An Advanced Hybrid Forecasting System for Wind Speed Point Forecasting and Interval Forecasting
Table 5
Prediction performance comparison table of the proposed model and hybrid models using the same data pretreatment technique.
Dataset
Model
One step
Two steps
MAE
MAPE
RMSE
MSE
DC
FICP
FINAW
AWD
MAE
MAPE
RMSE
MSE
DC
FICP
FINAW
AWD
Set 1
WACD-ARIMA
0.1662
3.9433
0.2296
0.0527
90.7850
89.4558
0.1017
0.0312
0.5469
12.9943
0.7321
0.5359
48.6301
53.5836
0.1074
0.3382
WACD-BPNN
0.1959
4.7382
0.2716
0.0737
85.6655
87.0748
0.1070
0.0412
0.4073
9.8769
0.5509
0.3035
56.1644
61.7747
0.1049
0.2207
WACD-GRNN
0.3930
9.5245
0.5161
0.2663
63.4812
55.1020
0.0899
0.2675
0.5288
12.8015
0.6925
0.4796
59.2466
42.6621
0.0836
0.5223
WACD-BILSTM
0.3165
7.0425
0.4150
0.1722
69.9659
65.9864
0.0946
0.1463
0.3312
7.9995
0.4088
0.1671
60.0683
66.6667
0.1060
0.0923
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
WACD-ARIMA
0.2273
7.3885
0.3126
0.0977
88.3959
90.1361
0.1346
0.0255
0.7532
24.1722
1.0796
1.1655
46.9178
51.1945
0.1373
0.2955
WACD-BPNN
0.3149
12.3639
0.4125
0.1702
80.5461
80.9524
0.1247
0.0480
0.6529
26.4495
0.8918
0.7954
56.1644
52.9010
0.1255
0.3144
WACD-GRNN
0.5112
17.3599
0.7541
0.5687
53.2423
69.7279
0.1418
0.1490
0.7939
32.0372
1.0743
1.1542
54.4521
31.7406
0.0849
1.4376
WACD-BILSTM
0.4272
12.8502
0.5800
0.3363
70.6485
72.1088
0.1276
0.0958
0.4335
14.7300
0.5962
0.3555
65.8703
72.1088
0.1282
0.1073
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
WACD-ARIMA
0.3021
8.7753
0.3828
0.1465
87.7133
84.6939
0.1904
0.0251
0.8911
25.1829
1.1431
1.3067
50.3425
49.1468
0.2216
0.2982
WACD-BPNN
0.3111
9.1970
0.3962
0.1570
87.7133
84.6939
0.1951
0.0196
0.5495
15.8400
0.7313
0.5347
75.6849
70.3072
0.2183
0.1445
WACD-GRNN
0.7059
18.9532
0.8934
0.7981
62.7986
46.9388
0.1650
0.2738
0.9215
25.7201
1.1458
1.3129
57.5342
33.1058
0.1515
0.5364
WACD-BILSTM
0.4087
10.8551
0.5195
0.2698
82.2526
74.4898
0.1758
0.0665
0.4533
11.8373
0.5721
0.3272
76.7918
73.1292
0.1872
0.0900
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. WACD is weight adaptive combined denoising. 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.
