# Predicting Geotechnical Parameters from Seismic Wave Velocity Using Artificial Neural Networks
## 7 Comparison between ANN and Regression Models  
Regression analysis is a conventional way to determine the relationship between independent and dependent variables. It determines how strongly the independent variables affect the depended variables. Multiple-linear regression analyses are performed using the same databases used for the ANN models. The performance of the models is determined based on RMSE, MARE, unnormalized ASE and R\({}^{2}\). For predicting seismic wave velocity three different data set: lab data, field data and both lab and field data are used. Input parameters for predicting seismic wave velocity models are LL, plasticity index, water content and dry density. For predicting water content LL, plasticity index, dry density and velocity are used as input parameters. Models are developed for lab, field and both lab and field data sets. For predicting dry density same type of data set and approach are used except the input parameters are LL, plasticity index, water content and seismic wave velocity. The results of regression analysis are shown in Table 7.  
Table 7 presents the statistics for ANN (without validation) and regression models. To compare ANN models with regression models the unnormalized ASE is calculated using the unnormalized actual and predicted values. Additionally, root mean squared error (RMSE) is also calculated using. \[\text{RMSE}=\sqrt{\frac{\sum_{i=1}^{N}\left(X_{i}^{\text{A}}-X_{i}^{\text{P}} \right)^{2}}{N}} \tag{9}\]  
For predicting seismic wave velocity, the regression model using laboratory data showed the higher R\({}^{2}\) value and lower MARE but higher. ASE and RMSE than field data models. Combining the field and lab data increased errors and a R\({}^{2}\) value in between the models using individual lab and field data. For predicting water content, the regression \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Source of Data**} & \multicolumn{4}{c}{**ANN**} & \multicolumn{4}{c}{**Regression**} \\  & & **RMSE** & **ASE** & **MAE** & **R\({}^{2}\)** & **RMSE** & **ASE** & **MAE** & **R\({}^{2}\)** \\ \hline \multirow{4}{*}{Predicting velocity} & F & 394 & 155,616 & 19.3 & 0.37 & 403 & 162,712 & 18.8 & 0.34 \\  & L & 403 & 162,650 & 13.3 & 0.80 & 465 & 216,368 & 15.4 & 0.72 \\  & F + L & 483 & 233,701 & 18.5 & 0.78 & 772 & 596,434 & 30.8 & 0.43 \\  & F & 1.0 & 1.0 & 7.7 & 0.85 & 1.5 & 2.3 & 12 & 0.66 \\ \multirow{4}{*}{Predicting water content} & L & 1.0 & 1.0 & 6.6 & 0.89 & 0.9 & 0.9 & 6.5 & 0.88 \\  & F + L & 1.6 & 2.6 & 11.6 & 0.67 & 1.6 & 2.7 & 12 & 0.66 \\ \multirow{4}{*}{Predicting dry density} & F & 2.7 & 7.5 & 1.8 & 0.91 & 4.9 & 24.2 & 3.3 & 0.69 \\  & L & 3.4 & 11.6 & 2.5 & 0.85 & 3.3 & 11.0 & 2.4 & 0.85 \\ \cline{1-1}  & F + L & 4.1 & 17.5 & 3 & 0.78 & 4.4 & 19.5 & 3.1 & 0.75 \\ \hline \hline \end{tabular} Note: Field (F), Lab (L).  
\end{table} 
Table 7: Comparison of ANN and regression models. models based on lab data also showed the best performance The performance of field data and field plus lab data are very close to each other. For predicting dry density, the best performance is also observed for the lab data model. The second-best model is field plus lab data and lowest performance is observed for the field data. For all the cases, ANN models resulted in better R2 values in comparison to regression analysis. Significant improvements are observed for the case of field data for predicting water content, the R2 increases 22.35%, using field data for predicting dry density the R2 increase 24.18% and for using field & lab data for predicting seismic wave velocity the R2 increase 44.87%. Errors are lower for ANN models in comparison to regression models with some minor exceptions. ANN models showed significantly reduced errors than regression models using with field data for predicting water content RMSE decreases 50%, ASE decreases 130%, MARE decreases 55.84%, for predicting dry density the RMSE decreases 81.48%, ASE decreases 222.67%, 83.33%.