基于区间分析的系统可靠性设计与优化

发布时间：2018-01-25 21:16

  本文关键词： 系统可靠性 冗余配置优化 区间分析 多元状态系统 元件重要度维修性　出处：《中国科学技术大学》2016年博士论文　论文类型：学位论文

【摘要】：系统可靠性作为工业系统中一个重要的性能评价指标,从上世纪初至今一直倍受国内外专家学者关注。在已有的系统可靠性设计和优化以及维修性的研究中,许多工作都是基于特定的假设,即系统或元件的可靠性及失效时间的概率特性或相关参数是准确可知的。然而,在实际情况中,受限于观测的难度,资源的限制以及系统复杂性等因素,不确定性问题在工业系统的建模过程中是不可避免的。对于许多工程系统,尤其是在系统设计周期的起始阶段,收集足够多的数据不仅难度大而且经济花费高。另外,随着科技更新换代的节奏越来越快,无论是工业领域还是电子科技领域,行业间的竞争也越来越激烈,导致在新产品的生产设计周期中往往没有充足的时间来搜集足够的信息和数据,因此难以避免出现不确定性的问题。对于一些不确定参数的概率分布可知的情况,虽然已有相应的研究成果和方法,但是仍有许多情况,我们只能获知不确定参数的上下界的相关信息。例如,工业零部件产品都存在一定范围内的容错误差,这些误差往往只有上下界的信息而且会被直接带入组成的系统。随着系统复杂化程度的增加,这种情况在实际系统中越来越多。因此,在这种情况下如何对系统可靠性问题进行定量分析和建模显得尤为重要,然而这在以往的研究中却鲜有涉及。本文以系统可靠性设计与优化问题以及系统维修性问题为研究目标,考虑系统及其组成元件的可靠度、失效时间以及性能状态的相关参数存在不确定性的情况,使用区间分析方法来研究具有区间值的不确定参数的问题,构建系统可靠性优化问题以及维修性问题的模型,分析系统的可靠性等指标,设计优化算法求解系统的最优策略。本篇论文主要呈现的具体工作可以分为以下三个部分：第一部分讨论了区间分析方法在系统可靠性优化问题中的应用。我们分别考虑了热备份系统中组成元件的可靠度存在不确定性的情况,冷备份系统中元件失效时间分布函数的参数存在不确定性的情况,以及温备份系统中备份元件在低负荷运转时工作寿命减速因子存在不确定性的情况,使用了区间分析方法处理不确定的参数,将这些参数表示成为具有上下界的区间值形式,基于区间分析理论,构建了对应于三种不同冗余配置方式的系统可靠性优化问题模型。对于具有区间值目标函数的优化问题,本文定义了新的基于决策者性格偏好的区间值排序关系用于比较区间值之间的优劣,设计了相应的遗传算法来求解系统可靠性优化问题的最优配置策略。同时,我们通过数值实例和对比实例的结果验证了区间分析方法的正确性和有效性,以及提出的遗传算法的优越性。第二部分针对一些实际系统的性能状态具有不确定性或动态变化特性的情况,提出了一种新的具有区间状态的多元状态系统模型,这种系统模型的区间状态表示该系统在当前状态下的性能范围。本文通过一个折叠门系统的示例引入了新的具有区间状态的多元状态系统模型,定义了该多元状态系统的状态空间,分析了该系统中元件状态之间的转移过程,讨论了该多元状态系统的状态分布特性以及可靠性,给出了计算该多元状态系统可靠性的迭代算法。此外,本文对一般的多元状态系统的元件重要度衡定方法进行了拓展,给出了四种适用于具有区间状态的多元状态系统的元件重要度衡定方法,并且通过数值实例讨论了系统的预设性能要求和元件重要度之间的关系。同时,数值实例的结果也表明了本文提出的四种元件重要度衡定方法得出的结论是一致的。第三部分研究了系统性能退化问题和系统维修性问题。首先,针对冷备份系统的冗余配置优化问题,考虑了冷备份元件在待命状态下的性能退化,在一般的冷备份系统的可靠性模型中引入了冷备份元件性能退化的情况,采用中心极限定理的方法给出了优化问题目标函数的近似表达,使用了遗传算法求解优化问题,讨论了冷备份元件在待命状态下的性能退化对系统冗余配置优化问题的影响。其次,继续深入研究了具有区间状态的多元状态系统模型,考虑了系统性能随工作时间推移而退化的情况以及系统在工作中可能发生随机失效的情况,同时也考虑了针对系统性能退化实施非完美修复以及针对系统随机失效实施最小修复,构建了系统状态转移过程的马尔可夫模型,通过求解对应的切普曼-柯尔莫哥洛夫方程计算系统的可靠性和可用性。在实例中,本文分析了在不同的修复率下的具有区间状态的多元状态系统的可靠性和可用性,实例的结果验证了本文所提出模型的正确性。
[Abstract]:The reliability of the system as an important index for evaluating the performance of the industrial system, from the beginning of the last century so far has always been the focus of experts and scholars at home and abroad. In the design and optimization of system reliability and maintainability of the existing research, many jobs are based on specific assumptions, the system reliability of system or component failure time and the probability characteristics or the relevant parameters are accurate. However, in reality, due to the difficulty of observing, resource constraints and system complexity and other factors, the uncertainty is unavoidable in the process of modeling in industrial system. For many engineering systems, especially in the initial stage of system design cycle, collect enough the data is not only difficult and high economic costs. In addition, with the development of science and technology upgrading in an increasingly fast pace, whether industry or electronic technology field, inter industry competition Competition has become increasingly fierce, resulting in the production of new product design cycles often do not have enough time to collect enough information and data, so it is difficult to avoid the problem of uncertainty. For some uncertain parameters of the probability distribution of the situation, although the research results and the existing methods of corresponding, but there are still many. We can only learn the related information of uncertain parameters of the upper and lower bounds. For example, industrial parts products are fault tolerance error within a certain range, the error is only the upper and lower bounds on the information and will be directly into the system. As the system complexity increases, this more and more in the actual system. Therefore, in in this case how to system reliability quantitative analysis and modeling is very important, however, that in previous studies in this department are rarely involved. Problems in the design and optimization of system reliability and maintainability problems as the research object, considering the reliability of the system and its components, the uncertainty of the relative parameters of failure time and performance status, to study with uncertain parameters of the problem of interval analysis method using interval, construction of system reliability and maintainability optimization problem model reliability index