Meta-models are increasingly used in wind energy as an alternative to time-domain aero-elastic simulations. These require only fractions of the computing time needed by time-domain simulations. In this work, Kriging and artificial neural networks (ANN) are investigated comprehensively for the approximation of fatigue loads of an offshore wind turbine. Both meta-models are already used in wind energy and provide good results, but a comparison is still pending. It was found that both meta-models can approximate the considered loads similarly well. Furthermore, Kriging partly requires a significantly smaller amount of training data than ANN to achieve the same approximation quality.


Aero-elastic simulations of offshore wind turbines in the time domain are very time-consuming, as many load cases have to be calculated due to controller-induced nonlinearities. Additionally, the simulation models of wind turbines are stochastic, e.g. wind loads, and this results in a further increase of computing times. Especially in the case of robust optimisation or probabilistic simulations, like probabilistic lifetime calculations, a simulation in the time domain is hardly possible. Consequently, meta-models are more frequently used as an alternative to simulations in the time domain.

Meta-models are used for sensitivity analyses, design optimisation or the prediction of ultimate and fatigue loads. Concerning sensitivity analyses, Hübler et al. (2017c), for example, used a Kriging meta-model to identify significant parameters of a substructure of an offshore wind turbine. Müller et al. (2018) applied an artificial neural network (ANN) for the sensitivity analysis of a floating wind turbine on a semi-submersible substructure. For design optimisation, for example, Yang et al. (2015) used Kriging for an optimisation of a tripod substructure. Häfele et al. (2018) and Stieng and Muskulus (2020) also utilised Kriging metamodels for the optimisation of substructures of offshore wind turbines. For fatigue load and stress estimations, Stewart (2016) used linear regression, Müller et al. (2017) applied an ANN, Wilkie (2020) used Kriging, and polynomial chaos expansion (PCE) was used by Murcia et al. (2018). In total, there are already some publications in this area. However, it is the case that there are only a few studies so far that investigate the meta-models in more detail with regard to different sampling methods, the amount of training data required as well as with regard to a comparison of different meta-models. Dimitrov et al. (2018), who investigated and compared five different meta-models, including Kriging and PCE, made a first step in this direction. Slot et al. (2020) also studied the two meta-models Kriging and PCE. In both studies, Kriging was found to have a higher accuracy than PCE. Another study by Schröder et al. (2018) compared three meta-models including PCE and ANN. Here it turned out that PCE and ANN lead to a similarly good approximation of the blade root moment for a large data set, but it is found that for ANN a smaller training data set is needed than for PCE to achieve the same approximation quality. With regard to the approximation performance of the meta-models mentioned, it can be seen that Kriging and ANN leads to good results, but a comparison of these two meta-models has not been carried out yet. Furthermore, the comparative studies mentioned were all carried out for onshore wind turbines. Meta-models are obviously already used for offshore wind turbines. However, to the authors' knowledge, there are otherwise no comprehensive comparative studies on the mentioned meta-models for the approximation of fatigue loads of offshore wind turbines. Compared to onshore wind turbines, there are additional effects such as waveinduced resonance or wind-wave interaction. Therefore, this study investigates and compares Kriging and ANN for an offshore wind turbine.

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