Probabilistic data-driven surrogate modeling of wind turbine damage equivalent loads

Abstract

As nations broaden their renewable energy portfolios, wind power is playing an increasingly important role in the energy landscape. Although onshore wind continues to dominate the wind energy mix in the EU, rising energy demand and ambitious climate targets have driven the development of offshore wind farms and spurred research into floating offshore wind turbines.

This thesis began with the goal of developing a data-driven modeling approach that maps site conditions to the load statistics on floating offshore wind turbines. The motivation for this research emerged from a need to accelerate the site-selection process, include more site variables, and achieve accurate load estimates while keeping the computational expense low.

Before installation, all modern wind turbines must be carefully assessed for structural loads to ensure safety and performance throughout their lifetimes. Floating turbines, in particular, introduce more complexity—more environmental variables to consider, and higher uncertainty in the dynamic response. This added complexity makes analyzing structural loads expensive and time-consuming, often more so than for fixed-bottom counterparts, and it makes understanding the behavior of floating wind turbines even more important. The process of fatigue damage calculation, in particular, is computationally intensive, often requiring thousands of costly simulations. Because it is not feasible to run simulations for every possible sea state, engineers typically reduce the problem by selecting a set of variables and binning or lumping sea states to limit the number of required simulations. However, for floating wind turbines, the choice of which variables to include and how to perform this binning remains an open question. This motivates the use of reliable data-driven surrogate models that can make quick estimates of loads on wind turbines while maintaining high accuracy.

Although most existing work relies on deterministic surrogate models, offshore wind environments exhibit strong stochasticity, making turbine loads inherently uncertain. This motivates the need for uncertainty quantification to characterize not only expected loads but also estimate their conditional variability. This dissertation, therefore, develops a probabilistic data-driven methodology that propagates environmental uncertainty to the 10-minute damage equivalent loads of onshore, offshore, and floating offshore wind turbines.

Several deterministic and probabilistic data-driven models are benchmarked on onshore and fixed-bottom offshore wind turbines. The evaluation consists not only of judging the accuracy of a model, but also of practical aspects such as the robustness of the model, sensitivity to hyperparameters, and ease of implementation. Compared to deterministic approaches, which require multiple seed repetitions prior to training, it is demonstrated that with probabilistic models, this step may not be necessary to achieve high accuracy predictions (𝑅2 > 0.95), thereby saving precious computational resources needed to generate the training database. Widely used Gaussian process regression is shown to accurately estimate the conditional mean of the response with a relatively small training dataset of Q102 - 103) samples. Wasserstein-conditional generative adversarial network is used as one of the probabilistic regression models. Despite learning the functional mapping with errors comparable to the best-performing models, it is found to be very complex to implement and requires extensive hyperparameter tuning. Simpler 4th-degree polynomials are shown to make good predictions in the onshore case, but are prone to overfitting and susceptible to the additional noise introduced by the hydrodynamic features. Overall, mixture density networks are shown to provide the best combination of consistency, accuracy, and practical ease of use.

Based on this analysis, the study extends the use of mixture density networks to a more sophisticated application of spar-type floating offshore wind turbine. It is shown to successfully capture the conditional response in terms of the normalized 2-Wasserstein distance despite the added complexity. The surrogate is further used to make probabilistic estimates of the lifetime damage equivalent loads on four potential floating wind turbine sites. Since the surrogate model is fast (order of milliseconds once trained), load predictions can be made over all sea states within seconds, without the need to lump or bin the sea states beforehand. The uncertainty in the aggregated lifetime fatigue loads due to stochastic inputs is extremely narrow, with variability on the order of only 0.1–0.5% of their mean values. This results from summing the 10-minute damage equivalent loads over a million occurrences, effectively nullifying the impact of the outliers. The use of a probabilistic surrogate that correctly captures the conditional distribution is still useful, as it minimizes the aggregation of error in the final response.

Through these analyses, it is demonstrated that surrogate models can be powerful tools for fatigue estimation in the site analysis process, especially for floating wind turbines, where the choice of variables and binning methods is still an open question. Additionally, using probabilistic surrogates like mixture density networks helps reduce bias in calculating the aggregate mean fatigue, as the conditional distributions are heteroscedastic and not always normally distributed.