The nonhomogeneous grey model has been seen as an effective method for forecasting time series with approximate nonhomogeneous index law, which has been widely used in diverse disciplines on account of its high prediction precision. However, there remains room for improvements. For this, this study presents an improved nonhomogeneous grey model by incorporating the dynamic integral mean value theorem and fractional accumulation simultaneously. In order to promote the efficacy of the optimised model, we apply the whale optimization algorithm (WOA) to ascertain its optimal parameter. In particular, two examples are conducted to validate the superiority of the proposed model in contrast with other benchmarks, and the experimental results show that the mean absolute percentage error of the proposed approach is 808692% and 6.0706%, respectively, indicating the proposed approach performs better than other competing models.
The remarkable prediction of petroleum consumption is of significance for energy scheduling and economic development. Considering the uncertainty and volatility of petroleum system, this paper
presents a nonlinear grey Bernoulli model with combined fractional accumulated generation operator to forecast China’s petroleum consumption and terminal consumption. The newly designed model introduces a combined fractional accumulated generation operator by incorporating the traditional fractional accumulation and conformable fractional accumulation; compared to the old accumulation, the newly optimized accumulation can enhance flexible ability to excavate the development patterns of time-series. In addition, to further improve the prediction performance of the new model, marine predation algorithm is applied to determine the optimal emerging coefficients such as fractional accumulation order. Furthermore, the proposed model is verified by a numerical example of coal consumption; and this newly established model is applied to predict China’s petroleum consumption and terminal consumption. Our tests suggest that the designed ONGBM(1,1,k,c) model outperforms the other benchmark models. Finally, we predict China’s petroleum consumption in the following years with the aid of the optimized model. According to the forecasts of this paper, some suggestions are provided for policy-makers in the relevant sectors.
Grey prediction models have been widely used in various fields of society due to their high prediction accuracy; accordingly, there exists a vast majority of grey models for equidistant sequences; however, limited research is focusing on nonequidistant sequence. The development of nonequidistant grey prediction models is very slow due to their complex modeling mechanism. In order to further expand the grey system theory, a new nonequidistant grey prediction model is established in this paper. To further improve the prediction accuracy of the NEGM (1, 1, t2) model, the background values of the improved nonequidistant grey model are optimized based on Simpson formula, which is abbreviated as INEGM (1, 1, t2). Meanwhile, to verify the validity of the proposed model, this model is applied in two real-world cases in comparison with three other benchmark models, and the modeling results are evaluated through several commonly used indicators. The results of two cases show that the INEGM (1, 1, t2) model has the best prediction performance among these competitive models.
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