基于马尔可夫过程的多部件系统劣化状态空间划分模型

Multi-component system state space partition model based on Markov process

工业系统的复杂性及智能化程度的不断提高使得系统的可靠性和安全性严重制约着系统正常的工作运转.长时间的工作运行会加大系统的故障风险,降低其安全稳定性.为了减少系统故障给产品质量和生产成本带来的影响,系统的最优维修决策问题逐渐成为研究的热点.分析系统的劣化状态有利于对系统做出正确的维修决策,延长系统的运行时间及减少经济损失.针对相同且劣化独立的多个部件组成的系统,建立离散状态建模下的多部件系统的多状态联合劣化空间划分模型.通过联合劣化状态空间的划分,给出所有维修需求组合及其概率计算通式,运用马尔科夫过程理论建立系统状态的平稳概率模型,并通过数值实验验证了该模型的正确性和有效性.

With the complexity of industrial systems and the increasing degree of intelligence,the normal operation of the system is seriously restried by the reliability and safety of the system.Long-term work operation will increase the risk of system failure and reduce its safety and stability.In order to reduce the impact of system failure on product quality and production cost,the optimal maintenance decision problem of the system has gradually become a research hot topic.Analyzing the degraded state of the system facilitates can help make correct maintenance decisions for the system,extending system uptime and reducing the economic losses.For system consisting of multiple components that are identical and degraded independently,a multi-state joint degradation space partition model for multi-component systems under discrete state modeling is established.According to the division of the joint degradation state space,the combination of all maintenance requirements and their probability calculation formula are given,a stationary probability model of the system state is established using Markov process theory.The correctness and effectiveness of the model are verified by numerical experiments.