基于多尺度仿真的长贮产品贮存寿命评估方法综述

doi:10.16182/j.issn1004731x.joss.25-0269

摘要/Abstract

摘要：

传统基于试验的长贮产品寿命评估方法存在耗时长、成本高、预测准确性低等缺陷，制约了长贮产品贮存寿命评估的实际应用效果。随着数字化仿真技术的发展，基于故障物理的仿真分析方法能够精准表征产品老化规律，成为贮存寿命评估领域的研究热点。分析了长贮产品的多尺度特征和典型贮存失效模式及失效机理；讨论了非金属材料、金属材料、元器件等基础产品贮存失效的多尺度建模与仿真分析方法；按照产品类别梳理了整机产品贮存寿命评估方法；提出了长贮产品贮存寿命评估未来发展方向，进一步丰富和完善了由微观损伤到宏观失效的贮存寿命仿真整体技术路线。

关键词: 多尺度仿真, 贮存失效, 老化规律仿真, 贮存寿命预测

Abstract:

Traditional experiment-based life assessment methods for long-term storage products suffer from drawbacks such as prolonged duration, high cost, and low prediction accuracy, greatly limiting the effectiveness of storage life assessment in practical applications. With the advancement of digital simulation technology, simulation analysis methods based on the physics of failure (PoF) have emerged as a research hotspot in the field of storage life assessment, as they can accurately characterize product aging behavior. The multi-scale characteristics of long-term storage products and their typical storage failure modes and mechanisms were analyzed. Multi-scale modeling and simulation analysis methods for storage failures of fundamental products were discussed, including non-metallic materials, metallic materials, and electronic components. Storage life assessment methods for complete equipment were reviewed by product categories. Future development directions for the storage life assessment of long-term storage products were proposed. This paper further enriched and refined the overall technical roadmap for storage life simulation from microscopic damage to macroscopic failure.

Key words: multi-scale simulation, storage failure, aging behavior simulation, storage life prediction

中图分类号:

TJ760.89

李宏民,韩笑,黄硕等 . 基于多尺度仿真的长贮产品贮存寿命评估方法综述[J]. 系统仿真学报, 2025, 37(8): 1907-1920.

Li Hongmin,Han Xiao,Huang Shuo,et al . Storage Life Assessment Methods for Long-term Storage Products Based on Multi-scale Simulation: A Review[J]. Journal of System Simulation, 2025, 37(8): 1907-1920.

