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双贮备系统冷/温/热贮备模型的优化选择研究

金海波 赵欣越 桑雨

金海波, 赵欣越, 桑雨. 双贮备系统冷/温/热贮备模型的优化选择研究. 自动化学报, 2020, 46(x): 1−16 doi: 10.16383/j.aas.c200533
引用本文: 金海波, 赵欣越, 桑雨. 双贮备系统冷/温/热贮备模型的优化选择研究. 自动化学报, 2020, 46(x): 1−16 doi: 10.16383/j.aas.c200533
Jin Hai-Bo, Zhao Xin-Yue, Sang Yu. Research on optimal selection for cold/warm/hot-standby patterns of dual-standby systems. Acta Automatica Sinica, 2020, 46(x): 1−16 doi: 10.16383/j.aas.c200533
Citation: Jin Hai-Bo, Zhao Xin-Yue, Sang Yu. Research on optimal selection for cold/warm/hot-standby patterns of dual-standby systems. Acta Automatica Sinica, 2020, 46(x): 1−16 doi: 10.16383/j.aas.c200533

双贮备系统冷/温/热贮备模型的优化选择研究

doi: 10.16383/j.aas.c200533
基金项目: 国家自然基金(61602226)资助
详细信息
    作者简介:

    金海波:辽宁工程技术大学软件学院副教授. 2014年获大连理工大学博士学位. 主要研究方向为复杂系统可靠性分析, 异常检测, 优化维护维修策略制定. 本文通信作者. E-mail: jinhaibo@lntu.edu.cn

    赵欣越:辽宁工程技术大学软件学院硕士研究生. 主要研究方向为智能信息处理、贮备系统可靠性分析、基于机器学习技术的网络安全防护. E-mail: zhaoxy1201@163.com

    桑雨:辽宁工程技术大学电子与信息工程学院副教授.2012年获大连理工大学博士学位. 主要研究方向为人工智能与计算机视觉. E-mail: sangyu2008bj@sina.com

Research on Optimal Selection for Cold/Warm/Hot-Standby Patterns of Dual-Standby Systems

Funds: Supported by National Natural Science Foundation of China (61602226)
  • 摘要: 对运行设备安装双贮备设备是实现系统高可靠性的有效方法. 在双贮备系统冷/温/热三种贮备模型中, 选择哪种贮备模型对系统性能指标和经济指标均有重要影响, 因此对如何选择双贮备系统的贮备模型从而使系统性能最优或经济效益最大的问题进行研究具有现实意义. 而现有研究成果很少涉及双贮备系统贮备模型的优化选择问题. 为此, 本文创新性地提出一种确定双贮备系统最优贮备模型的选择方法. 分别建立系统冷/温/热贮备模型, 分析每个模型的系统状态及系统半Markov核函数, 利用Markov更新方程、Laplace变换以及Laplace-Stieltjes变换技术推导系统稳态可用度、稳态平均维修次数、维修人员忙期稳态概率以及冷贮备模型的平均激活时间, 并从经济角度给出系统单位时间内的净收益函数. 最后分别以性能指标和经济指标作为研究目标, 通过模型对比分析给出不同条件下的系统贮备模型的优化选择算法, 并对每个研究目标下的优化选择算法进行实例计算. 计算结果表明以不同性能指标和不同费用作为参考得出的最优贮备模型不尽相同, 从而验证了所提方法能够有效的确定不同衡量标准下的系统最优贮备模型.
  • 图  1  冷贮备系统状态转移图

    其中○表示再生状态, □表示非再生状态. 表示失效状态.

    Fig.  1  State transition diagram of the cold-standby system

    图  2  温贮备系统状态转移图

    Fig.  2  State transition diagram of the warm-standby system

    图  3  双贮备冗余控制系统

    Fig.  3  Redundancy control system with dual-standby device

    图  4  ${\lambda _1}$ 对三个模型的稳态可用度的影响

    Fig.  4  Impact of ${\lambda _1}$ on steady-state available of the three models

    图  5  运行设备维修率对冷、热贮备系统中维修人员稳态忙期概率的影响

    Fig.  5  Impact of repair rate for the working device on steady-state probability of repairmen busy for cold, hot-standby system

    图  6  运行设备和温贮备设备的维修率对温贮备系统中维修人员稳态忙期概率的影响

    Fig.  6  Impact of repair rates for the working and warm-standy devices on steady-state probability of repairmen busy

