Properties of the GM(1,1) with fractional order accumulation

Wu, Lifeng; Liu, Sifeng; Fang, Zhigeng; Xu, Haiyan

doi:10.1016/j.amc.2014.12.014

Cited by 88 publications

(56 citation statements)

References 16 publications

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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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Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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“…The computational results demonstrated that the novel model outperformed the conventional GM(1,1) model. Later, Wu and his peers successfully applied fractional accumulation to the fuel production of China [41], tourism demand [42] and electricity consumption [43]. Subsequently, Xiao et al [44] studied the GM (1,1) model, in which they regarded the fractional accumulated generator matrix as a type of generalised accumulated generating operation.…”

Section: Introductionmentioning

confidence: 99%

Application of the novel fractional grey model FAGMO(1,1,k) to predict China's nuclear energy consumption

Wu¹,

Ma²,

Zeng³

et al. 2018

Energy

103

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At present, the energy structure of China is shifting towards cleaner and lower amounts of carbon fuel, driven by environmental needs and technological advances. Nuclear energy, which is one of the major low-carbon resources, plays a key role in China's clean energy development. To formulate appropriate energy policies, it is necessary to conduct reliable forecasts. This paper discusses the nuclear energy consumption of China by means of a novel fractional grey model FAGMO(1,1,k). The fractional accumulated generating matrix is introduced to analyse the fractional grey model properties. Thereafter, the modelling procedures of the FAGMO(1,1,k) are presented in detail, along with the transforms of its optimal parameters. A stochastic testing scheme is provided to validate the accuracy and properties of the optimal parameters of the FAGMO (1,1,k). Finally, this model is used to forecast China's nuclear energy consumption and the results demonstrate that the FAGMO(1,1,k) model provides accurate prediction, outperforming other grey models.

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“…The superiority of GMs over conventional statistical models manifests in the fact that only a limited amount of non-negative data is needed to predict the systems' behaviors without mathematical models. Grey forecasting models have been widely used in various problems such as foreign currency exchange rates [21], environmental pollution [22], power load [23], policy effectiveness [24], unemployment rates [25], and energy consumption [26]. Furthermore, the sliding mechanism was applied to improve the predicting accuracy of the original GM by updating the input data, and an optimization algorithm was used to optimize the adjustment coefficients of GMs during the sliding process [27].…”

Section: B Contributions Of the Studymentioning

confidence: 99%

A Novel State-of-Charge Estimation Method of Lithium-Ion Batteries Combining the Grey Model and Genetic Algorithms

Chen

Wang

Liu

et al. 2018

IEEE Trans. Power Electron.

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Abstract-In order to guarantee safe and reliable operation of electric vehicle batteries and to optimise their energy and capacity utilisation, it is indispensable to estimate their state-of-charge (SoC). This study aimed to develop a novel estimation approach based on the Grey model and Genetic Algorithms without the need of a high-fidelity battery model demanding high computation power. A SoC analytical model was established using the Grey System theory based on a limited amount of incomplete data in contrast to conventional methods. The model was further improved by applying a sliding window mechanism to adjust the model parameters according to the evolving operating status and conditions. In addition, the Genetic Algorithms were introduced to identify the optimal adjustment coefficient, λ, in a traditional Grey model (1, 1) model to further improve the source estimation accuracy. For experimental verification, two types of Lithium-ion batteries were used as the device-under-test that underwent typical passenger car driving cycles. The proposed SoC estimation method were verified under diverse battery discharging conditions and it demonstrated superior accuracy and repeatability compared to the benchmarking GM method.

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Properties of the GM(1,1) with fractional order accumulation

Cited by 88 publications

References 16 publications

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

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

Application of the novel fractional grey model FAGMO(1,1,k) to predict China's nuclear energy consumption

A Novel State-of-Charge Estimation Method of Lithium-Ion Batteries Combining the Grey Model and Genetic Algorithms

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