• • 上一篇    

具预警功能人机安全系统的可靠性分析

马丹, 乔兴, 郭爽, 赵国传   

  1. 大庆师范学院数学科学学院, 大庆 163712
  • 收稿日期:2021-10-15 修回日期:2022-01-15 发布日期:2022-08-31
  • 通讯作者: 乔兴,Email:xiaoqiao1502@163.com.
  • 基金资助:
    大庆师范学院自然科学基金项目(16ZR08,19ZR04),黑龙江省自然科学基金项目(QC2010024,LH2020A017)资助课题.

马丹, 乔兴, 郭爽, 赵国传. 具预警功能人机安全系统的可靠性分析[J]. 系统科学与数学, 2022, 42(7): 1891-1909.

MA Dan, QIAO Xing, GUO Shuang, ZHAO Guochuan. Reliability Analysis of Robot Safety System with Early Warning Function[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(7): 1891-1909.

Reliability Analysis of Robot Safety System with Early Warning Function

MA Dan, QIAO Xing, GUO Shuang, ZHAO Guochuan   

  1. School of Mathematical Science, Daqing Normal University, Daqing 163712
  • Received:2021-10-15 Revised:2022-01-15 Published:2022-08-31
为保证系统的安全可靠和避免突发事故的发生,依据随机过程理论,在可修复机器人安全系统中引入预警功能,此类系统的可靠性指标通常采用概率分析法、拉普拉斯变换和Tauber定理给出.运用马尔科夫过程理论和补充变量法构建具有预警功能的四机器人安全系统的数学模型.基于抽象柯西问题理论构建抽象柯西问题系统模型,从而运用半群理论研究此类系统解的适定性.运用分析法、共尾相关理论和现代泛函分析法验证系统的稳定性.进而从理论分析和数值模拟的角度验证了该系统的可靠性指标是一致的.运用本征值向量法给出四个主要可靠性指标.数值仿真和比较法揭示了提出的本征值向量法是有效的.
In order to ensure the safety and reliability of the system and avoid the occurrence of unexpected accidents, an early warning function is introduced into the repairable robot safety system. According to the process theory, the reliability index of this type of system usually adopts probability analysis, Laplace transform and Tauber's theorem gives the corresponding steady-state index. By using Markov process theory and supplementary variable method to construct a mathematical model of a four-robot safety system with early warning function. Construct an abstract Cauchy problem system model based on the abstract Cauchy problem theory. It is convenient to use semigroup theory to solve the well-posedness of the solution of this type of system. The stability of the system is verified by the pure analysis technique, the confinal related theory and functional analysis method. It is discussed that the different four reliability indices of the studied model by using eigenvalue vector method. Numerical simulation and comparison show that the proposed eigenvalue vector method is effective.

MR(2010)主题分类: 

