## 5 Results and Discussion  
### Comparison of Prediction Models from Rapidminer  
A sufficient list of numbers (\(\leq\)1000 data) of crack width data of seven RC beam-column joints was collected at every respective drift ratio level. The data were used for training and testing in the Rapidminer software based on the recommendations from literature as described in Section 4.1 [66]. Four different prediction models were developed and proposed as defined in Table 3 with potential input parameters.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**No** & **Model** & **Prediction Method** \\ \hline
1. & Deep learning (DL) & Max-out: Based on the maximum coordinate of the input vector. \\
2. & Deep learning (DL) & Rectifier: Rectifier Linear Unit (RLU), which chooses the maximum of (0, \(x\)) where x is the input value. \\
3. & Support Vector & Dot: The dot kernel is defined by \(k(x,y)=x\times y\), i.e., it is the inner product of \(x\) and \(y\). \\  & Machine (SVM) & Neural: The neural kernel is defined by a two-layered neural net \(\tanh\) (\(ax\times y+b\)), where a is alpha and b is the intercept constant. \\
4. & Support Vector & These parameters can be adjusted using the kernel \(a\) and kernel \(b\) \\  & Machine (SVM) & parameters. A common value for alpha is 1/N, where N is the data dimension. \\ \hline \hline \end{tabular}
\end{table}
Table 3: The details of four prediction models.  
Figure 9: The framework model applied for all four prediction models from Rapidminer machine learning.  
Figure 10 illustrates regression analysis plots for the distribution of predicted crack width. The figure includes the equity line as a guide, which for the predicted and measured crack widths reflects the state of equal value. The analysis shows that SVM model with dot prediction method presented better prediction with the smallest error, in which the distribution of predicted was below (27% error) and above (30% error) of the reference line compared to DL max-out (48% and 56%), DL rectifier (55% and 44%) and SVM--neural (29% and 48%). DL max-out and DL rectifier showed that almost all predicted points were distributed around the measured crack widths with the largest errors, due to over-fitting. These observed errors might be attributed to insufficient data as DL models require a large dataset for complex supported calculation/simulations [61; 72]. The accuracy of predicted crack widths by SVM--dot was consistently increased within equity line, thus demonstrating regression technique with input-output relationships. This was further supported by the regression technique developed for compressive strength and predicting autogenous shrinkage for concrete [62; 63]. Hence, in the field of machine learning, SVM is the best learning methodology for classification and regression tasks [79; 80; 81]. Though the SVM--neural showed a difference of 2%-18% from SVM--dot, however homogenous floats formed on top linear measured line at the area with more than 1.5 mm have shown uncorrelated and over-predicted values between the predicted and actual crack widths. Therefore, the SVM--dot model was selected for further analysis of optimization using data splitting, numbers of input parameters, and performance index and is described in the following sub-section.