基于GADSPN的复杂装备危险耦合传递模型
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摘要
针对装备危险耦合传递随机Petri网(stochastic Petri nets,SPN)模型存在指数分布限制、求解过程复杂的问题,提出广义任意分布SPN(general arbitrary distribution SPN,GADSPN)模型。通过引入熵概率密度函数、矩母函数(moment generating function,MGF)将变迁分布推广至一般任意分布;采用耦合度公式、极大熵模型分别求解GADSPN变迁使能概率及其危险度概率密度函数。基于GADSPN等效MGF性质改进传统SPN模型解析分析能力,提出了装备系统等效危险度、危险状态敏感度、危险路径恶化度等分析参数,并结合SPN模型的状态机、可达图、T-不变量,构建GADSPN分析步骤;最后,通过飞机大表速低空俯冲实例和基于蒙特卡罗与ExSpect平台仿真验证表明,GADSPN模型能充分反映装备危险活动耦合传递随机交互过程,具有较好的求解精度与适用性。
Aiming at the limitation of exponential distribution and complexity of solution in the traditional safety stochastic Petri nets(SPN)model,general arbitrary distribution SPN(GADSPN)for materiel hazard coupled conduction is proposed.Its transition distribution is generalized by entropy density function and moment generating function(MGF).The transition probability and interrelated hazard degree density function are got respectively by coupled degree formula,maximum entropy model,and the analysis performance of GADSPN is improved based on the character of equivalent MGF.The parameters of system equivalent hazard degree,hazard state sensitivity and hazard path deterioration are put forward,then the analysis process is constructed based on SPN state machine,reachability graph and T-invariant.Finally,an applied case of the battleplan"high velocity at low altitude"training subject and simulation based on Monte-Carlo &ExSpect are provided to illustrate the availability of GADSPN.The results show that the random influence relationship among the coupled conduction process of materiel hazard activities is reflected adequately by the GADSPN model,with good fitting accuracy and application.
Aiming at the limitation of exponential distribution and complexity of solution in the traditional safety stochastic Petri nets(SPN)model,general arbitrary distribution SPN(GADSPN)for materiel hazard coupled conduction is proposed.Its transition distribution is generalized by entropy density function and moment generating function(MGF).The transition probability and interrelated hazard degree density function are got respectively by coupled degree formula,maximum entropy model,and the analysis performance of GADSPN is improved based on the character of equivalent MGF.The parameters of system equivalent hazard degree,hazard state sensitivity and hazard path deterioration are put forward,then the analysis process is constructed based on SPN state machine,reachability graph and T-invariant.Finally,an applied case of the battleplan"high velocity at low altitude"training subject and simulation based on Monte-Carlo &ExSpect are provided to illustrate the availability of GADSPN.The results show that the random influence relationship among the coupled conduction process of materiel hazard activities is reflected adequately by the GADSPN model,with good fitting accuracy and application.
引文
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[2]VIOLETTE M G,SAFARIAN P,HAN N,et al.Transport airplane risk analysis[J].Journal of Aircraft,2015,52(2):395-402.
[3]SURYOPUTRO M R,SARI A D,KURNIA R D.Preliminary study for modeling train accident in Indonesia using Swiss Cheese model[J].Procedia Manufacturing,2015,3:3100-3106.
[4]张彤,刘东亮,徐浩军,等.基于系统仿真的装备故障后飞行风险定量评估[J].中国安全科学学报,2012,22(9):69-73.ZHANG T,LIU D L,XU H J,et al.Flight safety and reliability research based on system simulation[J].China Safety Science Journal,2012,22(9):69-73.
[5]刘东亮,徐浩军,张久星.多因素耦合复杂飞行情形风险定量评估方法[J].航空学报,2013,34(3):509-516.LIU D L,XU H J,ZHANG J X.Quantitative risk evaluation methods for multi-factor coupling complex flight situations[J].Acta Aeronautica et Astronautics Sinica,2013,34(3):509-516.
[6]ORTON J D,WEICK K E.Loosely coupled systems:a reconceptualization[J].Academy of Management Review,1990,2(8):203-223.
