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| 具有两种修复方法的可修复系统解的研究 |
| Fig.1 Repairable ,System Pattern with Two Types of Repair Facilities. |
| 投稿时间：2017-04-01 修订日期：2017-04-11 |
| DOI： |
| 中文关键词: 可修复系统 半离散化 收敛 数值计算. |
| 英文关键词: repairable system semi-discretization converge numerical calculation. |
| 基金项目:国家科技支撑计划课题(项目编号：2013BAK12B0803)；黑龙江省教育厅基本业务专项理工面上项目(项目编号：135109229) |
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| 中文摘要: |
| 本文将半离散算法应用到具有两种修复方法的可修系统模型中,在闭区间 上对其修复率进行离散,得到了该系统的半离散化模型.进一步利用泛函分析中算子半群理论将半离散后的偏微分方程转化为抽象Cauchy问题,即转化为矩阵常微分方程组；再根据Trotter逼近定理证明了矩阵常微分方程组的解是收敛于原方程的解.最后在故障率和修复率均为常数的前提下,利用Matlab数学软件对该系统的稳定性和可靠性等进行了数值试验并得到了该模型的数值解,同时给出了相应的图形趋势.结果表明,对具有两种修复方法的可修系统模型进行半离散化研究,既可以为利用计算机进一步进行数值计算打下理论基础,又有助于研究和分析系统的可靠性,因此具有重要的理论意义和实用价值. |
| 英文摘要: |
| In this paper, we apply the semi-discrete algorithm to the repairable system with two types of repair facilities,we discrete the repairable rate in and acquire the semi-discrete model of the system. Further more ,we use the operator semi-group to transform the model to the abstract Cauchy problems, i.e. the ordinary differential equations; then we prove the convergence of the matrix differential equations to the equation of the original equation according to Trotter theorem . At last,because the fuilure rate and the repairable rate are constant .we use the Matlab to prove the stability and the reliability of the system and acquire the numcrical simulation of the system.The results show that the repair system model is a semi-discrete study with two types of repair method, not only for the use of the computer for further numerical calculation to lay a theoretical foundation, but also help Therefore, it is of great theoretical significance and practical value to analyze and study the reliability of the system. |
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