Mathematical Problems in Engineering / 2016 / Article / Tab 11 / Research Article
Multistep Wind Speed Forecasting Using a Novel Model Hybridizing Singular Spectrum Analysis, Modified Intelligent Optimization, and Rolling Elman Neural Network Table 11 Performance evaluations of different models for the forecast of the one-hour wind speed series.
ā Error ARIMA BPNN RENN SSA-RENN SSA-PSO-RENN Proposed model ā ARIMA BPNN RENN SSA-RENN SSA-PSO-RENN Proposed model Spring 1-step MSE (m/s) 5.1762 4.5464 4.8944 1.6948 1.7761 1.5977 2-step 6.9013 5.7573 6.2777 2.6703 2.9233 2.3518 MAE (m/s) 1.8581 1.6491 1.7513 0.9221 0.9017 0.901 2.1454 1.8997 2.0602 1.1652 1.2252 1.0835 MAPE (%) 16.8 16.74 17.32 8.93 8.75 8.7 20.99 20.01 20.9 12 12.57 11.05 3-step MSE (m/s) 9.0442 6.9167 7.7342 3.7011 4.254 3.2441 5-step 12.4765 9.1089 10.1619 6.6403 7.6275 5.6975 MAE (m/s) 2.4758 2.069 2.2768 1.4621 1.5986 1.3514 2.9377 2.3763 2.613 1.9783 2.1813 1.8934 MAPE (%) 24.77 21.93 23.21 15.41 16.77 13.9 30.67 25.29 26.97 21.39 23.78 19.61 Summer 1-step MSE (m/s) 0.3986 0.2957 0.2727 0.2522 0.2437 0.2103 2-step 0.4336 0.3453 0.3165 0.3076 0.3052 0.24 MAE (m/s) 0.5323 0.453 0.4444 0.3861 0.3732 0.3495 0.5385 0.4741 0.4624 0.426 0.424 0.3665 MAPE (%) 15.19 13.55 13.48 11.67 11.34 10.63 15.31 14.32 14.24 12.81 12.89 11.11 3-step MSE (m/s) 0.4829 0.4236 0.3905 0.3509 0.3731 0.2917 5-step 0.5605 0.5792 0.5214 0.3982 0.4984 0.4136 MAE (m/s) 0.5713 0.5104 0.5026 0.4644 0.4754 0.4148 0.6208 0.6001 0.5815 0.5018 0.5576 0.5049 MAPE (%) 16.8 16 16.11 14.23 14.87 12.9 18.5 19.34 19.28 15.74 18.08 16.34 Fall 1-step MSE (m/s) 0.7161 0.54 0.5012 0.4865 0.4872 0.4901 2-step 0.8772 0.7482 0.6455 0.586 0.5816 0.5957 MAE (m/s) 0.7168 0.5844 0.5675 0.5727 0.5731 0.5733 0.7821 0.7098 0.6587 0.6175 0.6137 0.621 MAPE (%) 15.59 12.24 11.82 11.79 11.82 11.82 16.94 14.88 13.75 12.77 12.72 12.85 3-step MSE (m/s) 0.9588 0.8908 0.7079 0.6657 0.6553 0.68 5-step 0.8706 1.1014 0.7552 0.752 0.7259 0.7747 MAE (m/s) 0.8032 0.7729 0.6902 0.6707 0.6666 0.676 0.7562 0.8413 0.7071 0.703 0.6959 0.7108 MAPE (%) 17.46 16.3 14.46 13.91 13.86 14.03 16.41 18.06 15.04 14.51 14.43 14.7 Winter 1-step MSE (m/s) 1.6137 0.6872 0.6367 0.5746 0.5758 0.5683 2-step 2.079 0.7809 0.7208 0.6903 0.6766 0.678 MAE (m/s) 1.0548 0.6464 0.6414 0.641 0.6314 0.6306 1.1227 0.7051 0.7027 0.7059 0.6933 0.6993 MAPE (%) 21.17 12.57 12.5 12.31 12.03 12.02 23.1 14.09 13.95 13.77 13.45 13.55 3-step MSE (m/s) 2.4407 0.8516 0.781 0.7784 0.7552 0.7616 5-step 3.1868 0.9485 0.869 0.821 0.8172 0.816 MAE (m/s) 1.204 0.74 0.7345 0.7416 0.718 0.7279 1.3773 0.774 0.7643 0.7534 0.7495 0.7516 MAPE (%) 24.88 15.01 14.71 14.52 13.99 14.15 27.5 15.91 15.38 14.73 14.49 14.5