Marine and land economy–energy–environment systems forecasting by novel structural-adaptive fractional time-delay nonlinear systematic grey model

Abstract

Rapid economic growth and rising energy consumption have inevitably led to environmental problems, which is a cutting-edge issue of sustainable development. To distinguish the internal structure of marine and land economy–energy–environment (3E) systems and the non-linear relationships between the variables, a novel structural-adaptive fractional time-delay nonlinear systematic grey prediction model (FTDNSGM(1,m)) is established. Additionally, the solving process of each layer model of FTDNSGM(1,m) is described in detail, and the derived models of underlying layer FBTDGM(1,1) and upper layer FBTDGM(1,N) are deduced respectively, which constitute the nested grey difference equations. Furthermore, combined with comparative analysis and Monte-Carlo simulation, optimal non-linear parameters are determined by Beluga Whale Optimization (BWO) algorithm with robustness. Empirically, based on five case datasets under the national–regional dimensions, the FTDNSGM(1,m) model is scientifically verified to have superlative validity and stability. The results demonstrate that the average MAPEs of the proposed model in training and test sets are 0.38%, 0.28%, 0.34%, 0.26%, 0.21%, and 0.38%, 0.88%, 0.47%, 1.36%, 0.67%. Ulteriorly, the proposed model is of applicability to assess the impact on 3E systems attributed to the COVID-19 pandemic in 2020 and 2021. Predictably, from 2022 to 2025, with sustained economic growth, marine and land energy consumption will rise within reasonable limits, while coastal water quality will continue to grow and NOx emissions will keep going down.