## 4 Electromagnetic Exposure Safety Assessment and Uncertainty Quantification
### Uncertainty Quantification
Therefore, we considered a possible range of the overall mean by calculating a confidence interval. Table 5 shows the confidence intervals at different frequencies. The results of the confidence intervals were used to analyze the range of the mean and standard deviation. The results of maximum and minimum values, lower 90%, 95%, 99%, and upper 90%, 95%, 99% were obtained. The intervals of the SAR distribution were quantified, and the quantitative results of the SAR calculation were analyzed more accurately. The computer CPU used in this article was i9-13900K, the main frequency was 3 GHz, and the running memory was 64 GB. After obtaining the results reported in Table 6, under the premise of ensuring calculation accuracy, we found that compared with the calculation results of the 1000 runs of the MC method, the calculation time of the gPC method was greatly reduced. In terms of radiation uncertainty analysis, the gPC method not only ensured the accuracy of the calculation results, but also significantly improved the calculation efficiency compared with the Monte Carlo method. We then quantified the effect of mobile phones on the model by random input variables of the electromagnetic radiation to the human head. The global sensitivity indices for the different input parameters were calculated by combining the relevant theories of the Sobol global sensitivity method and the gPC method. By combining the calculated coefficients of the gPC, taking the SAR value generated by the electromagnetic simulation model subjected to mobile phone radiation as the index, the total sensitivity index and first-order sensitivity index of each input variable were obtained, as shown in Figure 9:  
At different frequencies, the results of combining the gPC method and the Sobol method to calculate the first-order sensitivity index and the global sensitivity index of each variable were basically consistent with the results of the MC method, and the dielectric constant of the shell had the greatest influence on the overall model. The dielectric constant of the battery jar had a relatively large effect on the overall model. Therefore, the dielectric \begin{table}
\begin{tabular}{c c} \hline \hline
**Computational Method** & **Computation Time** \\ \hline gPC & 35 min 20 s \\ MC & 16 h 36 min \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of the SAR calculation time. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Frequency** & **2.1 GHz** & **2.3 GHz** & **3.5 GHz** & **5.2 GHz** \\ \hline mean & 0.9580 & 1.4431 & 1.76  
constant of the shell and battery jar should be kept within reasonable limits when designing electromagnetic materials for mobile phones. In this way, the effect of mobile phones on the SAR of the electromagnetic radiation to the human head is diminished as much as possible. Figure 9: Comparison of the global sensitivity indices. Show are the (**a**) 2100 MHz first-order sensitivity index, (**b**) 2100 MHz total sensitivity index, (**c**) 2300 MHz first-order sensitivity index, (**d**) 2300 MHz total sensitivity index, (**e**) 3500 MHz first-order sensitivity index, (**f**) 3500 MHz total sensitivity index, (**g**) 5200 MHz first-order sensitivity index, (**h**) 5200 MHz total sensitivity index.