考虑溅射刻蚀的离子推力器可靠性建模与实验验证方法

陈世舜; 李晓阳; 李泊远; 李婧; 贾艳辉; 耿海; 康锐

doi:10.13224/j.cnki.jasp.20250561

考虑溅射刻蚀的离子推力器可靠性建模与实验验证方法

doi: 10.13224/j.cnki.jasp.20250561

陈世舜^1,,
李晓阳^1,*, ,,
李泊远¹,
李婧²,
贾艳辉²,
耿海²,
康锐^{1, 3}

1.
北京航空航天大学可靠性与系统工程学院，北京 100191
2.
兰州空间技术物理研究所真空技术与物理重点实验室，兰州 730000
3.
北京航空航天大学杭州创新研究院，杭州 310051

基金项目: 国家自然科学基金（62073009，51775020）

详细信息

作者简介:
陈世舜（1999-），男，博士生，主要从事确信可靠性建模、可靠性实验等方面的研究。E-mail：css1107@buaa.edu.cn

通讯作者:
李晓阳（1980-），女，博士，教授，主要从事确信可靠性建模、可靠性实验等方面的研究。E-mail：leexy@buaa.edu.cn

中图分类号: V43
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- 被引次数: 0
出版历程
- 收稿日期: 2025-12-04
- 网络出版日期: 2026-05-30

Reliability modeling and experimental verification method for ion thrusters considering sputtering erosion

Chen Shishun^1
,,
Li Xiaoyang^{1,*
, ,},
Li Boyuan¹,
Li Jing²,
Jia Yanhui²,
Geng Hai²,
Kang Rui^{1, 3}

1.
School of Reliability and Systems Engineering，Beihang University，Beijing 100191，China
2.
National Key Laboratory of Vacuum and Cryogenic Technology on Physics，Lanzhou Institute of Physics，Lanzhou 730000，China
3.
Hangzhou International Innovation Institute，Beihang University，Hangzhou 310051，China

摘要

摘要:
针对深空探测任务中具备多个工作模式的LIPS-300S离子推力器，构建从可靠性建模、实验设计到模型更新验证的确信可靠性建模与验证框架。基于确信可靠性理论，针对溅射刻蚀导致的加速栅电子反流失效，建立多模式离子推力器的可靠性模型。以准确验证退化规律为目标，提出离子推力器的实验设计方法。根据实验的控制与观测能力，对学科交叉方程进行等价性更新，避免难以验证的精细物理推导带来的模型偏差。另外，引入线性修正因子对退化方程进行校准，修正仿真模拟与实际之间的偏差。通过LIPS-300S离子推力器12 000 h的可靠性实验数据，验证所提方法的有效性。结果表明：更新校准后的性能模型能够准确表征不同工作模式下加速栅中心孔径与电子反流极限电压的关系，其中80%的预测偏差小于5%，而校准后的退化模型对加速栅中心孔径刻蚀的最大预测偏差不超过0.5%，支撑了多工作模式下可信的离子推力器可靠性评估，同时相比传统实验方法将验证可靠性所需的实验时间缩短了3倍。
- 多模式 /
- 离子推力器 /
- 电子反流失效 /
- 确信可靠性 /
- 可靠性实验 /
- 模型验证 /
- 等价性更新 /
- 可靠性评估
Abstract:
For the LIPS-300S ion thruster, which operates in multiple operating modes for deep space exploration missions, a belief reliability modeling, experiment design and verification framework was established. This framework encompassed reliability modeling, experimental design, and model updating and verification. A reliability model for the multi-mode ion thruster was constructed based on belief reliability theory considering sputtering erosion-induced electron backstreaming failure. An experimental design method was proposed with the aim of accurately verifying the degradation laws of the ion thruster. Subsequently, equivalence updating was applied to interdisciplinary equations based on the experimental controllable and measurable capabilities, mitigating model biases caused by unverified detailed physical derivations. Additionally, a linear correction factor was introduced to calibrate the degradation equations, addressing discrepancies between simulations and actual performance degradation. The effectiveness of the framework was validated using 12,000 h reliability experimental data from the LIPS-300S ion thruster. The results demonstrate that the updated and calibrated model can accurately characterize the performance and degradation patterns of the ion thruster across different operating modes, with 80% of the prediction errors within 5%. This work supports credible reliability evaluation for multi-mode ion thrusters, and effectively shortens the experimental time for reliability verification.
- multi-mode /
- ion thruster /
- electron backstreaming failure /
- belief reliability /
- reliability experiment /
- model validation /
- equivalence updating /
- reliability assessment

