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.

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.

scholarly journals An Improved Metabolism Grey Model for Predicting Small Samples with a Singular Datum and Its Application to Sulfur Dioxide Emissions in China

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Wei Zhou ◽  
Demei Zhang
Keyword(s):  
Sulfur Dioxide ◽  
Grey Model ◽  
Small Samples ◽  
Grey Prediction ◽  
Economic Data ◽  
Time Data ◽  
Sulfur Dioxide Emissions ◽  
Study Results ◽  
Standard Level

This study proposes an improved metabolism grey model [IMGM(1,1)] to predict small samples with a singular datum, which is a common phenomenon in daily economic data. This new model combines the fitting advantage of the conventional GM(1,1)in small samples and the additional advantages of the MGM(1,1)in new real-time data, while overcoming the limitations of both the conventional GM(1,1)and MGM(1,1)when the predicted results are vulnerable at any singular datum. Thus, this model can be classified as an improved grey prediction model. Its improvements are illustrated through a case study of sulfur dioxide emissions in China from 2007 to 2013 with a singular datum in 2011. Some features of this model are presented based on the error analysis in the case study. Results suggest that if action is not taken immediately, sulfur dioxide emissions in 2016 will surpass the standard level required by the Twelfth Five-Year Plan proposed by the China State Council.

scholarly journals The dynamics of a new chaotic system through the Caputo–Fabrizio and Atanagan–Baleanu fractional operators

2019 ◽  
Vol 11 (7) ◽  
pp. 168781401986654 ◽  
Author(s):  
Muhammad Altaf Khan
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Order Parameter ◽  
Numerical Procedure ◽  
Numerical Approach ◽  
Fractional Operators ◽  
Fundamental Properties ◽  
Chaotic Model ◽  
New Chaotic System ◽  
Model Apply

The aim of this article is to analyze the dynamics of the new chaotic system in the sense of two fractional operators, that is, the Caputo–Fabrizio and the Atangana–Baleanu derivatives. Initially, we consider a new chaotic model and present some of the fundamental properties of the model. Then, we apply the Caputo–Fabrizio derivative and implement a numerical procedure to obtain their graphical results. Further, we consider the same model, apply the Atangana–Baleanu operator, and present their analysis. The Atangana–Baleanu model is used further to present a numerical approach for their solutions. We obtain and discuss the graphical results to each operator in details. Furthermore, we give a comparison of both the operators applied on the new chaotic model in the form of various graphical results by considering many values of the fractional-order parameter [Formula: see text]. We show that at the integer case, both the models (in Caputo–Fabrizio sense and the Atangana–Baleanu sense) give the same results.

Adaptive Synchronization of a Stochastic Fractional-Order System

2015 ◽  
Vol 733 ◽  
pp. 939-942
Author(s):  
Xiao Jun Liu
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Stochastic System ◽  
Fractional Order System ◽  
Adaptive Synchronization ◽  
Order System ◽  
Unknown Parameters ◽  
Adaptive Laws

In this paper, adaptive synchronization of a stochastic fractional-order system with unknown parameters is studied. Firstly, the stochastic system is reduced into the equivalent deterministic one with Laguerre approximation. Then, the synchronization for the system is realized by designing appropriate controllers and adaptive laws of the unknown parameters. Numerical simulations are carried out to demonstrate the effectiveness of the controllers and laws.

Control of Sulfur Dioxide Emissions from Coal

Science ◽  
1975 ◽  
Vol 189 (4199) ◽  
pp. 253-253 ◽  
Author(s):  
P. H. Abelson
Keyword(s):  
Sulfur Dioxide ◽  
Sulfur Dioxide Emissions
Sign in / Sign up

Export Citation Format

Share Document