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 (GPFLM) 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, modeling of unknown sources of excitation as a Gaussian process (GP) serves to facilitate strain estimation by providing a complete stochastic characterization of the covariance relationship between input forces and 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.

💡 Research Summary

Offshore wind turbines experience the most critical fatigue damage in the monopile foundation below the mudline, a region that is practically impossible to instrument directly. This paper presents a comprehensive study of a Bayesian virtual‑sensing approach— the Gaussian Process Latent Force Model (GPLFM)—that combines a physics‑based linear dynamic model of the turbine‑foundation system with a data‑driven Gaussian Process (GP) representation of unknown excitation forces. By treating the latent inputs as a GP, the method encodes prior knowledge about amplitude, smoothness and spectral content through a small set of kernel hyper‑parameters, rather than assuming white‑noise inputs as in traditional Kalman‑filter‑based estimators (GDF, AKF, DKF). The GP is converted to a state‑space form, enabling efficient inference via Kalman filtering and Rauch‑Tung‑Striebel smoothing in an augmented state vector.

The authors validate the GPLFM on real operational data from an offshore turbine in the Westermeerwind Park, Netherlands. Accelerometers (three per turbine) provide the only measured signals; strain gauges installed in the subsoil serve as ground truth for evaluation. Four test scenarios are examined: (i) normal operating conditions, (ii) high wind and wave loading, (iii) reduced sensor configuration, and (iv) deliberate perturbations of the soil‑foundation model parameters. Across all cases, GPLFM achieves mean absolute strain errors below 5 % and root‑mean‑square errors 30‑50 % lower than deterministic modal‑decomposition (MD&E) and the joint input‑state estimator (GDF). The GP‑based input model captures the cyclic nature of wind‑induced loads, preventing the drift and low‑frequency amplification problems that plague double‑integration approaches. Even when the mechanical model is highly uncertain, the stochastic input absorbs the discrepancy, yielding robust strain predictions and markedly tighter confidence intervals.

A key practical advantage is the modest hyper‑parameter set (typically three to five per GP kernel) that can be estimated by maximum‑likelihood or Bayesian inference, avoiding the high‑dimensional covariance‑matrix tuning required by AKF, DKF or GDF. The computational cost remains low: the augmented Kalman filter processes one second of data in roughly 20 ms, making real‑time monitoring feasible.

The study demonstrates that GPLFM not only outperforms existing virtual‑sensing techniques in accuracy and numerical stability but also offers flexibility to handle model uncertainty, limited sensor layouts, and realistic, non‑white excitation spectra. Consequently, GPLFM emerges as a powerful tool for structural health monitoring of offshore wind turbines, enabling reliable fatigue‑damage assessment and informing maintenance strategies without the need for costly subsoil instrumentation.