单部件可修系统瞬时可用度的波动分析

发布时间：2018-02-08 23:07

本文关键词： 瞬时可用度波动更新模型波动抑制数值计算　出处：《南京理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文主要研究单部件可修系统的瞬时可用度波动问题。由于一个系统或部件在使用初期的工作状态呈现波动变化,所以研究波动产生的机理对系统或部件的日常运作有重要意义。作者主要对单部件两状态模型(工作,修理)与单部件三状态模型(工作,修理延迟,修理)中瞬时可用度的波动性进行了研究。首先,提出一套完整的波动理论,包括波动定义、波动判定定理以及波动初始幅度的定义。这些为研究不同分布下瞬时可用度的波动性提供了理论保障。其次,对于所研究的两类模型,运用把更新方程转化为常微分方程的方法,求解瞬时可用度的解析表达式。在此基础上,利用提出的波动理论判断其波动的存在性。其中当工作时间和修理时间都服从指数分布时,瞬时可用度不存在波动性;但当工作时间和修理时间都服从均匀分布或均匀与指数分布组合时,瞬时可用度存在波动性。推广为三状态模型时,当故障时间、修理延迟时间和修理时间都服从指数分布时,瞬时可用度在一定条件下存在波动性。然后,使用不同的方法研究波动抑制的问题。同时给出合理的物理解释,使得波动抑制方法具有可行性。其中对于两状态模型,使用优化参数的方法减小波动初始幅度,抑制波动的产生;对于三状态模型,对分布参数使用敏感性分析,分析某一参数对波动抑制的影响。在一定条件下,使用故障小修代替修理延迟的优化策略,简化了波动条件的同时提升了稳态可用度。最后,对于两状态模型中相关时间服从一般分布时,上述方法难以适用。通过对更新方程运用两次数值积分的方法,得到瞬时可用度的数值解,并对算法进行了误差分析。理论上的误差可控保证了判定波动性的正确性。
[Abstract]:In this paper, the transient availability fluctuation of a single component repairable system is studied. Therefore, it is important to study the mechanism of wave generation for the daily operation of the system or components. The author mainly studies the two-state model (work, repair) and the three-state model (work, repair delay) of single component. The volatility of instantaneous availability is studied. Firstly, a complete set of volatility theory, including the definition of volatility, is proposed. The determination theorem of fluctuation and the definition of initial amplitude of wave provide a theoretical guarantee for studying the volatility of instantaneous availability under different distributions. Secondly, for the two kinds of models studied, Using the method of transforming the renewal equation into ordinary differential equation, the analytical expression of instantaneous availability is solved. The volatility theory is used to judge the existence of the fluctuation. When the working time and repair time are distributed exponentially, there is no volatility in the instantaneous availability. However, when the working time and repair time are distributed uniformly or in combination with exponential distribution, the instantaneous availability fluctuates. When extended to a three-state model, when the failure time, repair delay time and repair time are all distributed exponentially, The instantaneous availability exists volatility under certain conditions. Then, different methods are used to study the problem of wave suppression. At the same time, a reasonable physical explanation is given to make the volatility suppression method feasible. The method of optimizing parameters is used to reduce the initial amplitude of fluctuation and suppress the occurrence of fluctuation. For the three-state model, sensitivity analysis is used to analyze the influence of a parameter on the fluctuation suppression. The optimal strategy of using minor repair instead of repair delay simplifies the fluctuation conditions and improves the steady-state availability. Finally, when the correlation time service in the two-state model is generally distributed, The above method is difficult to apply. By applying the method of twice numerical integration to the renewal equation, the numerical solution of instantaneous availability is obtained, and the error analysis of the algorithm is carried out. The theoretical error controllable ensures the correctness of judging volatility.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O213.2

【参考文献】