Generalized fractional grey system models: The memory effects perspective.

In recent years, grey models based on fractional-order accumulation and/or derivatives have attracted considerable research interest because they offer better performance in handling limited samples with uncertainty than integer-order grey models; however, there remains room for improvement. This paper considers a more flexible and general structure for the fractional grey model by incorporating a generalized fractional-order derivative (GFOD) that complies by memory effects, resulting in the development of a generalized fractional grey model (denoted as GFGM(1,1)). Specifically, we comprehensively analyse the modelling mechanism of the proposed GFGM(1,1) model, involving model parameter estimation and time response function derivation, and discuss the link between the proposed approach and existing special cases. Then, to further improve the efficacy of the proposed approach, four mainstream metaheuristic algorithms are employed to ascertain the orders of fractional accumulation and derivatives. Finally, we carry out a series of simulation studies and a real-world application case to demonstrate the applicability and advantage of the our approach. The numerical results show that GFGM(1,1) outperforms other benchmarks, and some significant insights are obtained from the numerical experiments.

[1]  Chong Liu,et al.  Continuous grey model with conformable fractional derivative , 2020, 2008.00803.

[2]  Mohammed Bennamoun,et al.  Linear Regression for Face Recognition , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Dingyu Xue,et al.  An actual load forecasting methodology by interval grey modeling based on the fractional calculus. , 2017, ISA transactions.

[4]  Somvir Singh Nain,et al.  Performance evaluation of fuzzy-logic and BP-ANN methods for WEDM of aeronautics super alloy , 2018, MethodsX.

[5]  Deng Ju-Long,et al.  Control problems of grey systems , 1982 .

[6]  Chong Liu,et al.  Forecasting fuel combustion-related CO2 emissions by a novel continuous fractional nonlinear grey Bernoulli model with grey wolf optimizer , 2020, Environmental Science and Pollution Research.

[7]  Chengli Zheng,et al.  Predictive analysis of quarterly electricity consumption via a novel seasonal fractional nonhomogeneous discrete grey model: A case of Hubei in China , 2021 .

[8]  Wenqing Wu,et al.  Forecasting short-term renewable energy consumption of China using a novel fractional nonlinear grey Bernoulli model , 2019, Renewable Energy.

[9]  Xinping Xiao,et al.  A novel fractional grey system model and its application , 2016 .

[10]  Lifeng Wu,et al.  Forecasting the renewable energy consumption of the European countries by an adjacent non-homogeneous grey model , 2021, Applied Mathematical Modelling.

[11]  Yanli Xiao,et al.  Using a novel multivariable grey model to forecast the electricity consumption of Shandong Province in China , 2018 .

[12]  Shu-hua Mao,et al.  Fractional derivative multivariable grey model for nonstationary sequence and its application , 2020, Journal of Systems Engineering and Electronics.

[13]  Andrew Lewis,et al.  The Whale Optimization Algorithm , 2016, Adv. Eng. Softw..

[14]  Julong Deng,et al.  Essential topics on grey system : theory and applications : a project supported by National Natural Science Foundation of China , 1988 .

[15]  Wenqing Wu,et al.  Application of the novel fractional grey model FAGMO(1,1,k) to predict China's nuclear energy consumption , 2018, Energy.

[16]  Andrew Lewis,et al.  Grey Wolf Optimizer , 2014, Adv. Eng. Softw..

[17]  B. Walczak,et al.  Particle swarm optimization (PSO). A tutorial , 2015 .

[18]  Peng Jiang,et al.  Forecasting tourism demand by incorporating neural networks into Grey–Markov models , 2019, J. Oper. Res. Soc..

[19]  Yanhui Chen,et al.  A novel grey wave forecasting method for predicting metal prices , 2016 .

[20]  Wai Keung Wong,et al.  A seasonal discrete grey forecasting model for fashion retailing , 2014, Knowl. Based Syst..

