考虑非平稳特性的多层多级备件时变凸优化研究

Both on practical time-varying mission sortie generation rate conditions as well as in realistic no failure passivation operation environment, if complex repairable systems available states located in forward time slot are neglected multi-indenture multi-echelon spare parts quantities are usually seriously overestimated or underestimated. In this project, spare parts status are described as demand, due-in pipeline and backorder, according to the three status stochastic process models are established on the consideration of internal-external alternate stress action abstracted from realistic complex system operation modes, and non-stationary characteristics are proved for the three stochastic processes. Analytic functional relations are modeled among the stochastic processes, and multi-indenture multi-echelon spare parts time-varying stock equation is established based on the non-stationary characteristics. Spare part time-varying demand rate and conditional backorder expectation function are analytically derived according to multi-indenture multi-echelon spare parts non-stationary demands. Transitive laws derived from the function relations are promulgated in cascade coupling maintenance net. Time-varying optimized model is build to multi-indenture multi-echelon spare parts, furthermore, optimized objective function is constructed, which depends on cumulative requirements of spare part in time domain. Constraint space is analyzed for making decision of convexity. Convex optimal operator is designed for objective function. The optimal resolution is searched in the inner-point set by means of differential operation under the gradient direction. Margin effect is analyzed in the adjacent time slots. Differential operational is iteratively implemented under the fastest decrease directions in order to complete convex optimization. Monte Carlo simulation experiments are implemented to validate the proposed time-varying convex optimization methodology. It can be concluded that the provided methology can be utilized to resolve the time-varying optimal problems effectively for multi-indenture multi-echelon spare parts.

在复杂可修系统时变任务强度及产品无故障休眠使用环境中,系统前时隙可用状态信息通常会产生后向影响，如果忽略这些影响将造成多层多级备件数量评估偏差较大。本项目综合考虑系统实际运行过程中这些内外交变应力影响，研究备件需求、备件在修及备件短缺非平稳随机过程，求证这些过程的非平稳特性，抽象这些过程分布函数族之间的解析关系，构建非平稳特性下多层多级备件时变库存平衡方程。推导多层多级备件级联时变需求率及条件短缺期望解析函数关系，揭示这些函数关系在时变级联维修网络中的耦合传递规律。建立多层多级备件时变凸优化模型，探索时域累积备件需求依赖的优化目标凸函数构造方法，对约束空间进行凸分析。设计目标函数凸优化算子，在梯度方向上对凸集中的内点进行搜索，分析其在相邻时隙上的边际效应，在目标函数最速下降方向上迭代差分运算实现凸优化。通过蒙特卡洛仿真实验进行验证。为大规模多层多级备件时变优化问题的高效求解提供科学方法。

在复杂可修系统时变任务强度及产品无故障休眠使用环境中,系统前时隙可用状态信息通常会产生后向影响，如果忽略这些影响将造成多层多级备件数量评估偏差较大。本项目综合考虑系统实际运行过程中这些内外交变应力影响，研究备件需求、备件在修及备件短缺非平稳随机过程，求证这些过程的非平稳特性，抽象这些过程分布函数族之间的解析关系，构建非平稳特性下多层多级备件时变库存平衡方程。推导多层多级备件级联时变需求率及条件短缺期望解析函数关系，揭示这些函数关系在时变级联维修网络中的耦合传递规律。建立多层多级备件时变凸优化模型，探索时域累积备件需求依赖的优化目标凸函数构造方法，对约束空间进行凸分析。设计目标函数凸优化算子，在梯度方向上对凸集中的内点进行搜索，分析其在相邻时隙上的边际效应，在目标函数最速下降方向上迭代差分运算实现凸优化。通过蒙特卡洛仿真实验进行验证。为大规模多层多级备件时变优化问题的高效求解提供科学方法。