Brittle Theory Of Complex System And Its Application On Coal Mine Accident System

With the development of science and technology, more and more systems related with people's life and work are becoming more complicated. But if the complex system collapses, it will lead people's lives inconvenience and the social unrest. However, the complicated coupled relationship of different subsystems can not be described easily. Therefore, in this paper, the concept of brittleness is introduced and developed to describe the process of complex system collapse induced by the internal or external interference. Brittleness is that if a subsystem of whole complex system collapse induced by the internal or external interference, as a chain response, whole complex system collapse.Based on the definition of brittleness, two conditions which denote that complex system is brittle are gained. And according to the other people's definition of brittle degree, the definition of brittle degree is developed to interzone from 0 to 1. Generally, complex system brittleness is hidden during the running process of complex system, brittleness of complex system can not be observed, but this does not mean that the brittleness does not exist. To describe the difference between subsystem state and collapse state, complex system state and brittle state, the subsystem collapse distance and complex system brittle distance are defined.In the brittle process of complex system, the first collapsed subsystems which are disturbed by internal or external factors are defined as the brittle source subsystems; moreover, the brittle source is the medium. This paper founded the brittle relation graph to describe the subsystems' brittle relation of complex system. We can get the brittle trees of brittle sources from brittle relation grapy and simplify them. To distinguish the different outcome of different subsystems to complex system, brittle source subsystems are graded with different power of set pair theory. With the increasing of the disorder degree of complex system, the complex system is collapsed, and the entropy theory can describe the disorder degree. For different levels of complex system, the subsystem brittle entropy, complex system brittle entropy, brittle contact entropy and brittle risk entropy are defined. According to the properties of brittle risk entropy function, the theorem of judging complex system collapse is founded. Brittleness theories of complex system are applied to analyze the coal mine accident system. Based on the brittle entropy theory, the brittle contact between coal mine accident system, subsystems and other subsystem from outside are analyzed, and the accident entropy and brittle risk entropy of coal mine accident system are analyzed. According to the properties of entropy function, the controlled strategy is acquired to the entropy function of coal mime accident system.Furthermore, though the analysis on the brittle process of coal mine accident system, this paper divided coal mine accident system into internal system and external system, that is the internal reason and the external reason. On the one hand, Influencing factors of internal systems are generalized to four factors that are the management factor, the human factor, the equipment factor and the technology factor. Moreover, The author simulates the change process of internal brittleness which has described the influence of four factors to coal mine accident system, and the different controlled result of different controlled aspect of government are discussed; On the other hand, Influencing factors of external systems also can come down to four factors that are the coal market, government policy to coal mine, local economy of coal mine and some enterprise about coal. According to the influence of four external systems to coal mine accident system, the external brittleness degree is gotten. Furthermore, the change processes of external brittleness are simulated.