Designing a Multi-Stage Expert System for daily ocean wave energy forecasting: A multivariate data decomposition-based approach

Accurate forecasting of the wave energy is crucial and has significant potential because every wave meter possesses an energy amount ranging from 30 to 40 kW along the shore. By harnessing, it does not produce toxic gases, which is a better alternative to the energies that use fossil fuels. In this research, a multi-stage Multivariate Variational Mode Decomposition (MVMD) integrated with Boruta-Extreme Gradient Boosting (BXGB) feature selection and Cascaded Forward Neural Network (CFNN) (i.e., MVMD-BXGB-CFNN) is proposed to forecast daily ocean wave energy in the regions of Queensland State, Australia. The modelling outcomes were benchmarked via three other robust intelligence-based alternatives comprised of Multigene Genetic Programming (MGGP), Least Square Support Machine (LSSVM), and Gradient Boosted Decision Tree (GBDT) models hybridized with MVMD and BXGB (i.e., MVMD-BXGB-MGGP, MVMD-BXGB-LSSVM, and MVMD-BXGB-GBDT), and their counterpart standalone CFNN, GBDT, LSSVM, and MGGP models. To develop the multi-step hybrid intelligent systems, first, the primary input signals were simultaneously decomposed into intrinsic mode functions (IMFs) and residual components using the MVMD pre-processing technique. Next, the significant lags at the t-1 and t-2 timescales computed using the cross-correlation function were imposed on the decomposed components and further filtered by the BXGB feature selection to identify the best IMFs and reduce the computational cost and enhance the accuracy. Finally, the filtered IMFs were incorporated into the machine learning (ML) models to forecast the wave energy. Forecasting performance of all the provided models (hybrid and counterpart standalone ones) was evaluated during the testing phase by several well-known metrics, infographic tools, and diagnostic analysis. The results showed that the MVMD-BXGB-CFNN technique, as a capable expert system, outperformed the other hybrid and counterpart standalone methods and has an adequate degree of reliability to forecast the daily wave energy in coastal regions.