Improvement And Application Of Grey Model Based On Beta And KPCA

As an important method of forecasting analysis,grey model is extensively used in various fields such as economy and energy.This paper focus on the calculation of grey action,background value and multidimensional grey model.Some practical cases are selected for comparison with other models.The main work is as follows:(1)Considering the nonlinearity and dispersion of the original data relationship,the fractional-order beta discrete grey FBDGM(1,1)model is proposed.To reduce the uncertainty of the raw data,fractional-order cumulative operation is employed to build the discrete grey model.Meanwhile,to improve the accuracy of the model,a revised probability density function of beta distribution with superior non-linear is introduced as the new grey action.Next,the recursive formulation of the model is derived by iteration.The validity of the proposed model is verified using real energy data from the existing literature.Then,the model is applied to simulate and forecast nuclear energy consumption for 13 countries from 2009-2020,and is compared with the existing one-dimensional models.The results show that the FBDGM(1,1)model can effectively improve the prediction accuracy and is practical.Finally,the model is utilized to predict the total nuclear energy consumption in the next 5 years.(2)For multidimensional nonlinear data,the multidimensional beta grey IBDGM(1,N)model based on the multiplicative method is proposed by convolutional integration theory.The multiplicative method is adopted to calculate the background value to reduce the model error.The grey action of the model is replaced by the probability density function of the beta distribution,which has more diverse trends.In the two-stage parameters identification of the model,the least squares method is applied to estimate the linear parameters and the particle swarm algorithm is utilized to select nonlinear parameters.At last,the model is validated with three real energy data and compared with existing multidimensional grey and non-grey models,and the results exhibit that the IBDGM(1,N)model has higher prediction accuracy.(3)To address the problems of small sample dimensional catastrophe and multicollinearity in multidimensional grey model,the multidimensional grey IKPGM(1,N,tα)model based on time power term and improved kernel principal component analysis(KPCA)is proposed.Considering the non-linearity of data relationship,KPCA is introduced to reduce the dimensionality of the cumulative series of the relevant variables,so that the correlation between the main relevant cumulative series and the original prediction sequence is maximised,and then the multidimensional grey model with time power term is built using the main relevant cumulative series.Next,the parameters are optimized using a particle swarm algorithm,and the multi-objective optimization problem is reduced to a single-objective optimization problem.Finally,the IKPGM(1,N,tα)model is validated using Chinese carbon emission data from 2004-2019.The results demonstrate that KPCA can achieve dimensionality reduction well,and the model is effective and has better performance in predicting carbon emission.