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图 1 论文研究方法

Figure 1. Technical scheme of the study

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图 2 离子推力器工作原理图

Figure 2. Working principle of the ion thruster

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图 3 离子推力器加速栅中心孔径的测量仪器

Figure 3. Instruments for measuring the accel grid central aperture diameter of ion thruster

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图 4 归一化后的加速栅中心孔直径实测值

Figure 4. Measurements of accel grid central aperture diameter after normalization

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图 5 归一化后不同工作模式下的电子反流极限电压实测值

Figure 5. Measurements of electron backstreaming voltage in different operating modes after normalization

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图 6 离子推力器在s₂₃条件下的电参数分布

Figure 6. Distribution of electrical parameters of the ion thruster at s₂₃ operating mode

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图 7 归一化后不同工作模式下的电子反流极限电压计算值与实测值对比

Figure 7. Comparison of calculated and measured electron backstreaming voltage in different operating modes after normalization

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图 8 归一化后的加速栅中心孔径预测值与实测值对比

Figure 8. Comparison of predicted and measured accel grid central aperture diameter after normalization

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图 9 离子推力器性能裕量随工作时间和工作模式的变化

Figure 9. Variation of performance margin of ion thruster with operating time and operating mode

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图 10 给定任务剖面下离子推力器的性能裕量退化和可靠度曲线

Figure 10. Performance margin degradation and reliability curves of the ion thruster for the given mission profile

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图 11 离子推力器电参数敏感性分析结果

Figure 11. Sensitivity analysis results of electric parameters of ion thrusters

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表 1 加速栅中心孔刻蚀速率的关键影响因素

Table 1. Key factors affecting the accel central aperture erosion rate

关键影响因素	对CEX离子的影响
V_s	能量
V_a	能量
l_g	能量、撞击角度
N_m	数量
d_a	撞击角度

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表 2 离子推力器设计参数

Table 2. Design parameters of an ion thruster

设计参数	数值	设计参数	数值
d_s/mm	1.9	l_d/mm	4
t_s/mm	0.4	V_d/V	30
A_s/cm²	706.86	t_a/mm	0.5
T_s	0.7	T_eu/eV	5
l_c/mm	1	d_a0/mm	1.25

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表 3 仿真实验影响因素及水平

Table 3. Impact factors and levels of simulation experiments

影响因素	因素型号	水平
影响因素	因素型号	−1	0	1
V_s/V	A	420	840	1260
V_a/V	B	−220	−200	−180
l_g/mm	C	0.4	0.6	0.8
N_m/10¹⁶	D	4	16	28
d_a/mm	E	1.25	1.575	1.9

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表 4 备选实验方案

Table 4. Optional accelerated experimental schemes

方案	实验时间/h
方案	s₂₃	s₁₅	s₆	s₃
方案1	3000	6000	1500	1500
方案2	3500	5500	1500	1500
方案3	4000	5000	1500	1500

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表 5 各工作模式的工作参数设置

Table 5. Operating parameter settings for each operating mode

参数	s₂₃	s₁₅	s₆	s₃
V_s/V	1260	1050	840	630
I_b/A	2.1	1.4	0.7	0.5
V_a/V	−200	−200	−200	−200
I_d/A	16	11	6.5	5

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表 6 各实验方案的指标结果

Table 6. Results of each experimental scheme

方案	s₂₃
方案	s₂₃	s₁₅	s₆	s₃	ϕ
方案1	3000	6000	1500	1500	0.6382
方案2	3500	5500	1500	1500	0.6798
方案3	4000	5000	1500	1500	0.6787

