北京航空航天大学学报 ›› 2004, Vol. 30 ›› Issue (12): 1168-1172.

• 论文 • 上一篇    下一篇

马尔可夫更新方程的迭代算法研究

王少萍, 陶建峰, 崔明山, 焦宗夏   

  1. 北京航空航天大学 自动化科学与电气工程学院 北京 100083
  • 收稿日期:2003-06-18 出版日期:2004-12-31 发布日期:2010-09-21
  • 作者简介:王少萍(1966-), 女, 山西阳泉人, 教授, shaopingwang@vip.sina.com.
  • 基金资助:

    国家自然科学基金资助项目(60371049); 北京市自然基金资助项目(4012009)

Study on iterative availability algorithm of Markov renewal equation

Wang Shaoping, Tao Jianfeng, Cui Mingshan, Jiao Zongxia   

  1. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
  • Received:2003-06-18 Online:2004-12-31 Published:2010-09-21

摘要: 冷储备系统的动态结构变化使得系统可用度分析必须基于瞬态求解,针对频域两部件冷储备系统马尔可夫更新方程解算困难的问题,提出基于时域伏尔特拉方程的迭代算法,证明了该迭代方程的唯一性和收敛性,并给出迭代算法的误差分析.理论和实例分析表明,当冷储备系统部件的工作寿命和维修时间分布是有界函数时,利用迭代算法可以容易实现时域马尔可夫更新方程的求解.

Abstract: Dynamic structure variance of cool spare system requires the dynamic availability analysis with transient solution. The traditional calculation method of Markov renewal equation based on Laplace transform and inverse Laplace transform makes many difficulties to complex system. The iterative availability algorithm based on Valterra series is presented in time domain to cool spare system with two units, and its uniqueness and convergence are proved. Comparing the iterative algorithm with the algorithm based on Laplace transform, it indicates that the iterative error is small and acceptable. Application results show that the iterative availability algorithm can easy realize the resolution for Markov renewal equation when the life distribution and repair time distribution are bounded function.

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