analysis, system design, optimal strategy optimization algorithm for solving the system. This paper mainly presents the specific work can be divided into the following three parts: the first part discusses the interval analysis method in the optimization of the reliability of the system. We consider the reliability of the components in the hot backup system does not exist the deterministic case, the uncertainty of the parameters of component failure time distribution function of cold backup system, and Backup temperature backup system in low load operation life of deceleration parameter uncertainty and parameters using interval analysis method to deal with uncertainty, these parameters will be expressed as interval with the upper and lower bounds of the value form of interval analysis based on the theory of system reliability optimization model is constructed corresponding to three different redundant configuration way. With interval valued objective function optimization problems, this paper introduces a new definition of interval decision character based on the preference value ordering relation for comparison between interval value quality, genetic algorithm is designed corresponding to the optimal allocation strategy of reliability optimization problem solving system. At the same time, we verify the correctness and validity of the interval analysis method through numerical examples and comparison results, and the superiority of the proposed genetic algorithm. In the second part, according to some actual The performance of state system has the characteristics of uncertainty or dynamic situation, put forward a new multi state system model with interval state, this state interval system model in the current state of the performance range of the system. In this paper, through a folding door system example introduced multiple state system model with interval the new definition of the state space, the multi state system, analyzes the transfer process between the state of the element in the system, discussed the distribution characteristics of the multi state system reliability calculation and the state, the multi state system reliability iteration algorithm is given. In addition, the multi state component importance scale system in general the method is extended to component importance weights are four applied to multi state systems with interval state setting method, and through the number The value of example discusses the relationship between the importance of preset performance requirements and system component. At the same time, numerical results also show that is consistent with four kinds of component importance weights is proposed in this paper will draw the conclusion. The third part studies the system performance degradation and system maintenance problems. Firstly, aiming at the cold backup the optimization problem of redundant configuration, considering the degradation performance of cold backup element in the standby state of the degradation of the performance of the cold backup components introduced in the reliability model of cold backup system in general, by the central limit theorem gives the approximate expression of the objective function of the optimization problem, using genetic algorithm to solve the optimization problem. The performance of cold backup components in the standby state under the effects of degradation on the optimization problem of system redundancy allocation. Secondly, further research with multi state interval State system model, considering the system performance with the working time and the degradation of the system at work may occur in random failure, but also consider the performance degradation for the system implementation and non perfect repair system for the random failure with minimal repair, construction of the Markov model process of system state transition, by solving the corresponding Karl Chapman - kolmogoroff equation to calculate the system reliability and availability. In the example, this paper analyzes the state of the multi state system with interval in different repair rates of reliability and availability, example results verify the correctness of the proposed model.

【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TB114.3
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本文编号：1463717