# Safety Assessment and Uncertainty Quantification of Electromagnetic Radiation from Mobile Phones to the Human Head

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## Abstract

**:**

## 1. Introduction

## 2. Parameter Uncertainty Quantification Method

#### 2.1. gPC Method

#### 2.2. Random Response Surface Method

- a.
- Construction of the generalized chaotic polynomial expansion model

- b.
- Estimation of the coefficient of interest

#### 2.3. Global Sensitivity Analysis

## 3. Electromagnetic Simulation Model and Electromagnetic Radiation Scenarios

#### 3.1. Mobile Phone Electromagnetic Simulation Model

#### 3.2. Electromagnetic Simulation Model of the Human Head

#### 3.3. Electromagnetic Radiation Scenarios

## 4. Electromagnetic Exposure Safety Assessment and Uncertainty Quantification

#### 4.1. Safety Assessment

#### 4.2. Uncertainty Quantification

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Mobile phone antenna return loss S-parameters. (

**a**) S11, (

**b**) S22, (

**c**) S33, (

**d**) S44, (

**e**) S55 (

**f**) S66.

**Figure 6.**Radiation pattern at four frequencies. Shown are (

**a**) 2100 MHz, (

**b**) 2300 MHz, (

**c**) 3500 MHz, (

**d**) 5200 MHz.

**Figure 7.**SAR results at four frequencies. The chosen frequencies were (

**a**) 2100 MHz, (

**b**) 2300 MHz, (

**c**) 3500 MHz, (

**d**) 5200 MHz.

**Figure 8.**Comparison of the probability density function of the SAR at four frequencies, i.e., (

**a**) 2100 MHz, (

**b**) 2300 MHz, (

**c**) 3500 MHz, (

**d**) 5200 MHz.

**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.

Distribution Pattern | Orthogonal Polynomial Basis | Weight Function | Variable Range | |
---|---|---|---|---|

normal | $\frac{1}{\sqrt{2\pi}}{e}^{-{x}^{2}/2}$ | Hermite ${H}_{n}\left(x\right)$ | ${e}^{-{x}^{2}/2}$ | $\left[-\infty ,+\infty \right]$ |

uniform | 1/2 | Legendre ${P}_{n}\left(x\right)$ | 1 | $\left[-1,1\right]$ |

exponential | ${e}^{-x}$ | Legendre ${L}_{n}\left(x\right)$ | ${e}^{-x}$ | $\left[0,+\infty \right]$ |

γ | $\frac{{x}^{\alpha}{e}^{-x}}{\Gamma \left(\alpha +1\right)}$ | generalized Legendre ${L}_{n}^{\left(\alpha ,\beta \right)}\left(x\right)$ | ${x}^{\alpha}{e}^{-x}$ | $\left[0,+\infty \right]$ |

Component | Relative Permittivity | Conductivity |
---|---|---|

antenna | 1.00 | PEC |

battery | 1.00 | PEC |

battery jar | 5.00 | PEC |

display screen | 4.80 | 0.01 |

PCB | 1.00 | PEC |

phone receiver | 1.00 | PEC |

loudspeaker | 1.00 | PEC |

speaker connector | 1.00 | PEC |

inner shell | 2.30 | PEC |

shell | 2.20 | PEC |

camera | 1.90 | PEC |

casing pipe | 3.00 | 0.01 |

vibrator | 1.00 | PEC |

**Table 3.**Variables of the mobile phone electromagnetic radiation safety assessment for the human head.

Dielectric Constant | Distribution Pattern | Distribution Interval |
---|---|---|

camera | uniform | [1.8,2.0] |

battery jar | uniform | [4.8,5.2] |

inner shell | normal | [2.3,0.52] |

shell | uniform | [2.0,2.4] |

Frequency | Output Mean | Standard Deviation | ||
---|---|---|---|---|

MC | gPC | MC | gPC | |

2.1 GHz | 0.9576 | 0.9580 | 0.0274 | 0.0277 |

2.3 GHz | 1.4436 | 1.4431 | 0.0159 | 0.0165 |

3.5 GHz | 1.7621 | 1.7622 | 0.0511 | 0.0501 |

5.2 GHz | 1.7737 | 1.7731 | 0.0119 | 0.0117 |

Frequency | 2.1 GHz | 2.3 GHz | 3.5 GHz | 5.2 GHz |
---|---|---|---|---|

mean | 0.9580 | 1.4431 | 1.7622 | 1.7731 |

STD | 0.0277 | 0.0165 | 0.0501 | 0.0117 |

minimum | 0.8804 | 1.3993 | 1.6557 | 1.7380 |

maximum | 1.0098 | 1.4885 | 1.8662 | 1.8078 |

lower 90% | 0.9051 | 1.4159 | 1.6846 | 1.7548 |

upper 90% | 0.9985 | 1.4706 | 1.8443 | 1.7928 |

lower 95% | 0.8978 | 1.4122 | 1.6756 | 1.7529 |

upper 95% | 1.0019 | 1.4749 | 1.8513 | 1.7962 |

lower 99% | 0.8885 | 1.4056 | 1.6633 | 1.7502 |

upper 99% | 1.0062 | 1.4807 | 1.8607 | 1.8016 |

Computational Method | Computation Time |
---|---|

gPC | 35 min 20 s |

MC | 16 h 36 min |

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**MDPI and ACS Style**

Yi, M.; Wu, B.; Zhao, Y.; Su, T.; Chi, Y.
Safety Assessment and Uncertainty Quantification of Electromagnetic Radiation from Mobile Phones to the Human Head. *Appl. Sci.* **2023**, *13*, 8107.
https://doi.org/10.3390/app13148107

**AMA Style**

Yi M, Wu B, Zhao Y, Su T, Chi Y.
Safety Assessment and Uncertainty Quantification of Electromagnetic Radiation from Mobile Phones to the Human Head. *Applied Sciences*. 2023; 13(14):8107.
https://doi.org/10.3390/app13148107

**Chicago/Turabian Style**

Yi, Miao, Boqi Wu, Yang Zhao, Tianbo Su, and Yaodan Chi.
2023. "Safety Assessment and Uncertainty Quantification of Electromagnetic Radiation from Mobile Phones to the Human Head" *Applied Sciences* 13, no. 14: 8107.
https://doi.org/10.3390/app13148107