图/表 5

参考文献 80

[1]	王凯. 导弹武器系统贮存环境监测及贮存可靠性评定方法研究[D]. 哈尔滨: 哈尔滨理工大学, 2012.
	Wang Kai. Missile Weapon System Environmental Monitoring and Storage Reliability Assessment Methods[D]. Harbin: Harbin University of Science and Technology, 2012.
[2]	于运治, 李建林, 龚红良. 导弹贮存的失效模式及失效机理[J]. 四川兵工学报, 2009, 30(4): 27-29.
[3]	李锴, 高军, 李小兵, 等. 装备贮存寿命综合评价方案[J]. 电子产品可靠性与环境试验, 2015, 33(4): 50-54.
	Li Kai, Gao Jun, Li Xiaobing, et al. Comprehensive Evaluation Scheme for the Storage Life of Equipment[J]. Electronic Product Reliability and Environmental Testing, 2015, 33(4): 50-54.
[4]	蒙上阳, 杨晓红, 杨军辉. 野战火箭发动机结构完整性评估数值方法[M]. 北京: 国防工业出版社, 2015.
	Meng Shangyang, Yang Xiaohong, Yang Junhui. Numerical Method of Structural Integrity Evaluation of Field Rocket Motor[M]. Beijing: National Defense Industry Press, 2015.
[5]	周永康. Nb521合金高温蠕变-疲劳交互多尺度损伤机制及寿命预测[D]. 西安: 西安理工大学, 2024.
	Zhou Yongkang. Multi-scale Creep-fatigue Interaction Failure Mechanism and Life Prediction of Nb521 Alloy at High Temperature[D]. Xi'an: Xi'an University of Technology, 2024.
[6]	周金宇, 陈逸飞. 基于多尺度模拟的SLM金属件疲劳性能预测[J/OL]. 中国机械工程. (2025-01-17) [2025-03-02]. .
	Zhou Jinyu, Chen Yifei. Prediction of Fatigue Property of SLM Metal Parts Based on Multi-scale Simulation[J/OL]. China Mechanical Engineering. (2025-01-17) [2025-03-02]. .
[7]	吴佰建, 李兆霞, 汤可可. 大型土木结构多尺度模拟与损伤分析-从材料多尺度力学到结构多尺度力学[J]. 力学进展, 2007, 37(3): 321-336.
	Wu Baijian, Li Zhaoxia, Tang Keke. Multi-scale Modeling and Damage Analyses of Large Civil Structure-multi-scale Mechanics from Material to Structure[J]. Advances in Mechanics, 2007, 37(3): 321-336.
[8]	Liu Xuan, Furrer D, Kosters J, et al. Vision 2040: A Roadmap for Integrated, Multiscale Modeling and Simulation of Materials and Systems[EB/OL]. (2018-03-01) [2025-03-02]. .
[9]	李宏伟, 高佳, 孙新新, 等. 面向高性能塑性成形的多尺度建模仿真研究进展[J]. 机械工程学报, 2024, 60(1): 27-43.
	Li Hongwei, Gao Jia, Sun Xinxin, et al. Research Developments on Multiscale Modeling and Simulation towards High-performance Plastic Forming[J]. Journal of Mechanical Engineering, 2024, 60(1): 27-43.
[10]	肖李军, 李实, 冯根柱, 等. 增材制造三维微点阵材料力学性能表征与细观优化设计研究进展[J]. 固体力学学报, 2023, 44(6): 718-754.
	Xiao Lijun, Li Shi, Feng Genzhu, et al. Research Progress in Mechanical Characterization and Mesoscopic Optimal Design of Additively-manufactured 3D Microlattice Materials[J]. Chinese Journal of Solid Mechanics, 2023, 44(6): 718-754.
[11]	徐会会, 奥妮, 吴圣川, 等. 金属结构材料腐蚀疲劳寿命预测模型的研究进展[J]. 固体力学学报, 2023, 44(1): 1-33.
	Xu Huihui, Ao Ni, Wu Shengchuan, et al. Research Progress on Corrosion Fatigue Life Prediction Models of Metal Structural Materials[J]. Chinese Journal of Solid Mechanics, 2023, 44(1): 1-33.
[12]	张生鹏, 马小兵, 刘浩然, 等. 导弹产品贮存寿命多源信息融合评估技术综述[J]. 装备环境工程, 2023, 20(10): 39-46.
	Zhang Shengpeng, Ma Xiaobing, Liu Haoran, et al. A Review on Multi-source Information Fusion Evaluation Techniques for Missile Products Storage Life[J]. Equipment Environmental Engineering, 2023, 20(10): 39-46.
[13]	侯晓, 张旭, 刘向阳, 等. 固体火箭发动机药柱结构完整性研究进展[J]. 宇航学报, 2023, 44(4): 566-579.
