## 3 Application Results and Discussion
### Estimation of RCCP Mechanical Characteristics Using Classification-Based Regression Methods  
Application of the decision tree classification system, which is based on artificial intelligence, is a recent method proposed for solving engineering problems. The final properties of models are recaptured on the basis of network calibration. Then, the network can generalize those learned in a similar condition [67]. In the present study, the modelling methods included are four classification-based regression methods, namely RF, CHAID, M5 rule, and M5 prime, which were explored for the prediction of the characteristics of RCCP.  
Definition of the matrix, consisting of _CA, FA, SCM, W, B_, and _AS_ datasets, indicated the independent variables, and the dependent variables were CS, TS, and FS, which were used in each decision tree-based regression model. RF, M5 rule, and M5p were performed using WEKA 3.9 and CHAID was implemented using STATISTICA software on an AMD A-12 9700, 10-core 2.5 GHz computer system.  
To implement the _RF_ model, the default Bagger algorithm was used with bag size percent set to 200, leaf number was set to eight, and delta criterion set to 0.1007. No mathematical formulation was utilized to fine the optimum number of trees. Commonly, a larger number of trees produces more precise results, but increases computational cost.  
The M5 tree procedure for simulation of RCCP properties was generated using a set of tuning parameters to initialize the proposed model. A pruning factor of 4.0 and smoothing option were selected to evaluate the performance of the M5 model towards proposing the mathematical linear formulations for RCCP. After classifying, the developed M5p model, consisting of six input variables and three output variables, was used for simulation of CS, TS, and FS of RCCP using 12, 18, and 3 rules, respectively. The proposed models have the optimum number of decision trees (linear models (LMs)) as this value achieves the lowest error in the training stage. These LMs (rules), on the basis of conditional sentences, are illustrated in Figure 3. Furthermore, the estimated CS, TS, and FS values are presented for AS smaller and greater than 10.5, 21, and 17.5 respectively, as in the M5p rule. Estimated coefficients for LMs based on proposed mathematical linear equation of RCCP properties (i.e., CS, TS, and FS) are presented in Tables A1-A3 in Appendix A. All inputs were included in the simulation of the mechanical characteristics of RCCP; they are significant in implementation of the developed LMs.  
other ensemble tree-based techniques, such as CHAID (R = 0.925, NSE = 0.857 and RSD = 2.570 MPa). Moreover, the M5 rule model attained lower performance in terms of R (0.855), NSE (0.731), RSME (74.480 MPa), and RSD (5.460 MPa) than M5p (R = 0.896, NSE = 0.797, RSME = 56.142 MPa, and RSD = 4.122 MPa).  
In the testing phase, it is obvious that the CS values simulated by RF performed the best with the highest NSE (0.931) and lowest RSD (1.181 MPa) values in comparison with other ML methods. Figure 5 plots the observed and simulated CS of RCCP and their relative error using the tree-based techniques. The estimated CS of RF and CHAID models were in coherence with the observed data points. However, RF could only roughly simulate extreme CS values.  
Figure 4: Scatter plots of observed and simulated CS values for training (light color) and testing (dark color) of the proposed models.  
Figure 3: Tree diagram of the proposed M5p model; (**A**) CS, (**B**) TS, (**C**) FS.