# Predicting Geotechnical Parameters from Seismic Wave Velocity Using Artificial Neural Networks
## 6 ANN Models
### ANN Models for Predicting Seismic Wave Velocity  
Six different models are developed to predict seismic wave velocity. Models are using lab data, field data and both lab and field data together following the two approaches, with validation and without validation. Correlation matrix analysis was used before selecting the input and output parameters for prediction model development. The best three networks selected based on the statistical measures and optimal hidden nodes to predict seismic velocity using field data from LL, plasticity index, water content, and dry density are presented in Table 3. The best model is the model which has lower the ASE, MARE and higher the R\({}^{2}\). The statistics show that ASE, MARE and R\({}^{2}\) of all three networks are very close to each other in training, testing, and all-trained. From these three networks, network 4_(_4_3100)_1 (where network structure is denoted as input_ (initial hidden nodes_final hidden nodes_iteration)_output) is chosen as the best model depending on the best statistics in testing. The predicted versus actual graph is shown in Figure 1a. The statistics and predicted versus actual graph indicate that the accuracy of predicting velocity is marginal. The best model for predicting velocity using field data without the validation stage is network 4_(_2\(4\)2900)_1. The predicted versus actual graph for network 4_(_2\(4\)2900)_1 is shown in Figure 1b. The statistics are presented in Table 4. The accuracy of predicting velocity is increased after omitting validation, but the overall performance is still marginal. The best model using lab data to predict velocity is network 4_(_2\(2\)200)_1. The statistics in Table 4 and predicted versus actual graph shown in Figure 1c indicate that the accuracy of the velocity prediction is good. The best model to predict velocity without validation is network 4_(_1\(5\)100)_1. The predicted versus actual graph shown in Figure 1d and the statistics presented in Table 4 indicate that the accuracy of the velocity predictions is good. Again, excluding the validation helps to slightly minimize the errors and increases the R\({}^{2}\) values. The results also show that the errors are much lower, and the R\({}^{2}\) values are much higher for the networks trained using lab data in comparison to the network trained using field data. \begin{table}
\begin{tabular}{c c c c} \hline
**Model Architecture** & **4_(1\(1\)2100)_1** & **4_(2\(2\)2100)_1** & **4_(4\(4\)3100)_1** \\ \hline Training & & & \\ ASE & 0.0151 & 0.0152 & 0.0152 \\ MARE & 19.61 & 19.87 & 19.75 \\ R\({}^{2}\) & 0.30 & 0.30 & 0.30 \\ Testing & & & \\ ASE & 0.0122 & 0.0121 & 0.0121 \\ MARE & 21.72 & 21.70 & 21.56 \\ R\({}^{2}\) & 0.26 & 0.28 & 0.27 \\ Validation & & & \\ ASE & 0.0153 & 0.0149 & 0.0147 \\ MARE & 18.54 & 18.63 & 18.49 \\ R\({}^{2}\) & 0.25 & 0.28 & 0.29 \\ All & & & \\ ASE & 0.0132 & 0.0132 & 0.0133 \\ MARE & 18.87 & 19.01 & 19.04 \\ R\({}^{2}\) & 0.34 & 0.34 & 0.34 \\ \hline \end{tabular}
\end{table} 
Table 3: Statistical accuracy measures of model for predicting seismic wave velocity using field data, with validation). Figure 1: Graphical prediction accuracy of model for predicting seismic wave velocity, (**a**) field, with validation, (**b**) field, without validation, (**c**) lab, with validation, (**d**) lab, without validation, (**e**) field, plus lab, with validation, (**f**) field plus lab, without validation. The best model using field and lab data together to predict the seismic wave velocity is network 4_(_1\(2\)2900). The statistics are shown in Table 4. and the predicted versus actual graphs for the best network shown in Figure 1e. indicates that the accuracy is marginal. The ASE and MARE are higher after combining lab and field data in comparison to the models trained with lab and field data separately. The R\({}^{2}\) values are improve. The model developed without the validation stage is network 4_(_5_10_20000)_1 The statistics are shown in Table 4. and the predicted versus actual graphs for the best network shown in Figure 1f.