# Experimental Test and Prediction Model of Soil Thermal Conductivity in Pernafrost Regions
## 6 Discussion  
### Error Analysis of Thermal Conductivity Prediction Models  
To compare the precisions of three prediction models, the mean absolute percent error (MAPE) of different thermal conductivity intervals has been calculated and analyzed:  
\[MAPE=\sum_{i=1}^{n}\left|\frac{\lambda_{ei}-\lambda_{pi}}{\lambda_{ei}}\right| \times\frac{100}{n} \tag{4}\]  
where \(\lambda_{ei}\) and \(\lambda_{pi}\) is the experimental and predictive thermal conductivity respectively; \(n\) is the total sample numbers of certain thermal conductivity value.  
The MAPE distribution of HWHCS is shown in Figure 14. This shows that the MAPE distribution curve of the binary fitting method is steeper. Its bilateral MAPE can be up to 21% and 16% for frozen and unfrozen soils, and its small MAPE interval is narrow which restricts its application in the large or small thermal conductivity prediction. While the MAPE of the RBF neural network method  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Prediction** \\ **Model** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Abnormal** \\ **Sample** \\ **Rejection Ratio** \\ \end{tabular} } & \multicolumn{5}{c}{\begin{tabular}{c} **HWHCS** \\ **Unfrozen** \\ \end{tabular} } & \multicolumn{5}{c}{\begin{tabular}{c} **MWHCS** \\ **Frozen** \\ \end{tabular} } & \multicolumn{5}{c}{\begin{tabular}{c} **LWHCS** \\ **Frozen** \\ \end{tabular} } \\ \hline \begin{tabular}{c} Binary fitting \\ RBF neural \\ network \\ \end{tabular} & 10\%–15\% & 0.561 & 0.512 & 0.475 & 0.432 & 0.532 & 0.487 \\ \
\begin{tabular}{c} RBF neural \\ network \\ \end{tabular} & 10\% & 0.79 & 0.79 & 0.82 & 0.75 & 0.81 & 0.8 \\
\begin{tabular}{c} Ternary fitting \\ \end{tabular} & 2\%–3\% & — & 0.77 & — & 0.8 & — & 0.88 \\ \hline \hline \end{tabular}
\end{table}
Table 6: \(R^{2}\) for three prediction models.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Prediction Model** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Fitting** \\ **Parameters** \\ \end{tabular} } & \multicolumn{5}{c}{\begin{tabular}{c} **HWHCS** \\ **Unfrozen** \\ \end{tabular} } & \multicolumn{5}{c}{\begin{tabular}{c} **MWHCS** \\ **Unfrozen** \\ \end{tabular} } & \multicolumn{5}{c}{\begin{tabular}{c} **LWHCS** \\ **Frozen** \\ \end{tabular} } \\ \hline \begin{tabular}{c} Binary fitting \\ RBF neural \\ network \\ \end{tabular} & \(w\), \(\rho_{d}\) & 59.8 & 43.6 & 42.5 & 39.6 & 60.3 & 54.6 \\ \
\begin{tabular}{c} RBF neural \\ network \\ \end{tabular} & \(w\), \(\rho_{d}\) & 77.9 & 65.1 & 81.4 & 70.1 & 71.6 & 63.2 \\
\begin{tabular}{c} Ternary fitting \\ \end{tabular} & \(w\), \(\rho_{d}\), \(\lambda_{u}\) & — & 65.7 & — & 70.5 & — & 74.5 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Quantitative proportion of relative error within \(\pm 10\%\) for three prediction models.  
and ternary fitting method are much lower, comparatively, and can be applied to the entire thermal conductivity distribution interval. Additionally, it should be mentioned that the relative accurate thermal conductivity predictive intervals (MAPE \(<\) 10%) of binary fitting method for three clusters is 1.24-1.62 W/(m \(\cdot\) K), 1.4-1.7 W/(m \(\cdot\) K), 1.54-2.06 W/(m \(\cdot\) K) (unfrozen) and 1.7-2.08 W/(m \(\cdot\) K), 1.9-2.3 W/(m \(\cdot\) K), 1.96-2.64 W/(m \(\cdot\) K) (frozen), respectively, which is roughly overlapped with main thermal conductivity probability range as shown in Figure 7. Therefore, considering easily accessed dry density and water content data, the binary fitting method definitely has certain application value in engineering.