复杂系统崩溃过程的分析与控制
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摘要
随着科学技术和社会经济的发展,现实中许多复杂系统的规模越来越大,子系统之间的关联关系越来越紧密、复杂。这些复杂系统在运行过程中,不可避免的受到系统外部和内部的干扰。一旦复杂系统中的一个或多个子系统崩溃而不能正常工作,由于子系统之间的相互作用,危害将在系统内部扩散,最终可能会导致整个系统崩溃、丧失其应有的功能。现实生活中复杂系统崩溃而造成巨大损失的例子数不胜数,因此深入研究复杂系统的崩溃过程,并探讨相应的控制策略显得十分重要。本文利用控制理论、系统理论以及复杂网络等理论对复杂系统的崩溃过程进行了深入分析。主要工作与内容如下:
(1)给出了复杂系统崩溃过程的分析方法。根据现实生活中复杂系统崩溃的案例,总结崩溃过程的特点,将复杂系统的崩溃过程分为两个阶段:崩溃初期与崩溃扩散期。崩溃初期是环境要素与子系统性能共同作用,直到初始崩溃出现的阶段。利用控制论以及系统理论,本文给出崩溃初期的分析方法。崩溃扩散期是初始崩溃在整个系统中扩散的阶段。针对崩溃扩散期的特点,利用复杂网络理论,本文给出了崩溃扩散期的形式化描述模型。此外,以胶济铁路火车对撞事故为例,分析了初始崩溃(T195火车出轨)的各种致因及改进措施,同时对崩溃扩散过程(T195火车与5034火车相撞)进行了建模。
(2)给出了复杂系统崩溃扩散过程的离散状态模型。现实生活中许多复杂系统的状态是离散的,而且许多连续状态的系统演化机制不明确但若从宏观上把握系统的崩溃扩散过程,系统状态也可以看成离散值。基于崩溃扩散过程的形式化描述模型,结合这类复杂系统崩溃的特有特征,本文提出了复杂系统崩溃扩散过程的离散状态模型并给出了相应的解析分析方法。从模型参数、系统拓扑结构以及系统结构复杂性增加三个方面分析了它们对崩溃扩散过程的影响,而且给出了几种控制崩溃扩散的方案并探讨了各方案的效果。
(3)给出了复杂系统崩溃扩散过程的连续状态模型。现实生活中大量复杂系统的状态值与状态变化均是连续的,基于崩溃扩散过程的形式化描述模型并参考几个存在的连续状态崩溃扩散模型,本文给出了复杂系统崩溃扩散过程的一种考虑冗余系统的普适性连续状态模型。从模型参数、冗余策略以及系统结构复杂性增加三个方面分析了它们对系统崩溃扩散过程的影响,并从外部资源调用的角度,给出了控制崩溃扩散的资源分配策略并分析了各策略的有效性。
(4)以关联基础设施为案例,给出了关联基础设施崩溃扩散过程的分析方法。基础设施中,天然气网的子系统状态演化与邻居子系统的状态相关,符合复杂系统崩溃扩散的形式化描述模型,而电网的子系统状态演化受到系统中其它所有子系统状态以及系统拓扑结构的影响,不符合形式化描述模型。本文以关联的电网与天然气网为例,分析它们的崩溃扩散过程,重点仿真分析了基础设施之间的关联影响,而且给出几种控制崩溃扩散的方案,并探讨了各个方案的效果。
With the development of scientific technology and social economy,many complex systems in our life become more and more complicated.These complex systems are unavoidably disturbed by external and internal perturbations.Once one or more subsystems can not operate normally and collapse,due to interaction among subsystems, disaster caused by initial collapsed subsystems will spread in the whole system,which may cause the whole system lose its function and collapse.The cases of immense loss caused by complex system collapse are numerous,so in-depth studies on complex system collapse are very important.By use of control theories,system theories and complex network theories,collapse process of complex system has been analyzed.Main works of this dissertation are summarized as follow:
(1)A methodical approach has been proposed to analyze the collapse process of complex system.According to the cases of complex system collapse in our life,collapse process characteristics have been summarized and the process can be divided into two stages:Initial Collapse Stage and Collapse Spreading Stage.In the Initial Collapse Stage, environmental factors and some subsystems together cause initial collapse.By use of control theories and system theories,a method has been introduced to analyze this stage. In the Collapse Spreading Stage,disaster caused by initial collapsed subsystems spreads in the whole systems.According to the characteristics of this stage,by use of complex network theory,a formal description model has been given to describe this stage.Finally, Taking the China-Jiaoji Railway Accident as an example,all factors causing the initial collapse(Derailment of Train T195 ) have been identified and many improvement measures have been proposed.In addition,the disaster spreading mechanism(Collision between Train T195 and Train 5034 after Train T195 collapsed) has also been modeled.
