# Misalignment Fault Prediction of Wind Turbines Based on Combined Forecasting Model
## 4 Fault Prediction Results and Discussion
### Fault Prediction Results and Discussion of Current Signal  
#### 4.2.1 The Results of IMGM (1, _n_)  
The collected 60 current signal samples are also divided into the first 45 samples and the last 15 samples according to the ratio of 3:1. The first 45 samples are also used to construct an IMGM (1, _n_) prediction model. Eleven feature parameters of the current signal are used as inputs and the kurtosis is used as output. The indexes of the posteriori error test of current signal are listed in Table 10.  
In Table 10, MGM (1,11) is barely qualified grade and IMGM (1,11) belongs to the qualified grade. Therefore, IMGM (1,11) is more suitable for predicting the kurtosis of the current signal than MGM (1,11). The prediction results of MGM (1,11) and IMGM (1,11) of the current signal are shown in Figure 6.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & \(C\) & \(P\) & **Precision Grade** \\ \hline MGM (1,11) & 0.6378 & 0.7632 & Barely qualified \\ IMGM (1,11) & 0.4002 & 0.8857 & Qualified \\ \hline \hline \end{tabular}
\end{table}
Table 10: The precision grade of MGM (1,11) and IMGM (1,11) for the current signal.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Data Set** & **RMSE** & **MAE** & \(\mathbf{R^{2}}\) & **Time(s)** \\ \hline \multirow{2}{*}{Combined prediction} & Training Set & 0.0179 & 0.0150 & 0.9973 & \multirow{2}{*}{1.6025} \\  & **Testing Set** & **0.0840** & **0.0688** & **0.9100** & \\ \hline \multirow{2}{*}{QGA\_LSSVM} & Training Set & 0.0148 & 0.0118 & 0.9981 & \multirow{2}{*}{1.8286} \\  & **Testing Set** & **0.1175** & **0.0975** & **0.7229** & \\ \hline \multirow{2}{*}{IMGM (1,9)} & Fitted values & 0.1959 & 0.1232 & 0.9053 & \multirow{2}{*}{1.6780} \\  & **Predicted values** & **0.4349** & **0.3358** & **0.5673** & \\ \hline \hline \end{tabular}
\end{table}
Table 9: The forecasting evaluation indexes of the vibration signal.  
By comparing the prediction results in Figure 6a,b, the predicted fluctuation range of IMGM (1,11) is obviously smaller than that of MGM (1,11). It is because when predicting the last 15 points, the data used to establish the MGM (1,11) has always been the first 45 points, and the data has not been updated with the increase prediction steps. However, the modelling data of IMGM (1,11) is updated by adding the actual value corresponding to the previous step of the current prediction point. The modelling data is updated every time the model outputs one predicted value. Hence, when predicting the kurtosis of a current signal with a large rising slope, the IMGM (1,11) has significantly better prediction accuracy than that of MGM (1,11). The forecasting evaluation indexes of IMGM (1,11) and MGM (1,11) are listed in Table 11. For the fitted values, the RMSE of IMGM (1,11) is nearly the same to that of MGM (1,11), while the MAE and \(R^{2}\) of IMGM (1,11) in the table is better than those of MGM (1,11). For the predicted values, the RMSE, MAE and running time of the IMGM (1,11) are smaller than those of MGM (1,11). The \(R^{2}\) of IMGM (1,11) is much larger than that of MGM (1,11). Therefore, compared with MGM (1,11), IMGM (1,11) improves the prediction accuracy and stability of the current signal, and it can be one of the single prediction models input to the combined forecasting model for current signal.