## 5 Results and Discussion
### Analysis on Input Parameters Selection for SVM--Dot Model  
To define the optimal functional type of regression models, the choice of input variables is central and crucial. The role of selecting input variables is common to the creation of most models of regression and depends on the discovery of relationships within the available data to identify acceptable model output predictors. The difficulty of the input variable selection task is somewhat alleviated in the case of parametric or semi-parametric empirical models by a-priori assumption of the model's functional form, which is based on some physical interpretation of the underlying system or process being modeled. In the case of ANN, however, there is no such inference about the model's structure. The input variables are instead chosen from the available data, and the model is subsequently developed [88]. Consequently, three different types of input variables are used, as seen in Table 4, to integrate flexibility and prevent duplication, providing a more reliable model of prediction. The results for variable input vectors in determining the correlation and consistency between predicted and measured crack widths are presented in Figure 12.  
Figure 11: The distribution of predicted results according to every split ratio (**a**) 70:30, (**b**) 75:25, and (**c**) 80:20. Several important parameters that were omitted for seven inputs resulted in overfitting (52-58%), due to the discrepancy of data between predicted and measured crack widths. The smaller number in sample size with the smaller number of inputs does not \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**List of Inputs**} & **7 Inputs Vector** & **9 Inputs Vector** & **11 Inputs Vector** \\  & **(X\({}_{1}\)–X\({}_{7}\))** & **(Y\({}_{1}\)–Y\({}_{9}\))** & **(Z\({}_{1}\)–Z\({}_{11}\))** \\ \hline \multirow{4}{*}{\begin{tabular}{c} \(\mathrm{A_{s}}\) \\ \(\mathrm{OL_{B/C}}\) \\ \(\mathrm{SSL_{B}}\) \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} \(\mathrm{A_{s}}\) \\ \(\mathrm{OL_{B/C}}\) \\ \(\mathrm{SSL_{B}}\) \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} \(\mathrm{OL_{B/C}}\) \\ \(\mathrm{SSL_{B}}\) \\ \(\mathrm{SSL_{C}}\) \\ \(\mathrm{AL}\) \\ \(\mathrm{C_{c}}\) \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} \(\mathrm{OL_{B/C}}\) \\ \(\mathrm{SSL_{B}}\) \\ \(\mathrm{C_{c}}\) \\ \(\mathrm{Q_{max(-ve)}}\) \\ \end{tabular} } \\  & & & \(\mathrm{Q_{max(-ve)}}\) \\ \hline Output & \multicolumn{2}{c}{Crack width (C.W.)} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Inputs variable vector (7, 9, and 11 inputs). Figure 12: The distribution of predicted results are dependent on inputs vector: (**a**) Seven inputs vector, (**b**) nine inputs vector, and (**c**) eleven inputs vector. effectively cover the prediction observed in the broader domain. This can seen in Figure 12a, where a large variance developed in the regression model based on the smaller number of inputs dataset. As seen in Figure 12b, the load parameter (\(\text{Q}_{\text{max(+ve)}}\) and \(\text{Q}_{\text{max(-ve)}}\)) played a significant role, thus showing how important the parameters are correlated in engineering terms to approach with experimental crack widths data. Even though the prediction model with nine inputs was sufficient (21-25% difference between measured to predicted), however in contrast to previous studies [63; 65], Figure 12c with additional concrete tensile strength (\(\text{C}_{\text{t}}\)) and reinforcement tensile strength (\(\text{T}_{\text{t}}\)) had proved that the smaller number of datasets with an increased number of inter-related inputs parameter had drawn back less than 20% consistency of predicted points varied and equally within above and under the reference lines. Several studies found it difficult to pick input variables because of the number of variables available; associations between possible input variables will establish overlap and variables with little or no predictive power [89; 90].