A Novel Fractional-Order Grey Prediction Model and Its Modeling Error Analysis

Meng, Wei; Zeng, Bo; Li, Shuliang

doi:10.3390/info10050167

Cited by 21 publications

(37 citation statements)

References 12 publications

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“…[ 5 ] . Assume that

is the original sequence,

is called the accumulating generation sequence with order “r” of

, where

…”

Section: Building the Optimal Fractional Order Grey Gm (11) Modelmentioning

confidence: 99%

“…[ 5 ] . Assume that

is the original sequence,

is called the accumulating generation sequence with order “r” of

is called the reducing generation sequence with order “r” of

, the accumulating generation operator and the reducing generation operator with order “r” are inverse operation, that is

…”

Section: Building the Optimal Fractional Order Grey Gm (11) Modelmentioning

confidence: 99%

“…[ 5 ] . Assume

is stated as Theorem 4,

, then The answer for the whitenization differential equation

of GM (1,1) model for fractional order operator, that is the time response function as follows:

The time response sequence for

of GM (1,1) model for fractional order operator is as follows:

The reduced value is as follows:

…”

Section: Building the Optimal Fractional Order Grey Gm (11) Modelmentioning

confidence: 99%

“…However, the grey prediction model based on the integer order cumulating generation method belongs to the integer order derivative model and it also belongs to the ideal memory model. Therefore, it is not suitable for describing some irregular phenomena [ 5 ]. In order to reveal the essential characteristics under behaviour of objects clearly, it is necessary to construct a more general fractional grey accumulating generation method.…”

Section: Introductionmentioning

confidence: 99%

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Forecasting the Amount of Waste-Sewage Water Discharged into the Yangtze River Basin Based on the Optimal Fractional Order Grey Model

Meng

Xie³

2017

IJERPH

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With the rapid development of the Yangtze River economic belt, the amount of waste-sewage water discharged into the Yangtze River basin increases sharply year by year, which has impeded the sustainable development of the Yangtze River basin. The water security along the Yangtze River basin is very important for China, It is something about water security of roughly one-third of China’s population and the sustainable development of the 19 provinces, municipalities and autonomous regions among the Yangtze River basin. Therefore, a scientific prediction of the amount of waste-sewage water discharged into Yangtze River basin has a positive significance on sustainable development of industry belt along with Yangtze River basin. This paper builds the fractional DWSGM (1,1) (DWSGM (1,1) model is short for Discharge amount of Waste Sewage Grey Model for one order equation and one variable) model based on the fractional accumulating generation operator and fractional reducing operator, and calculates the optimal order of “r” by using particle swarm optimization (PSO) algorithm for solving the minimum average relative simulation error. Meanwhile, the simulation performance of DWSGM (1,1) model with the optimal fractional order is tested by comparing the simulation results of grey prediction models with different orders. Finally, the optimal fractional order DWSGM (1,1) grey model is applied to predict the amount of waste-sewage water discharged into the Yangtze River basin, and corresponding countermeasures and suggestions are put forward through analyzing and comparing the prediction results. This paper has positive significance on enriching the fractional order modeling method of the grey system.

show abstract

“…[ 5 ] . Assume that

is the original sequence,

is called the accumulating generation sequence with order “r” of

, where

…”

Section: Building the Optimal Fractional Order Grey Gm (11) Modelmentioning

confidence: 99%

“…[ 5 ] . Assume that

is the original sequence,

is called the accumulating generation sequence with order “r” of

is called the reducing generation sequence with order “r” of

, the accumulating generation operator and the reducing generation operator with order “r” are inverse operation, that is

…”

Section: Building the Optimal Fractional Order Grey Gm (11) Modelmentioning

confidence: 99%

“…[ 5 ] . Assume

is stated as Theorem 4,

, then The answer for the whitenization differential equation

of GM (1,1) model for fractional order operator, that is the time response function as follows:

The time response sequence for

of GM (1,1) model for fractional order operator is as follows:

The reduced value is as follows:

…”

Section: Building the Optimal Fractional Order Grey Gm (11) Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Forecasting the Amount of Waste-Sewage Water Discharged into the Yangtze River Basin Based on the Optimal Fractional Order Grey Model

Meng

Xie³

2017

IJERPH

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, in Brazil, China, India, and South Africa, energy consumption exhibits positive growth rates. On the other hand, Russia is reducing its energy consumption, and it follows the global decreasing trend 1 .…”

Section: Introductionmentioning

confidence: 99%

Comparison of Forecasting Ability for Energy Consumption in BRICS: ARIMA (1,1,1) and FGM (1, 1) Models

Khan¹,

Osińska²

2021

Preprint

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Brazil, Russia, China, India, and the Republic of South Africa (BRICS) represent developing economies facing different energy and economic development challenges. The current study aims to forecast energy consumption in BRICS at aggregate and disaggregate levels using the annual time series data set from 1992 to 2019 and to compare results obtained from a set of models. The time-series data are from the British Petroleum (BP-2019) Statistical Review of World Energy. The forecasting methodology bases on a novel Fractional-order Grey Model (FGM) with different order parameters. This study contributes to the literature by comparing the forecasting accuracy and the forecasting ability of the FGM(1,1) with traditional ones, like standard GM(1,1) and ARIMA(1,1,1) models. Also, it illustrates the view of BRICS's nexus of energy consumption at aggregate and disaggregates levels using the latest available data set, which will provide a reliable and broader perspective. The Diebold-Mariano test results confirmed the equal predictive ability of FGM(1,1) for a specific range of order parameters and the ARIMA(1,1,1) model and the usefulness of both approaches for energy consumption efficient forecasting.

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Prediction of Water Consumption in 31 Provinces of China Based on FGM(1,1) Model

Qiao

Yang

2022

CLEAN Soil Air Water

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Human production activities and social development cannot be separated from the indispensable water resources. In recent years, with the increasing speed of China's economic development, the consumption of water resources has gradually become the focus of attention of the Chinese government and the public. Based on the original data of water use of 31 provinces (municipalities and autonomous regions) in China from 2014 to 2018, a fractional order accumulative gray prediction model (FGM(1,1)) is established to predict the water use of 31 provinces (municipalities and autonomous regions) in China in the short term, and the applicability of the model is verified by the mean absolute percentage error (MAPE) value. According to the MAPE value, the data obtained by the FGM(1,1) model is relatively accurate. The prediction results show that in case of little change in total water consumption, agricultural water and industrial water use show a downward trend, while domestic water use shows an upward trend. The government's water management policy for urban residents needs to be adjusted, and the publicity work to improve the water-saving awareness of urban residents needs to be improved.

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A Novel Fractional-Order Grey Prediction Model and Its Modeling Error Analysis

Cited by 21 publications

References 12 publications

Forecasting the Amount of Waste-Sewage Water Discharged into the Yangtze River Basin Based on the Optimal Fractional Order Grey Model

Forecasting the Amount of Waste-Sewage Water Discharged into the Yangtze River Basin Based on the Optimal Fractional Order Grey Model

Comparison of Forecasting Ability for Energy Consumption in BRICS: ARIMA (1,1,1) and FGM (1, 1) Models

Prediction of Water Consumption in 31 Provinces of China Based on FGM(1,1) Model

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