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表 7 学科交叉方程中各个参数的可控可测性

Table 7. Controllability and measurability of each parameter in the interdisciplinary equations

公式	输出	输出是否可观测	可控参数	可测参数	常量	不可控且不可测参数	未知参数
（1）	V_m	√	t_a, l_d, I_b	d_a		∆V, V_bp, V_dp, l_e
（2）	∆V	×		d_a	m_i, ε₀, e	I_bs, d_b, V_dp, V_sp
（3）	I_bs	×	V_a		m_i, ε₀, e	d_b, V_dp, l_e
（4）	V_sp	×	t_a, l_d, V_a	d_a		V_bp, V_dp, l_e
（5）	V_bp	×	I_b		m_i, m_e	V_f	p₁, p₂
（6）	V_dp	×	V_s, V_d
（7）	l_e	×	t_s, l_c, d_s, V_d, I_d				x₁, x₂

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表 8 裕量模型未知参数估计结果

Table 8. Estimation results of unknown parameters in the margin model

未知参数	估计值	未知参数	估计值
x₁	7.771 8×10⁻⁴	x₄	0.8625
x₂	−0.1068	x₅	6.6372
x₃	0.1047	x₆	13.1378

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表 9 电参数不确定性量化结果

Table 9. Uncertainty quantization results of electrical parameters

参数	数值
$C_{V_{\mathrm{s}}} $	0.00399
$C_{I_{\mathrm{b}}} $	0.0097
$C_{I_{\mathrm{d}}} $	0.0509
$C_{V_{\mathrm{a}}} $	0.0073

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表 10 离子推力器任务剖面

Table 10. Mission profile of the ion thruster

序号	工作模式	屏栅电压/V	屏栅电流/A	加速栅电压/V	阳极电流/A	工作时间/h
1	s₂₃	1260	2.1	−200	16	50000
2	s₂₀	1050	1.9	−200	14.5	40000
3	s₁₅	1050	1.4	−200	11	80000

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参考文献(35)

