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动态系统失效的不确定性分析及其高效算法

巩祥瑞 吕震宙 刘辉 周易成

巩祥瑞, 吕震宙, 刘辉, 等 . 动态系统失效的不确定性分析及其高效算法[J]. 北京航空航天大学学报, 2017, 43(7): 1460-1469. doi: 10.13700/j.bh.1001-5965.2016.0533
引用本文: 巩祥瑞, 吕震宙, 刘辉, 等 . 动态系统失效的不确定性分析及其高效算法[J]. 北京航空航天大学学报, 2017, 43(7): 1460-1469. doi: 10.13700/j.bh.1001-5965.2016.0533
GONG Xiangrui, LYU Zhenzhou, LIU Hui, et al. Uncertainty analysis of failure of dynamic system and its efficient algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(7): 1460-1469. doi: 10.13700/j.bh.1001-5965.2016.0533(in Chinese)
Citation: GONG Xiangrui, LYU Zhenzhou, LIU Hui, et al. Uncertainty analysis of failure of dynamic system and its efficient algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(7): 1460-1469. doi: 10.13700/j.bh.1001-5965.2016.0533(in Chinese)

动态系统失效的不确定性分析及其高效算法

doi: 10.13700/j.bh.1001-5965.2016.0533
基金项目: 

国家自然科学基金 51475370

中央高校基本科研业务费专项资金 3102015BJ(Ⅱ)CG009

详细信息
    作者简介:

    巩祥瑞  男, 硕士研究生。主要研究方向:飞行器设计及可靠性工程

    吕震宙  女, 博士, 教授, 博士生导师。主要研究方向:飞行器设计及可靠性工程

    通讯作者:

    吕震宙, E-mail:zhenzhoulu@nwpu.edu.cn

  • 中图分类号: V215.7;TB114.3

Uncertainty analysis of failure of dynamic system and its efficient algorithm

Funds: 

National Natural Science Foundation of China 51475370

the Fundamental Research Funds for the Central Universities 3102015BJ(Ⅱ)CG009

More Information
  • 摘要:

    为了分析在不确定性元器件失效率影响条件下动态系统的失效问题,提出了满足工作时间要求的系统失效概率和满足失效概率限制的系统正常工作时间的分析方法。同时,为了研究元器件失效率对动态系统失效的影响程度,提出了元器件失效率对系统失效概率以及系统正常工作时间不确定性影响的重要性分析方法,建立了元器件失效率对系统失效概率和系统正常工作时间方差贡献的重要性测度指标。首先给出了指标求解的直接蒙特卡罗方法,然后采用基于分数矩的极大熵方法来高效估计系统失效的概率密度函数,采用乘法降维积分建立了2种重要性测度指标的高效解法。阀门控制系统和民用飞机电液舵机系统的算例结果表明所提方法的合理性和算法的高效性。

     

  • 图 1  系统失效概率随系统工作时间变化曲线

    Figure 1.  Variation of system failure probability with system function time

    图 2  阀门控制系统[17]

    Figure 2.  Valve control system[17]

    图 3  阀门控制系统失效概率的概率密度曲线

    Figure 3.  Probability density curves of failure probability of valve control system

    图 4  阀门控制系统工作时间的概率密度曲线

    Figure 4.  Probability density curves of function time of valve control system

    图 5  空客A系列飞机电液舵机结构[18]

    Figure 5.  Aircraft electro-hydraulic actuator structure of Airbus A[18]

    图 6  空客A系列飞机电液舵机系统故障树[18]

    Figure 6.  Fault tree of aircraft electro-hydraulic actuator system of Airbus A[18]

    图 7  飞机电液舵机系统失效概率的概率密度曲线

    Figure 7.  Probability density curves of failure probability of aircraft electro-hydraulic actuator system

    图 8  飞机电液舵机系统工作时间的概率密度曲线

    Figure 8.  Probability density curves of function time of aircraft electro-hydraulic actuator system

    表  1  阀门控制系统元器件失效率分布参数

    Table  1.   Distribution parameters of components' failure rates in valve control system

