一般概率分布下系统瞬时可用度离散时间建模分析与应用
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摘要
装备战备完好性与任务持续性是装备战斗力的重要组成要素。装备可用度是描述装备战备完好性与任务持续性的重要参数。在实际使用过程中,装备可用度参数一般分为稳态可用度参数和瞬时可用度参数。长期以来,稳态可用度的研究和应用一直受到广泛的重视。然而,随着装备功能日益复杂,装备的故障规律、保障规律等也变得越来越难以把握,装备的可用度在装备使用过程中,出现了一系列的波动现象。这一现象己无法运用传统的稳态可用度来解释和研究。
针对上述问题,论文在分析总结当前装备瞬时可用度模型研究工作的基础上,着重对装备瞬时可用度模型建模、模型的求解以及模型的具体应用等方面进行了较为系统深入的研究。具体工作主要包括:
(1)为了展开瞬时可用度的相关分析,论文首先对一般概率分布下已有连续系统的可用度模型及其离散化近似解方法进行了研究。结果表明:虽然近似解具有较好的计算精度,但由于受到模型变化的限制,离散化近似解的求解过程较为复杂,不利于进一步的研究和分析。同时,连续模型也不便于描述系统在实际维护中的离散时间特点。
(2)为了改善所发现的求解复杂度问题,以及适应系统在实际维护中的离散时间特点,论文转而尝试直接在离散时间下对瞬时可用度模型进行建模。建立了单部件可修系统、考虑延迟的单部件可修系统、串联可修系统、两部件并联可修系统以及考虑预防性维修可修系统的瞬时可用度模型。
(3)分析和探讨了所建离散时间瞬时可用度模型与传统的连续时间可用度模型之间的关系。对指数分布下,离散时间模型的数值解、连续时间模型的数值解和连续时间模型的解析解进行了详细的比较研究。通过比较发现离散时间模型的数值解具有计算精度高、消耗时间少的优点,在一定的采样时间要求下,完全可以替代连续时间模型的数值解。
(4)基于所建离散时间瞬时可用度模型,提出了系统优化设计的两类问题:即最小可用度波动问题和跟踪问题,并运用粒子群算法对单部件可修系统和考虑延迟的单部件可修系统进行了实例演示运算。研究结果表明:在容许范围内,针对系统故障率、修复率和转修率等因素的恰当匹配设计,可以有效地抑制瞬时可用度的波动现象,使装备系统得以更加快速平稳地形成稳定的战斗力。
Equipment Operational Readiness and continuity of mission are important elements of equipment combat power. Availability of equipment is an important parameter of well describing equipment Operational Readiness and continuity of mission. In practical using, equipment availability parameters can be generally divided into steady-state availability parameters and instantaneous availability parameters. For a long time, the research and application of steady-state availability has brought wide attention. However, with equipment's function being more and more complicated, the fault-mechanism and maintaining-rules become more and more difficult to be understood and controlled. The equipment availability presents a series of fluctuation phenomenon in the using process. Obviously, these phenomena can be neither explained nor further studied via the traditional methodology of steady-state availability.
Based on a careful analysis and discussions of the current existing equipment instantaneous availability model, this dissertation focuses on the problems of the equipment instantaneous availability modeling and its specific application on the instantaneous availability analysis and designs. The main works are as follows.
First, in order to study the issue of instantaneous availability in details, the existing continuous-time model of availability and its approximate solution are discussed under the general distribution. The studies reveal that the computational accuracy of the discretelized solving methodology is satisfactory, but the expression as well as the computation of the approximate solution is usually very complicated and hence not very convenient for the further applications. Especially, the discrete-time characteristic of the practical maintenance is not very applicable for the descriptions of continuous-time availability models either.
Then, in order to overcome the shortcomings of the existing continuous-time models of the instantaneous availability, a kind of new discrete-time instantaneous availability model is proposed for one-unit repairable systems, two-unit series and parallel-connected repairable systems with repair-delays, and the repairable system with preventive maintenance.
Moreover, the relationship between the continual-time and the discrete-time of instantaneous availability model is investigated. The numerical solutions of the proposed discrete-time models are compared with exactly analytic solutions of the continual-time models under the exponential distribution. The comparison shows that the discrete-time model has the advantages of satisfactory computational-precision and less time-consuming. Under suitable sampling-rate, the proposed discrete-time models can substitute for the continual-time model.