[1]	朱智春, 林庆国, 杭观荣, 等. 我国空间推进技术研究现状及发展[J]. 上海航天, 2021, 38(3): 178-188. Zhu Zhichun, Lin Qingguo, Hang Guanrong, et al. Research status and development of space propulsion technology in China[J]. Aerospace Shanghai, 2021, 38(3): 178-188. (in Chinese doi: 10.19328/j.cnki.2096-8655.2021.03.020 Zhu Zhichun, Lin Qingguo, Hang Guanrong, et al. Research status and development of space propulsion technology in China[J]. Aerospace Shanghai, 2021, 38(3): 178-188. (in Chinese) doi: 10.19328/j.cnki.2096-8655.2021.03.020
[2]	张天平, 耿海, 张雪儿, 等. 离子电推进技术的发展现状与未来[J]. 上海航天, 2019, 36(6): 88-96. Zhang Tianping, Geng Hai, Zhang Xueer, et al. Current status and future development of ion electric propulsion[J]. Aerospace Shanghai, 2019, 36(6): 88-96. (in Chinese doi: 10.19328/j.cnki.1006-1630.2019.06.013 Zhang Tianping, Geng Hai, Zhang Xueer, et al. Current status and future development of ion electric propulsion[J]. Aerospace Shanghai, 2019, 36(6): 88-96. (in Chinese) doi: 10.19328/j.cnki.1006-1630.2019.06.013
[3]	Polk J, Anderson J, Brophy J, et al. An overview of the results from an 8200 hour wear test of the NSTAR ion thruster[R]. AIAA 1999-2446, 1999.
[4]	Van Noord J. Lifetime assessment of the NEXT ion thruster[R]. AIAA-2007-5274, 2007.
[5]	Zhong Lingwei, Liu Yu, Li Juan, et al. Numerical simulation of characteristics of CEX ions in ion thruster optical system[J]. Chinese Journal of Aeronautics, 2010, 23(1): 15-21. doi: 10.1016/S1000-9361(09)60182-5
[6]	Sun Anbang, Mao Genwang, Yang Juan, et al. Particle simulation of three-grid ECR ion thruster optics and erosion prediction[J]. Plasma Science and Technology, 2010, 12(2): 240-247. doi: 10.1088/1009-0630/12/2/21
[7]	Wirz R E, Anderson J R, Goebel D M, et al. Decel grid effects on ion thruster grid erosion[J]. IEEE Transactions on Plasma Science, 2008, 36(5): 2122-2129. doi: 10.1109/TPS.2008.2001041
[8]	Kaufman H R. Technology of electron-bombardment ion thrusters[M]//Advances in Electronics and Electron Physics. Amsterdam: Elsevier, 1975: 265-373.
[9]	Peng Xiaohang, Ruyten W M, Friedly V J, et al. Particle simulation of ion optics and grid erosion for two-grid and three-grid systemsa)[J]. Review of Scientific Instruments, 1994, 65(5): 1770-1773. doi: 10.1063/1.1144823
[10]	任军学, 谢侃, 汤海滨, 等. 离子发动机加速栅极孔扩大腐蚀的粒子模拟[J]. 推进技术, 2013, 34(10): 1432-1440. Ren Junxue, Xie Kan, Tang Haibin, et al. Particle simulation of the acceleration grid aperture erosion in ion thruster[J]. Journal of Propulsion Technology, 2013, 34(10): 1432-1440. (in Chinese doi: 10.13675/j.cnki.tjjs.2013.10.019 Ren Junxue, Xie Kan, Tang Haibin, et al. Particle simulation of the acceleration grid aperture erosion in ion thruster[J]. Journal of Propulsion Technology, 2013, 34(10): 1432-1440. (in Chinese) doi: 10.13675/j.cnki.tjjs.2013.10.019
[11]	贾艳辉, 王聪, 李娟, 等. 三栅极离子推力器电子反流失效影响参数的敏感性研究[J]. 推进技术, 2020, 41(1): 140-148. Jia Yanhui, Wang Cong, Li Juan, et al. Parameter sensitivity analysis of electron backstreaming failure mode for 3-grid system ion thruster[J]. Journal of Propulsion Technology, 2020, 41(1): 140-148. (in Chinese doi: 10.13675/j.cnki.tjjs.190337 Jia Yanhui, Wang Cong, Li Juan, et al. Parameter sensitivity analysis of electron backstreaming failure mode for 3-grid system ion thruster[J]. Journal of Propulsion Technology, 2020, 41(1): 140-148. (in Chinese) doi: 10.13675/j.cnki.tjjs.190337
[12]	Chaplin V H, Goebel D M, Lewis R A, et al. Accelerator grid life modeling of T6 ion thruster for BepiColombo[J]. Journal of Propulsion and Power, 2021, 37(3): 436-449. doi: 10.2514/1.B37938
