Radiation Shielding Structure Multi-objective Optimization of Imagine Sensors Based on Monte-Carlo Variance Reduction Method

doi:10.3969/j.issn.1004-132X.2026.05.004

Abstract

Abstract:

The radiation simulation method and shielding structure multi-objective optimization design method were proposed based on MC variance reduction for the radiation shielding problems of image sensors in nuclear radiation environments. According to the principles of coupled neutron and photon transport， a multi radiation source composite shielding model was constructed for image sensors， and a shielding simulation method of characteristic interpolation weight window MC variance reduction was proposed for the thick-shielding micro-detection structure characteristics， effectively improving the computational efficiency and accuracy of the shielding simulation. By combining the genetic algorithms with parameterized geometric modeling of radiation shielding structures， a multi-objective optimization design method for image sensors was constructed to obtain the optimal solution under volume， mass， and dose rate parameters and obtain a non-dominated solution combination of Pareto front. Numerical experiments verified the effectiveness of the imagine sensor radiation shielding structure optimization design method.

Key words: imagine sensor, radiation shielding, multi-objective optimization, Monte-Carlo（MC） particle transport, variance reduction method

摘要：

针对核辐射环境下图像传感器辐射屏蔽问题，提出基于蒙特卡罗（MC）减方差的辐射仿真方法和屏蔽结构多目标优化设计方法。根据中子和光子耦合输运原理构建图像传感器的多辐射源复合屏蔽模型，并针对其厚屏蔽微探测结构特征提出特征插值权窗MC减方差的屏蔽仿真方法，有效提高了其屏蔽仿真的计算效率与精度；通过将遗传算法与辐射屏蔽结构参数化几何建模结合，构建图像传感器的多目标优化设计方法，以获得体积、质量和剂量率参数下最优解并得到Pareto前沿的非劣解组合。数值实验验证了该图像传感器辐射屏蔽结构优化设计方法的有效性。

关键词: 图像传感器, 辐射屏蔽, 多目标优化设计, 蒙特卡罗粒子输运, 减方差方法

CLC Number:

TP182

FU Haocheng, WU Shaowei, JIANG Chao. Radiation Shielding Structure Multi-objective Optimization of Imagine Sensors Based on Monte-Carlo Variance Reduction Method[J]. China Mechanical Engineering, 2026, 37(5): 1045-1053.

付昊成, 吴少伟, 姜潮. 基于蒙特卡罗减方差方法的图像传感器辐射屏蔽结构多目标优化设计[J]. 中国机械工程, 2026, 37(5): 1045-1053.

Figures/Tables 26

Fig.1 Straight tube composite shielding structure

Fig.2 Simplified CSG model

Fig.3 Sampling process diagram of spherical shell source

Fig.4 Spatial flux distribution of spherical shell source

Fig.5 Prior weight windows

Fig.6 Characteristics weight window

Fig.7 Comparison with different sampling numbers

Fig.8 Comparation of FOM factor relative scale

Fig.9 Comparation of relative standard error

Fig.10 Comparation of calculation time

Fig.11 Design of optimization variable

Tab.1 Code of material selections

材料编号	二进制编码	材料	密度/（g·cm $- 3$ ）
0	0000	玻璃	2.40
1	0001	含硼玻璃	2.23
2	0010	铅玻璃	6.22
3	0011	石英玻璃	2.20
4	0100	铅	11.35
5	0101	锻钢	7.70
6	0110	灰铸铁	7.15
7	0111	302不锈钢	7.86
8	1000	铝	2.73
9	1001	钨	19.30
10	1010	PE	0.93
11	1011	PET	1.38
12	1100	含硼PE	1.00

Tab.1 Code of material selections

材料编号	二进制编码	材料	密度/（g·cm $- 3$ ）
0	0000	玻璃	2.40
1	0001	含硼玻璃	2.23
2	0010	铅玻璃	6.22
3	0011	石英玻璃	2.20
4	0100	铅	11.35
5	0101	锻钢	7.70
6	0110	灰铸铁	7.15
7	0111	302不锈钢	7.86
8	1000	铝	2.73
9	1001	钨	19.30
10	1010	PE	0.93
11	1011	PET	1.38
12	1100	含硼PE	1.00

Tab.2 Parameter combination

组号	C_R	C_V	C_W
1	0.8	0.1	0.1
2	0.7	0.2	0.1
3	0.6	0.3	0.1
4	0.6	0.2	0.2
5	0.5	0.4	0.1
6	0.5	0.3	0.2

Fig.12 Iterative optimization results of objective function

Fig.13 Iterative optimization results of dose rate

Fig.14 Iterative optimization results of volume

Fig.15 Iterative optimization results of mass

Tab.3 Optimization results of different group

组号	剂量率/（Gy·h $- 1$ ）	体积/cm³	质量/kg	x₁/cm	x₂/cm	x₃/cm	x₄/cm	x₅/cm	x₆/cm	m₁	m₂	m₃	m₄
1	0.040	5931	50.509	3.82	1.90	4.07	1.41	4.09	3.67	2	1	10	9
2	0.055	4730	23.123	4.11	1.74	0.79	3.92	3.80	2.70	2	3	9	12
3	0.052	4476	15.508	3.30	4.14	0.11	4.69	2.43	2.70	3	2	9	10
4	0.047	5300	22.425	4.19	2.98	0.83	4.00	2.67	4.30	3	2	9	12
5	0.065	3090	35.300	0.90	3.29	1.82	1.92	1.22	3.45	1	2	10	9
6	0.054	4223	15.017	2.78	4.80	0.06	4.54	2.55	0.53	2	1	9	12

Tab.3 Optimization results of different group

组号	剂量率/（Gy·h $- 1$ ）	体积/cm³	质量/kg	x₁/cm	x₂/cm	x₃/cm	x₄/cm	x₅/cm	x₆/cm	m₁	m₂	m₃	m₄
1	0.040	5931	50.509	3.82	1.90	4.07	1.41	4.09	3.67	2	1	10	9
2	0.055	4730	23.123	4.11	1.74	0.79	3.92	3.80	2.70	2	3	9	12
3	0.052	4476	15.508	3.30	4.14	0.11	4.69	2.43	2.70	3	2	9	10
4	0.047	5300	22.425	4.19	2.98	0.83	4.00	2.67	4.30	3	2	9	12
5	0.065	3090	35.300	0.90	3.29	1.82	1.92	1.22	3.45	1	2	10	9
6	0.054	4223	15.017	2.78	4.80	0.06	4.54	2.55	0.53	2	1	9	12

Fig.16 Relative rate of optimization results

Tab.4 Weight factor correlation coefficient

	C_R	C_V	C_M
剂量率	$-$ 0.74	0.82	0.57
体积	$-$ 0.97	$-$ 0.97	$-$ 0.42
质量	$-$ 0.15	0.11	$-$ 0.46

Tab.4 Weight factor correlation coefficient

	C_R	C_V	C_M
剂量率	$-$ 0.74	0.82	0.57
体积	$-$ 0.97	$-$ 0.97	$-$ 0.42
质量	$-$ 0.15	0.11	$-$ 0.46

Fig.17 Distribution of non-inferior solutions in Group 1

Fig.18 Distribution of non-inferior solutions in Group 2

Fig.19 Distribution of non-inferior solutions in Group 3

Fig.20 Distribution of non-inferior solutions in Group 4

Fig.21 Distribution of non-inferior solutions in Group 5

Fig.22 Distribution of non-inferior solutions in Group 6

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