Reliability analysis of an electromechanical integrated transmission system based on Copula correlation modeling
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摘要:
针对机电复合传动装置中多子系统在载荷传递、控制回路和功能协同作用下呈现的相关失效特性，在保持各子系统边缘可靠性模型不变的前提下，引入 Copula 方法对系统内部依赖结构进行建模。该方法通过累积分布函数将子系统寿命数据映射至统一的概率空间，实现边缘分布与相关结构的解耦描述。结合工程失效机理分析不同 Copula 模型的依赖特性，选取 Gaussian Copula 构建系统联合失效模型，并给出失效时间样本的生成流程。通过 Kendall
τ 秩相关系数对样本相关性进行验证，结果表明，生成数据与预设依赖结构一致。进一步分析识别出电机驱动子系统与驱动电机控制器之间的强耦合关系，并定位了联合失效的高风险区域。研究结果表明，Copula 建模方法能够有效刻画系统层相关失效特征，为协同监测与维护决策提供可靠依据。Abstract:Considering the correlated failure characteristics of multiple subsystems in an electromechanical integrated transmission system arising from load transfer, control loops, and functional coupling, this study introduces a Copula-based approach to model the internal dependency structure while preserving the marginal reliability models of individual subsystems. By mapping subsystem lifetime data into a unified probability space via cumulative distribution functions, the proposed method achieves decoupled modeling of marginal distributions and dependency structures. The process for creating failure time samples is described, and a Gaussian Copula is chosen to build the system-level joint failure model based on an examination of the dependency characteristics of several Copula families combined with engineering failure mechanisms. The dependency structure of the generated samples is validated using the Kendall τ rank correlation coefficient, and the results show good consistency with the predefined correlation matrix. Additional investigation finds high-risk areas of joint failure and reveals a significant coupling link between the drive motor controller and the motor drive subsystem. The results demonstrate that the Copula-based framework can effectively characterize system-level correlated failures, providing quantitative support for coordinated monitoring and maintenance decision-making.
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图 1 Copula 相关性可靠性建模与验证流程
Figure 1. Copula correlation reliability modeling and validation process
图 3 机电复合传动装置原理
Figure 3. Schematic diagram of electromechanical integrated transmission device
图 4 串联模式下各子系统的失效率与平均无故障时间对比
Figure 4. Comparison of failure rates and mean time between failures of each subsystem in series configuration
图 5 基于串联模型的系统可靠度函数曲线
Figure 5. System reliability function curve based on series model
图 6 基于 Copula 空间的子系统依赖结构分析图
Figure 6. Dependency structure analysis diagram of subsystems based on Copula space
图 8 2组强相关子系统的 Copula 空间分析图
Figure 8. Copula space analysis diagram for two sets of strongly correlated subsystems
图 9 2组强相关子系统的联合分布等高线图
Figure 9. Contour map of joint distribution for two sets of strongly correlated subsystems
表 1 常用Copula函数特性对比
Table 1. Comparison of common Copula function features
Copula函数 数学表达式（二元形式） 依赖结构 尾部相关性 适用场景 Gaussian Copula $ C_{\rho }^{{\mathrm{Ga}}}({u}_{1},{u}_{2})={\varPhi }_{\rho }({\varPhi }^{-1}({u}_{1}),{\varPhi }^{-1}({u}_{2})) $ 对称 零 线性依赖，无显著极端共现 t-Copula $ C_{\rho ,v}^{t}({u}_{1},{u}_{2})={t}_{\rho ,v}(t_{v}^{-1}({u}_{1}),t_{v}^{-1}({u}_{2})) $ 对称 对称 冲击载荷等引起的极端并发失效 克莱顿 Copula $ {C}_{{\mathrm{Cl}}}({u}_{1},{u}_{2};\theta )={({u_{1}^{-\theta }}+{u_{2}^{-\theta }}-1)}^{-1/\theta } $ 非对称 下尾相关 共同缺陷导致的早期失效 甘力克 Copula $ \begin{array}{c}{C}_{{\mathrm{Gu}}}({u}_{1},{u}_{2};\theta )=\exp(-[(-\ln{{u}_{1}})^{\theta }+\\ (-\ln{{u}_{2}})^{\theta }{]}^{1/\theta })\end{array} $ 非对称 上尾相关 共同磨损/老化导致的耗损失效 
