## Materials and Methods
### Description of Performance Indices  
To evaluate the accuracy of proposed estimator models, the performance indices such as mean square error (_RMSE_), Standardized Root Mean Square Error (SRMSE), mean absolute error (_MAE_),  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Models** & **Data** & \(d\) & \(a\) & \(a_{g}\) & \(fc\) & \(\rho\) & \(a\)/\(d\) & \(a_{g}\)/\(d\) \\ \hline Model-1 & Not Pre-processed & ✓ & ✓ & ✓ & ✓ & ✓ & - & - \\ \hline Model-2 & Not Pre-processed & - & ✓ & ✓ & ✓ & ✓ & - & - \\ \hline Model-3 & Not Pre-processed & ✓ & - & ✓ & ✓ & ✓ & - & - \\ \hline Model-4 & Not Pre-processed & ✓ & ✓ & - & ✓ & ✓ & - & - \\ \hline Model-5 & Not Pre-processed & ✓ & ✓ & ✓ & - & ✓ & - & - \\ \hline Model-6 & Not Pre-processed & ✓ & ✓ & ✓ & ✓ & - & - & - \\ \hline Model-7 & Pre-processed & ✓ & ✓ & ✓ & ✓ & ✓ & - & - \\ \hline Model-8 & Pre-processed & - & ✓ & ✓ & ✓ & ✓ & - & - \\ \hline Model-9 & Pre-processed & ✓ & - & ✓ & ✓ & ✓ & - & - \\ \hline Model-10 & Pre-processed & ✓ & ✓ & - & ✓ & ✓ & - & - \\ \hline Model-11 & Pre-processed & ✓ & ✓ & ✓ & - & ✓ & - & - \\ \hline Model-12 & Pre-processed & ✓ & ✓ & ✓ & ✓ & - & - & - \\ \hline Model-13 & Pre-processed & ✓ & - & - & ✓ & ✓ & ✓ & ✓ \\ \hline Model-14 & Pre-processed & - & - & - & ✓ & ✓ & ✓ & ✓ \\ \hline Model-15 & Pre-processed & ✓ & - & - & ✓ & ✓ & - & ✓ \\ \hline Model-16 & Pre-processed & ✓ & - & - & ✓ & ✓ & ✓ & - \\ \hline Model-17 & Pre-processed & ✓ & - & - & - & ✓ & ✓ & ✓ \\ \hline Model-18 & Pre-processed & ✓ & - & - & ✓ & - & ✓ & ✓ \\ \hline \hline \end{tabular}
\end{table}
Table 1: The input combinations constructed for building the proposed hybrid estimator models for both pre-processed and non-preprocessed dataset.  
Legate and McCabe's index (_LMI_), correlation coefficient (_CC_), _PBIAS_, [PERSON]'s index (_WI_), and relative root mean square error (_RRMSE_) are employed as following equations [27; 97; 98; 99; 100]:  
\[RMSE=\sqrt{\frac{1}{N_{s}}\sum\
olimits_{j=1}^{N_{s}}\left(\left(Ss\right)_{ exp}-\left(Ss\right)_{Sim}\right)^{2}} \tag{14}\]  
\[SRMSE=\frac{\sqrt{\frac{1}{N_{s}}\sum\
olimits_{j=1}^{N_{s}}\left(\left(Ss \right)_{exp}-\left(Ss\right)_{Sim}\right)^{2}}}{\left(\frac{d_{s}}{D}\right)_ {Obs}} \tag{15}\]  
\[MAE=\frac{1}{N_{s}}\sum\
olimits_{j=1}^{N_{s}}\left|\left(Ss\right)_{exp}-\left(Ss \right)_{Sim}\right| \tag{16}\]  
\[CC=\frac{\sum\
olimits_{j=1}^{N_{s}}\left(\left(Ss\right)_{exp}-\overline{ \left(Ss\right)_{exp}}\right)\left(\left(Ss\right)_{Sim}-\overline{\left(Ss \right)_{Sim}}\right)}{\sqrt{\sum\
olimits_{j=1}^{N_{s}}\left(\left([PERSON] \right)_{exp}-\overline{\left([PERSON]\right)_{exp}}\right)^{2}\sum\
olimits_{j=1}^ {N_{T}}\left(\left([PERSON]\right)_{Sim}-\overline{\left([PERSON]\right)_{Sim}}\right)^ {2}}} \tag{17}\]  
\[WI=1-\left[\frac{\sum\
olimits_{i=1}^{N_{s}}\left(\left([PERSON]\right)_{exp}-\left([PERSON] \right)_{Sim}\right)^{2}}{\sum\
olimits_{i=1}^{N_{s}}\left(\left|\left([PERSON] \right)_{Sim}-\overline{\left([PERSON]\right)_{exp}}\right|+\left|\left([PERSON]\right)_{ exp}-\overline{\left([PERSON]\right)_{exp}}\right|\right)^{2}}\right] \tag{18}\]  
\[LMI=1-\left[\frac{\sum\
olimits_{i=1}^{N_{s}}\left|\left([PERSON]\right)_{exp}- \left([PERSON]\right)_{Sim}\right|}{\sum\
olimits_{i=1}^{N_{s}}\left|\left([PERSON]\right) _{exp}-\overline{\left([PERSON]\right)_{exp}}\right|}\right] \tag{19}\]  
\[PBIAS=\left[\frac{\sum\
olimits_{i=1}^{N_{s}}\left(\left(Ss\right)_{exp}- \left(Ss\right)_{Sim}\right)}{\sum\
olimits_{i=1}^{N_{s}}\left(Ss\right)_{ exp}}\right]\times 100 \tag{20}\]  
where the \(\left(Ss\right)_{exp}\) and \(\left(Ss\right)_{Sim}\) are the experimental and simulated shear strength, \(\overline{\left(Ss\right)_{exp}}\) and \(\overline{\left(Ss\right)_{Sim}}\) are their mean values, and \(N_{s}\) is the sample size.