	Hou Xiao, Zhang Xu, Liu Xiangyang, et al. Research Progress on Structural Integrity of Solid Rocket Motor Grain[J]. Journal of Astronautics, 2023, 44(4): 566-579.
[14]	李维燕. 基于应力松弛的弹用电磁继电器贮存可靠性分析方法研究[D]. 镇江: 江苏科技大学, 2021.
	Li Weiyan. Study on Storage Reliability Analysis Method of Elastic Electromagnetic Relay Based on Stress Relaxation[D]. Zhenjiang: Jiangsu University of Science and Technology, 2021.
[15]	魏薪, 董超芳, 徐奥妮, 等. 金属腐蚀的多尺度计算模拟研究进展[J]. 中国材料进展, 2018, 37(1): 1-8.
	Wei Xin, Dong Chaofang, Xu Aoni, et al. Progress in Multi-scale Calculation and Simulation of Metal Corrosion[J]. Materials China, 2018, 37(1): 1-8.
[16]	Sood B, Das D, Azarian M, et al. Failure Site Isolation on Passive RFID Tags[C]//2008 15th International Symposium on the Physical and Failure Analysis of Integrated Circuits. Piscataway: IEEE, 2008: 1-5.
[17]	黄姣英, 曹阳, 高成. 微电子封装焊点疲劳失效研究综述[J]. 电子元件与材料, 2020, 39(10): 11-16, 24.
	Huang Jiaoying, Cao Yang, Gao Cheng. Fatigue Failure of Microelectronic Packaging Solder Joints: A Review[J]. Electronic Components and Materials, 2020, 39(10): 11-16, 24.
[18]	李国忠, 曾江, 赵慧. 弹用涡轮发动机贮存失效模式及失效机理分析[J]. 飞航导弹, 2014(6): 76-80.
[19]	Chaube Suryanaman, Mishra Shashank, Maiti Soumyadipta, et al. Multiscale Analysis of Large-strain Deformation Behaviour of Random Cross-linked Elastomers[J]. Molecular Simulation, 2019, 45(2): 111-119.
[20]	Joshi S Y, Deshmukh S A. A Review of Advancements in Coarse-grained Molecular Dynamics Simulations[J]. Molecular Simulation, 2021, 47(10/11): 786-803.
[21]	袁斌. 纳米颗粒填充橡胶的粗粒化分子动力学模拟及跨尺度研究[D]. 哈尔滨: 哈尔滨工业大学, 2022.
	Yuan Bin. Coarse-grained Molecular Dynamics Simulation and Cross-scale Research of Nanoparticle-filled Rubber[D]. Harbin: Harbin Institute of Technology, 2022.
[22]	Ernst Gerald, Vogler Matthias, Hühne Christian, et al. Multiscale Progressive Failure Analysis of Textile Composites[J]. Composites Science and Technology, 2010, 70(1): 61-72.
[23]	翟军军. 基于多尺度理论的三维编织复合材料力学性能研究[D]. 哈尔滨: 哈尔滨理工大学, 2018.
	Zhai Junjun. Investigation of Mechanical Properties of 3D Braided Composites Based on Multi-scale Theory[D]. Harbin: Harbin University of Science and Technology, 2018.
[24]	曾翔龙, 王奇志. 二维机织C/SiC复合材料非线性力学行为数值模拟[J]. 宇航材料工艺, 2017, 47(1): 29-36.
	Zeng Xianglong, Wang Qizhi. Numerical Simulation of Nonlinear Mechanics Behavior for 2D Weave Composites[J]. Aerospace Materials & Technology, 2017, 47(1): 29-36.
[25]	吕晋书, 马玉钦, 庞利沙, 等. 基于ANSYS的多尺度GO-CF/EP复合材料弯曲性能仿真及试验验证[J]. 复旦学报(自然科学版), 2024, 63(4): 481-491.
	Jinshu Lü, Ma Yuqin, Pang Lisha, et al. Simulation and Experimental Verification of Multi-scale GO-CF/EP Composites Based on ANSYS[J]. Journal of Fudan University(Natural Science), 2024, 63(4): 481-491.
[26]	王奇志, 林慧星, 许赟泉. 二维编织陶瓷基复合材料偏轴拉伸力学性能预测[J]. 复合材料学报, 2018, 35(12): 3423-3432.
	Wang Qizhi, Lin Huixing, Xu Yunquan. Mechanical Properties Prediction of 2D Braided Ceramic Matrix Composites Under off-axial Tension[J]. Acta Materiae Compositae Sinica, 2018, 35(12): 3423-3432.
[27]	王晓峰. 含能材料的多尺度结构及其研究意义[J]. 含能材料, 2024, 32(10): 1011-1013.
