An approach to increase prediction precision of GM(1,1) model based on optimization of the initial condition

Wang, Yuhong; Dang, Yaoguo; Li, Yueqing; Liu, Sifeng

doi:10.1016/j.eswa.2010.02.048

Cited by 123 publications

(77 citation statements)

References 8 publications

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“…Hence, when a modelling sequence has the characteristic of approximately homogeneous exponential growth, the model shows better performance for simulation and prediction [22][23][24]. However, the real world is full of complexity and uncertainty, and a sequence with approximately exponential growth is only a special case.…”

Section: Introductionmentioning

confidence: 99%

Forecasting the Energy Consumption of China’s Manufacturing Using a Homologous Grey Prediction Model

2017

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Abstract:With the rapid development of China's manufacturing, energy consumption has increased rapidly, and this has become a major bottleneck affecting the sustainable development of China's economy. This paper deduces and constructs a homologous grey prediction model with one variable and one first order equation (HGEM(1,1)) for forecasting the total energy consumption of China's manufacturing based on the Grey system theory. Both parameter estimation (PE) and the deduction of the final restored expression (FRE) of the HGEM(1,1) model are all from the time response expression of the whitenization differential equation, which solves the 'non-homologous' defects of PE and FRE with traditional grey prediction models. HGEM(1,1) has good performance and can unbiasedly simulate a homogeneous/non-homogeneous exponential function sequence and a linear function sequence. Then, the HGEM(1,1)model is used to simulate and forecast the total energy consumption of China's energy manufacturing, and the results show that the comprehensive performance of this model is much better than that of the classic Grey Model with one variable and single order equation, GM(1,1) for short and the frequently-used Discrete Grey Model with one variable and single order equation, DGM(1,1) for short. Finally, we forecast the total energy consumption of China's manufacturing industry during the years 2018-2024. The results show that the total energy consumption in China's manufacturing is slowing down but is still too large. For this, some measures, such as optimizing the manufacturing structure and speeding up the development and promotion of energy saving and emission reduction technologies, to ensure the effective supply of energy in China's manufacturing industry are suggested.

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Section: Introductionmentioning

confidence: 99%

Forecasting the Energy Consumption of China’s Manufacturing Using a Homologous Grey Prediction Model

2017

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“…Xie and Liu [12] discussed the influence of different fitting points and proposed optimization model fitting point contributes to the model. Another study by Wang et al, [13] introduced a new approach for grey model improvement based on a modified initial condition using the first item and the last item of X (1) to enhance prediction accuracy of a traditional GM(1,1) model. Chen and Li [14] also proposed a new technique for a GM(1,1) model using an optimal weighted combination with a different initial value.…”

Section: Introductionmentioning

confidence: 99%

An Initial Condition Optimization Approach for Improving the Prediction Precision of a GM(1,1) Model

Madhi

Mohamed

2017

MCA

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Grey model GM(1,1) has attained excellent prediction accuracy with restricted data and has been broadly utilized in a range of areas. However, the GM(1,1) forecasting model sometimes yields large forecasting errors which directlyaffect the simulation and prediction precision directly. Therefore, the improvement of the GM(1,1) model is an essential issue, and the current study aims to enhance the prediction precision of the GM(1,1) model. Specifically, in order to improve the prediction precision of GM(1,1) model, it is necessary to consider improving the initial condition in the response function of the model. Consequently, the purpose of this paper is to put forward a new method to enhance the performance of the GM(1,1) model by optimizing its initial condition. The minimum sum of squared error was used to optimize the new initial condition of the model. The numerical outcomes show that the improved GM(1,1) model provides considerably better performance than traditional grey model GM(1,1) . The result demonstrates that the improved grey model GM(1,1) achieves the objective of minimizing the forecast errors.

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“…Meanwhile, many scholars have improved the GM (1, 1) model a lot [11][12][13][14][15][16][17][18][19], thus enhancing its simulative accuracy and predictive accuracy. However, during the processes of both practical application and theoretical research of the GM (1, 1) model, GM (1, 1) model directly jumped from discrete form to continuous form, which resulted in failing in completely fitting homogeneous exponential sequence in simulation and prediction.…”

Section: Introductionmentioning

confidence: 99%

Research on the Stability of NDGM Model with the Fractional Order Accumulation and Its Optimization

Duan

Shao

Xiao

et al. 2017

Mathematical Problems in Engineering

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The grey forecasting model has been successfully applied in numerous fields since it was proposed. The nonhomogeneous discrete grey model (NDGM) was approximately constructed based on the nonhomogeneous index trend; it increased the applicability of discrete grey model. However, the NDGM required accurate data and better effect when the original data did not meet the conditions and fitting and prediction errors were larger. For this, the NDGM with the fractional order accumulating operator (abbreviated as NDGM 푝/푞 ) has higher performance. In this paper, the matrix perturbation bound of the parameters was used to analyze the stability of NDGM 푝/푞 and the NDGM 푝/푞 can decrease the disturbance bound. Subsequently, the parameter estimation method of NDGM 푝/푞 was studied and the Particle Swarm Optimization algorithm was employed to optimize the order number of NDGM 푝/푞 and some steps were provided. In addition, the results of two practical examples demonstrated that the perturbation of NDGM 푝/푞 was smaller than that of NDGM and provided remarkable predication performance compared with the traditional NDGM model and DGM model.

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An approach to increase prediction precision of GM(1,1) model based on optimization of the initial condition

Cited by 123 publications

References 8 publications

Forecasting the Energy Consumption of China’s Manufacturing Using a Homologous Grey Prediction Model

Forecasting the Energy Consumption of China’s Manufacturing Using a Homologous Grey Prediction Model

An Initial Condition Optimization Approach for Improving the Prediction Precision of a GM(1,1) Model

Research on the Stability of NDGM Model with the Fractional Order Accumulation and Its Optimization

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