## 4 Discussion  
For the first experiment (Section 3.1), the results shown in Table 4 indicate that the models using 60-min aggregation are the ones that best fit the data. Note that in this experiment, the target to be estimated is a slowly varying temperature with a dynamic range of variation from 0 \({}^{\circ}\)C to 55 \({}^{\circ}\)C. In this case, the model fits very well, possibly due to the fact that one of the input variables is also a temperature value in the same transmission chain, as shown in Figure 7, although the dynamic range of the target is from 0 \({}^{\circ}\)C to 55 \({}^{\circ}\)C, for the input variable the range is from 10 \({}^{\circ}\)C to 70 \({}^{\circ}\)C (see Figure 3). Another way to visually observe the results presented in Table 4 is by means of the regression line obtained when training and testing a model. Figure 9 compares, for the WT#81, the regression line obtained using 5-min and 60-min data. As can be seen, the best adjustment is obtained when using 60-min data, with a regression value of \(R=0.99745\), while \(R=0.99682\) using 5-min data. When these models are tested with the second half of the available data, the difference is even more visible in favour of the model using 60-min data. In Figure 10, the curve on the left shows the line obtained in the test of the 5-min model, obtaining a regression value of \(R=0.9224\), while on the right the 60-min model obtains a better result with \(R=0.9487\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{RMSE} \\ \hline  & **WT\_id** & **5 min** & **10 min** & **15 min** & **30 min** & **60 min** \\ \hline \multirow{4}{*}{**Training**} & 80 & 3.2367 & 3.1966 & 3.1894 & 3.0865 & **2.9774** \\  & 81 & 2.6836 & 2.6648 & 2.6396 & 2.5883 & **2.5166** \\  & 82 & 4.5850 & 4.6142 & 4.5633 & 4.4968 & **4.3784** \\  & 83 & 3.1191 & 3.1055 & 3.0547 & 3.0083 & **2.9019** \\ \hline \multirow{4}{*}{**Test**} & 80 & 4.0724 & 3.9918 & 3.9882 & 3.8870 & **3.7598** \\  & 81 & 5.0538 & 5.0294 & 5.0006 & 4.8525 & **4.6026** \\ \cline{1-1}  & 82 & 4.8108 & 4.7921 & 4.7446 & 4.6730 & **4.5200** \\ \cline{1-1}  & 83 & 4.6635 & 4.6540 & 4.5470 & 4.4431 & **4.2168** \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results obtained by averaging the RMSE of 25 models both in the training and test steps when trained with data of different temporal aggregation. In all cases, the trained network is a SLFN with 40 hidden nodes. The minimum values, highlighted in bold, are obtained when 60-min time aggregation is used in all WTs. Notice that now the results are less accurate than those in Table 3.  
This same result can be visualised in terms of the deviation of the regression lines of the output data with respect to the 45-degree line that would represent the perfect estimation. Note that in these two representations the data and target axes have been extended beyond the dynamic range of the data in order, first, to make the deviation of the regression lines more evident and, second and more importantly, to show how the two models detect the presence of inconsistent values between the prediction made of the target and the measurement obtained from it. This happens when the variables are changing because of a failure (warning or alarm), which generates a bad estimation detected by our normality model, or are due to a miss-function of some sensor. Indeed, in some cases the problem is due to a failure of the sensors that is particularly difficult to detect in other ways. It occurs when the signals are'stuck' and the sensor sends the same value every 5 min. This can happen both in the variables and in the target. This type of failure is not detected by the outlier tests, and hence it is transparent in the pre-processing stages, but the normality model can allow one to detect them. Results obtained for experiment 2 (Section 3.2) show that 60-min aggregation obtains the best results in all the cases, except for a couple of cases in which 30-min aggregation is proven to be better, only for the WT#80.