Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model

This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.

A self-adaptive grey forecasting model and its application

GM(1,1)models have been widely used in various fields due to their high performance in time series prediction.However,some hypotheses of the existing GM(1,1)model family may reduce their prediction performance in some cases.To solve this problem,this paper proposes a self-adaptive GM(1,1)model,termed as SAGM(1,1)model,which aims to solve the defects of the existing GM(1,1)model family by deleting their modeling hypothesis.Moreover,a novel multi-parameter simultaneous optimization scheme based on firefly algorithm is proposed,the proposed multi-parameter optimization scheme adopts machine learning ideas,takes all adjustable parameters of SAGM(1,1)model as input variables,and trains it with firefly algorithm.And Sobol’sensitivity indices are applied to study global sensitivity of SAGM(1,1)model parameters,which provides an important reference for model parameter calibration.Finally,forecasting capability of SAGM(1,1)model is illustrated by Anhui electricity consumption dataset.Results show that prediction accuracy of SAGM(1,1)model is significantly better than other models,and it is shown that the proposed approach enhances the prediction performance of GM(1,1)model significantly.

Expansion modelling of discrete grey model based on multi-factor information aggregation

This paper aims to study a novel expansion discrete grey forecasting model, which could aggregate input information more effectively. In general, existing multi-factor grey forecasting models, such as one order and h variables grey forecasting model （GM （1, h））, always aggregate the main system variable and independent variables in a linear form rather than a nonlinear form, while a nonlinear form could be used in more cases than the linear form. And the nonlinear form could aggregate collinear independent factors, which widely lie in many multi-factor forecasting problems. To overcome this problem, a new approach, named as the Solow residual method, is proposed to aggregate independent factors. And a new expansion model, feedback multi-factor discrete grey forecasting model based on the Solow residual method （abbreviated as FDGM （1, h））, is proposed accordingly. Then the feedback control equation and the parameters＇ solution of the FDGM （1, h） model are given. Finally, a real application is used to test the modelling accuracy of the FDGM （1, h） model. Results show that the FDGM （1, h） model is much better than the nonhomogeneous discrete grey forecasting model （NDGM） and the GM （1, h） model.

A novel fractional grey forecasting model with variable weighted buffer operator and its application in forecasting China's crude oil consumption

Oil is an important strategic material and civil energy.Accurate prediction of oil consumption can provide basis for relevant departments to reasonably arrange crude oil production,oil import and export,and optimize the allocation of social resources.Therefore,a new grey model FENBGM(1,1)is proposed to predict oil consumption in China.Firstly,the grey effect of the traditional GM(1,1)model was transformed into a quadratic equation.Four different parameters were introduced to improve the accuracy of the model,and the new initial conditions were designed by optimizing the initial values by weighted buffer operator.Combined with the reprocessing of the original data,the scheme eliminates the random disturbance effect,improves the stability of the system sequence,and can effectively extract the potential pattern of future development.Secondly,the cumulative order of the new model was optimized by fractional cumulative generation operation.At the same time,the smoothness rate quasi-smoothness condition was introduced to verify the stability of the model,and the particle swarm optimization algorithm(PSO)was used to search the optimal parameters of the model to enhance the adaptability of the model.Based on the above improvements,the new combination prediction model overcomes the limitation of the traditional grey model and obtains more accurate and robust prediction results.Then,taking the petroleum consumption of China's manufacturing industry and transportation,storage and postal industry as an example,this paper verifies the validity of FENBGM(1,1)model,analyzes and forecasts China's crude oil consumption with several commonly used forecasting models,and uses FENBGM(1,1)model to forecast China's oil consumption in the next four years.The results show that FENBGM(1,1)model performs best in all cases.Finally,based on the prediction results of FENBGM(1,1)model,some reasonable suggestions are put forward for China's oil consumption planning.

Forecasting of dissolved oxygen in the Guanting reservoir using an optimized NGBM(1,1) model

An optimized nonlinear grey Bernoulli model was proposed by using a particle swarm optimization algorithm to solve the parameter optimization problem. In addition, each item in the first-order accumulated generating sequence was set in turn as an initial condition to determine which alternative would yield the highest forecasting accuracy. To test the forecasting performance, the optimized models with different initial conditions were then used to simulate dissolved oxygen concentrations in the Guantlng reservoir inlet and outlet （China）. The empirical results show that the optimized model can remarkably improve forecasting accuracy, and the particle swarm optimization technique is a good tool to solve parameter optimization problems. What＇s more, the optimized model with an initial condition that performs well in in-sample simulation may not do as well as in out-of-sample forecasting.