# Fuzzy and Neural Network Approaches to Wind Turbine Fault Diagnosis
## 3 Data-Driven Strategies for Fault Diagnosis
### Fault Estimators via FS and NN Tools
This paper considers an alternative data-driven approach, which exploits NNs used as fault approximators in the scheme of Figure 2. Therefore, in the same way of the FSs, a bank of NNs is employed to reconstruct the faults affecting the WT system using a proper selection of the input and the output measurements. This NN structure consists of a feed-forward MLP architecture with 3 layers of neurons [19]. However, as MLP NNs represent static relations, the paper suggests to implement these structures with a tapped delay line. Therefore, this quasi-static NN represents a powerful way for estimating nonlinear dynamic regressions between the input and output measurements from the WT process and its fault functions. This solution allows to obtain another Nonlinear ARX (NARX) description among the data. Moreover, when properly trained, these NARX NNs are able to reconstruct the fault function \(\hat{f}(k)\) using a suitable selection of the past measurements of the WT system inputs and outputs \(u_{l}(k)\) and \(y_{j}(k)\), respectively. The example of the general solution is sketched in Figure 3, which can be implemented by means of FIS or NARX NN structures. Figure 3: General scheme for fault reconstruction. Similarly to the fuzzy scheme, with reference to the \(i\)-th fault reconstructor, a bank of NARX NNs is exploited, where the generic NARX system models the relation of Equation (9):  
\[\hat{f}(k)=F\big{(}\dots,\,u_{j}(k),\,\dots,\,u_{j}(k-d_{u}),\,\dots\,y_{l}(k-1), \,\dots,\,y_{l}(k-d_{y}),\,\dots\big{)} \tag{9}\]  
the signal \(\hat{f}(k)\) represents the estimate of the general \(i\)-th fault in Table 3, whilst \(u_{j}(\cdot)\) and \(y_{l}(\cdot)\) indicate the components of the measured inputs and outputs from the WT process. These signals are selected again by means of the solution of the fault sensitivity problem reported in Table 3. The accuracy of the fault reconstruction depends on the number of neurons per layer, their weights and their activation functions. In order to summarise the overall procedure exploited for the implementation of the FDI schemes, Figure 4 reports the different phases involved in the proposed methods and a summary of the complete design flows. In particular, once the measurements have been selected according to the procedure addressed in Section 2.3, the design of the FIS requires the clustering of the data into \(n_{C}\) regions, the selection of the model structure (order \(o\)) and the estimation of the consequent parameters \(\mathbf{a}_{i}\) and \(b_{i}\), as well as the membership functions \(\lambda_{i}\) in Equation (6). The data are usually divided into three sets, i.e., the training, the validation and the test sets. This solution leads to improve the estimation capabilities of the identified fuzzy prototypes. The FIS models can be thus organised into the bank structure that allows for fault isolation. Moreover, the fault identification is also accomplished. Figure 4: Tasks involved in the design of the proposed FDI schemes. On the other hand, the same procedure can be performed for the NARX NN models. After the measurement selection, the data are divided into the training, the validation and the test sets. Also in this case, this partition improves the generalisation capabilities of these systems. The derivation of the NARX NN prototypes requires the selection of the delays \(d_{u}\) and \(d_{y}\) in Equation (9), as well as the the number of neurons per layers. Once these NARX NN models are estimated, they can be organised into the bank structure for achieving the fault identification task. The results of the selection of the optimal structure of the fault reconstructors for FDI and the achieved performances will be shown in Section 4.