A Novel Power-Driven Grey Model with Whale Optimization Algorithm and Its Application in Forecasting the Residential Energy Consumption in China

Table 12

Evaluation result of different grey models for fitting and forecasting China’s total residential energy consumption in Case 1.

Fitting	GM(1,1)	ARGM	DGM	NGM	NIGM	FGM(1,1)	SAIGM	GM(1,1,)
RMSE	390.9308897	592.0396847	390.5257193	4998.407423	433.8786898	393.6339653	366.3717398	729.3183711
MAE	304.3361034	454.5790022	305.3384416	3115.451246	359.0785841	264.2156166	266.0438679	555.9520645
NRMSE	0.001442512	0.034214153	0.000188067	0.215925463	3.43E − 16	0.001570568	3.22E − 05	0.04351679
MAPE	0.917567213	1.41907916	0.923604391	10.00319848	1.17303263	0.838592869	0.833461064	1.695028338
RMSPE	1.219447364	1.958309635	1.219282349	17.31812039	1.471344436	1.287221758	1.186116654	2.227857299
MSE	152826.9605	350510.9882	152510.3374	24984076.77	188250.7174	154947.6986	134228.2517	531905.2864
IA	0.998469768	0.996464675	0.998474462	0.832432082	0.998113113	0.99844636	0.998656649	0.994674042
U1	0.005725206	0.008618064	0.005717969	0.07547321	0.006352639	0.005765005	0.005364149	0.010598626
U2	0.011447175	0.01733601	0.011435311	0.146362557	0.012704766	0.011526326	0.010728038	0.021355782
Prediction	GM(1,1)	ARGM	DGM	NGM	NIGM	FGM(1,1)	SAIGM	GM(1,1,)
RMSE	1129.146983	3095.192957	1147.235089	8999.707111	2574.222417	1881.723156	2346.09186	547.909444
MAE	1027.709741	2664.610899	1037.636147	8817.91821	2104.938825	1507.948278	1922.28879	448.704651
NRMSE	0.02676036	0.096930345	0.027692398	0.320768731	0.076571197	0.054778092	0.069926951	0.0163225
MAPE	2.123843293	5.478528089	2.143125482	18.4001908	4.309109234	3.083818646	3.936570679	0.94784892
RMSPE	2.307063232	6.299170718	2.343113335	18.64536826	5.227933254	3.828372361	4.768440944	1.16691584
MSE	1274972.909	9580219.441	1316148.349	80994728.08	6626621.053	3540882.034	5504147.015	300204.759
IA	0.941388626	0.738632316	0.939683635	0.267264603	0.797293581	0.866620632	0.819041097	0.9797724
U1	0.011752671	0.031568432	0.011937749	0.104105989	0.026407079	0.019427025	0.024114228	0.00577616
U2	0.02369601	0.064954984	0.024075603	0.188865715	0.05402202	0.039489395	0.049234526	0.0114983