# Fuzzy and Neural Network Approaches to Wind Turbine Fault Diagnosis
## 4 Simulation Results, Experimental Validation, Comparisons and Discussion
### Discussion and Final Remarks  
This section discusses the results shown in Section 4.2 relying on model-based and data-driven methods. In particular, the FS and NN models were compared to the SMO, the RFS and the NLGA-AF, already proposed for WTs, and applied to the considered benchmark. SMO was designed on the basis of a linearised model of the WT process. In this case, the design procedure is based on the selection of an appropriate switching manifold, and then on the determination of an input, including a discontinuous term, that ensures the sliding motion in this manifold. This strategy can manage disturbance and modelling errors, which represent the effect of both the linearisation and measurement errors. The RFS approach used a recursive identification method for synthesising the residual generators for FDI, under the assumption of LPV modes. In fact, the considered WT system has varying parameters caused by the nonlinearity of the aerodynamic relation along the nominal operating trajectory and due to the model uncertainty. In particular, the instantaneous partial derivatives of the aerodynamic torque are part of the linearised model and change along the nominal operating trajectory. These changes were approximated using an affine description in the wind speed. The NLGA-AF is obtained using differential geometry and nonlinear system analysis tools. In particular, the NLGA-AF methodology, which was developed for the more general problem of FDI, relies on adaptive filters designed with a nonlinear geometric approach to obtain the disturbance de-coupling property. In order to provide a brief but clear insight into the above mentioned techniques, the comparisons were performed in the same previous working conditions, and based on the RMSE index, when the realistic WT simulator is considered. It is worth noting that the FDI schemes implemented via SMO, FS and NN do not exploit any adaptation mechanism. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Fault Case** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline TS FSs & 1.69\% & 2.29\% & 2.01\% & 1.94\% & 1.99\% & 2.22\% & 1.81\% & 2.21\% & 2.03\% \\ NARX NN & 0.99\% & 0.98\% & 0.99\% & 1.28\% & 1.21\% & 1.69\% & 1.02\% & 1.01\% & 1.51\% \\ \hline NLGA-AF & 1.37\% & 1.45\% & 1.73\% & 1.75\% & 1.56\% & 1.99\% & 1.45\% & 1.54\% & 1.76\% \\ RFS & 1.99\% & 2.67\% & 2.44\% & 2.56\% & 2.67\% & 2.97\% & 2.23\% & 2.78\% & 2.82\% \\ SMO & 1.87\% & 1.82\% & 2.11\% & 2.01\% & 1.91\% & 2.34\% & 1.95\% & 2.08\% & 2.23\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: RMSE % index for the HIL analysis and comparisons. In fact, the SMO strategy is able to decouple the uncertainty via the sliding motion, whilst NNs and FSs were designed to passively tolerate disturbance and modelling errors via the acquired off-line learning. The comparisons among the different FDI solutions summarised in Table 7 highlighted that schemes using adaptive strategies, such as RFS and NLGA-AF, allowed to achieve acceptable performances in terms of estimation errors. The SMO solution can require considerable computational time with respect to the other solutions, without any parameter change, whilst the RFS strategy can lead to larger computational effort at the design stage. On the other hand, when the mathematical description of the monitored system can be perfectly obtained, in general model-based strategies such as NLGA-AF are preferred. However, when modelling errors and uncertainty are present, alternative schemes relying on adaptation mechanisms, or passive robust methods, showed interesting robustness properties in the presence of unmodelled disturbance, modelling mismatch, and measurement errors. With reference to data-driven methodologies, and in particular to FS and NN, in the case of a monitored system with modelling errors, the off-line learning can lead to very good results.