复杂系统脆性理论及在煤矿事故系统中的应用
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摘要
随着社会经济以及科学技术的发展,与人们的生活工作息息相关的一些系统越来越复杂,这些系统的崩溃常常会给人们的生活造成不便,严重的甚至可以引起人心不稳,社会动荡等。系统内部各个系统之间复杂的耦合关系给我们的研究造成了很大的困难,要很好的描述复杂系统在干扰下最终引起系统崩溃的这个性质,本文引入并发展了脆性的概念。脆性是指复杂系统中某个子系统在受到内外界的干扰而崩溃,引起了复杂系统内部崩溃的连锁反应,从而导致了整个系统的崩溃。
基于复杂系统脆性的定义,得到复杂系统易脆的两个条件;并根据以往脆性度的定义,将其定义扩展到[0,1]区间,完善了脆性度的定义。复杂系统脆性具有一定的隐藏性。一般地,在复杂系统运行过程中,脆性虽然没有显现出来,但并不能就否认脆性的存在性,为了更好的描述系统状态与崩溃状态的差别,分别定义子系统崩距以及复杂系统脆距。
在复杂系统脆性过程中,首先受到干扰而崩溃的子系统也就是脆性源子系统,复杂系统内部崩溃的传播也是以脆性源为媒介,若能够分清各个脆性源对整个复杂系统所造成的后果,并对其进行区别对待,就能很好的阻止复杂系统内部各子系统的继续崩溃。为了更好的描述复杂系统内部各个子系统之间的脆性联系,论文建立了脆性关系图,从脆性关系图中得到与各个脆性源子系统相对应的脆性树,并根据最简脆性树的特点对其进行简化,对各个脆性源子系统进行分级。对复杂系统脆性过程进行分析,建立描述复杂系统不同侧面不确定性的脆性熵函数,研究脆性风险熵函数的性质,进而得到判断复杂系统崩溃的判定定理。
将复杂系统脆性理论应用于分析煤矿事故系统。基于脆性熵理论研究煤矿事故系统,分析煤矿事故系统以及各子系统与其它外部子系统之间的脆性关联,以及分析煤矿事故系统的事故熵以及脆性风险熵,根据熵函数的性质,得到对煤矿事故系统各个熵函数的控制策略。
进而,基于煤矿事故系统的脆性过程,将煤矿事故系统分为内部系统和外部系统,即煤矿事故发生的内部原因以及外部原因。内部系统主要分析煤矿本身所具有的问题,从管理因素、人为因素、设备因素、技术因素四个方面进行考虑,并根据它们之间的作用方式得到煤矿事故系统的内部脆性度,仿真内部脆性度的变化过程,讨论政府对不同方面进行控制的控制结果;同时,分析煤炭市场、国家政策、当地经济和煤炭相关产业发展情况影响等外部环境对煤矿事故系统的影响,并根据这四个外部系统对煤矿事故系统的作用方式,得到煤矿事故系统的外部脆性度,仿真外部脆性度的变化曲线。
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.
基于复杂系统脆性的定义,得到复杂系统易脆的两个条件;并根据以往脆性度的定义,将其定义扩展到[0,1]区间,完善了脆性度的定义。复杂系统脆性具有一定的隐藏性。一般地,在复杂系统运行过程中,脆性虽然没有显现出来,但并不能就否认脆性的存在性,为了更好的描述系统状态与崩溃状态的差别,分别定义子系统崩距以及复杂系统脆距。
在复杂系统脆性过程中,首先受到干扰而崩溃的子系统也就是脆性源子系统,复杂系统内部崩溃的传播也是以脆性源为媒介,若能够分清各个脆性源对整个复杂系统所造成的后果,并对其进行区别对待,就能很好的阻止复杂系统内部各子系统的继续崩溃。为了更好的描述复杂系统内部各个子系统之间的脆性联系,论文建立了脆性关系图,从脆性关系图中得到与各个脆性源子系统相对应的脆性树,并根据最简脆性树的特点对其进行简化,对各个脆性源子系统进行分级。对复杂系统脆性过程进行分析,建立描述复杂系统不同侧面不确定性的脆性熵函数,研究脆性风险熵函数的性质,进而得到判断复杂系统崩溃的判定定理。
将复杂系统脆性理论应用于分析煤矿事故系统。基于脆性熵理论研究煤矿事故系统,分析煤矿事故系统以及各子系统与其它外部子系统之间的脆性关联,以及分析煤矿事故系统的事故熵以及脆性风险熵,根据熵函数的性质,得到对煤矿事故系统各个熵函数的控制策略。
进而,基于煤矿事故系统的脆性过程,将煤矿事故系统分为内部系统和外部系统,即煤矿事故发生的内部原因以及外部原因。内部系统主要分析煤矿本身所具有的问题,从管理因素、人为因素、设备因素、技术因素四个方面进行考虑,并根据它们之间的作用方式得到煤矿事故系统的内部脆性度,仿真内部脆性度的变化过程,讨论政府对不同方面进行控制的控制结果;同时,分析煤炭市场、国家政策、当地经济和煤炭相关产业发展情况影响等外部环境对煤矿事故系统的影响,并根据这四个外部系统对煤矿事故系统的作用方式,得到煤矿事故系统的外部脆性度,仿真外部脆性度的变化曲线。
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.
引文
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