# Improvement of ANFIS Model for Prediction of Compressive Strength of Manufactured Sand Concrete
## 4 Results and Discussions
### Comparison with Existing Models in the Literature  
In this section, the prediction performance of ANFIS-TLBO/P model is compared with existing formula in literature. In the work of [PERSON] et al. [14], an empirical equation has been proposed in order to estimate the MSC compressive strength based on the cement compressive strength at 28 days, the cement density and the water to cement ratio. Table 6 indicates the value of performance indicators such as R, RMSE, MAE, Error standard deviation and slope, using ANFIS-TLBO/P and the formula proposed by [PERSON] et al. [14]. The comparison is presented for 7, 28, 56 and all curing age, respectively. For other curing ages such as 14, 60, 70, 84, 90 and 180, the number of samples is lower than 10 and thus not be considered in the comparison. In Table 6, \(\Delta\) is the deviation (in %) of performance indicators between the present work ANFIS-TLBO/P model and [PERSON] et al. [14]. Noting that the values of \(\Delta\) with respect to R and slope were calculated based on the deviation around 1, whereas the values of \(\Delta\) corresponding to RMSE, MAE and Error Std were computed based on changes regarding zero, as indicated by the following equation:  
\[\Delta=\left\{\begin{array}{llllll}\left(\left(\lambda^{\text{our-model}}-1 \right)-\left(\lambda^{\text{original-model}}-1\right)\right)\times 100\text{ in case of : R, Slope}\\ \left(\left(\lambda^{\text{our-model}}-\lambda^{\text{other-model}}\right)/ \lambda^{\text{original-model}}\right)\times 100\text{ in case of : RMSE, MAE and Error}_{\text{std}}\end{array}\right. \tag{5}\]  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Curing Age** & **Model** & **R** & **RMSE** & **MAE** & **Error Std** & **Slope** \\ \hline \multirow{3}{*}{7 days} & [PERSON] et al. [14] (Equation (6) in [14]\({}^{*}\)) & 0.61 & 14.42 & 10.25 & 10.41 & 1.77 \\ \cline{2-8}  & Our model & 0.90 & 7.43 & 5.22 & 6.06 & 0.99 \\ \cline{2-8}  & \(\Delta\) (\%) & +29.00 & +48.49 & +49.03 & +41.78 & +76.00 \\ \hline \multirow{3}{*}{28 days} & [PERSON] et al. [14] (Equation (5)) & 0.92 & 5.31 & 4.44 & 5.32 & 0.94 \\ \cline{2-8}  & Our model & 0.95 & 5.20 & 4.08 & 5.18 & 0.87 \\ \cline{2-8}  & \(\Delta\) (\%) & +3.00 & +2.07 & +8.11 & +2.63 & \textIn cases of curing age of 7 and 28 days, the developed ANFIS-TLBO/P model provided better performance indicators than the proposed exponential functions in [PERSON] et al. [14]. In case of curing age of 56 days, negative effects were observed regarding to R and MAE. However, in terms of RMSE, error Std and slope, the proposed model gave the better prediction performance. Overall, from 3-388 days of curing age, the proposed ANFIS-TLBO/P model outperforms the empirical formulas in [PERSON] et al. [14], with respect to R, RMSE, MAE, error Std and slope. It is worth noticed that [PERSON] et al. [14] have optimized their equations based on only three variables, such as cement compressive strength at 28 days, cement density and water to cement ratio. Other factors have not been considered in the exponential equation form. Consequently, the influence of sand's characteristic, especially stone powder content, have not been investigated. In addition, it is worth mentioned that as reported in [PERSON] et al. [13], stone powder content in sand had a major effect on the compressive strength of MSC. Moreover, the impact of other sand's characteristics on the compressive behavior of MSC is also discussed in the works of [PERSON] et al. [1] and [PERSON] et al. [2]. In short, the ANFIS-TLBO/P model developed in this study provided better prediction capability of compressive strength of MSC than other approaches and models in taking into account the variation of sand's characteristics in the simulation.