基于随机函数Petri网的系统动力学关联分析模型

发布时间：2019-03-20 08:47

【摘要】：针对系统动力学(SD)模型既无法表达延迟具有随机性,又无法描述不同状态之间存在的条件转移,以及随机Petri网(SPN)本身存在计算能力不足等问题,首先,将SPN进行扩展,提出了随机函数Petri网(SFPN)模型;然后,将SFPN与SD相结合,提出了一种SFPN-SD模型。因SFPN模型中的变迁本身能精确描述随机延迟,故解决了SD模型存在的第一个问题;因SFPN模型中的条件弧能表达库所之间的有条件转移,故解决了SD模型存在的第二个问题;最后,在SPN的库所和变迁中定义一些状态变量及其状态转移方程,而状态变量及其状态转移方程就是SD模型中的水平变量、辅助变量、速率变量、水平方程和速率方程的不同解释,状态转移方程可以实现复杂的计算,于是解决了SPN模型的计算能力不足的问题。SFPN-SD模型很好地继承了SD模型的全部特征,同时又将随机Petri网的全部特征融入到SFPN-SD模型中。与SD模型相比,SFPN-SD模型具有系统的状态及其类型的含义更明确、状态演变过程更明确的特点,且其描述的系统变化动态性是通过事件激发的,从而更逼真地描述了复杂系统的自主动态随机演变行为。实例研究表明,SFPN-SD模型比SD模型具有更强、更全面的对复杂系统的描述关联分析与模拟能力。
[Abstract]:In view of the problem that the (SD) model of system dynamics can not express the randomness of delay, nor describe the conditional transition between different states, as well as the lack of computing ability of random Petri net (SPN) itself, firstly, the SPN is extended. A stochastic function Petri net (SFPN) model is proposed. Then, a SFPN-SD model is proposed by combining SFPN with SD. Because the transition in the SFPN model itself can accurately describe the random delay, the first problem of the SD model is solved, and the second problem of the SD model is solved because the conditional arc in the SFPN model can express the conditional transfer between the libraries. Finally, some state variables and their state transition equations are defined in the library and transition of SPN, and the state variables and their state transition equations are horizontal variables, auxiliary variables and rate variables in the SD model. With the different interpretation of the horizontal equation and the rate equation, the state transition equation can realize the complicated calculation, so the problem of the insufficient computing ability of the SPN model is solved. The SFPN-SD model inherits all the characteristics of the SD model well. At the same time, all the features of stochastic Petri nets are incorporated into the SFPN-SD model. Compared with the SD model, the SFPN-SD model has a clearer meaning of the state and its type, and a clearer state evolution process. Moreover, the dynamic nature of the system change described by the SFPN-SD model is triggered by the event. Thus, the autonomous and dynamic stochastic evolution behavior of complex system is described more realistically. The case study shows that the SFPN-SD model is more powerful than the SD model in describing correlation analysis and simulation of complex systems.
【作者单位】：西安建筑科技大学管理学院;
【基金】：教育部人文社会科学研究规划基金资助项目(15YJA910002) 陕西省自然科学基础研究计划-重点项目(2015JZ010) 陕西省教育厅服务地方专项计划项目(16JF015) 陕西省社会科学基金资助项目(2014P07) 西安市科技计划项目:社发引导-软科学(SF1505(9))~~
【分类号】：TP301.1;N941.3

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