# Energy Evaluation of Triggering Soil Liquefaction Based on the Response Surface Method
## 6 The RSM Equations
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Test No** & **Log W** & **BB** & **CC** & **HCC** & **BB28** & **CC28** & **HCC28** \\ \hline
1 & 2.568 & 2.370 & 2.167 & 2.133 & 2.456 & 2.943 & 3.102 \\
2 & 2.690 & 2.369 & 2.205 & 2.175 & 2.503 & 2.965 & 3.129 \\
3 & 2.771 & 2.531 & 2.350 & 2.276 & 2.612 & 3.065 & 3.236 \\
4 &  
BB28 equation and the CC with 0.830, closely followed by the HCC and CC28 equations, with 0.792 and 0.722, respectively, demonstrated the highest precision. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **R** & **RMSE** & **MAE** \\ \hline LGP & 0.627 & 0.402 & 0.369 \\ MEP & 0.584 & 0.182 & 0.157 \\ GP & 0.664 & 0.259 & 0.227 \\ Zhang & 0.614 & 0.620 & 0.600 \\ BB & 0.693 & 0.251 & 0.207 \\ CC & 0.830 & 0.376 & 0.348 \\ HCC & 0.792 & 0.476 & 0.456 \\ BB28 & 0.911 & 0.218 & 0.203 \\ CC28 & 0.722 & 0.173 & 0.139 \\ HCC28 & 0.508 & 0.293 & 0.244 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Summary of comparison between six new RSM equations and four available models. Figure 3: Capacity energy predicted by RSM equation on the basis of the central composite (CC) design of experiment (DOE) and the first ANN model versus the measured values of laboratory tests. Figure 2: Capacity energy predicted by RSM equation on the basis of the Box-Behnken DOE and the first ANN model versus the measured values of laboratory tests. Figure 4: Capacity energy predicted by RSM equation on the basis of the half central composite (HCC) design of experiment (DOE) and the first ANN model versus the measured values of laboratory tests. Figure 5: Capacity energy predicted by RSM equation on the basis of the Box-Behnken (BB) design of experiment (DOE) and the second ANN model versus the measured values of laboratory tests. Figure 6: Capacity energy predicted by RSM equation on the basis of the central composite (CC) and design of experiment (DOE) and the second ANN model versus the measured values of laboratory tests. Figure 8: Capacity energy predicted by genetic programming (LGP) versus the measured values of laboratory tests. Figure 7: Capacity energy predicted by RSM equation on the basis of half central composite (HCC) and design of experiment (DOE) and the second ANN model versus the measured values of laboratory tests. Figure 9: Capacity energy predicted by multi expression programming (MEP) versus the measured values of laboratory tests. On the other hand, with RSME and MAE values of 0.173 and 0.139, respectively, CC28 demonstrated less inaccuracy. Considering the graphs, BB28 and CC28 were the most capable and accurate models among all six equations presented in this study as well as the four extra inspected models, as shown in Figures 2-7. Moreover, five of the six RSM models demonstrated a higher R than the extra four models. The RMSEs of CC28, MEP, and BB28 were 0.173, 0.182, and 0.218, respectively, displaying the highest accuracy to predict \(W\), as demonstrated in Table 14. In addition, the MAEs of CC28, MEP, and BB28--0.139, 0.157, and 0.203, respectively--revealed the most accuracy. As can be seen from Figures 2-11, among all models evaluated in this study, CC and HCC present underpredicted values for \(W\). In contrast, HCC28 and LGP overestimated \(W\) in their predictions. Furthermore, BB28 shows the highest accuracy in predicting \(W\). industry, medicine, and science, according to the literature review, it has not been used to investigate soil liquefaction by other researchers. To examine the complicated influence of fine content (_FC_), two sets of databases were arranged and an artificial neural network (ANN) model was developed for each. Finally, three RSM equations were developed based on each ANN model, with each equation belonging to a specific design of experiment (DOE).