Finally, based on the proposed discrete-time instantaneous availability model, two types of optimization design problems, namely, the smallest availability fluctuation problem and the track problem, are well formulated. Some numerical analysis is carried out on the discrete-time one-unit repairable system and the discrete-time one-unit repairable system with repair delays using the Particle Swarm Optimization Algorithm.Studies reveal that the fluctuation phenomenon of instantaneous availability can be refrained by matching-design the fault-rate, maintaining rate, and delays-repair rate appropriately in a pre-specific extent.
针对上述问题,论文在分析总结当前装备瞬时可用度模型研究工作的基础上,着重对装备瞬时可用度模型建模、模型的求解以及模型的具体应用等方面进行了较为系统深入的研究。具体工作主要包括:
(1)为了展开瞬时可用度的相关分析,论文首先对一般概率分布下已有连续系统的可用度模型及其离散化近似解方法进行了研究。结果表明:虽然近似解具有较好的计算精度,但由于受到模型变化的限制,离散化近似解的求解过程较为复杂,不利于进一步的研究和分析。同时,连续模型也不便于描述系统在实际维护中的离散时间特点。
(2)为了改善所发现的求解复杂度问题,以及适应系统在实际维护中的离散时间特点,论文转而尝试直接在离散时间下对瞬时可用度模型进行建模。建立了单部件可修系统、考虑延迟的单部件可修系统、串联可修系统、两部件并联可修系统以及考虑预防性维修可修系统的瞬时可用度模型。
(3)分析和探讨了所建离散时间瞬时可用度模型与传统的连续时间可用度模型之间的关系。对指数分布下,离散时间模型的数值解、连续时间模型的数值解和连续时间模型的解析解进行了详细的比较研究。通过比较发现离散时间模型的数值解具有计算精度高、消耗时间少的优点,在一定的采样时间要求下,完全可以替代连续时间模型的数值解。
(4)基于所建离散时间瞬时可用度模型,提出了系统优化设计的两类问题:即最小可用度波动问题和跟踪问题,并运用粒子群算法对单部件可修系统和考虑延迟的单部件可修系统进行了实例演示运算。研究结果表明:在容许范围内,针对系统故障率、修复率和转修率等因素的恰当匹配设计,可以有效地抑制瞬时可用度的波动现象,使装备系统得以更加快速平稳地形成稳定的战斗力。
Equipment Operational Readiness and continuity of mission are important elements of equipment combat power. Availability of equipment is an important parameter of well describing equipment Operational Readiness and continuity of mission. In practical using, equipment availability parameters can be generally divided into steady-state availability parameters and instantaneous availability parameters. For a long time, the research and application of steady-state availability has brought wide attention. However, with equipment's function being more and more complicated, the fault-mechanism and maintaining-rules become more and more difficult to be understood and controlled. The equipment availability presents a series of fluctuation phenomenon in the using process. Obviously, these phenomena can be neither explained nor further studied via the traditional methodology of steady-state availability.
Based on a careful analysis and discussions of the current existing equipment instantaneous availability model, this dissertation focuses on the problems of the equipment instantaneous availability modeling and its specific application on the instantaneous availability analysis and designs. The main works are as follows.
First, in order to study the issue of instantaneous availability in details, the existing continuous-time model of availability and its approximate solution are discussed under the general distribution. The studies reveal that the computational accuracy of the discretelized solving methodology is satisfactory, but the expression as well as the computation of the approximate solution is usually very complicated and hence not very convenient for the further applications. Especially, the discrete-time characteristic of the practical maintenance is not very applicable for the descriptions of continuous-time availability models either.
Then, in order to overcome the shortcomings of the existing continuous-time models of the instantaneous availability, a kind of new discrete-time instantaneous availability model is proposed for one-unit repairable systems, two-unit series and parallel-connected repairable systems with repair-delays, and the repairable system with preventive maintenance.
Moreover, the relationship between the continual-time and the discrete-time of instantaneous availability model is investigated. The numerical solutions of the proposed discrete-time models are compared with exactly analytic solutions of the continual-time models under the exponential distribution. The comparison shows that the discrete-time model has the advantages of satisfactory computational-precision and less time-consuming. Under suitable sampling-rate, the proposed discrete-time models can substitute for the continual-time model.
Finally, based on the proposed discrete-time instantaneous availability model, two types of optimization design problems, namely, the smallest availability fluctuation problem and the track problem, are well formulated. Some numerical analysis is carried out on the discrete-time one-unit repairable system and the discrete-time one-unit repairable system with repair delays using the Particle Swarm Optimization Algorithm.Studies reveal that the fluctuation phenomenon of instantaneous availability can be refrained by matching-design the fault-rate, maintaining rate, and delays-repair rate appropriately in a pre-specific extent.
引文
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