## 5 The Experiments and Discussion
To model the vertical data partition across process facilities, the following data preprocessing were implemented:  
* grouping data by the technological processes based on the sensors' names because initial data do not contain information on the technological processes;
* data normalization;
* removing timestamps due to the type of the analysis model;
* data partitioning on the test and training samples followed by stratification i.e., preserving the class structure of labels in datasets. Table 1 shows that the partition of the data across the nodes as well as a description of sensor types designated to different process facilities. The labels are stored on the aggregation server. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Client** & **No. of Parameters** & **List of Parameters** & **Description of Parameters** \\ \hline \multirow{3}{*}{Process facility PF1} & \multirow{3}{*}{5} & FIT101 & \\  & & LIT101 & \\  & & MV101 & \\  & & P101, P102 & \\ \hline \multirow{3}{*}{Process facility PF2} & \multirow{3}{*}{11} & AIT201, AIT202, AIT203, & \\  & & MV201 & \\  & & P201, P202, P203, P204, P205, P206 & \\ \hline \multirow{3}{*}{Process facility PF3} & \multirow{3}{*}{9} & DPIT301 & FIT–Flow Meter \\  & & FIT301 & LIT–Level Transmitter \\  & & LIT301 & MV–Motorized Valve \\  & & MV301, MV302, MV303, MV304 & P–Pomp \\  & & P301, P302 & AIT—Analyzer \\ \hline \multirow{3}{*}{Process facility PF4} & \multirow{3}{*}{9} & AIT401, AIT402, & PIT–Pressure Meter \\  & & FIT401, & DPI—Differential Pressure \\  & & LIT401 & Indicating Transmitter \\  & & P401, P402, P403, P404 & UV—Dechlorinator \\  & & UV401 & \\ \hline \multirow{3}{*}{Process facility PF5} & \multirow{3}{*}{13} & AIT501, AIT502, AIT503, AIT504 & \\  & & FIT501, FIT502, FIT503, FIT504 & P501, P20 \\ \cline{1-1}  & & PIT501, PIT502, PIT503 & \\ \hline \multirow{3}{*}{Process facility PF6} & \multirow{3}{*}{4} & FIT601, & \\  & & P601, P602, P603 & \\ \hline Aggregation server & \multirow{3}{*}{1} & AIT501, AIT502, AIT503, AIT504 & \\  & & FIT501, FIT502, FIT503, FIT504 & \\ \cline{1-1}  & & P501, P20 & \\ \hline \multirow{3}{*}{Process facility PF5} & \multirow{3}{*}{13} & FIT601, & \\ \cline{1-1}  & & P601, P602, P603 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The partition of SWaT dataset parameters among process facilities. Tables 2 and 3 provide the results of the conducted experiments. Table 2 shows the results of training the GBDT model in federated mode. During this series of experiments, the authors changed the settings of the SecureBoost algorithm by varying the number of constructed trees and types of encryption algorithms. When training in a federated mode, we also measured the time of the training and inference process. The authors also performed the experiments with a centralized machine learning model to compare the accuracy of the obtained models (Table 3). The settings of the GBDT model were similar; to train and test the model, the initial data set was split in a ratio of 0.7 to 0.3. The training was performed using the scikit-learn library [50]. The experiments demonstrated that the obtained accuracy is comparable with the results of GBDT in the case of centralized learning: as the number of trees increases, the accuracy increases. However, the training time is measured in hours, while training decision trees in centralized manner takes less than 1 min. It is also clearly seen that the training time of the model also depends linearly on the number of trees. The use of a fast implementation of the homomorphic encryption algorithm can significantly speed up the training process (up to three times). The gain in training time increases with an increase in the number of trees, but the accuracy of training decreases in this case. Figure 4 summarizes obtained results and shows the comparison of the accuracy of the gradient boosting decision tree constructed in a centralized and decentralized manner, and shows the duration of training process in the federated mode for different encryption settings.