具有两种修复方法的可修复系统解研究

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周莉,芦雪娟,王伟华.具有两种修复方法的可修复系统解研究[J].,2017,57(4):424-429

具有两种修复方法的可修复系统解研究

Study of solution of repairable system with two types of repair facilities

DOI：10.7511/dllgxb201704014

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 convergence numerical calculation

基金项目:国家科技支撑计划课题资助项目(2013BAK12B0803)；黑龙江省教育厅基本业务专项理工面上项目(135109229).

作者	单位
周莉,芦雪娟,王伟华

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中文摘要:

将半离散算法应用到具有两种修复方法的可修复系统模型中，在 0， x 0 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复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．

英文摘要:

The semi-discrete algorithm is applied to the repairable system with two types of repair facilities, the repairable rate in 0, x 0 is discretized and the semi-discrete model of the system is acquired. Furthermore, by using the operator semi-group theory in functional analysis, the semi-discrete partial differential equation is transformed to the abstract Cauchy problems, i. e. the matrix ordinary differential equations. Then the solution of the matrix ordinary differential equations is proved to converge to the solution of the original equation according to Trotter approximate theorem. At last, because the failure rate and the repairable rate are constants, using Matlab the stability and the reliability of the system are proved and the numerical solution of the system is acquired, the corresponding graph trend is given. The results show that semi-discrete study of the repairable system model with two types of repair facilities can not only lay a theoretical foundation for the use of the computer for further numerical calculation, but also have practical value to analyze and study the reliability of the system.

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