[13]	李军星, 张勇波, 王治华, 等. 基于加速栅溅射腐蚀失效的离子推力器寿命预测[J]. 航空动力学报, 2016, 31(5): 1047-1052. Li Junxing, Zhang Yongbo, Wang Zhihua, et al. Life prediction of ion thruster based on sputtering erosion failure of accelerator grid[J]. Journal of Aerospace Power, 2016, 31(5): 1047-1052. (in Chinese doi: 10.13224/j.cnki.jasp.2016.05.004 Li Junxing, Zhang Yongbo, Wang Zhihua, et al. Life prediction of ion thruster based on sputtering erosion failure of accelerator grid[J]. Journal of Aerospace Power, 2016, 31(5): 1047-1052. (in Chinese) doi: 10.13224/j.cnki.jasp.2016.05.004
[14]	赵以德, 吴宗海, 张天平, 等. 离子推力器多模式化研究[J]. 推进技术, 2020, 41(1): 187-193. Zhao Yide, Wu Zonghai, Zhang Tianping, et al. Research on multi-mode realization of ion thruster[J]. Journal of Propulsion Technology, 2020, 41(1): 187-193. (in Chinese doi: 10.13675/j.cnki.tjjs.190357 Zhao Yide, Wu Zonghai, Zhang Tianping, et al. Research on multi-mode realization of ion thruster[J]. Journal of Propulsion Technology, 2020, 41(1): 187-193. (in Chinese) doi: 10.13675/j.cnki.tjjs.190357
[15]	李建鹏, 靳伍银, 赵以德. 多模式离子推力器输入参数设计及工作特性研究[J]. 物理学报, 2022, 71(7): 265-273. Li Jianpeng, Jin Wuyin, Zhao Yide. Design of input parameters and operating characteristics for multi-mode ion thruster[J]. Acta Physica Sinica, 2022, 71(7): 265-273. (in Chinese Li Jianpeng, Jin Wuyin, Zhao Yide. Design of input parameters and operating characteristics for multi-mode ion thruster[J]. Acta Physica Sinica, 2022, 71(7): 265-273. (in Chinese)
[16]	Chen Shishun, Li Xiaoyang, Li Boyuan, et al. Belief reliability modeling and analysis for the three-grid ion thruster[C]//2021 5th International Conference on System Reliability and Safety. Piscataway, US: IEEE, 2021: 58-65.
[17]	李婧, 陈世舜, 贾艳辉, 等. 基于确信可靠度的离子推力器可靠性分析和试验设计[J]. 真空与低温, 2022, 28(5): 524-531. Li Jing, Chen Shishun, Jia Yanhui, et al. Reliability analysis and test design of ion thruster based on belief reliability theory[J]. Vacuum and Cryogenics, 2022, 28(5): 524-531. (in Chinese doi: 10.3969/j.issn.1006-7086.2022.05.004 Li Jing, Chen Shishun, Jia Yanhui, et al. Reliability analysis and test design of ion thruster based on belief reliability theory[J]. Vacuum and Cryogenics, 2022, 28(5): 524-531. (in Chinese) doi: 10.3969/j.issn.1006-7086.2022.05.004
[18]	Zhang Xueer, Zhang Tianping, Li Detian. Quantification of the lifetime and reliability of dual-mode ion thrusters[J]. Journal of Aerospace Technology and Management, 2022, 14: e0422. doi: 10.1590/jatm.v14.1247
[19]	Zhang Xueer, Zhang Tianping, Li Detian. Lifetime and Mission reliability assessment of multi-mode ion thruster[J]. Journal of Electric Propulsion, 2022, 1(1): 5. doi: 10.1007/s44205-022-00006-x
[20]	康锐. 确信可靠性理论与方法[M]. 北京: 国防工业出版社, 2020. Kang Rui. Belief reliability theory and methodology[M]. Beijing: National Defense Industry Press, 2020. (in Chinese Kang Rui. Belief reliability theory and methodology[M]. Beijing: National Defense Industry Press, 2020. (in Chinese)
[21]	Lu Chang, Zhang Tianping, Qiu Pei, et al. Barrel erosion of ion thruster accelerator grid under different operating conditions[J]. IEEE Transactions on Plasma Science, 2018, 46(12): 4065-4077. doi: 10.1109/TPS.2018.2865600
[22]	Jia Yanhui, Chen Juanjuan, Guo Ning, et al. 2D hybrid-PIC simulation of the two and three-grid system of ion thruster[J]. Plasma Science and Technology, 2018, 20(10): 105502. doi: 10.1088/2058-6272/aace52
[23]	Goebel D M, Katz I. Fundamentals of electric propulsion: ion and hall thrusters[M]. New York: John Wiley & Sons, 2008.
