## 4 Results and Discussion
### Building of Stress-Strain Relationship Model  
#### 4.2.1 Development of the Proposed Models  
The primary target is to develop stress-strain models that are based on the PSO approach's ability to predict the best matching parameters. It is well established that models developed utilizing soft-computing exhibit predictive capability within the data range used in their creation. The amount of data that may be gathered is of paramount importance, since it has a substantial impact on the trustworthiness of the resulting models. The entire database was partitioned into a building dataset and a validation dataset for post-construction validation. A 24 (80%) of the 30 tested concrete combinations were used  
Figure 7: Compressive strength. to develop the model, while the remaining six testing samples (20%) were used to verify the suggested model. The minimum ratio of objects to specified variables is three for model acceptability. Scholars claim that a value of five is more secure [42]. In this study, the adopted ratio is 30/3, or about ten, which is significantly greater than the stated threshold. The PSO method was run by obtaining the aimd function for 40, 60, 80, and 100 swarms using the PSO parameter settings stated in Section 3.2.1 as displayed in Figure 10. The PSO method is able to pick the swarms with the smallest error and the shortest time by implementing several swarms. With the RMSE as an objective function, a suitable goal was chosen. As a result, four different swarms of varying sizes were evaluated. When the given convergence condition is met, the PSO search strategy continues. According to the results in Figure 10, the search became stable after 4100 iterations since the goal functions could only handle a maximum of 5000 iterations. To find the swarms with the lowest error and fastest convergence, a variety of swarms were tested. As shown in Figure 10, the optimal solution for the PSO method is achieved by using 100 swarms. According to the proposed model, variables that have optimum coefficients are shown in Table 6. Per the data in the table, the stress-strain relationship predicted by the suggested model is accurate. To demonstrate its accuracy and consistency, as depicted in Figure 11, the acceptable model predicts output with an average value of 0.93, standard deviation of 0.122, and covariance of 12.67%. In addition, the following final description of the proposed model is obtained after rounding the coefficients for simplicity and replacing them into Equations (4)-(8):  
\[f^{\prime}_{HFRC}=1.54\;f^{\prime}_{c}-0.0024\;(RI_{\text{ws}})^{1.09}+6\;(RI_ {\text{wp}})^{9.17} \tag{9}\]  
\[\varepsilon^{\prime}_{HFRC}=0.031\;\varepsilon^{\prime}_{c}+0.82\;RI_{\text{ws }}-38.45\;RI_{\text{wp}} \tag{10}\]  
\[\beta=-0.29+80.39(RI_{\text{ws}})^{31.42}-23.51\big{(}RI_{\text{wp}}\big{)}^{61.91} \tag{11}\]  
\[\frac{f_{HFRC}}{f^{\prime}_{HFRC}}=\left[\frac{-6.40\beta\Big{(}\frac{ \varepsilon}{\varepsilon_{o}}\Big{)}}{-4.31\beta-0.09+\Big{(}\frac{ \varepsilon}{\varepsilon_{o}}\Big{)}^{-17.86\beta}}\right] \tag{12}\]  
Figure 8: Maximum strain. Figure 9: Stress-strain curves of cubic specimens with various fiber content percentages. Based on these factors, a model's performance can be evaluated using the following criteria [44; 45]: