论文摘要
系统signature是研究可靠性的一个强大工具,它是一组仅与系统结构有关的概率向量,因此可以在不依赖于元件寿命分布的情况下对系统可靠性进行分析和研究。另外,通过对某一关联系统signature的计算,可以了解该系统中元件的失效情况和系统寿命。近几年来,signature方法由于其在可靠性分析方面展现出的强大的分析能力而备受关注,应用signature对二态系统进行可靠性建模以及寿命对比等研究层出不穷,相关理论日趋成熟完善,但由于signature自身定义的限制,应用signature分析多态系统可靠性的讨论与研究尚有不足。实际上,在许多工程实践中,系统和元件并不是简单地呈现为成功、失败两种状态,而是存在着多种处于完美工作状态与完全失效状态之间的中间状态。如果仅仅把系统或元件划分为成功、失败两个状态,有可能导致严重的分析误差。因此,本文的核心问题在于应用系统signature分析多状态系统的可靠性并且求解其剩余寿命,研究对象包括以下两类系统:第一类系统由多个二态元件组成,元件失效对系统性能的影响具有累积效应。该系统的性能水平取决于可用元件的数量——可用元件的数量越多,系统的性能水平也越高。第二类系统由多状态元件组成的。当组成系统的元件随着使用时间而发生恶化(疲劳、部分失效)或者因为外部环境的变化而导致元件性能下降时,系统的性能水平随之下降。针对第一类系统,首先把传统signature的定义和使用范围拓展到多维的情形,应用多维signature,在多状态系统理论框架下对多态关联系统可靠性进行建模与分析,得到系统在每一状态下的联合生存函数表达式。之后进一步探究了系统在某一时刻t的动态signature,其实质是元件失效导致系统性能衰退的条件失效概率,所基于的条件事件是:多状态系统在时刻t仍在工作,经检查发现系统处于l(t)状态并且恰好已发生了q(t)次元件失效。在此基础上,求解得出了动态signature的计算公式以及系统剩余寿命的表达式,给出的数值算例验证了这一模型的有效性。针对第二类系统,同一元件在不同状态层上的寿命并不独立,因此首先从生存signature着手。生存signature是对系统signature的拓展,它适用于分析由多种类型元件组成的系统。把多态元件看作M种类型的二态元件,由此导出了多态系统在j层上的生存signature及其计算公式,并求解得出系统在j层上的生存函数表达式。然后,借用多态系统生存signature这一概念反向定义系统的m阶signature,并给出了相应的计算公式,通过m阶signature,求出多态系统的寿命分布函数。最后,进一步讨论了在时刻t系统基于条件事件下的动态signature,分别给出了第二类系统的动态signature计算公式及其剩余寿命的表达式。选取的数值算例是多状态连续n中取k的F系统,计算结果验证了这一方法的可行性。
论文目录
文章来源
类型: 硕士论文
作者: 徐凡启
导师: 贾旭杰
关键词: 多态关联系统,系统,动态,剩余寿命
来源: 中央民族大学
年度: 2019
分类: 基础科学,工程科技Ⅱ辑
专业: 数学,数学,工业通用技术及设备
单位: 中央民族大学
分类号: TB114.3
总页数: 70
文件大小: 2491K
下载量: 37
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