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[1] Bai X N, Li Y H, Zhang D X, et al. A structural reliability analysis method considering multiple correlation features[J]. Machines, 2024, 12(3): 210. [2] 魏晨竹. 不同情形下的机电设备可靠性信息融合[D]. 成都: 电子科技大学, 2021: 1-10.Wei C Z. Reliability information fusion of electromechanical equipment under different scenarios[D]. Chengdu: University of Electronic Science and Technology of China, 2021: 1-10(in Chinese). [3] 王蕾, 程世娟, 韩雨. 基于时变Copula函数的多部件系统可靠性评估[J]. 计算机应用, 2024, 44(3): 953-959.Wang L, Cheng S J, Han Y. Reliability evaluation of multi-component systems based on time-varying Copula functions[J]. Journal of Computer Applications, 2024, 44(3): 953-959(in Chinese). [4] Gu Y K, Fan C J, Liang L Q, et al. Reliability calculation method based on the Copula function for mechanical systems with dependent failure[J]. Annals of Operations Research, 2022, 311(1): 99-116. [5] Adès M, Provost S B, Zang Y S. Four measures of association and their representations in terms of Copulas[J]. Applied Math, 2024, 4(1): 363-382. [6] Xia E D, Zhou F P, Kun-Chieh W, et al. A novel reliability analysis methodology based on IPSO-MCopula model for gears with multiple failure modes[J]. Advances in Mechanical Engineering, 2024, 16(2): 16878132241228194. [7] 帅志斌, 贺帅, 李国辉, 等. 特种履带车辆机电复合传动装置低温启动过程建模与优化控制[J]. 兵工学报, 2023, 44(1): 117-128.Shuai Z B, He S, Li G H, et al. Modeling and optimal control of low-temperature start-up process for electromechanical integrated transmission of special tracked vehicles[J]. Acta Armamentarii, 2023, 44(1): 117-128(in Chinese). [8] 付善强, 王孟夏, 杨明, 等. 架空导线载流量的多时段联合概率密度预测[J]. 电力系统自动化, 2019, 43(17): 102-108.Fu S Q, Wang M X, Yang M, et al. Multi-period joint probability density forecasting of ampacity for overhead conductors[J]. Automation of Electric Power Systems, 2019, 43(17): 102-108(in Chinese). [9] Arriaza A, Navarro J, Sordo M Á, et al. A variance-based importance index for systems with dependent components[J]. Fuzzy Sets and Systems, 2023, 467: 108482. [10] Genest C, Okhrin O, Bodnar T. Copula modeling from Abe Sklar to the present day[J]. Journal of Multivariate Analysis, 2024, 201: 105278. [11] Zhou L, He Z X. Application research on reliability modeling of multi-failure modes correlation system based on time varying Copula model[J]. IOP Conference Series: Materials Science and Engineering, 2020, 964(1): 012031. [12] 周松. 基于Vine Copula的机械结构系统失效模式相关可靠性分析及拓扑优化[D]. 重庆: 重庆交通大学, 2018: 1-6.Zhou S. Correlation reliability analysis and topology optimization of mechanical structural systems with failure-mode dependence based on Vine Copula[D]. Chongqing: Chongqing Jiaotong University, 2018: 1-6(in Chinese). [13] 张根保, 张定飞, 冉琰, 等. 基于Gamma和混合Copula的元动作单元性能可靠性分析[J]. 湖南大学学报(自然科学版), 2021, 48(4): 113-125.Zhang G B, Zhang D F, Ran Y, et al. Performance reliability analysis of meta-action unit based on Gamma process and hybrid Copula function[J]. Journal of Hunan University (Natural Sciences), 2021, 48(4): 113-125(in Chinese). [14] Lyu H, Li Z H, Qiao X H, et al. Reliability analysis for multi-component system considering failure propagation and dependent competing failure process[J]. Reliability Engineering & System Safety, 2025, 259: 110930. [15] 冯钧, 刘伟, 谭龙, 等. 高维Copula函数的动态系统可靠性模型研究[J]. 机械强度, 2022, 44(1): 86-94.Feng J, Liu W, Tan L, et al. Research on dynamic system reliability model of high-dimensional Copula function[J]. Journal of Mechanical Strength, 2022, 44(1): 86-94(in Chinese) . [16] Khanthaporn R, Wichitaksorn N. Bayesian estimation of R-Vine Copula with Gaussian-mixture GARCH margins: an MCMC and machine learning comparison[J]. Mathematics, 2025, 13(23): 3886. [17] Torre E, Marelli S, Embrechts P, et al. A general framework for data-driven uncertainty quantification under complex input dependencies using Vine Copulas[J]. Probabilistic Engineering Mechanics, 2019, 55: 1-16. [18] Wei W. Copula-based high dimensional dependence modelling[D]. Sydney: University of Technology Sydney, 2014: 1-12. -
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