Multi-objective optimized signal decomposition with explainable and reliable hybrid models for multistep significant wave height forecasting in ocean wave energy applications

Abstract

Accurate forecasting of significant wave height (Hs) is vital for marine safety, coastal engineering, and renewable energy production. This study presents an effective integrated model system to forecast Hs for two distinct sites in Australia, Gladstone and Palm Beach, over various time horizons from 30-min to 24-h ahead during the period of 2018 to 2022. In the first stage, a novel multi-objective Optuna is developed to optimize the decomposition parameters using two criteria of compactness, bandwidth, and peakedness of a signal's frequency spectrum. The proposed methodology is utilized for hyperparameter tuning of Singular Spectrum Analysis (SSA) and De-mixing Multivariate Variational Mode Decomposition (D-MVMD) techniques. This enables an optimal data decomposition process by eliminating the need for manual parameter selection. In the second stage, an explainable artificial intelligence (XAI) approach, SHAPley Additive Explanations (SHAP), is used to identify the most influential components and analyze their interactions. These optimized and interpretable decomposed signals are then used as inputs to standalone forecasting models, including Long Short-Term Memory (LSTM), deep Random Vector Functional Link (RVFL), and eXtreme Gradient Boosting (XGBoost). These optimized and interpretable decomposed signals are then used as inputs to the Long Short-Term Memory (LSTM), deep Random Vector Functional Link (RVFL), and eXtreme Gradient Boosting (XGBoost) models to forecast. In the final stage, a comprehensive Monte Carlo Simulation (MCS) is employed to quantify uncertainties and perform reliability analysis. The SHAP-based feature selection reduced the input variables from 37 to 48 decomposed components to a single dominant predictor while maintaining nearly identical predictive accuracy across all forecast horizons, significantly lowering computational costs. Among the models, the SSA-RVFL demonstrated superior performance, with lower computational cost and the highest forecasting accuracy across all time horizons. This model achieved the highest Index of Agreement (IA: 0.81-1) and determination coefficient (R 2 : 0.49-0.98), and lowest Root Mean Square Error (RMSE: 0.04-0.33) across stations and horizons. In addition, the results confirm operational reliability exceeding 88% for forecasts up to 6 h ahead. Overall, the fully optimized SSA integrated with the SHAP-RVFL-MCS results provides a robust framework for enhancing decision-making in coastal hazard and wave energy planning.