## 4 Environmental Impact on Temperature Distribution of Thin-Walled Concrete  
Sensitivity Analysis of Thin-Walled Concrete to Environmental Factors Based on Random Forest Regression  
According to the previous analysis, the temperature distribution composed of the mean temperature and gradient temperature is significantly influenced by environmental factors. Thus, it is necessary to evaluate the impact and importance of each environmental factor. However, due to complex combined effects from various factors, it is difficult to assess and quantify the effects without a powerful tool. Therefore, random forest regression [29; 30], as a machine learning method to predict targets and classify multiple parameters in a nonlinear way, was introduced as a powerful statistical tool to conduct the sensitivity analysis of thin-walled concrete to environmental factors. In this study, random forest regression was performed using MATLAB, and the whole execution process is shown in Figure 8. Firstly, each target in the sample corresponds to several features. The target can be regarded as the dependent variable, and the features as the potential influencing factors. Secondly, all the features were normalized to avoid errors caused by different statistical units. Thirdly, by using bootstrap sampling, the normalized original samples were extracted as multiple random subsamples to establish a forest composed of decision trees. Finally, the prediction of targets and the importance of features were obtained by the majority vote of all the decision trees. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Pattern** & **Parameter** & **Spring** & **Summer** & **Autumn** & **Winter** \\ \hline \multirow{2}{*}{\(T_{\text{g}}^{+}\)} & \(m\) & \(-1.64\) & \(-1.84\) & \(-1.00\) & \(-0.37\) \\ \cline{2-6}  & \(n\) & \(6.68\) & \(7.50\) & \(4.62\) & \(2.98\) \\ \hline \multirow{2}{*}{\(T_{\text{g}}^{-}\)} & \(m\) & \(0.02\) & \(-0.20\) & \(0.23\) & \(0.45\) \\ \cline{2-6}  & \(n\) & \(-1.29\) & \(-1.51\) & \(-1.83\) & \(-2.02\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Value of \(m\) and \(n\) in different seasons. Figure 7: Seasonal changes in extreme vertical gradient temperature \(T_{\text{g}}^{+}\) and \(T_{\text{g}}^{-}\): (**a**) in spring; (**b**) in summer; (**c**) in autumn; and (**d**) in winter. In the practical procedure, the measured environmental factors, including wind speed, solar radiation, and air temperature, were set as features, while \(T_{\rm m}\), \(T_{\rm gb}\), and \(T_{\rm gt}\) were set as the three different targets. In addition, to avoid distortion of the results due to transient fluctuations in the measured environmental factors, all data were input as average values throughout the day. By screening the measured data from the experiments, 273 valid samples were obtained. Because the main goal of random forest regression is to search for important factors, all 273 valid samples were used as the training set as well as the test set for RF regression. To verify the correctness of the algorithm, the measured data were compared to the results of the prediction (Figure 9). For the three targets, all the prediction results were consistent with the measured results. Therefore, both the accuracy and practicality of the random forest regression were verified. Figure 8: Execution diagram of random forest regression. Figure 9: Comparison of the measured data with the results predicted by random forest regression: (**a**) \(T_{\rm m}\); (**b**) \(T_{\rm gb}\); (**c**) \(T_{\rm gt}\). The normalized influence of the environmental factors on \(T_{\rm m}\), \(T_{\rm gb}\), and \(T_{\rm gt}\) are illustrated in Figure 10. The influence value of a feature represents its contribution ratio when voting for the prediction, and a larger importance value indicates that the target is more sensitive to the feature. The influence of wind speed was negligible for all the concrete temperature characteristics. Moreover, air temperature and solar radiation produced different effects on the concrete temperature field.