    λi 均值/10-2 方差/10-5
    λ1 4 2
    λ2 2 1
    λ3 1 0.5
    下载: 导出CSV

    表  2  阀门控制系统失效概率的概率密度函数特征

    Table  2.   Characteristics of probability density function about failure probability of valve control system

    方法 μPf σPf 置信区间(95%) 计算量
    MCS-KDE 0.489 3 0.045 1 [0.401 2, 0.578 0] 1×103
    MaxEnt-FMD 0.489 4 0.045 6 [0.400 0, 0.578 8] 16
    下载: 导出CSV

    表  3  基于系统失效概率的元器件失效率重要性测度指标

    Table  3.   Importance measure indices of components' failure rates based on failure probability of system

    方法 λ1 λ2 λ3 计算量
    MCS 0.090 2 0.353 1 0.569 0 4×106
    本文方法 0.089 8 0.354 0 0.567 1 181
    下载: 导出CSV

    表  4  阀门控制系统正常工作时间概率密度函数特征

    Table  4.   Characteristics of probability density function about function time of valve control system

    方法 μt σt 置信区间(95%) 计算量
    MCS-KDE 13.058 6 1.424 8 [10.266 0, 15.851 2] 142 172
    MaxEnt-FMD 13.010 3 1.511 5 [10.047 8, 15.972 8] 2 279
    下载: 导出CSV

    表  5  基于系统正常工作时间的元器件失效率重要性测度指标

    Table  5.   Importance measure indices of components' failure rates based on function time of system

    方法 λ1 λ2 λ3 计算量
    MCS 0.060 2 0.201 2 0.786 5 2.36×108
    本文方法 0.067 9 0.189 9 0.780 3 26 656
    下载: 导出CSV

    表  6  民用飞机电液舵机系统底事件失效率分布参数

    Table  6.   Distribution parameters of basic events' failure rates in civil aircraft electro-hydraulic actuator system

    λi 均值/10-7 方差/10-14
    λ1 3.5 2
    λ2 2 1
    λ3 3 1.5
    λ4 10 5
    λ5 6 5
    λ6 2.5 1
    下载: 导出CSV

    表  7  民用飞机电液舵机系统失效概率的概率密度函数特征

    Table  7.   Characteristics of probability density function about failure probabilityof civil aircraft electro-hydraulic actuator system

    方法 μPf σPf 置信区间(95%) 计算量
    MCS-KDE 0.068 1 0.004 0 [0.060 3, 0.075 9] 1×105
    MaxEnt-FMD 0.068 1 0.003 9 [0.060 5, 0.075 7] 31
    下载: 导出CSV

    表  8  底事件失效率重要性测度指标(t0=5 000 h)

    Table  8.   Importance measure indices of failure rates of basic events (t0=5 000 h)

    方法 λ1 λ2 λ3 λ4 λ5 λ6 计算量
    MCS 0.068 2 0.032 3 0.050 2 0.165 2 0.655 1 0.031 5 7×107
    本文方法 0.065 2 0.032 6 0.048 9 0.162 9 0.651 7 0.032 0 811
    下载: 导出CSV

    表  9  民用飞机电液舵机系统正常工作时间的概率密度函数特征

    Table  9.   Characteristics of probability density function about function time of civil aircraft electro-hydraulic actuator system

    方法 μt σt 置信区间(95%) 计算次数
    MCS-KDE 3 111.78 207.21 [2 705.65, 3 517.91] 132 178
    MaxEnt-FMD 3 115.26 203.46 [2 716.48, 3 514.04] 5 894
    下载: 导出CSV

    表  10  底事件失效率重要性测度指标(Pf0=0.01)

    Table  10.   Importance measure indices of failure rates of basic events (Pf0=0.01)

    方法 λ1 λ2 λ3 λ4 λ5 λ6 计算量
    MCS 0.040 8 0.031 2 0.059 2 0.145 2 0.621 1 0.031 5 5.97×109
    本文方法 0.043 8 0.029 6 0.058 6 0.147 1 0.614 4 0.029 7 42 851
    下载: 导出CSV
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出版历程
  • 收稿日期:  2016-06-21
  • 录用日期:  2016-07-05
  • 刊出日期:  2017-07-20

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