Deep random vector functional link transformer network with multiple output layers for significant wave height forecasting

Accurate control of wave energy devices relies heavily on precise forecasts of wave heights, yet the dynamic and fluctuating nature of historical wave data presents significant challenges to achieving this precision. Neural networks help address this issue by extracting meaningful patterns from past observations to improve wave height predictions. This paper introduces a novel random vector functional link transformer (RFT) and ensemble deep random vector functional link transformer (edRFT) networks to capture the dynamic characteristics of significant wave heights. The model employs hidden blocks based on transformer encoders to effectively capture complex sequential dependencies in the data. The proposed model incorporates randomly initialized and fixed weights for the hidden layers to ensure stability during training. Stacked hidden layers are incorporated to facilitate deep representation learning, allowing the extraction of complex patterns from the data. Forecasts are generated by integrating the outputs of each layer using an ensemble approach. The computational results demonstrate the superiority of the proposed models through a comparative analysis against state-of-the-art approaches across fifteen significant wave height time series, validated by three error metrics and a statistical test. • Random Vector Functional Link Transformer (RFT) network is proposed for significant wave height time series forecasting. • Multiple output deep Random Vector Functional Link Transformer (edRFT) network is introduced to improve RFT using ensemble learning and deep transformer encoder architectures. • The proposed models utilize the layerwise Bayesian optimization technique for hyperparameter tuning. • The research evaluates the proposed models against benchmark models, including statistical, machine learning, and deep learning approaches, using fifteen wave height time series datasets. • Three error metrics and statistical tests are used to assess performance, highlighting the superior performance of the proposed models.