## 4 Results and Discussion
### Comparison Between the Training and Synthetic Data
#### 3.2.3 Case Study 3: Generation of Synthetic Power Consumption Data for a Printing House  
The third case study concerns the power consumption of a printing house. Using the same methodology, the probabilistic and statistical measures of the generated data with different numbers of states are summarized in Figure 12.  
It can be seen that both Frobenius distances had their lowest average values at 10, 11, and 12 states. Thereafter, they had local minimums at 22 and 25 states. It can be noticed that in all cases, they did not surpass 0.4. Analogous observations can be made for the average hourly and hour-change \(R^{2}\) coefficients, which did not fall below 0.94 and 0.95, respectively. The variance changed between 10% and 19% and had local minimums at 11,  
Figure 11: Seven days of sample data from the original time series for a pig house (**a**), and from the generated synthetic data for 12 states (**b**), 17 states (**c**), and 23 states (**d**).  
16, and 22 states. Similarly, the standard deviation changed between 5% and 10% and had local minimums at 11, 16, and 22 states.  
Considering the abovementioned, the following situations were selected for closer examination (Table 4):  
* the generated data with 11 states, for which all indicators have peaks or close-to-optimal values;
* the generated data with 16 states, for which the statistical measures have local minimums and the probabilistic measures are close to optimal;
* the generated data with 22 states, for which the Frobenius distances and the \(R^{2}\) coefficients have local peaks, and the statistical measures have minimums.  
It can be seen that the metrics for the three cases were very similar, and once again, the probabilistic ones became slightly worse with the increase in the number of states, while the statistical ones improved. Therefore, seven days of data were generated for each scenario to get a better understanding of their performance (Figure 13). The main problem that can be observed with fewer states was the wider scattering of the data for non-working hours, when it should have been close to zero. The problem was mitigated for the situation with 22 states, which can be explained by the narrower width of the zone. Once again, it can be  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metric** & \begin{tabular}{c} **Synthetic Data** \\ **with 11 States** \\ \end{tabular} & \begin{tabular}{c} **Synthetic Data** \\ **for 16 States** \\ \end{tabular} & \
\begin{tabular}{c} **Synthetic Data** \\ **for 22 States** \\ \end{tabular} \\ \hline
\begin{tabular}{c} Average Frobenius distance of the \\ hourly matrices (F.avg h) \\ Average Frobenius distance of the \\ hour-change matrices (F.avg h-ch) \\ Average \(R^{2}\) of the hourly matrices \\ (R^{2}.avg h) \\ Average \(R^{2}\) of the hour-change \\ matrices (R^{2}.avg h-ch) \\ Relative error of the variance \\ (\(\sigma^{2}\).rel.diff) \\ Relative error of the standard \\ deviation (\(\sigma\).rel.diff) \\ \end{tabular} & 0.12 & 0.21 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison between the metrics of the three generated datasets of the industrial consumer with 11, 16, and 22 states.  
Figure 12: Dependency of the average Frobenius distances, average \(R^{2}\)s, the relative differences of variance, and standard deviation for the different number of states of the synthetic data for a printing house.  
concluded that when the evaluation metrics are similar, it is better to generate the synthetic data with a higher number of states.