Development of pyramid neural networks for prediction of significant wave height for renewable energy farms

Significant wave height (Hs) is a critical parameter in the design, operation, and maintenance of nearshore and offshore wind and wave farms. In this study, the original pyramid neural network (PNN) was introduced and applied to predict Hs for North Sea renewable energy farms. The performance of PNN was compared with state-of-the-art algorithms. The results show that the machine learning (ML) models trained by the network datasets can accurately predict Hs at any point of nearshore or offshore energy farms, significantly reducing wave monitoring costs. The PNN models predict Hs with high accuracy. The results predicted by PNN, with SRMSE of 0.256 and R2 of 0.873, are more accurate than the corresponding results obtained by the deep neural network (DNN) model, which show that PNNs with their far simpler structures and lower number of parameters are attractive alternatives for complex and time-consuming DNN models. The ensemble of regular models, with SRMSE of 0.247, is ranked as the most accurate method. The results also show that the applied state-of-the-art algorithms including MLR, SNN, DNN, ANFIS, and SVR models predict non-physical negative values of Hs. The PNNs developed in this study predict Hs with positive values. Moreover, the analysis shows that the scatter of the results obtained by the derived nonlinear models is less pronounced than the scatter of corresponding results obtained by other methods. The results also show that to evaluate the performance of nonlinear ML methods for large datasets, the analysis of standard statistical indices is not sufficient. For large datasets standard statistical indices provide inadequate or insufficient information and additional calculations, and statistical analysis are required.