A non-linear systematic grey model for forecasting the industrial economy-energy-environment system

To estimate the internal structure and forecast dynamic trends in the industrial economy-energy-environment (3E) system, a non-linear systematic grey model (NSGM(1, m)) is proposed. This model is derived from a non-linear grey Bernoulli model (NGBM(1, 1)) and consisted of multiple non-linear equations in an embedded manner. To minimise the mean absolute percentage error (MAPE), a particle swarm optimisation (PSO) algorithm is used to optimise the parameters of the model. The empirical analysis based on a dataset of Zhejiang Province, China from 2000 to 2018 shows that the NSGM(1, m) model can identify a non-linear relationship among industrial economic growth, energy consumption, and pollutant emissions. The MAPEs of training sets of three industrial 3E systems are 2.95%, 4.90%, and 3.75%, while those of test sets are 1.36%, 6.94%, and 1.72%, respectively. From 2019 to 2023, it is predicted that, with constant industrial and economic growth, industrial energy consumption and discharge of exhaust and solid waste will continue to increase while industrial wastewater discharge will decline. Moreover, efficiency indices indicate that the economic efficiency of the industrial 3E systems in Zhejiang Province will increase.