# Neural Network-Based Cost-Effective Estimation of Useful Variables to Improve Wind Turbine Control
## 3 Neural Network Based Estimators
### Estimation Results  
#### 3.3.1 Aerodynamic Torque  
Figures 6 and 7 show, in black, the aerodynamic torque estimated using the NN-based estimator for Scenario 1 in both the time (left column) and frequency (right column) domains, compared to that estimated using the conventional aerodynamic torque estimator (Section 3.1) (in blue) and the actual measurements (in red). Figures 6 and 7 show the results for Turbines 1 and 5, respectively, which were selected randomly because Turbines 2 to 4 produce similar results. In real world scenarios, the measurements would only be available from Turbine 1 (i.e., the turbine with the sensor); however, the measurements from Turbine 5 are also included for comparison purposes. Note that this also applies to Figures 8 and 9 for Scenario 2 and Figures 10 and 11 for Scenario 3 in the following:  
Figure 8: Scenario 2: Aerodynamic torque estimation from Turbine 1.  
Figure 7: Scenario 1: Aerodynamic torque estimation from Turbine 5.  
Figure 10: Scenario 3: Aerodynamic torque estimation from Turbine 1.  
Figure 9: Scenario 2: Aerodynamic torque estimation from Turbine 5.  
In Scenario 1, for both turbines, the time domain results demonstrate that the aerodynamic torque estimated by the NN-based estimator tracks the measurements more closely than that estimated by the conventional aerodynamic torque estimator; however, the improvement shown by the corresponding power spectra is not as significant.  
For Scenario 2, Figures 8 and 9 demonstrate similar results to those observed in Scenario 1 in the time-domain, that is, for both turbines, the aerodynamic torque estimated by the NN-based estimator tracks the measurements more closely than that estimated by the conventional aerodynamic torque estimator. The corresponding power spectra shown in Figures 8 and 9 illustrate that the aerodynamic torque estimated by the NN-based estimator tracks the measurements more closely than that estimated by the conventional aerodynamic torque estimator in the frequency domain. The power spectra also exhibit improved results compared to those of Scenario 1, which implies that the combination of variables used to train the NN in Scenario 2 is better than the combination used in Scenario 1.  
For Scenario 3, Figures 10 and 11 show similar results to those obtained for Scenarios 1 and 2 in the time domain, that is, for both turbines, the aerodynamic torque estimated by the NN-based estimator tracks the measurements more closely than that estimated by the conventional aerodynamic torque estimator in the time domain. The corresponding power spectra shown in Figures 8 and 9 demonstrate that the aerodynamic torque estimated by the NN-based estimator tracks the measurements more closely than that estimated by the conventional aerodynamic torque estimator in the frequency domain. In addition, the corresponding power spectra illustrate more improved results than those obtained in Scenarios 1 and 2, which indicates that the combination of variables used to train the NN in Scenario 3 is better than the combinations of variables used in Scenarios 1 and 2.  
Figure 11: Scenario 3: Aerodynamic torque estimation from Turbine 5.  
In summary, the NN-based estimator performs best in Scenario 3 (of Scenarios 1 to 3); that is, when fore-aft acceleration, rotor speed and TBM are used as the inputs to train the NN. The NN-based estimator outperforms the conventional aerodynamic torque estimator in each scenario, which could be due to the fact that the conventional aerodynamic torque estimator includes a low-pass filter as described by Equation (9), which is required to ensure that the estimator is practically feasible.