[21]  Hsien-Che Lai,et al.  A variable P value rolling Grey forecasting model for Taiwan semiconductor industry production , 2005 .

[22]  C. Lewis.  Industrial and business forecasting methods : a practical guide to exponential smoothing and curve fitting , 1982 .

[23]  Mark Goh,et al.  Parameter optimization for nonlinear grey Bernoulli model on biomass energy consumption prediction , 2020, Appl. Soft Comput..

[24]  Zhang Yong-hong,et al.  Variable order fractional grey model and its application , 2021 .

[25]  Jianghui Wen,et al.  Fractal derivative fractional grey Riccati model and its application , 2021 .

[26]  Yan Chen,et al.  An unequal adjacent grey forecasting air pollution urban model , 2021 .

[27]  Weijie Zhou,et al.  A novel discrete grey seasonal model and its applications , 2020, Commun. Nonlinear Sci. Numer. Simul..

[28]  Naiming Xie,et al.  A nonlinear grey forecasting model with double shape parameters and its application , 2019, Appl. Math. Comput..

[29]  Jianliang Wang,et al.  Predicting monthly natural gas production in China using a novel grey seasonal model with particle swarm optimization , 2021, Energy.

[30]  Bangzhu Zhu,et al.  Forecast of biofuel production and consumption in top CO2 emitting countries using a novel grey model , 2020 .

[31]  Xiang-Sun Zhang,et al.  Introduction to Artificial Neural Network , 2000 .

[32]  Shuo-Pei Chen,et al.  Forecasting of foreign exchange rates of Taiwan’s major trading partners by novel nonlinear Grey Bernoulli model NGBM(1, 1) , 2008 .

[33]  Chaoqing Yuan,et al.  On novel grey forecasting model based on non-homogeneous index sequence , 2013 .

[34]  Sifeng Liu,et al.  Grey system model with the fractional order accumulation , 2013, Commun. Nonlinear Sci. Numer. Simul..

[35]  G. Lugosi,et al.  On the Strong Universal Consistency of Nearest Neighbor Regression Function Estimates , 1994 .

[36]  R. Rajesh,et al.  Forecasting supply chain resilience performance using grey prediction , 2016, Electron. Commer. Res. Appl..

[37]  M. Goh,et al.  A novel fractional grey Riccati model for carbon emission prediction , 2020 .

[38]  Liang Zeng,et al.  A novel discrete grey Riccati model and its application , 2020, Grey Syst. Theory Appl..

[39]  Yong Wang,et al.  The novel fractional discrete multivariate grey system model and its applications , 2019, Applied Mathematical Modelling.

[40]  Sifeng Liu,et al.  Discrete grey forecasting model and its optimization , 2009 .

[41]  Dazhi Zhao,et al.  Representations of acting processes and memory effects: General fractional derivative and its application to theory of heat conduction with finite wave speeds , 2019, Appl. Math. Comput..

[42]  Bo Zeng,et al.  A new-structure grey Verhulst model: Development and performance comparison , 2020 .

[43]  Li Ye,et al.  A novel time-delay multivariate grey model for impact analysis of CO2 emissions from China’s transportation sectors , 2021 .

[44]  Wu Lifeng,et al.  Fractional Hausdorff grey model and its properties , 2020 .

[45]  Naiming Xie,et al.  On unified framework for discrete-time grey models: Extensions and applications. , 2020, ISA transactions.

[46]  Xinping Xiao,et al.  Fractional grey model based on non-singular exponential kernel and its application in the prediction of electronic waste precious metal content. , 2020, ISA transactions.

[47]  Xin Ma,et al.  A novel Grey Bernoulli model for short-term natural gas consumption forecasting , 2020 .

[48]  Lifeng Wu,et al.  The damping accumulated grey model and its application , 2021, Commun. Nonlinear Sci. Numer. Simul..

[49]  Wenqing Wu,et al.  The conformable fractional grey system model. , 2018, ISA transactions.

