## 5 Results
The \(\gamma\) shows the scatter of data in the same manner as the mean square error or standard deviation. These parameters determine the control quality in the most intuitive way, but their values are significantly different from the day to day values. Changes in the power signal cause variations in the operating point which introduces noise into the whole facility. By analysing the power waveforms and the errors in the vacuum maintenance system, a certain correlation of trends is observed. The noise and control signal characteristics were analysed and the sum of the signal changes for each hour and for each day were counted. The best fit to the control error is shown by the fuel change signal calculated for the day, as shown in Figure 8.  
The results over 20 days for the calculated mean absolute error (MAE) and mean squared error (MSE) are shown in Table 1. The max/min ratio shows that the same metric can vary by almost 2 times for the MAE and by more than 4 times for the MSE. A simple normalization was proposed as a first step to reduce the variation. Both the MAE and MSE were normalized. For each day, the MAE and MSE were divided by the sum of the fuel signal changes from that day (FUEL_changes(\(day\))) and multiplied by the average value of fuel signal changes counted for 20 days (FUEL_changes(\(20 days\))), see Equation (10). \[\text{MAE}_{n}(day)=\frac{\text{MAE}(day)\cdot\text{mean}(\text{FUEL\_changes (20 days)})}{\text{FUEL\_changes(day)}} \tag{10}\]  
Additionally, the normalized \(\text{MSE}_{n}\) is used as an analogical metric (11)  
\[\text{MSE}_{n}(day)=\frac{\text{MSE}(day)\cdot\text{mean}(\text{FUEL\_changes (20 days)})}{\text{FUEL\_changes(day)}} \tag{11}\]  
Table 1 shows the minimum, maximum and standard deviation for 20 days, calculated for the normalized indexes \(\text{MAE}_{n}\) and \(\text{MSE}_{n}\). The value of the normalized metric has less variability for individual days. The max/min ratio is reduced to 1.5924 for \(\text{MAE}_{n}\) and 1.9882 for \(\text{MSE}_{n}\). The results for each day are presented in Figure 5:0 \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **Min** & **Max** & **Max/Min** & **Standard Deviation** \\ \hline \multirow{3}{*}{direct} & MAE & 0.0222 & 0.0436 & 1.9563 & 0.0055 \\  & MSE & 0.0008 & 0.0034 & 4.2332 & 0.0007 \\ \hline \multirow{2}{*}{normalized} & \(\text{MAE}_{n}\) & 0.0023 & 0.0370 & 1.5940 & 0.0044 \\  & \(\text{MSE}_{n}\) & 0.0012 & 0.0023 & 1.9882 & 0.0003 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Obtained statistics for 20 days of operation: direct and normalized. Figure 8: Sum of changes for the steam and fuel signals (disturbance variables). Based on these early results, it can be concluded that normalization allows for more reliable monitoring of the regulation quality considering the variability of the operating conditions. The study used data recorded over 20 days and counted the average for the period. When running the proposed method in an online mode, the number of days should be long enough for the obtained average to be stable. The window length over which the average is calculated is a tuning parameter, and there is no optimal value for all cases. The value depends on the nature of the leading variables and how the process is run. The presented approach requires verification on other control loops and more data collection from the plant.