Abstract: Many critical infrastructures and services, such as power, communications and transportation systems, depend on the proper functioning of the network. The interdependence of the system improves the performance and efficiency of the system to a certain extent. However, this interdependence also brings certain risks. When there is interaction between different networks, if a network or a node within it fails, it will cause the other network nodes that depend on it to also fail, causing cascading failures and eventually leading to the complete collapse of these interdependent networks. If these interdependent networks cascade down, it can lead to power outages, communication outages, traffic jams and other serious consequences, which can have a significant impact on social stability and people’s daily lives. Therefore, we should not only study the system composed of a single network, but should focus on multiple network systems that interact with each other to have a more comprehensive understanding of the operating mechanism of network systems in reality.
Based on the classical cascading failure model, this paper introduces a load-sharing coupling system for the dependence between coupled systems. Specifically, when a system experiences a failure, its component load will increase due to the existence of propagation pressure. This paper quantifies this pressure as the load amount, that is, the evolution of cascading failure of the coupling system is caused by the steadily increasing load, and through the quantitative analysis of load growth, the strength and speed of fault propagation within and between different subsystems are better measured. Based on the dynamic Markov model, a stochastic dynamic model of cascaded failure propagation in an interdependent system is established. In order to more accurately assess system reliability, the traditional two-state model is extended to classify component states into normal operation, overload operation and fault state. In this paper, the multi-stage characteristics of the dynamic failure rate are considered, and the influence of multiple factors such as component life, component overload and interdependence between systems on the failure rate is analyzed in the model, and the law of overload probability and failure rate with the number of failures of the two subsystems is given, the repair time and the number of repair equipment are included in the model, and the state transfer rate matrix of the coupling system and the analytical expression of the system reliability are given.
The effectiveness of the proposed method is verified by numerical analysis, and a coupled dependent system is constructed, and each subsystem has a repair equipment. Since the subsystem needs to assume its own load and responsibility when performing its own tasks, the coupled system plays more of a coordinating and regulating role in this case, and therefore, in the cascade process, each subsystem has its own pressure, which is higher than the pressure exerted on it by the coupled system. It is calculated that when the number of faults in systems A and B increases, the amount of additional load required by the remaining working parts of the entire coupled system increases, and the failure rate increases accordingly. The results show that system A is more likely to fail than system B when subject to the same overload. Finally, the state transition rate matrix and reliability of the coupling system are calculated.
The influence of the initial load, the life of the component itself, the number of faults in the subsystem where the component is located, the dependence between the systems and the repairability of the component on the cascading failure propagation process are considered, and the Markov load-sharing coupling system model is established by using the continuous Markov process, which makes the reliability model closer to reality. It can be extended to different network topologies, coupling strengths and different load sharing modes to further study the cascading failure mechanism of the system and its reliability analysis.

Key words: reliability, Markov process, multi-state coupled systems, cascading failure, load dependency

摘要： 基础设施系统彼此之间功能上的关联决定了不同系统之间的各个组件在物理和逻辑层面上的依赖性。本文基于经典的级联失效模型,针对耦合系统间的相依性,建立了非时齐的马尔可夫负载共享耦合系统模型。为了更准确评估系统可靠性,对传统的二态模型进行了扩展,将部件状态划分为运行态、过载态和故障态。本文考虑了动态故障率的多阶段特征,在模型中分析了组件寿命、组件过载以及系统间的相互依存关系等多重因素对故障率的影响,并给出了过载概率和故障率随着两子系统故障数变化的规律,分析了系统的可维修性,将修理时间和修理设备数量纳入了模型,给出了耦合系统的状态转移率矩阵和系统可靠度的解析表达,并通过数值分析验证了本方法的有效性。

关键词: 可靠性, 马尔可夫过程, 多状态耦合系统, 级联失效, 负载相依