(2)A discrete state model has been proposed to analyze the Collapse Spreading Stage. States of many complex systems in our life are discrete,and for many continuous-state complex systems whose evolving mechanisms are unclear,system states can be also considered as discrete values so that some results can be still found for these systems. Based on the characteristics of these systems and the formal description model for Collapse Spreading Stage,a discrete state model has been proposed.For this model, several kinds of analytical method have been introduced,and then effects of model parameters,system topologies and topological complexity on collapse spreading process have been analyzed.Finally,several strategies have been formulated to control the spreading process and their effectiveness has been also discussed.
(3)A continuous-state model has been proposed to analyze the Collapse Spreading Stage.States and evolving processes of many complex systems in our life are continuous. Based on the formal description model and several existing continuous-state models,a continuous-state model considering redundant systems has been proposed.For this model, effects of model parameters,redundant strategies and topological complexity on collapse spreading processes have been discussed,and from the point of view of mobilizing external resources,several emergent strategies used to control collapse spreading have been formulated and their effectiveness has also been discussed.
(4)Taking the interdependent critical infrastructures as an example,a methodological approach has been proposed to analyze their collapse spreading process.Among all types of infrastructures,for gas pipeline network,each subsystem state is affected by its neighboring subsystems,which satifies the formal description model.But for power network,each subsystem state is affected by all other subsystems and system topology, which can not be modeled according to the formal description model.Taking interdependent power network and gas pipeline network as an example,by means of simulation,the Collapse Spreading Stage has been analyzed and the interdependent effects have been mainly discussed.In addition,several control strategies have been formulated and their effectiveness has also been discussed.
(1)给出了复杂系统崩溃过程的分析方法。根据现实生活中复杂系统崩溃的案例,总结崩溃过程的特点,将复杂系统的崩溃过程分为两个阶段:崩溃初期与崩溃扩散期。崩溃初期是环境要素与子系统性能共同作用,直到初始崩溃出现的阶段。利用控制论以及系统理论,本文给出崩溃初期的分析方法。崩溃扩散期是初始崩溃在整个系统中扩散的阶段。针对崩溃扩散期的特点,利用复杂网络理论,本文给出了崩溃扩散期的形式化描述模型。此外,以胶济铁路火车对撞事故为例,分析了初始崩溃(T195火车出轨)的各种致因及改进措施,同时对崩溃扩散过程(T195火车与5034火车相撞)进行了建模。
(2)给出了复杂系统崩溃扩散过程的离散状态模型。现实生活中许多复杂系统的状态是离散的,而且许多连续状态的系统演化机制不明确但若从宏观上把握系统的崩溃扩散过程,系统状态也可以看成离散值。基于崩溃扩散过程的形式化描述模型,结合这类复杂系统崩溃的特有特征,本文提出了复杂系统崩溃扩散过程的离散状态模型并给出了相应的解析分析方法。从模型参数、系统拓扑结构以及系统结构复杂性增加三个方面分析了它们对崩溃扩散过程的影响,而且给出了几种控制崩溃扩散的方案并探讨了各方案的效果。
(3)给出了复杂系统崩溃扩散过程的连续状态模型。现实生活中大量复杂系统的状态值与状态变化均是连续的,基于崩溃扩散过程的形式化描述模型并参考几个存在的连续状态崩溃扩散模型,本文给出了复杂系统崩溃扩散过程的一种考虑冗余系统的普适性连续状态模型。从模型参数、冗余策略以及系统结构复杂性增加三个方面分析了它们对系统崩溃扩散过程的影响,并从外部资源调用的角度,给出了控制崩溃扩散的资源分配策略并分析了各策略的有效性。
(4)以关联基础设施为案例,给出了关联基础设施崩溃扩散过程的分析方法。基础设施中,天然气网的子系统状态演化与邻居子系统的状态相关,符合复杂系统崩溃扩散的形式化描述模型,而电网的子系统状态演化受到系统中其它所有子系统状态以及系统拓扑结构的影响,不符合形式化描述模型。本文以关联的电网与天然气网为例,分析它们的崩溃扩散过程,重点仿真分析了基础设施之间的关联影响,而且给出几种控制崩溃扩散的方案,并探讨了各个方案的效果。
With the development of scientific technology and social economy,many complex systems in our life become more and more complicated.These complex systems are unavoidably disturbed by external and internal perturbations.Once one or more subsystems can not operate normally and collapse,due to interaction among subsystems, disaster caused by initial collapsed subsystems will spread in the whole system,which may cause the whole system lose its function and collapse.The cases of immense loss caused by complex system collapse are numerous,so in-depth studies on complex system collapse are very important.By use of control theories,system theories and complex network theories,collapse process of complex system has been analyzed.Main works of this dissertation are summarized as follow:
(1)A methodical approach has been proposed to analyze the collapse process of complex system.According to the cases of complex system collapse in our life,collapse process characteristics have been summarized and the process can be divided into two stages:Initial Collapse Stage and Collapse Spreading Stage.In the Initial Collapse Stage, environmental factors and some subsystems together cause initial collapse.By use of control theories and system theories,a method has been introduced to analyze this stage. In the Collapse Spreading Stage,disaster caused by initial collapsed subsystems spreads in the whole systems.According to the characteristics of this stage,by use of complex network theory,a formal description model has been given to describe this stage.Finally, Taking the China-Jiaoji Railway Accident as an example,all factors causing the initial collapse(Derailment of Train T195 ) have been identified and many improvement measures have been proposed.In addition,the disaster spreading mechanism(Collision between Train T195 and Train 5034 after Train T195 collapsed) has also been modeled.
(2)A discrete state model has been proposed to analyze the Collapse Spreading Stage. States of many complex systems in our life are discrete,and for many continuous-state complex systems whose evolving mechanisms are unclear,system states can be also considered as discrete values so that some results can be still found for these systems. Based on the characteristics of these systems and the formal description model for Collapse Spreading Stage,a discrete state model has been proposed.For this model, several kinds of analytical method have been introduced,and then effects of model parameters,system topologies and topological complexity on collapse spreading process have been analyzed.Finally,several strategies have been formulated to control the spreading process and their effectiveness has been also discussed.
(3)A continuous-state model has been proposed to analyze the Collapse Spreading Stage.States and evolving processes of many complex systems in our life are continuous. Based on the formal description model and several existing continuous-state models,a continuous-state model considering redundant systems has been proposed.For this model, effects of model parameters,redundant strategies and topological complexity on collapse spreading processes have been discussed,and from the point of view of mobilizing external resources,several emergent strategies used to control collapse spreading have been formulated and their effectiveness has also been discussed.
(4)Taking the interdependent critical infrastructures as an example,a methodological approach has been proposed to analyze their collapse spreading process.Among all types of infrastructures,for gas pipeline network,each subsystem state is affected by its neighboring subsystems,which satifies the formal description model.But for power network,each subsystem state is affected by all other subsystems and system topology, which can not be modeled according to the formal description model.Taking interdependent power network and gas pipeline network as an example,by means of simulation,the Collapse Spreading Stage has been analyzed and the interdependent effects have been mainly discussed.In addition,several control strategies have been formulated and their effectiveness has also been discussed.
引文
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