An Advanced Hybrid Forecasting System for Wind Speed Point Forecasting and Interval Forecasting
Table 7
Prediction performance comparison table of the proposed model and classic individual models.
Dataset
Model
One step
Two steps
MAE
MAPE
RMSE
MSE
DC
FICP
FINAW
AWD
MAE
MAPE
RMSE
MSE
DC
FICP
FINAW
AWD
Set 1
ARIMA
0.4011
9.5513
0.5344
0.2856
53.9249
63.9456
0.1042
0.1969
0.6462
15.7336
0.8202
0.6727
53.0822
41.9795
0.1042
0.4227
BPNN
0.4065
9.7395
0.5467
0.2989
53.9249
56.1224
0.1042
0.2433
0.5395
13.4091
0.7108
0.5052
55.1370
47.0990
0.0978
0.4435
ELMAN
0.5378
12.9708
0.6828
0.4662
51.5358
44.2177
0.1002
0.4116
0.6125
14.8276
0.7740
0.5990
51.7123
41.9795
0.1052
0.4647
GRNN
0.4559
11.4420
0.5919
0.3504
55.2901
46.9388
0.0941
0.3536
0.5698
14.4080
0.7385
0.5454
56.8493
38.2253
0.0887
0.6553
ELMNN
0.3976
9.6203
0.5314
0.2824
59.3857
59.5238
0.1015
0.2135
0.5391
13.3873
0.6952
0.4833
51.0274
44.3686
0.0967
0.4563
Proposed model
0.1648
3.8354
0.2284
0.0498
92.0139
93.4028
0.0984
0.0193
0.2435
5.6317
0.3329
0.1109
85.9589
83.2765
0.1284
0.0494
Set 2
ARIMA
0.5104
16.0071
0.7449
0.5549
53.9249
71.7687
0.1348
0.1530
0.8363
27.6248
1.1928
1.4228
52.0548
44.0273
0.1169
0.4541
BPNN
0.6360
26.6598
0.8468
0.7171
54.6075
48.6395
0.1221
0.3209
0.7450
27.5824
1.0728
1.1509
53.0822
47.4403
0.1265
0.4329
ELMAN
0.6979
22.7232
0.9921
0.9843
53.5836
50.0000
0.1175
0.3213
0.7994
26.1353
1.1322
1.2819
53.4247
46.0751
0.1178
0.4054
GRNN
0.6720
27.8385
0.9280
0.8612
54.6075
40.8163
0.0896
0.6960
0.7864
30.3558
1.0922
1.1928
55.1370
34.1297
0.0912
0.9722
ELMNN
0.4948
16.0898
0.7033
0.4946
68.6007
61.2245
0.1069
0.2164
0.7516
28.8463
1.0630
1.1299
54.7945
42.6621
0.1207
0.4272
Proposed model
0.2159
6.94987
0.3065
0.0937
90.2778
94.2177
0.1260
0.0128
0.3974
11.6754
0.5477
0.2999
80.4795
81.5700
0.1987
0.0533
Set 3
ARIMA
0.7076
20.4992
0.9131
0.8338
59.3857
59.5238
0.2155
0.2166
1.1537
33.8070
1.4614
2.1358
53.7671
37.8840
0.1978
0.4784
BPNN
0.7149
20.3467
0.9188
0.8442
56.3140
57.4830
0.2029
0.2235
0.9870
28.4973
1.2463
1.5532
53.7671
39.2491
0.1831
0.4745
ELMAN
0.9611
27.7013
1.2250
1.5005
56.6553
42.8571
0.1853
0.4171
1.3019
37.0247
1.6473
2.7137
57.1918
40.6143
0.2449
0.4282
GRNN
0.7658
23.3317
0.9823
0.9648
58.7031
48.9796
0.1773
0.3137
1.0044
31.0281
1.2558
1.5771
57.1918
33.7884
0.1629
0.6429
ELMNN
0.6912
20.5330
0.9017
0.8131
61.0922
60.2041
0.1983
0.2272
0.9731
29.5352
1.2352
1.5257
54.1096
40.2730
0.1863
0.4719
Proposed model
0.2946
8.2657
0.3794
0.1456
89.9305
94.5578
0.1860
0.0072
0.3655
9.6888
0.4736
0.2243
85.6164
88.7372
0.2349
0.0188
The most notable results are bolded. MAPE is the average of absolute percentage error. MAE is the mean absolute error of forecasting results. RMSE is the square root of the average of the error squares. MSE is mean squared error. DC is directional change. FICP is forecast interval coverage probability. FINAW is forecast interval normalized average width. AWD is accumulated width deviation of testing dataset.
