To estimate the dynamic trend of industrial water-waste-energy (hereinafter referred to as WWE) system, this paper proposes a new method for forecasting specific indicators in such a system. First, the fractional accumulated generation operator, fractional derivative and classic nonlinear grey Bernoulli model are simultaneously coupled to develop an optimised nonlinear grey Bernoulli model that identifies the nonlinear trends in industrial WWE systems. Second, the particle swarm optimization algorithm is employed to determine the optimal model parameters in the newly-designed model. Based on this, simulation studies are conducted to examine the stability of the proposed model. Finally, the model is applied in the industrial WWE system. The results demonstrate that (1) the proposed model outperforms other competitive models in terms of error-value metrics and (2) industrial water use and industrial energy consumption will increase, whereas industrial wastewater discharge will decline. Furthermore, the rationality of the predicted results redis analyzed from a policy perspective.
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