## 4 Results
The assessed probability is an added value for operational planning and day-to-day scheduling purposes. For the purpose of applying SVM-based classification to a real-life dataset describing formwork assembly works, this study assumed a critical value of \(x_{c}=Me\). Note that \(Me\) was taken separately for each element type (column, wall, or slab) according to the fitted triangular distributions. It is also important to note that for \(Me\), it can be assessed that the probability of achieving an efficiency greater than \(Me\) is 0.5, and the same probability would be for achieving an efficiency lower than \(Me\). Based on these assumptions, all cases in the dataset were labelled as follows:  
* A (above the median value) for efficiency \(>Me\),
* B (below the median value) for efficiency \(<Me\). Thus, for the purpose of supervised training, two classes, A or B, were defined to represent \(y_{i}\). It is important to mention that the vector \(x_{i}\) consisted of eight variables, namely \"Element\", \"Level\", \"Number of workers\", \"Gang experience and skills\", \"Duration\", \"Temperature\", \"Falls\", and \"Day of the week\", as presented in Table 2. SVM models for classification problem type 1 (Equations (7) and (8)), as well as type 2 (Equations (9) and (10)), were trained using the TIBCO(r) Statistic(tm) 13.3 software suite (developed by TIBCO Software Inc. 3307 Hillview Avenue, Palo Alto, CA 94304, USA, distributed by StatSoft Polska Sp. z o.o., 30-110 Cracow, Kraszewskiego 36, Poland). Before initiating the training, the dataset was randomly divided into training and testing subsets in the ratio of 70% to 30%, respectively. All variable values were automatically scaled for the purpose of SVM training. The models' parameters were determined using the grid method and 10-fold cross-validation, with a maximum of 2000 epochs for the training process. For the purposes of cross-validation, the dataset was randomly divided into 10 equal-sized subsets. In each fold, a single subset was retained as the validating data, and the remaining 9 subsets were used for training. The cross-validation process was repeated ten times for each point on the grid, which was defined by the lower and upper boundary of parameter values and the step size. The goal was to find the optimal value of the \(C\) parameter for the type 1 and \(\
u\) parameter for the type 2 SVM-based classification. The considered range of parameters, including lower and upper boundary values and the step size, is presented in Table 9.  
The considered kernel functions \(\varphi\) included: polynomial, Gaussian radial basis and sigmoid. The best results and performance, however, were obtained in the case of the Gaussian radial basis kernel function implementation. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Element** & \(x_{c}\) & \(P(X>x_{c})\) & **Number of Workers** & **Duration 1 [Hours /Day]** & **Total Quantity 1 [m2]** \\ \hline COLUMN & 0.8 & 0.798 & 2 & 8 h & 12.8 m2 \\  & 1.0 & 0.667 & 2 & 8 h & 16 m2 \\  & 1.2 & 0.502 & 2 & 8 h & 19.2 m2 \\ WALL & 1.6 & 0.759 & 3 & 8.33 h & 40 m2 \\  & 1.8 & 0.641 & 3 & 7.41 h & 40 m2 \\  & 2.0 & 0.498 & 3 & 6.67 h & 40 m2 \\ SLAB & 1.2 & 0.827 & 5 & 7.5 h & 45 m2 \\  & 1.4 & 0.751 & 4 & 9 h & 50.4 m2 \\  & 1.6 & 0.661 & 3 & 6.5 h & 31.2 m2 \\ \hline \hline \end{tabular}  
* Some of the values were assumed and some computed; the latter are underlined.  
\end{table} 
Table 8: Results of probabilistic analysis for hypothetical critical values of formwork assembly works efficiencies. As a result of the supervised training, two SVM-based models were obtained--one for each of the classification problem types. The models are later referred to as SVMct1 (developed as a result of solving type 1 problem) and SVMct2 (developed as a result of solving type 2 problem).