Water wave height prediction using a novel hybrid deep learning model with output uncertainty quantification

Articles in Press

Document Type : Research/Original/Regular Article

Authors

1 Associate Professor, Department of the Water Engineering, Faculty of Agriculture, Shahrekord University, Shahrekord, Iran

2 Ph.D. Department of Hydraulic Structures, Semnan University, Semnan, Iran

Abstract

Accurate significant wave height (SWH) prediction is essential for improving the safety and efficiency of maritime operations. Thus, our study develops the Gaussian data augment (GDA) technique- Meerkat optimization algorithm (MOA)- variational mode decomposition (VMD)- complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN)- bidirectional long short-term memory neural network model (BILSTM)- attention mechanism (AT)- gated recurrent unit (GRU) model to accurately predict SWH and overcome the limitations of the GRU model. First, the GDA method addresses the problem of data scarcity by providing new data points. Next, MOA is used to adjust the parameters of the components of the hybrid model. The VMD method then reduces the intricacy of the time series by converting them into subseries with lower complexity named intrinsic mode functions (IMFs). However, as the first IMF retains the complex characteristics of the original time series, the CEEMDAN method is applied to decompose it into secondary IMFs with reduced complexity. Subsequently, the BILSTM model extracts forward and backward temporal features from the secondary IMFs and the initial remaining IMFs. An attention mechanism is then applied to assign the attention weights to the extracted features. Each attention weight indicates the importance of a feature, enabling the GRU model to identify the most important time series features for predicting SWH. Finally, the weighted features are fed into the GRU model to predict SWH accurately. Our study also couples the kernel density estimation method with the GDA- MOA-VMD-CEEMDAN-BILSTM- attention mechanism-GRU (GMVCBAG) model to quantify the uncertainty of the model outputs. The new model is benchmarked against multiple predictive models. Our study also uses various performance metrics to evaluate the accuracy of predictions. Our findings indicate that Nash–Sutcliffe efficiency (NSE), mean absolute error (MAE), standard deviation of the relative error (STDRE), and explained variance of the GMVCBAG model are 0.973, 0.245, 1.245, and 0.899, respectively. Results indicate that GMVCBAG provides reliable SWH predictions. Moreover, the outputs of the new model have a lower uncertainty than those of the other predictive models. Thus, GMVCBAG is a suitable model for predicting SWH in the different regions of the world.  

Keywords

Main Subjects

Water and Soil Management and Modelling

Articles in Press, Accepted Manuscript
Available Online from 27 November 2025

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History

  • Receive Date: 25 October 2025
  • Revise Date: 26 November 2025
  • Accept Date: 27 November 2025

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