	Wang Xiaofeng. Multi Scale Structure of Energetic Materials and Its Research Significance[J]. Chinese Journal of Energetic Materials, 2024, 32(10): 1011-1013.
[28]	梁蔚, 吕庆山, 陈雄, 等. 温度对HTPB推进剂疲劳特性的影响[J]. 含能材料, 2017, 25(3): 184-190.
	Liang Wei, Qingshan Lü, Chen Xiong, et al. Effect of Temperature on Fatigue Properties of HTPB Propellant[J]. Chinese Journal of Energetic Materials, 2017, 25(3): 184-190.
[29]	顾志旭, 郑坚, 彭威, 等. 基于不可逆热力学的宏细观粘弹性损伤本构模型[J]. 推进技术, 2018, 39(2): 396-403.
	Gu Zhixu, Zheng Jian, Peng Wei, et al. A Marco-micro Viscoelastic Damage Constitutive Model Based on Irreversible Thermodynamic[J]. Journal of Propulsion Technology, 2018, 39(2): 396-403.
[30]	张鑫, 胡翔, 徐星星, 等. GAP黏合剂基体与ε-CL-20界面作用[J].含能材料, 2021, 29(11): 1099-1105.
	Zhang Xin, Hu Xiang, Xu Xingxing, et al. Surface Interaction Between GAP Binder Matrix and ε-CL-20[J]. Chinese Journal of Energetic Materials, 2021, 29(11): 1099-1105.
[31]	强洪夫, 王稼祥, 王哲君, 等. 复合固体推进剂强度、损伤与断裂失效研究进展[J]. 火炸药学报, 2023, 46(7): 561-588.
	Qiang Hongfu, Wang Jiaxiang, Wang Zhejun, et al. Research Progress on Strength, Damage and Fracture Failure of Composite Solid Propellants[J]. Chinese Journal of Explosives & Propellants, 2023, 46(7): 561-588.
[32]	张淇钧. 基于晶体塑性的P91钢高温蠕变细观力学模拟研究[D]. 哈尔滨: 哈尔滨工业大学, 2019.
	Zhang Qijun. Crystal Plasticity Based Micromechanical Simulation and Investigation of Creep for P91 Steels[D]. Harbin: Harbin Institute of Technology, 2019.
[33]	Xiao Xiazi, Li Shilin, Yu Long. A General Steady-state Creep Model Incorporating Dislocation Static Recovery for Pure Metallic Materials[J]. International Journal of Plasticity, 2022, 157: 103394.
[34]	Tawqeer Nasir Tak, Prakash Aditya, Keralavarma Shyam M, et al. A Discrete Dislocation Dynamics Model of Creep in Polycrystals[J]. Journal of the Mechanics and Physics of Solids, 2023, 179: 105385.
[35]	李凯尚, 王润梓, 张显程, 等. 基于多尺度建模方法的蠕变-疲劳寿命预测[J]. 压力容器, 2021, 38(11): 73-81.
	Li Kaishang, Wang Runzi, Zhang Xiancheng, et al. Creep-fatigue Life Prediction Based on Multi-scale Modelling Approach[J]. Pressure Vessel Technology, 2021, 38(11): 73-81.
[36]	Li Z X, Chan T H T, Yu Y, et al. Concurrent Multi-scale Modeling of Civil Infrastructures for Analyses on Structural deterioration-part I: Modeling Methodology and Strategy[J]. Finite Elements in Analysis and Design, 2009, 45(11): 782-794.
[37]	Curtin W A, Miller R E. Atomistic/Continuum Coupling in Computational Materials Science[J]. Modelling and Simulation in Materials Science and Engineering, 2003, 11(3): R33-R68.
[38]	陆新征, 林旭川, 叶列平. 多尺度有限元建模方法及其应用[J]. 华中科技大学学报(城市科学版), 2008, 25(4): 76-80.
	Lu Xinzheng, Lin Xuchuan, Ye Lieping. Multiscale Finite Element Modeling and its Application in Structural Analysis[J]. Journal of Huazhong University of Science and Technology(Urban Science Edition), 2008, 25(4): 76-80.
[39]	夏大海, 邓成满, 陈子光, 等. 金属材料局部腐蚀损伤过程的近场动力学模拟: 进展与挑战[J]. 金属学报, 2022, 58(9): 1093-1107.
	Xia Dahai, Deng Chengman, Chen Ziguang, et al. Modeling Localized Corrosion Propagation of Metallic Materials by Peridynamics: Progresses and Challenges[J]. Acta Metallurgica Sinica, 2022, 58(9): 1093-1107.