[24]	贾艳辉, 冯杰, 王亮, 等. LIPS-300多模式离子推力器中和器优化研究[J]. 真空与低温, 2018, 24(1): 15-18. Jia Yanhui, Feng Jie, Wang Liang, et al. The studying of neutralizer characterization of lips-300 multi-mode ion thruster[J]. Vacuum and Cryogenics, 2018, 24(1): 15-18. (in Chinese Jia Yanhui, Feng Jie, Wang Liang, et al. The studying of neutralizer characterization of lips-300 multi-mode ion thruster[J]. Vacuum and Cryogenics, 2018, 24(1): 15-18. (in Chinese)
[25]	Chen Juanjuan, Jia Yanhui, Geng Hai, et al. Investigation of variable aperture on the performance and lifetime of ion thruster[J]. Plasma Science and Technology, 2021, 23(10): 104002. doi: 10.1088/2058-6272/ac11af
[26]	Sun Mingming, Wang Liang, Yang Juntai, et al. Study of the key factors affecting the triple grid lifetime of the LIPS-300 ion thruster[J]. Plasma Science and Technology, 2018, 20(4): 045504. doi: 10.1088/2058-6272/aaa66a
[27]	陶有俊, Daniel Tao, 赵跃民, 等. 采用Design-Expert设计进行优化Falcon分选试验[J]. 中国矿业大学学报, 2005, 34(3): 343-348. Tao Youjun, Tao Daniel, Zhao Yuemin, et al. Design and optimization of falcon separation test using design-expert software[J]. Journal of China University of Mining & Technology, 2005, 34(3): 343-348. (in Chinese Tao Youjun, Tao Daniel, Zhao Yuemin, et al. Design and optimization of falcon separation test using design-expert software[J]. Journal of China University of Mining & Technology, 2005, 34(3): 343-348. (in Chinese)
[28]	Williams J, Goebel D, Wilbur P. Analytical model of electron backstreaming for ion thrusters[R]. AIAA 2003-4560, 2003.
[29]	Nadvornick W, Chang H Y, Alvarado A, et al. A linked-scale coupled model of mass erosion and redistribution in plasma-exposed micro-foam surfaces[J]. Journal of Nuclear Materials, 2021, 553: 153010. doi: 10.1016/j.jnucmat.2021.153010
[30]	Brooks J N. Modeling and analysis of erosion and redeposition for limiter and divertor impurity control systems[J]. Nuclear Technology: Fusion, 1983, 4(1): 33-45. doi: 10.13182/FST83-A22772
[31]	张天平, 张雪儿, 赵志伟, 等. 离子推力器寿命试验总结与展望[J]. 真空与低温, 2022, 28(1): 1-13. Zhang Tianping, Zhang Xue’er, Zhao Zhiwei, et al. Review and prospect of ion thruster life tests[J]. Vacuum and Cryogenics, 2022, 28(1): 1-13. (in Chinese doi: 10.3969/j.issn.1006-7086.2022.01.001 Zhang Tianping, Zhang Xue’er, Zhao Zhiwei, et al. Review and prospect of ion thruster life tests[J]. Vacuum and Cryogenics, 2022, 28(1): 1-13. (in Chinese) doi: 10.3969/j.issn.1006-7086.2022.01.001
[32]	Chen Dayu, Li Yao, Shangguan Yiyang, et al. Belief reliability modeling and analysis for TPS considering physical principles, degradation mechanism and epistemic uncertainties[J]. Chinese Journal of Aeronautics, 2025, 38(5): 103385. doi: 10.1016/j.cja.2024.103385
[33]	Tao Zhao, Chen Wenbin, Li Xiaoyang, et al. Belief reliability modeling of coarse tracking system for satellite optical communication[J]. Reliability Engineering & System Safety, 2025, 256: 110763. doi: 10.1016/j.ress.2024.110763
[34]	Tao Zhao, Chen Wenbin, Li Xiaoyang, et al. Reliability modelling and assessment of CMOS image sensor under radiation environment[J]. Chinese Journal of Aeronautics, 2024, 37(9): 297-311. doi: 10.1016/j.cja.2024.05.008
[35]	康锐, 李晓阳. 可靠性科学实验[J]. 航空学报, 2025, 46(5): 531706. Kang Rui, Li Xiaoyang. Reliability science experiments[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(5): 531706. (in Chinese Kang Rui, Li Xiaoyang. Reliability science experiments[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(5): 531706. (in Chinese)