# Experimental Test and Prediction Model of Soil Thermal Conductivity in Pernafrost Regions
## 5 Thermal Conductivity Prediction for Three Soil Clusters
### Thermal Conductivity Prediction Models
#### 5.1.2 Radial Basis Function (RBF) Neural Network  
The radial basis function (RBF) neural network has the characteristics of simple structure, fast learning speed and good convergence, and is widely used in the field of nonlinear function approximation [46; 47]. Thus, this method has been applied for three clusters' thermal conductivity prediction. The dry density and water content is respectively used as the input layer of the RBF neural network, and the thermal conductivity is used as the output layer. The settings of the neural network structure in JMP Pro 13.0 software mainly include the activation function, the number of hidden layers, and the number of nodes in each layer. Considering the calculation accuracy and amount, the radial Gaussian function is selected as the activation function, the number of hidden layers is set as 2, and the number of nodes in each layer is 10. The established relationship diagram of the RBF neural network is shown in Figure 11.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Soil Type**} & **Operation** & \multirow{2}{*}{**Application Range**} & \multicolumn{3}{c}{**Parameters**} \\ \cline{3-6}  & **Condition** & & & \(a_{1}\) & \(b_{1}\) & \(c_{1}\) \\ \hline \multirow{4}{*}{HWHCS} & Unfrozen & \(\rho_{d}\leq 1.7\) g/cm\({}^{3}\) & 0.3441 & 0.7152 & 0.6865 \\  & & \(\rho_{d}>1.7\) g/cm\({}^{3}\) & 0.4158 & 0.5942 & 0.7932 \\  & Frozen & \(\rho_{d}\leq 1.7\) g/cm\({}^{3}\) & 0.3385 & 0.8262 & 1.1973 \\  & & \(\rho_{d}>1.7\) g/cm\({}^{3}\) & 0.4569 & 0.6011 & 1.4366 \\ \hline \multirow{4}{*}{MWHCS} & Unfrozen & \(\rho_{d}\leq 1.7\) g/cm\({}^{3}\) & 0.5338 & 0.5586 & 0.751 \\  & Frozen & \(\rho_{d}>1.7\) g/cm\({}^{3}\) & 0.8478 & 0.2332 & 1.44 \\  & Frozen & \(\rho_{d}\leq 1.7\) g/cm\({}^{3}\) & 0.4906 & 0.586 & 1.9327 \\  & & \(\rho_{d}>1.7\) g/cm\({}^{3}\) & 0.88 & 0.2748 & 1.7438 \\ \hline \multirow{4}{*}{LWHCS} & Unfrozen & \(\rho_{d}\leq 1.9\) g/cm\({}^{3}\) & 0.298 & 0.8404 & 1.4741 \\  & & \(\rho_{d}>1.9\) g/cm\({}^{3}\) & 0.6675 & 0.3675 & 2.912 \\ \cline{1-1}  & Frozen & \(\rho_{d}\leq 1.9\) g/cm\({}^{3}\) & 0.4351 & 0.6979 & 2.366 \\ \cline{1-1}  & & \(\rho_{d}>1.9\) g/cm\({}^{3}\) & 0.9374 & 0.2549 & 3.8056 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Binary fitting parameters for three soil clusters.  
Figure 11: Schematic diagram of radial basis function (RBF) neural network.  
Besides, all of thermal conductivity measurement results of three soil clusters are randomly divided into 9:1 ratio; 90% of the sample data were used for training samples of the neural network model, and the remaining 10% were used as the validation of RBF neural network predictive model. Additionally, based on the feedback of training results, small samples with larger deviations are eliminated in the calculation to improve the prediction accuracy. Figure 12 is the predictive values of unfrozen MWHCS. It can be seen that the predicted results of RBF neural network method are in good agreement with the experimental results (\(R^{2}=0.82\)).