In this study, a new adaptive conformable fractional order grey prediction model with a time power term is constructed to further advance the field of grey prediction. In the modeling process, the discretization operation and ridge regression are considered to optimize the unbiasedness and adaptive performance of the model, respectively. Then, the particle swarm optimization is used to search for suitable hyperparameters. The research findings reveal that the proposed model possesses both uniformity and unbiasedness, highlighting its theoretical superiority. To verify the effectiveness of the proposed method, the real case is used. Experimental results show that the proposed method is superior to all benchmark algorithms, which verifies its effectiveness.
ChenJ.HuY.ZhuQ.RashidH.LiH. (2023). A novel battery health indicator and PSO-LSSVR for LiFePO4 battery SOH estimation during constant current charging. Energy, 282, 128782. https://doi.org/10.1016/j.energy.2023.128782
2.
ChenY.LianyiW.LiuL. Y.KaiZ. (2020). Fractional Hausdorff grey model and its properties. Chaos, Solitons & Fractals, 138, 109915. https://doi.org/10.1016/j.chaos.2020.109915
HoerlA. E.KennardR. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55–67.
5.
IzadyaraN.OngaH.ShamshirbandS.GhadamianH.TongC. W. (2015). Intelligent forecasting of residential heating demand for the District Heating System based on the monthly overall natural gas consumption. Energy and Buildings, 104, 208–214. https://doi.org/10.1016/j.enbuild.2015.07.006
LaoT. F.SunY. R. (2022). Predicting the production and consumption of natural gas in China by using a new grey forecasting method. Mathematics and Computers in Simulation, 202, 295–315. https://doi.org/10.1016/j.matcom.2022.05.023
8.
LiM. W.XuR. Z.YangZ. Y.HongW.-C.AnX.-G.YehY.-H. (2024). Optimization approach of berth-quay crane-truck allocation by the tide, environment and uncertainty factors based on chaos quantum adaptive seagull optimization algorithm. Applied Soft Computing, 152, 111197. https://doi.org/10.1016/j.asoc.2023.111197
9.
LiuC.LaoT. F.WuW. Z.XieW.ZhuH. (2022). An optimized nonlinear grey Bernoulli prediction model and its application in natural gas production. Expert Systems with Applications, 194, 116448. https://doi.org/10.1016/j.eswa.2021.116448
10.
LiuX. M.LiS. H.GaoM. N. (2024). A discrete time-varying grey Fourier model with fractional order terms for electricity consumption forecast. Energy, 296, 131065. https://doi.org/10.1016/j.energy.2024.131065
11.
LiuC.WuW. Z.XieW. L.ZhangT.ZhangJ. (2021b). Forecasting natural gas consumption of China by using a novel fractional grey model with time power term. Energy Reports, 7(3), 788–797. https://doi.org/10.1016/j.egyr.2021.01.082
MaX.XieM.WuW. Q.ZengB.WangY.WuX. X. (2019). The novel fractional discrete multivariate grey system model and its applications. Applied Mathematical Modelling, 70, 402–424. https://doi.org/10.1016/j.apm.2019.01.039
14.
QianW. Y.DangY. G.LiuS. F. (2012). Grey GM(1,1,t() model with time power and its application. Systems Engineering - Theory & Practice, 32(10), 2247–2252.
15.
ŞahinU.ChenY. (2023). Assessing the current and future effects of COVID-19 on energy related-CO2 emissions in the United States using seasonal fractional grey model. Energy Strategy Reviews, 50, 101234. https://doi.org/10.1016/j.esr.2023.101234
16.
SaxenaA. (2023). Optimized fractional overhead power term polynomial grey model (OFOPGM) for market clearing price prediction. Electric Power Systems Research, 214, 108800. https://doi.org/10.1016/j.epsr.2022.108800
17.
WangW.YangR.ZhangJ.SunL.XiaoW.SaxenaA. (2024). A novel structure adaptive discrete grey Bernoulli prediction model and its applications in energy consumption and production. Energy, 291, 130368. https://doi.org/10.1016/j.energy.2024.130368
18.
WuL. F.LiuS. F.CuiW.YaoT.-X. (2014a). Non-homogenous discrete grey model with fractional-order accumulation. Neural Computing and Applications, 25(5), 1215–1221. https://doi.org/10.1007/s00521-014-1605-1
19.
WuL.LiuS.YaoL. (2014b). Discrete grey model based on fractional order accumulate. Systems Engineering-Theory & Practice, 34, 1822–1827.
20.
WuL. F.LiuS. F.YaoL. G.YanS.LiuD. (2013). Grey system model with the fractional order accumulation. Communications in Nonlinear Science and Numerical Simulation, 18, 1775–1785. https://doi.org/10.1016/j.cnsns.2012.11.017
21.
WuW. Q.MaX.ZengB.ZhangY.LiW. (2020). Forecasting short-term solar energy generation in Asia Pacific using a nonlinear grey Bernoulli model with time power term. Energy & Environment, 32, 0958305X2096070.
22.
XieN. M.LiuS. F. (2005). Discrete GM(1,1) and mechanism of grey forecasting model. Systems Engineering - Theory & Practice, 25(1), 93–99.
23.
XieN. M.LiuS. F.YangY. J.YuanC.-Q. (2013). On novel grey forecasting model based on non-homogeneous index sequence. Applied Mathematical Modelling, 37(7), 5059–5068. https://doi.org/10.1016/j.apm.2012.10.037
24.
XuJ.WuW. Z.LiuC.XieW.ZhangT. (2024). An extensive conformable fractional grey model and its application. Chaos, Solitons & Fractals, 182, 114746. https://doi.org/10.1016/j.chaos.2024.114746
25.
YanS. L.SuQ.WuL. F.XiongP. (2023). A damping grey multivariable model and its application in online public opinion prediction. Engineering Applications of Artificial Intelligence, 118, 105661. https://doi.org/10.1016/j.engappai.2022.105661