()
[1] Dhillon B S, AnudeIncome O C.Optimization of a repairable and redundant system.Microelectronics and Reliab., 1994, 34(11):1709-1720.
[2] Yang N, Dhillon B S.Stochastic analysis of a general standby system with constant human error and arbitrarily system repair rates.Microelectron.Reliab., 1995, 35(9):1037-1045.
[3] Liu H, Wang Y, Ji W, et al.A context-aware safety system for human-robot collaboration.Procedia Manufacturing, 2018,(17):238-245.
[4] Zheng K, Hu Y, Wu B.Intelligent fuzzy sliding mode control for complex robot system with disturbances.European Journal of Control, 2020,(51):95-109.
[5] Ajoudani A, Zanchettin A M, Ivaldi S, et al.Progressand prospects of the human-robot collaboration.Autonomous Robots, 2018, 42(5):957-975.
[6] Leite A, Pinto A, Matos A.A safety monitoring model for a faulty mobile robot.Robotics, 2018, 7(3):1-20.
[7] 凤宝林,乔兴.具有预警功能的四机器人安全系统数学模型构建.牡丹江师范学院学报(自然科学版), 2021,(1):37-40.(Feng B L, Qiao X.Construction of mathematics model of four-robot safety system with early warning function.Journal of Mudanjiang Normal University, 2021,(1):37-40.)
[8] 乔兴.具有预警功能的四类故障可修复系统主算子的性质.数学的实践与认识, 2018, 48(3):247-254.(Qiao X.Properties of the system main operator of a repairable system with four type of failures.Journal of Mathematics in Practice and Theory, 2018, 48(3):247-254.)
[9] 马艳英,李秀珍,乔兴.具有四类故障可修复系统非负弱解存在唯一性.吉林工程技术师范学院学报, 2008,(4):78-80.(Ma Y Y, Li X Z, Qiao X.The existence and uniqueness of the none-negative weak solution of a repairable system with four kind of failures.Journal of Jilin Teachers Institute of Engineering and Technology, 2008,(4):78-80.)
[10] 乔兴.具有预警功能的四类故障系统的可靠性分析.齐齐哈尔大学学报(自然科学版), 2018, 34(1):91-94.(Qiao X.Reliability analysis of four type of failures repairable system with warning function.Journal of Qiqihar University (Natural Science Edition), 2018, 34(1):91-94.)
[11] 乔兴,凤宝林,马丹,等.具有预警功能三机器人安全系统模型的渐近稳定性分析.数学的实践与认识, 2021, 51(8):138-145.(Qiao X, Feng B L, Ma D, et al.The asymptotic stability analysis of three-robot safety system with early warning function.Journal of Mathematics in Practice and Theory, 2021, 51(8):138-145.)
[12] Jain M, Rakhee M S.Bilevel control of degraded machining system with warm standbys, setup and vacation.Applied Mathematical Modelling, 2004,(28):1015-1026.
[13] Ke J C, Wang K H.Vacation policies for machine repair problem with two type spares.Applied Mathematical Modelling, 2007,(31):880-894.
[14] Gaver D P.Time to failure and availability of paralleled systems with repair.IEEE Transactions on Reliability, 1963, 12(2):30-38.
[15] Pazy A.Semigroup of Linear Operators and Application to Partial Differential Equations.Applied Mathematical Science.Berlin, Germany:Springer, 2012.
[16] Gurtin M E, MacCamy R C.Non-linear age-dependent population dynamics.Archive for Rational Mechanics and Analysis, 1974, 54(3):281-300.
[17] Dunford N, Schwartz J T.Linear Operators Part I:General Theory.New York:Interscience Publishers, 1958.
[18] Arendt W.Resolvent positive operators.Proceedings of the London Mathematical Society, 1987, 3(2):321-349.
[19] Zhang X.Reliability analysis of a cold standby repairable system with repairman extra work.Journal of Systems Science and Complexity, 2015, 28(5):1015-1032.
[20] Wang Y, Qiao X, Zhan B J, et al.The stability and reliability analysis of a system containing two redundant robots.2014 Sixth International Conference on Intelligent Human-Machine Systems and Cybernetics.IEEE, 2014,(1):288-291.
[21] Yuan W Z, Wu G Q.Spectral analysis of a two unit deteriorating standby system with repair.WSEAS Transactions on Mathematics, 2011, 10(4):125-138.
[22] Qiao X, Ma D.Reliability and numerical analysis of a robot safety system.Journal of Systems Science and Complexity, 2019, 32(4):1072-1092.
[23] Taylor A E, Lay D C.Introduction to Functional Analysis.UK:Clarendon Press, 1980.
[24] Lyubich Y I, Phông Q V.Asymptotic stability of linear differential equations in Banach spaces.Studia Mathematica, 1988, 88(1):37-42.
[1] 杨建华, 丁肇炜. 考虑警情处置可靠性的警力备勤选址研究[J]. 系统科学与数学, 2022, 42(6): 1519-1536.
[2] 祁雪萍, 阿不都克热木·阿吉. 具有小修和一般型更换策略的多状态退化系统的定性分析[J]. 系统科学与数学, 2021, 41(9): 2571-2594.
[3] 杨坤一, 董云宁. 时滞反馈控制下五维能源供需系统的稳定性分析及Hopf分支性质[J]. 系统科学与数学, 2021, 41(8): 2113-2136.
[4] 卢威威, 刘安东, 仇翔, 俞立. 基于视觉的机器人滚动时域位姿估计[J]. 系统科学与数学, 2021, 41(7): 1772-1787.
[5] 张婷婷, 胡林敏, 王桂荣. 离散时间随机不确定多状态系统可靠性分析[J]. 系统科学与数学, 2021, 41(7): 2006-2017.
[6] 余凯. 矩形区域热-板耦合系统的稳定性分析[J]. 系统科学与数学, 2021, 41(6): 1481-1492.
[7] 左凯, 吴文青, 张元元. 修理工多重休假且修理设备可更换的$n$中取$k$温贮备系统研究[J]. 系统科学与数学, 2021, 41(6): 1729-1741.
[8] 罗小丽, 戴璐, 练红海, 李谟发, 邓鹏. 具有时滞概率分布的电力系统负荷频率稳定性分析[J]. 系统科学与数学, 2021, 41(5): 1245-1255.
[9] 张兴贤, 王应明. 一种考虑证据权重和可靠性的混合型多属性群决策方法[J]. 系统科学与数学, 2021, 41(5): 1305-1327.
[10] 李斌, 杨豪中, 甘旭升, 李琦. 改进PSO算法融合人工势场法的工业机器人路径规划设计[J]. 系统科学与数学, 2021, 41(4): 939-952.
[11] 练红海,覃事刚,肖伸平,肖会芹. 基于采样区间分割的线性系统稳定准则[J]. 系统科学与数学, 2021, 41(2): 310-324.
[12] 陈洋, 赵秋红. 考虑双向路网的车辆异常聚集监测预警算法[J]. 系统科学与数学, 2021, 41(11): 3065-3077.
[13] 张德金, 向淑文, 邓喜才, 杨彦龙. 约束图像拓扑下的向量值拟变分不等式解集的通有稳定性[J]. 系统科学与数学, 2021, 41(1): 115-125.
[14] 傅金波, 陈兰荪. 具有免疫应答和吸收效应的病毒感染模型分析[J]. 系统科学与数学, 2021, 41(1): 280-290.
[15] 吴红星,程国飞,王胜华. 细菌种群增生中Rotenberg模型解的渐近稳定性研究[J]. 系统科学与数学, 2020, 40(9): 1539-1549.
阅读次数
全文


摘要