本文關(guān)鍵詞： 瞬時可用度 波動 更新模型 波動抑制 數(shù)值計算　出處：《南京理工大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：本文主要研究單部件可修系統(tǒng)的瞬時可用度波動問題。由于一個系統(tǒng)或部件在使用初期的工作狀態(tài)呈現(xiàn)波動變化,所以研究波動產(chǎn)生的機理對系統(tǒng)或部件的日常運作有重要意義。作者主要對單部件兩狀態(tài)模型(工作,修理)與單部件三狀態(tài)模型(工作,修理延遲,修理)中瞬時可用度的波動性進行了研究。首先,提出一套完整的波動理論,包括波動定義、波動判定定理以及波動初始幅度的定義。這些為研究不同分布下瞬時可用度的波動性提供了理論保障。其次,對于所研究的兩類模型,運用把更新方程轉(zhuǎn)化為常微分方程的方法,求解瞬時可用度的解析表達式。在此基礎(chǔ)上,利用提出的波動理論判斷其波動的存在性。其中當(dāng)工作時間和修理時間都服從指數(shù)分布時,瞬時可用度不存在波動性;但當(dāng)工作時間和修理時間都服從均勻分布或均勻與指數(shù)分布組合時,瞬時可用度存在波動性。推廣為三狀態(tài)模型時,當(dāng)故障時間、修理延遲時間和修理時間都服從指數(shù)分布時,瞬時可用度在一定條件下存在波動性。然后,使用不同的方法研究波動抑制的問題。同時給出合理的物理解釋,使得波動抑制方法具有可行性。其中對于兩狀態(tài)模型,使用優(yōu)化參數(shù)的方法減小波動初始幅度,抑制波動的產(chǎn)生;對于三狀態(tài)模型,對分布參數(shù)使用敏感性分析,分析某一參數(shù)對波動抑制的影響。在一定條件下,使用故障小修代替修理延遲的優(yōu)化策略,簡化了波動條件的同時提升了穩(wěn)態(tài)可用度。最后,對于兩狀態(tài)模型中相關(guān)時間服從一般分布時,上述方法難以適用。通過對更新方程運用兩次數(shù)值積分的方法,得到瞬時可用度的數(shù)值解,并對算法進行了誤差分析。理論上的誤差可控保證了判定波動性的正確性。
[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.
【學(xué)位授予單位】：南京理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O213.2

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