## 12 Influencing Factors of Laboratory Specim Temperature Variation
### Importance Analysis for Influencing Factors  
The effects of mixture gradations, mixture components, radial and axial regions on the temperature field of asphalt mixture laboratory specimens were discussed above. However, the importance of each influencing factor on temperature field variations is not the same. Therefore, a random forest algorithm proposed by [PERSON] [40] was introduced to evaluate the importance of various influencing factors on TA value. Figure 13: Asphalt mixtures coefficient of TA variation during cooling and heating processes. Firstly, the Bootstrap resampling method was used to randomly extract multiple autogenous data sets from the original data sets (such as shown in Figures 11 and 12) and generate N training samples to construct N classifier trees (called base classifiers). In each process of building the base classifier, data other than training samples were used as test data, which was called out of bag data sets (OOB). Through the error rate based variable importance measures (VIM_ER) on OOB, the importance of variables was scored and ranked. The basic principle of VIM_ER is to calculate the difference of OOB error rates before and after randomly substituting each variable so as to measure the importance of the variables. Specifically, in order to obtain the importance score of variables, a random forest from training samples was constructed first, and the error rates of all OOB samples were estimated. Then, one variable in all OOB samples was randomly replaced, and the change of prediction error of OOB samples was calculated before and after the replacement of the independent variable. The greater the change of error, the higher the importance of the independent variable. VIM_ER can be expressed as follows. \[VIM_{i}^{ER}=\frac{1}{Ntree}\sum\
olimits_{t=1}^{Ntree}\left(ER_{it}-ER_{it}^ {\prime}\right) \tag{11}\]  
where \(Ntree\) is the number of decision trees in random forests, \(ER_{it}\) is the error rate corresponding to the No_t_ tree before variable replacement and \(ER_{it}^{\prime}\) is the error rate corresponding to the No. \(t\) tree after variable replacement. According to the VIM_ER formula, if \(X_{i}\) is not related to the result, the error rate of OOB samples corresponding to the random replacement of \(X_{i}\) will not change, and \(VIM_{i}^{ER}=0\) in theory; on the contrary, if \(VIM_{i}^{ER}>0\), the variable \(X_{i}\) is related to the result. Contribution degree (CD) is used to measure the importance of influencing factors to the results, calculated according to the following formula:  
\[CD_{i}=\frac{VIM_{i}^{ER}}{\sum\limits_{i=1}^{n}VIM_{i}^{ER}} \tag{12}\]  
where \(CD_{i}\) is the contribution degree of no. \(i\) influencing factor to the results,\(0\leq CD_{i}\leq 1\), and \(\sum\limits_{i=1}^{n}CD_{i}=1\). In this paper, the random forest method was used to evaluate the importance of influencing factors on the asphalt mixture laboratory specimen temperature field, and the contribution degrees of influencing factors were calculated, as shown in Table 5.  
Table 5 shows that among these four factors, asphalt mixture gradation was the main factor affecting the temperature field of laboratory specimens, and its contribution degrees during cooling and heating processes were 53.59% and 76.83, respectively. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Influencing Factor** & \multicolumn{3}{c}{**CD to TA**} \\
**Cooling Process** & \multicolumn{2}{c}{**Heating Process**} \\ \hline Mixture gradation & & \\ (AC-13, AC-20, AC-25 and PAC-13) & 53.59\% & 76.83\% \\ Region r (A, B, C, D) & 38.87\% & 21.04\% \\ Region h (1,2,3,4,5) & 6.56\% & 1.53\% \\ Component (aggregate, asphalt mortar, void) & 0.98\% & 0.60\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Contribution degrees of influencing factors. Secondly, the radial region (Region r) of cylindrical specimens had a significant effect on the specimen temperature field.