# Experimental Test and Prediction Model of Soil Thermal Conductivity in Pernafrost Regions
## 5 Thermal Conductivity Prediction for Three Soil Clusters
### Comparison of Thermal Conductivity Prediction Models  
The predictive results of three prediction models are shown in Figure 13. It should be noted that the prediction models of different soil clusters remove some abnormal sample points for feasible  
Figure 12: Predictive values of unfrozen MWHCS using RBF neural network method.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **HWHCS** & **MWHCS** & **LWHCS** \\ \hline \(a_{2}\) & 1.254 & 1.167 & 1.178 \\ \(b_{2}\) & 0.413 & 0.599 & 0.634 \\ \(c_{2}\) & 0.273 & 0.332 & 0.312 \\ \(d_{2}\) & 0.2 & 0.354 & 0.22 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Ternary fitting parameters for three soil clusters.  
calculation, which account for 2%-15% of the total samples number (seen in Table 5). Moreover, for the large quantity of sample points and clear exhibition, only 1/3 randomly selected sample points are shown in Figure 13. It can be seen that most sample points are within the \(\pm\)10% error bars for all three prediction models, which proves their predictive availability and engineering application values. Furthermore, the sample points of the binary fitting method are mainly concentrated in the medium thermal conductivity range, and there is almost no distribution at both high- and low-value intervals. Conversely, the sample distribution range of the RBF neural network method and the ternary fitting method is much broader, which is distributed throughout the thermal conductivity interval. Compared with the quantitative proportion of predictive values deviating severely from experimental values, it can be found that the binary fitting method is much more than that of the RBF neural network method and the ternary fitting method.  
Figure 13: Predictive results of three prediction models.  
The \(R^{2}\) and quantitative proportion of relative error within \(\pm 10\%\) (\(P_{\pm 10\%}\)) for three prediction models is shown in Tables 6 and 7. It can be seen that the fitting degree of the RBF neural network method and the ternary fitting method is much higher than that of the binary fitting method. The maximum \(R^{2}\) and \(P_{\pm 10\%}\) of the ternary fitting method reaches up to 0.88 and 74.5%, while binary fitting method is only 0.561 and 39.6%. Besides, the abnormal sample rejection ratio of three predictive models is 10%-15%, 10% and 2%-3%, respectively. This demonstrates that the ternary fitting is the most accurate thermal conductivity prediction method. However, the ternary fitting method has some methodological limitations: (1) the fitting formulas are based on a large amount of test data, which cannot completely avoid high costs and a lengthy thermal conductivity experiment; (2) it can only be used to predict thermal conductivity of frozen soils, which limits its application scope. The RBF neural network method, meanwhile, has comparative \(R^{2}\) and \(P_{\pm 10\%}\) as well as the ternary fitting method, and it can also be used for unfrozen soils. It also can be noted that the \(R^{2}\) and \(P_{\pm 10\%}\) of MWHCS is usually lower than that of HWHCS and LWHCS with binary or ternary fitting models, while the prediction results of the RBF neural network method for MWHCS is more accurate. Therefore, it can be concluded that the RBF neural network method can better identify soil's complex composition characteristics and be the optimal thermal conductivity prediction method.