Using fractional order accumulation to reduce errors from inverse accumulated generating operator of grey model

Wu, Lifeng; Liu, Sifeng; Yao, Ligen; Xu, Ruiting; Xun-ping, Lei

doi:10.1007/s00500-014-1268-y

Cited by 64 publications

(27 citation statements)

References 18 publications

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“…Although a large variety types of grey prediction models can be studied, the most widely used grey prediction model is a GM(1,1) model because of its high computational efficiency [32]. So far, the GM(1,1) model has been widely applied to a broad spectrum of fields, including economics [33,34], environment [35], tourism [36,37], industry [38,39], education [40], transportation [41] and energy [29,[42][43][44][45]. Wang et al [33] presented an improved grey model, named PRGM(1,1), to forecast tertiary industry in Beijing City in China.…”

Section: Background and Motivationmentioning

confidence: 99%

Forecasting Electricity Consumption Using an Improved Grey Prediction Model

Zhang

2018

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Prediction of electricity consumption plays critical roles in the economy. Accurate electricity consumption forecasting is essential for policy makers to formulate electricity supply policies. However, limited data and variables generally cannot provide sufficient information to gain satisfactory prediction accuracy. To address this problem, we propose a novel improved grey forecasting model, which combines data transformation for the original data sequence and combination interpolation optimization of the background value of the GM(1,1) model, and is therefore named DCOGM(1,1). To evaluate the simulation and prediction performance of DCOGM(1,1), two case studies are carried out. In addition, the results show that DCOGM(1,1) outperforms most existing improved grey models in terms of forecasting accuracy. Finally, DCOGM(1,1) is employed to predict the total electricity consumption of Shanghai City in China from 2017 to 2021. In addition, the results suggest that DCOGM(1,1) performs well compared with the traditional GM(1,1) model and other grey modification models in this context and Shanghai's electricity consumption will increase stably in the following five years. In summary, DCOGM(1,1) proposed in our study has competent exploration and exploitation ability, and could be utilized as an effective and promising tool for short-term planning for other forecasting issues with limited source data as well.The forecast accuracy of electricity consumption is affected by many factors, such as economic development [8], population [9], power facilities [10] and climate factors [11], and thus the data sequence of electricity consumption often presents to be highly nonlinear, stochastic, time-changeable,

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Section: Background and Motivationmentioning

confidence: 99%

Forecasting Electricity Consumption Using an Improved Grey Prediction Model

Zhang

2018

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“…With high performance of improving the grey models and innovative methodology, the FOA and FGM soon appealed considerable interest of research in nearly 5 years, and have been widely used in the realworld applications, such as the weapon system costs [38], gas emission [39], etc. According to Wu's results, the FOA can perform as an error reducer to the grey models [40], and the FGM is also effective in time series forecasting with small samples. It was noticed that the basic structure of the FGM models would not be changed when introducing the FOA, thus it can also be used for building other commonly used grey models.…”

Section: Introductionmentioning

confidence: 99%

The conformable fractional grey system model

et al. 2020

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The fractional order grey models (FGM) have appealed considerable interest of research in recent years due to its higher effectiveness and flexibility than the conventional grey models and other prediction models. However, the definitions of the fractional order accumulation (FOA) and difference (FOD) is computationally complex, which leads to difficulties for the theoretical analysis and applications. In this paper, the new definition of the FOA are proposed based on the definitions of Conformable Fractional Derivative, which is called the Conformable Fractional Accumulation (CFA), along with its inverse operation, the Conformable Fractional Difference (CFD). Then the new Conformable Fractional Grey Model (CFGM) based on CFA and CFD is introduced with detailed modelling procedures. The feasibility and simplicity and the CFGM are shown in the numerical example. And the at last the comprehensive real-world case studies of natural gas production forecasting in 11 countries are presented, and results show that the CFGM is much more effective than the existing FGM model in the 165 subcases.

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“…Numerical results show that the fractional grey prediction models have much higher precision than the traditional GM(1,1) model. Modeling mechanism of the fractional grey models has been studied, see [17,29,35,[39][40][41].…”

Section: Introductionmentioning

confidence: 99%

A Novel Weighted Fractional GM(1,1) Model and Its Applications

et al. 2020

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Based on the ideas of the new information priority principle and the fractional-accumulation generating operator, in this paper we propose a novel weighted fractional GM(1,1) (WFGM(1,1)) prediction model. In the new model, the original sequence is first transformed by using the weighted fractional-accumulation generating operator, which involves two parameters. With special choices of these parameters, the proposed WFGM(1,1) model reduces to the classical GM(1,1) model and the fractional GM(1,1) (FGM(1,1)) model, as well as the new information priority GM(1,1) (NIPGM(1,1)) model studied recently. Stability property of the WFGM(1,1) model is studied in detail. In practice, the quantum particle swarm optimization algorithm is adopted to choose the quasi-optimal parameters for the new model so as to get the best fitting accuracy. Finally, four numerical examples from different practical applications are present. Numerical results show that the new proposed prediction model is very efficient and has both the best fitting accuracy and the best prediction accuracy compared with the GM(1,1) and the FGM(1,1) as well as the NIPGM(1,1) prediction models.

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Using fractional order accumulation to reduce errors from inverse accumulated generating operator of grey model

Cited by 64 publications

References 18 publications

Forecasting Electricity Consumption Using an Improved Grey Prediction Model

Forecasting Electricity Consumption Using an Improved Grey Prediction Model

The conformable fractional grey system model

A Novel Weighted Fractional GM(1,1) Model and Its Applications

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