[51]  Yanhui Chen,et al.  Multi-step-ahead crude oil price forecasting using a hybrid grey wave model , 2018, Physica A: Statistical Mechanics and its Applications.

[52]  Mohd Saqib.  Forecasting COVID-19 outbreak progression using hybrid polynomial-Bayesian ridge regression model , 2020, Applied Intelligence.

[53]  Zheng-xin Wang,et al.  Grey forecasting method of quarterly hydropower production in China based on a data grouping approach , 2017 .

[54]  Xin Ma,et al.  A novel fractional time delayed grey model with Grey Wolf Optimizer and its applications in forecasting the natural gas and coal consumption in Chongqing China , 2019, Energy.

[55]  Zheng-xin Wang,et al.  A seasonal GM(1,1) model for forecasting the electricity consumption of the primary economic sectors , 2018, Energy.

[56]  Dingyu Xue,et al.  Continuous fractional-order grey model and electricity prediction research based on the observation error feedback , 2016 .

[57]  Song Ding,et al.  A novel adaptive discrete grey model with time-varying parameters for long-term photovoltaic power generation forecasting , 2021 .

[58]  Yaoguo Dang,et al.  Using a self-adaptive grey fractional weighted model to forecast Jiangsu’s electricity consumption in China , 2020 .

[59]  Yong Wang,et al.  A novel conformable fractional non-homogeneous grey model for forecasting carbon dioxide emissions of BRICS countries. , 2019, The Science of the total environment.

[60]  Nannan Ma,et al.  Optimize production allocation for the oil-gas field basing on a novel grey model , 2019, Journal of Natural Gas Geoscience.

[61]  Tzu-Li Tien,et al.  The indirect measurement of tensile strength of material by the grey prediction model GMC(1, n) , 2005 .

[62]  Mark Goh,et al.  A novel grey Riccati-Bernoulli model and its application for the clean energy consumption prediction , 2020, Eng. Appl. Artif. Intell..

[63]  Zheng-Xin Wang,et al.  A novel grey prediction model based on quantile regression , 2020, Commun. Nonlinear Sci. Numer. Simul..

[64]  Shuhua Mao,et al.  An improved seasonal rolling grey forecasting model using a cycle truncation accumulated generating operation for traffic flow , 2017 .

[65]  Seyed Mohammad Mirjalili,et al.  The Ant Lion Optimizer , 2015, Adv. Eng. Softw..

[66]  Jiao-feng Pan,et al.  Application of a novel discrete grey model for forecasting natural gas consumption: A case study of Jiangsu Province in China , 2020, Energy.

[67]  Tao Liu,et al.  Grey system theory trends from 1991 to 2018: a bibliometric analysis and visualization , 2019, Scientometrics.

[68]  Roshdi Khalil,et al.  SOLUTION OF SOME CONFORMABLE FRACTIONAL DIFFERENTIAL EQUATIONS , 2015 .

[69]  Tzu-Li Tien,et al.  A research on the grey prediction model GM(1, n) , 2012, Appl. Math. Comput..

[70]  Xinping Xiao,et al.  A new grey model for traffic flow mechanics , 2020, Eng. Appl. Artif. Intell..

[71]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[72]  Wei Cui,et al.  Non-homogenous discrete grey model with fractional-order accumulation , 2014, Neural Computing and Applications.

[73]  Yingjie Yang,et al.  Using a novel multi-variable grey model to forecast the electricity consumption of Shandong Province in China , 2018 .

[74]  Chong Liu,et al.  APPLICATION OF OPTIMIZED FRACTIONAL GREY MODEL-BASED VARIABLE BACKGROUND VALUE TO PREDICT ELECTRICITY CONSUMPTION , 2020 .

[75]  Naiming Xie,et al.  Parameter estimation for grey system models: A nonlinear least squares perspective , 2021, Commun. Nonlinear Sci. Numer. Simul..