[40]	Roy Krishanu, Ho Lau Hieng, Fang Zhiyuan, et al. Effects of Corrosion on the Strength of Self-drilling Screw Connections in Cold-formed Steel Structures-experiments and Finite Element Modeling[J]. Structures, 2022, 36: 1080-1096.
[41]	Qin Guojin, Cheng Yufeng, Zhang Peng. Finite Element Modeling of Corrosion Defect Growth and Failure Pressure Prediction of Pipelines[J]. International Journal of Pressure Vessels and Piping, 2021, 194, Part A: 104509.
[42]	Karpenko O, Oterkus S, Oterkus E. Peridynamic Analysis to Investigate the Influence of Microstructure and Porosity on Fatigue Crack Propagation in Additively Manufactured Ti6Al4V[J]. Engineering Fracture Mechanics, 2022, 261: 108212.
[43]	Nikolaev P, Sedighi M, Jivkov A P, et al. Analysis of Heat Transfer and Water Flow with Phase Change in Saturated Porous Media by Bond-based Peridynamics[J]. International Journal of Heat and Mass Transfer, 2022, 185: 122327.
[44]	Jafarzadeh S, Chen Ziguang, Bobaru F. Computational Modeling of Pitting Corrosion[J]. Corrosion Reviews, 2019, 37(5): 419-439.
[45]	周文栋, 王学梅, 张波, 等. IGBT模块键合线失效研究[J]. 电源学报, 2016, 14(1): 10-17.
	Zhou Wendong, Wang Xuemei, Zhang Bo, et al. Research on Failures of Bonding Wire in IGBTs Module[J]. Journal of Power Supply, 2016, 14(1): 10-17.
[46]	Ji Bing, Song Xueguan, Sciberras E, et al. Multiobjective Design Optimization of IGBT Power Modules Considering Power Cycling and Thermal Cycling[J]. IEEE Transactions on Power Electronics, 2015, 30(5): 2493-2504.
[47]	赵旭州, 朱戈, 吴馨. 基于壳温的IGBT模块键合引线疲劳寿命预测[J]. 高压电器, 2017, 53(7): 167-173.
	Zhao Xuzhou, Zhu Ge, Wu Xin. Fatigue Life Prediction of Bonding Wires in IGBT Modules Based on Case Temperature[J]. High Voltage Apparatus, 2017, 53(7): 167-173.
[48]	张亮, 韩永典, 尹立孟, 等. 电子互连无铅钎料及焊点蠕变行为研究进展[J]. 稀有金属材料与工程, 2023, 52(12): 4307-4324.
	Zhang Liang, Han Yongdian, Yin Limeng, et al. Development of Creep Behavior of Lead-free Solders and Solder Joints in Electronic Interconnection[J]. Rare Metal Materials and Engineering, 2023, 52(12): 4307-4324.
[49]	Zhang Yue, Wang Chenxi, Yuan Zhitian, et al. Investigation of Moisture Diffusion in Plastic Electronic Packages by Molecular Dynamics Simulation[C]//2017 18th International Conference on Electronic Packaging Technology (ICEPT). Piscataway: IEEE, 2017: 1626-1630.
[50]	Guo F L, He B B, Niu X. Analysis of Vapor Pressure and Void Volume Fraction Evolution in Porous Polymers: A Micromechanics Approach[J]. International Journal of Solids and Structures, 2015, 66: 133-139.
[51]	Due J, Robinson Anthony J. Reliability of Thermal Interface Materials: A Review[J]. Applied Thermal Engineering, 2013, 50(1): 455-463.
[52]	Mao Dasha, Chen Jiahui, Ren Linlin, et al. Spherical Core-shell Al@Al₂O₃ Filled Epoxy Resin Composites as High-performance Thermal Interface Materials[J]. Composites Part A: Applied Science and Manufacturing, 2019, 123: 260-269.
