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

Table 15

Evaluation result of different grey models for fitting and forecasting China’s residential thermal energy consumption in Case 2.

Fitting	GM(1,1)	ARGM	DGM	NGM	NIGM	FGM(1,1)	SAIGM	GM(1,1,)
RMSE	1117.216715	1084.839675	1117.196143	9369.107976	1008.424292	1112.393086	995.4137672	2159.813561
MAE	833.481874	774.6359237	831.2695007	4997.562392	727.3628862	644.5599287	739.7103295	1676.346441
NRMSE	0.000311765	0.008800034	0.000138821	0.21331217	4.44E − 16	0.005034	2.05E − 05	0.054996175
MAPE	1.309080795	1.26220759	1.305378066	8.486704395	1.196710704	1.046859636	1.198515175	2.688266118
RMSPE	1.762923227	1.821901401	1.764262819	16.38324835	1.673963545	1.83762531	1.632581987	3.487383104
MSE	1248173.188	1176877.121	1248127.222	87780184.26	1016919.552	1237418.377	990848.5679	4664794.619
IA	0.991453209	0.991823554	0.991452721	0.70140632	0.99308751	0.991283835	0.993269893	0.971417611
U1	0.008969537	0.008695398	0.00896862	0.077822239	0.008095409	0.008923061	0.00799091	0.017509782
U2	0.017936366	0.017416568	0.017936035	0.150416426	0.016189757	0.017858925	0.015980879	0.034674746
Prediction	GM(1,1)	ARGM	DGM	NGM	NIGM	FGM(1,1)	SAIGM	GM(1,1,)
RMSE	7127.875052	15537.08007	7138.65228	21828.1977	14334.23205	10884.47247	13027.7043	2666.27728
MAE	6579.37576	14174.77901	6588.258311	20426.62949	13043.67981	10068.06587	11830.2122	2461.54694
NRMSE	0.167934454	0.361802375	0.168161176	0.521376951	0.332931775	0.256981089	0.301958773	0.06282945
MAPE	7.297904145	15.66808266	7.307428738	22.72386382	14.40941604	11.1683294	13.06301736	2.74950079
RMSPE	7.69811988	16.70857475	7.709280273	23.69867698	15.40101991	11.76115179	13.9871564	2.91164244
MSE	50806602.76	241400857	50960356.37	476470215	205470208.5	118471740.9	169721079.4	7109034.54
IA	0.770969645	0.473466789	0.770285171	0.372333584	0.502732671	0.618658116	0.538683921	0.96778228
U1	0.042144608	0.096270537	0.042210649	0.140714021	0.088194495	0.065740224	0.079555449	0.01537902
U2	0.081048357	0.176666229	0.0811709	0.248200135	0.162989102	0.123763197	0.148133072	0.03031723