    图  7  设备维修率对冷、热贮备系统稳态平均维修次数的影响

    Fig.  7  Impact of repair rate on mean repair number of the cold, hot-standby systems in steady-state

    图  8  运行设备的维修率和温贮备设备的失效率对系统稳态维修次数的影响

    Fig.  8  Impact of repair rate of the working device and failure rate of the warm-standby device on repair number of the system in steady-state

    表  1  模型中主要变量说明

    Table  1  Main variables involved in models

    变量符号 变量含义
    λ 运行设备失效率
    λ1 温贮备设备失效率
    X 冷备份模型中设备运行时的寿命
    Z 冷贮备模型中设备失效后的维修时间
    Xi 温贮备模型中第i个设备运行时的寿命
    Yi 温贮备模型中第i个设备贮备时的寿命
    Zi 温贮备模型中第i个设备失效后的维修时间
    μi 系统在状态Si的平均停留时间
    Qij(t) 系统从进入状态Si开始经过时间t后
    直接进入状态Sj的概率分布函数
    Qij(k)(t) 系统从进入状态Si开始经过时间t后中间经过
    状态Sk后再进入状态Sj的概率分布函数
    qij(t) Qij(t)的导数, 系统由状态Si到状态Sj的转移率
    F(t;λ) 参数为λ的指数分布函数
    $G(t)$ , ${G_1}(t)$ 分别为运行设备失效后和温贮备设备
    失效后的维修时间分布函数
    W(t) 激活时间分布函数
    Pi(t) 系统在状态Si的存活函数, 即Pi(t)=P{X>t}
    F*(s) 函数F(t)经Laplace变换后的象函数
    $\hat F(s)$ 函数F(t)经Laplace-Stieltjes变换后的象函数
    Ai(t) 系统从进入状态Si开始(t=0)在时刻t时的可用度
    ${\bar A_1}$ , ${\bar A_2}$ , ${\bar A_3}$ 分别为冷、温、热贮备系统稳态可用度
    Bi(t) 系统从进入状态Si开始(t=0)维修人员
    t时刻正在维修(既忙期)的概率
    ${\bar B_1}$ , ${\bar B_2}$ , ${\bar B_3}$ 分别为冷、温、热贮备系统稳态维修
    概率, 既维修人员忙期稳态概率
    Vi(t) 系统从进入状态Si开始(t=0)维修
    人员在(0,t]期间的维修次数
    ${\bar V_1}$ , ${\bar V_2}$ , ${\bar V_3}$ 分别为冷、温、热贮备系统稳态平均维修次数
    ${\omega _i}(t)$ 系统从进入状态Si开始(t=0)在t
    时刻处于激活状态的概率
    ${\bar \omega _1}$ 冷贮备系统稳态激活概率
    下载: 导出CSV

    表  2  模型中主要符号说明

    Table  2  Main symbols involved in models

    符号 符号含义
    Si 系统状态(i=0,1,···)
    Op 设备处于运行状态
    Cs 设备处于冷贮备状态
    Ws 设备处于温贮备状态
    Fr 运行设备失效后处于维修状态
    Fr1 温贮备设备失效后处于维修状态
    FR 失效后的运行设备继续维修的状态
    FR1 失效后的温贮备设备继续维修的状态
    Fwr 运行设备失效后处于等待维修状态
    Fwr1 温贮备设备失效后处于等待维修状态
    Fra 正在维修的设备暂停维修的状态
    Csa 冷贮备设备处于被激活状态
    下载: 导出CSV

    表  3  系统稳态可用度

    Table  3  System steady-state available

    系统模型 模型Ⅰ 模型Ⅱ 模型Ⅲ
    ${\bar A_i}$ 1.0000 0.9967 0.9845
    下载: 导出CSV

    表  4  维修人员忙期稳态概率

    Table  4  Steady-state probability of repairmen busy

    系统模型 模型Ⅰ 模型Ⅱ 模型Ⅲ
    ${\bar B_i}$ 0.0110 0.0131 0.0323
    下载: 导出CSV

    表  5  系统稳态平均维修次数

    Table  5  Mean repair number of the system in steady-state

    系统模型 模型Ⅰ 模型Ⅱ 模型Ⅲ
    ${\bar V_i}$ 0.00056 0.00077 0.0017
    下载: 导出CSV
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