Improved Fractional-order Accumulation Grey Model in Data Prediction

2018 ◽  
Author(s):  
Yang Yang ◽  
Xiuqin Wang ◽  
Zhen Zhao
Keyword(s):  
Fractional Order ◽  
Grey Model ◽  
Data Prediction

A novel fractional discrete grey model with an adaptive structure and its application in electricity consumption prediction

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yitong Liu ◽  
Yang Yang ◽  
Dingyu Xue ◽  
Feng Pan
Keyword(s):  
Fractional Order ◽  
Electricity Consumption ◽  
Grey Model ◽  
The Novel ◽  
Raw Data ◽  
Content Type ◽  
Power Load ◽  
Grey Models ◽  
Novel Model ◽  
Consumption Prediction

PurposeElectricity consumption prediction has been an important topic for its significant impact on electric policies. Due to various uncertain factors, the growth trends of electricity consumption in different cases are variable. However, the traditional grey model is based on a fixed structure which sometimes cannot match the trend of raw data. Consequently, the predictive accuracy is variable as cases change. To improve the model's adaptability and forecasting ability, a novel fractional discrete grey model with variable structure is proposed in this paper.Design/methodology/approachThe novel model can be regarded as a homogenous or non-homogenous exponent predicting model by changing the structure. And it selects the appropriate structure depending on the characteristics of raw data. The introduction of fractional accumulation enhances the predicting ability of the novel model. And the relative fractional order r is calculated by the numerical iterative algorithm which is simple but effective.FindingsTwo cases of power load and electricity consumption in Jiangsu and Fujian are applied to assess the predicting accuracy of the novel grey model. Four widely-used grey models, three classical statistical models and the multi-layer artificial neural network model are taken into comparison. The results demonstrate that the novel grey model performs well in all cases, and is superior to the comparative eight models.Originality/valueA fractional-order discrete grey model with an adaptable structure is proposed to solve the conflict between traditional grey models' fixed structures and variable development trends of raw data. In applications, the novel model has satisfied adaptability and predicting accuracy.

Non-homogenous discrete grey model with fractional-order accumulation

2014 ◽  
Vol 25 (5) ◽  
pp. 1215-1221 ◽  
Author(s):  
Li-Feng Wu ◽  
Si-Feng Liu ◽  
Wei Cui ◽  
Ding-Lin Liu ◽  
Tian-Xiang Yao
Keyword(s):  
Fractional Order ◽  
Grey Model

scholarly journals A Predictive Analysis of the Business Environment of Economies along the Belt and Road Using the Fractional-Order Grey Model

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Lingling Pei ◽  
Jun Liu
Keyword(s):  
Particle Swarm Optimization ◽  
Fractional Order ◽  
Particle Swarm Optimization Algorithm ◽  
Business Environment ◽  
Grey Model ◽  
Predictive Analysis ◽  
Optimal Order ◽  
Swarm Optimization ◽  
Belt And Road ◽  
The Belt And Road

This paper determined the optimal order of FGM (1, 1) model through particle swarm optimization algorithm and combined with the World Bank business environment data to predict and analyze the business environment of economies along the Belt and Road. The empirical results show that the FGM (1, 1) model has a good predicting effect on the business environment. In terms of prediction accuracy, the FGM (1, 1) model based on particle swarm optimization algorithm to determine the optimal order is significantly better than the traditional GM (1, 1) model. The predict results show that the business environment level of economies along the Belt and Road will increase year by year from 2021 to 2022, but the overall level is still relatively low. The main innovation of this paper lies in the introduction of the fractional-order grey model into the predictive analysis of the business environment, which is of great significance to the extension and application of fractional-order models in management and economic systems.

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

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Huiming Duan ◽  
Kailiang Shao ◽  
Xinping Xiao ◽  
Jinwei Yang
Keyword(s):  
Fractional Order ◽  
Estimation Method ◽  
Original Data ◽  
Grey Model ◽  
Prediction Errors ◽  
Matrix Perturbation ◽  
Perturbation Bound ◽  
Grey Forecasting ◽  
The Matrix ◽  
The Stability

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 NDGMp/q) has higher performance. In this paper, the matrix perturbation bound of the parameters was used to analyze the stability of NDGMp/q and the NDGMp/q can decrease the disturbance bound. Subsequently, the parameter estimation method of NDGMp/q was studied and the Particle Swarm Optimization algorithm was employed to optimize the order number of NDGMp/q and some steps were provided. In addition, the results of two practical examples demonstrated that the perturbation of NDGMp/q was smaller than that of NDGM and provided remarkable predication performance compared with the traditional NDGM model and DGM model.

scholarly journals Prediction of China’s Sulfur Dioxide Emissions by Discrete Grey Model with Fractional Order Generation Operators

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Wei Meng ◽  
Daoli Yang ◽  
Hui Huang
Keyword(s):  
Sulfur Dioxide ◽  
Fractional Order ◽  
Current Trend ◽  
Grey Model ◽  
Order System ◽  
Fractional Operators ◽  
Sulfur Dioxide Emissions ◽  
Forecast Result ◽  
Grey Models ◽  
Improved Performance

Sulfur dioxide is an important source of atmospheric pollution. Many countries are developing policies to reduce sulfur dioxide emissions. In this paper, a novel prediction model is proposed, which could be used to forecast sulfur dioxide emissions. To improve the modeling procedure, fractional order accumulating generation operator and fractional order reducing generation operator are introduced. Based on fractional order operators, a discrete grey model with fractional operators is developed, which also makes use of genetic algorithms to optimize the modeling parameter r. The improved performance of the model is demonstrated via comparison studies with other grey models. The model is then used to predict China’s sulfur dioxide emissions. The forecast result shows that the amount of sulfur dioxide emissions is steadily decreasing and the policies of sulfur dioxide reduction in China are effective. According to the current trend, by 2020, the value of China’s sulfur dioxide emissions will be only 86.843% of emissions in 2015. Fractional order generation operators can be used to develop other fractional order system models.

scholarly journals Prediction of Agricultural Water Consumption in 2 Regions of China Based on Fractional-Order Cumulative Discrete Grey Model

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Yunhong Xu ◽  
Huadong Wang ◽  
Nga Lay Hui
Keyword(s):  
Fractional Order ◽  
Water Consumption ◽  
Optimization Model ◽  
Historical Data ◽  
Grey Model ◽  
Optimal Order ◽  
Agricultural Water ◽  
Forecasting Method ◽  
Best Fitting ◽  
Matlab Programming

In this paper, a new forecasting method of agricultural water demand, fractional-order cumulative discrete grey model, is proposed. Firstly, the best fitting of historical data is used to construct the optimization model. MATLAB programming is applied to solve the optimization model and obtain the optimal order. Secondly, the fractional-order cumulative discrete grey model in this paper is compared with GM (1, 1) model to verify the performance of the model. Finally, Handan region of Hebei Province and Jingzhou region of Hubei Province were selected as the study areas to predict their agricultural water consumptions. The results show that the fractional-order cumulative discrete grey model has better prediction performance than the GM (1, 1) model. It can be used as an effective method for forecasting agricultural water consumption.

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