关键词: 相依关系, 耦合系统, 级联失效, 连续时间马尔可夫过程, 可靠度

Abstract: The phenomenon that natural disasters or man-made failures cause small perturbations in the system, which in turn trigger chain reaction failures in the system, leading to the rapid spread of the disaster in the system and the collapse of part or the whole system, is called cascade failure. Because cascade failure can carry out one-to-many failure transmission, the failure is exponentially fast propagation, so the propagation speed is fast and the scope is wide. In real life, most of the systems are not isolated, such as communication networks and power grids, which are interdependent and interact with each other, and this coupling relationship between the systems makes the scope of cascade failure wider, resulting in a more complex cascade process, which affects the reliability of the entire system and its normal operation.
Aiming at this problem, taking the power communication coupled system as the research object, this paper considers the interaction between the component failure rate and the state of the coupled system to more accurately assess the dynamic performance of the components. A continuous-time Markov process is utilized to establish a coupled cascade failure system reliability model, which describes a more generalized and universally applicable coupled cascade failure system in which inter-system failures and intra-system failures act at the same time. The subsystems are not only affected by component failures that lead to load redistribution, but also the states of other subsystems coupled to them. In this paper, firstly, a stochastic model is established by using the continuous-time Markov process to describe the coupling relationship of the subsystems with the system state transfer. The occurrence of cascade failure of the coupled system is a series of transfers of the coupled system in the state space, which gives the analytical expression of the transfer rate of the coupled system. Then the paper analyzes the effect of cascade failure that the increase in the component load affects the failure rate of the component and the dependence relationship between the subsystems, establishes a reliability model of the coupled cascade failure system, and proves the reliability model of the coupled cascade failure system. The reliability model of the coupled cascade failure system is established, and the calculation method and analytical expression results of the system reliability are proved. Based on the arithmetic example, the specific process of cascade failure occurring in the coupled system is demonstrated to verify the validity and feasibility of the method, the Laplace transform and inverse transform of the coupled system reliability are performed to find the average time before failure of the coupled system, the uncoupled system in which the line failure rate of the electric power system is not affected by the degree of line loading or the state of the communication system is considered, and the indexes of the coupled system and the independent system are compared and analyzed. The results show that the reliability of the coupled system is less than the reliability of the uncoupled system when the number of lines and the line failure rate are the same, and the mean time before failure of the coupled system is smaller than that of the uncoupled system. The comparative results show that the coupling relationship in the system has a significant effect on the system reliability. Therefore, the dependencies between subsystems significantly increase the instability and the risk of the overall system and accelerate the propagation of cascading failures.
The propagation process of cascade failure is deeply analyzed by using the method of continuous-time Markov process and the idea of recursion, which provides a research method for the cascade study of coupled systems based on load and time and can be extended to different coupling relationships, coupling strengths, and different load distribution modes to further study the cascade failure process of the system as well as the reliability analysis. In further studies, the types of system life distributions and coupling relationships can be expanded, such as multilevel coupling relationships and intersystem life nonlinear dependencies.

Key words: dependence relation, coupled system, cascading failure, continuous-time Markov process, reliability