[53]	Wahyu Jati Kusuma, Fadarina, Hasan Abu. Sodium Silicate Composite Filled by Zinc Oxide as Low Resistance Thermal Grease[J]. Journal of Physics: Conference Series, 2019, 1167(1): 012045.
[54]	Tong Zhen, Liu Meng, Bao Hua. A Numerical Investigation on the Heat Conduction in High Filler Loading Particulate Composites[J]. International Journal of Heat and Mass Transfer, 2016, 100: 355-361.
[55]	Li Hongkun, Zheng Weidong. Enhanced Thermal Conductivity of Epoxy/Alumina Composite Through Multiscale-disperse Packing[J]. Journal of Composite Materials, 2021, 55(1): 17-25.
[56]	Ding Tongyu, Zhang Liang, Trinchero R, et al. Worst-case Analysis of Electrical and Electronic Equipment Via Affine Arithmetic[C]//2017 International Conference on Electromagnetics in Advanced Applications (ICEAA). Piscataway: IEEE, 2017: 991-993.
[57]	Sopelana J, Cea L, Ruano S. Multisim Simulation Software Application in Electronic Measurement Course[J]. Natural Hazards, 2018, 36(4): 135-139.
[58]	吴义忠, 刘敏, 陈立平. 多领域物理系统混合建模平台开发[J]. 计算机辅助设计与图形学学报, 2006, 18(1): 120-124.
	Wu Yizhong, Liu Min, Chen Liping. Development of Hybrid Modeling Platform for Multi-domain Physical System[J]. Journal of Computer-Aided Design & Computer Graphics, 2006, 18(1): 120-124.
[59]	周一飞. 基于Simulink的步进电机控制系统仿真[D]. 成都: 西南交通大学, 2014.
	Zhou Yifei. Simulation of Stepper Motor Control System Based on Simulink[D]. Chengdu: Southwest Jiaotong University, 2014.
[60]	Goswami Somdatta, Ghosh Shyamal, Chakraborty Subrata. Reliability Analysis of Structures by Iterative Improved Response Surface Method[J]. Structural Safety, 2016, 60: 56-66.
[61]	张星宇, 刘迪. 基于Simulink仿真的无线电引信信号处理器性能退化研究[J]. 电子测试, 2021(18): 40-43.
	Zhang Xingyu, Liu Di. Research on Performance Degradation of Radio Fuze Signal Processor Based on Simulink Simulation[J]. Electronic Test, 2021(18): 40-43.
[62]	胡晓青, 张鑫, 邢亮. 飞机液压系统关键部件性能退化建模与仿真[J]. 机电信息, 2023(6): 70-72.
[63]	牛晓鹏, 朱顺鹏, 高杰维, 等. 多源不确定性下叶盘结构疲劳可靠性分析与优化设计[J]. 推进技术, 2022, 43(2): 222-230.
	Niu Xiaopeng, Zhu Shunpeng, Gao Jiewei, et al. Fatigue Reliability Analysis and Optimization Design of Turbine Blade Disks Under Multi-source Uncertainties[J]. Journal of Propulsion Technology, 2022, 43(2): 222-230.
[64]	张卫. 考虑多失效机理耦合的电子产品寿命预测方法研究[D]. 长沙: 国防科学技术大学, 2014.
	Zhang Wei. Research on Life Prediction Method of Electronic Product Combined Multiple-failure Mechanism[D]. Changsha: National University of Defense Technology, 2014.
[65]	Steinberg D S. Preventing Thermal Cycling and Vibration Failures in Electronic Equipment[M]. Hoboken: John Wiley & Sons, Inc., 2001.
[66]	栾家辉, 朱兴高, 陈皓, 等. 基于综合应力的电子产品寿命预测仿真方法研究[J]. 机械工程与自动化, 2020(2): 25-28.
	Luan Jiahui, Zhu Xinggao, Chen Hao, et al. Research on Simulation Method of Life Prediction for Electronic Products Based on Comprehensive Stress[J]. Mechanical Engineering & Automation, 2020(2): 25-28.
[67]	张宁, 刘庭伟, 徐洪武. 基于失效物理的电子产品寿命预计方法及工程应用[J]. 质量与可靠性, 2016(5): 43-47.
[68]	文歆磊, 张金栋, 叶茂, 等. 仿真与试验结合的电子产品可靠性评估方法[J]. 机电产品开发与创新, 2023, 36(3): 19-21, 32.
