitation are modeled as a Gaussian process (GP) and endowed with a structured covariance relationship with response states, using properties of the GP covariance kernel as well as correlation information supplied by the mechanical model. It is shown that posterior inference of the latent inputs and states is performed by Gaussian process regression of measured accelerations, computed efficiently using Kalman filtering and Rauch-Tung-Striebel smoothing in an augmented state-space model. While the GPLFM has been previously demonstrated in numerical studies to improve upon other virtual sensing techniques in terms of accuracy, robustness, and numerical stability, this work provides one of the first cases of in-situ validation of the GPLFM. The predicted strain response by the GPLFM is compared to subsoil strain data collected from an operating offshore wind turbine in the Westermeerwind Park in the Netherlands. A number of test cases are conducted, where the performance of the GPLFM is evaluated for its sensitivity to varying operational and environmental conditions, to the instrumentation scheme of the turbine, and to the fidelity of the mechanical model. In particular, this paper discusses the capacity of the GPLFM to achieve relatively robust strain predictions under high model uncertainty in the soil-foundation system of the offshore wind turbine by attributing sources of model error to the estimated stochastic input.