## 2 Materials and Methods
### Application and Analysis  
We allocated our variables into three subsets: the training, selection, and testing datasets. Overall, our dataset had 510 records, from which 306 records accounted for the training subset, 102 records for the selection subset, and 102 records for the testing subset. The training subset was 60% of the whole dataset, the selection subset 20%, and the testing subset 20%. Training and testing the datasets allowed us to feed the ANN with data and find out what the model's performance is. \begin{table}
\begin{tabular}{c c c c c} \hline
**Ordinal Number** & **Parameter** & **Codename** & **Type** & **Description** \\ \hline
1 & Foundation failure occurrence & foundations\_failure\_occurrence & target & Foundation failure: 1-yes, 0-no \\ \hline
2 & Machine failure occurrence & machine\_failure\_occurrence & input & Machine failure: 1-yes, 0-no \\ \hline
3 & Concrete cover thickness & cover\_thickness & input & Concrete cover thickness (cm) \\ \hline
4 & Machine gravity center distortion & gravity\_center\_distortion & input & Deviation of the foundation with the machine from the calculated center of gravity “e” (mm) \\ \hline
5 & Angular frequency of vertical self-excited vibrations & vibrations\_ar & input & Angular frequency of vertical self-excited vibrations \(var\) (s\({}^{-1}\)) \\ \hline
6 & Angular frequency of horizontal self-excited vibrations & vibrations\_as & input & Angular frequency of horizontal self-excited vibrations \(\varphi\) (s\({}^{-1}\)) \\ \hline
7 & Amplitudes of oscillation & vibrations\_at & input & (imulates of oscillation (\(x\)-\(y\) plane (imul)), the horizontal upper surface of the block \\ \hline
8 & Foundation area & fund\_area & input & Foundation area (m\({}^{2}\)) \\ \hline
9 & Foundation volume & fund\_volume & input & Foundation volume (m\({}^{3}\)) \\ \hline \end{tabular}
\end{table} 
Table 1: The parameters we adopted for our dataset. \begin{table}
\begin{tabular}{c c c c} \hline
**Input Features** & **Minimum (-)** & **Maximum (-)** & **Average (-)** \\ \hline Foundation failure occurrence & 0.00 & 1.00 & - \\ Machine failure occurrence & 0.00 & 1.00 & - \\ Concrete cover thickness & 2.00 & 5.00 & 3.89 \\ Machine gravity center distortion & 6.00 & 744.00 & 98.16 \\ Angular frequency of vertical self-excited vibrations & 73.13 & 147.72 & 118.96 \\ Angular frequency of horizontal self-excited vibrations & 61.18 & 123.59 & 99.53 \\ Amplitudes of oscillation & 0.04 & 36.51 & 4.87 \\ Foundation area & 0.60 & 25.20 & 2.76 \\ Foundation volume & 1.02 & 156.24 & 6.85 \\ \hline \end{tabular}
\end{table} 
Table 2: Ranges of database input and target features. In Figure 3, we show scatter plots that represent data from input variables in relation to the failure occurrence rate. Our dataset consisted of records corresponding to the individual foundations, with several parameters and information on whether the failure occurred: [1] means that the failure occurred, and [0] means that the failure did not happen. For the needs of our analysis, we found a correlation matrix and performed a logistic correlation. We also performed a principal components analysis to identify the underlying structure in the dataset to make a predictive model. In this procedure, we performed an orthogonal transformation to change a set of potentially correlated variables into a set of values of linearly uncorrelated variables. Simplifying this issue, we tried to find directions in which there was the most variance and where the data were most dispersed. The results of the analysis were determinations of principal components. In Figure 4, we present a cumulative sum of explained variance for the eight principal components. Figure 3: The scatter plots: targets versus input variables. The vertical axis is the foundation failure occurrence rate (FFOR—foundation failure occurrence rate; YES—failure occurred; NO—failure did not occur). The horizontal axis is the considered parameter, and the units depend on the parameter.