	Wen Xinlei, Zhang Jindong, Ye Mao, et al. Reliability Assessment for Electronic Products by Combination of Simulation and Test[J]. Development & Innovation of Machinery & Electrical Products, 2023, 36(3): 19-21, 32.
[69]	蒋京. 航空电子产品故障诊断与寿命预测技术研究[D]. 成都: 四川大学, 2021.
	Jiang Jing. Research on Fault Diagnosis and Life Prediction of Avionics[D]. Chengdu: Sichuan University, 2021.
[70]	谢里阳. 机械可靠性理论、方法及模型中若干问题评述[J]. 机械工程学报, 2014, 50(14): 27-35.
	Xie Liyang. Issues and Commentary on Mechanical Reliability Theories, Methods and Models[J]. Journal of Mechanical Engineering, 2014, 50(14): 27-35.
[71]	Dong Wenjie, Liu Sifeng, Suk Joo Bae, et al. Reliability Modelling for Multi-component Systems Subject to Stochastic Deterioration and Generalized Cumulative Shock Damages[J]. Reliability Engineering & System Safety, 2021, 205: 107260.
[72]	郭伟. 机械产品仿真与试验相结合的可靠性评估方法研究[D]. 西安: 西北工业大学, 2016.
	Guo Wei. Research on Methods of Reliability Evaluation Through Combination of Simulation and Test for Mechanical Products[D]. Xi'an: Northwestern Polytechnical University, 2016.
[73]	孔雪峰, 潘骏, 钱萍, 等. 机械产品多变量相依退化建模方法研究综述[J]. 机械工程学报, 2023, 59(20): 470-488.
	Kong Xuefeng, Pan Jun, Qian Ping, et al. Review of Multivariate Dependent Degeneration Modeling Methods for Mechanical Products[J]. Journal of Mechanical Engineering, 2023, 59(20): 470-488.
[74]	Kong Xuefeng, Yang Jun, Li Lei. Remaining Useful Life Prediction for Degrading Systems with Random Shocks Considering Measurement Uncertainty[J]. Journal of Manufacturing Systems, 2021, 61: 782-798.
[75]	员婉莹. 结构可靠性及全局灵敏度分析算法研究[D]. 西安: 西北工业大学, 2019.
	Yun Wanying. Research on Algorithms of Reliability Analysis and Global Sensitivity Analysis of the Structures[D]. Xi'an: Northwestern Polytechnical University, 2019.
[76]	Opgenoord M M J, Allaire D L, Willcox K E. Variance-based Sensitivity Analysis to Support Simulation-based Design Under Uncertainty[J]. Journal of Mechanical Design, 2016, 138(11): 111410.
[77]	钟云龙, 何宗科, 王学孔, 等. 机电产品故障模式及可靠性特点分析[J]. 电子产品可靠性与环境试验, 2023, 41(6): 43-48.
	Zhong Yunlong, He Zongke, Wang Xuekong, et al. The Analysis of Failure Modes and Reliability Characteristics of Electromechanical Products[J]. Electronic Product Reliability and Environmental Testing, 2023, 41(6): 43-48.
[78]	晁代宏, 马静, 陈淑英. 应用多元性能退化量评估光纤陀螺贮存的可靠性[J]. 光学精密工程, 2011, 19(1): 35-40.
	Chao Daihong, Ma Jing, Chen Shuying. Assessment of Storage Reliability for FOGs by Multivariate Degradation Data[J]. Optics and Precision Engineering, 2011, 19(1): 35-40.
[79]	苏春, 汪千程. 基于改进多层级嵌套Copula方法的机电产品可靠性评估[J]. 东南大学学报(自然科学版), 2022, 52(5): 981-989.
	Su Chun, Wang Qiancheng. Reliability Evaluation for Electromechanical Products Based on Improved Multi-level Nested Copula Method[J]. Journal of Southeast University(Natural Science Edition), 2022, 52(5): 981-989.
[80]	石磊, 许胜刚, 李劲, 等. 导弹机电产品可靠性和寿命考核方法研究[J]. 电子产品可靠性与环境试验, 2020, 38(5): 40-43.
	Shi Lei, Xu Shenggang, Li Jin, et al. Study on Reliability and Life Assessment Method of Missile Electromechanical Products[J]. Electronic Product Reliability and Environmental Testing, 2020, 38(5): 40-43.