[7]SIGNORET J P.Dependability&safety modeling and calculation:Petri nets[C]∥Proc.of the 2nd IFAC Workshop on Dependable Control of Discrete Systems,2009:203-208.
[8]LEVESON N G.STOLZY J L.Safety analysis using Petri nets[J].IEEE Trans.on Software Engineering,1987,13(3):386-397.
[9]CHO S M,HONG H S,CHA S D.Safety analysis using colored Petri nets[C]∥Proc.of the IEEE Asia-Pacific Software Engineering Conference,1996:176-183.
[10]MARIANA D.Fault tolerant control multiprocessor systems modeling using advanced stochastic Petri nets[J].Procedia Technology,2016,22:623-628.
[11]ZHANG Y Y,WU W H.Flight mission modeling based on BDI Petri nets[J].Journal of Systems Engineering and Electronics,2017,28(4):776-783.
[12]彭颖,姚淑珍,谭火彬.基于随机时间Petri网的安全性分析方法[J].计算机科学,2016,43(11):61-65.PENG Y,YAO S Z,TAN H B.Safety analysis method based on stochastic time Petri nets[J].Computer Science,2016,43(11):61-65.
[13]LIU Z K,LIU Y H,CAI B P,et al.RAMS analysis of hybrid redundancy system of subsea blowout preventer based on stochastic Petri nets[J].International Journal of Security and its Applications,2013,7(4):159-166.
[14]陈翔,刘军丽.基于矩母函数的工作流网性能分析方法[J].计算机集成制造系统,2009,15(12):2467-2472.CHEN X,LIU J.Workflow nets performance analysis approach based on moment generating function[J].Computer Integrated Manufacturing Systems,2009,15(12):2467-2472.
[15]张磊,向德全.基于任意分布随机Petri网的装备维修保障建模与分析[J].火力与指挥控制,2009,34(9):158-160.ZHANG L,XIANG D Q.Modeling and analysis of equipment maintenance support systems based on arbitrary distribution stochastic Petri nets[J].Fire Control&Command Control,2009,34(9):158-160.
[16]WANG H,ZHAO L M,WANG Y G.Risk integrated assessment of the project schedule and cost based on maximum entropy and the random network[C]∥Proc.of the International Conference on Management Science and Engineering,2010:247-251.
[17]CHING J Y,HSIEH Y H.Local estimation of failure probability function and its confidence interval with maximum entropy principle[J].Probabilistic Engineering Mechanics,2007,22(1):39-49.
[18]JIU D,LAWRENCE R M.The maximum entropy method applied to stationary density computation[J].Applied Mathematics and Computation,2007,185(1):658-666.
[19]XIE N,DUAN M L,RATNA B C,et al.An energy modeling and evaluation approach for machine tools using generalized stochastic Petri nets[J].Journal of Cleaner Production,2016,113:523-531.
[20]兰丽,张友鹏.基于随机Petri网的铁路时间同步网协议脆弱性分析[J].铁道学报,2017,39(8):85-92.LAN L,ZHANG Y P.Vulnerability analysis of railway time synchronization network protocol based on stochastic Petri nets[J].Journal of the China Railway Society,2017,39(8):85-92.
[21]SIDALL N.Probabilistic engineering design[M].New York:Marcel Dekker,1992:79-90.
[22]QU J F,LI G,ZHANG S L.Study on system coupling effects of ecological and economic in mining subsidence reclamation area[C]∥Proc.of the 2nd International Conference on Energy,Environment and Sustainable Development,2013:1315-1320.
[23]林嘉豪,李克武,张兵.基于风险耦合理论的航空装备本质安全管理研究[J].中国安全生产科学技术,2011,7(9):75-79.LIN J H,LI K W,ZHANG B.Inherent safety management of aviation equipment based on risk coupling theory[J].Journal of Safety Science and Technology,2011,7(9):75-79.
[24]陈翔.基于Petri网及矩母函数的计划评审技术[J].北京理工大学学报,2010,30(9):1121-1125.CHEN X.Program evaluation and review technique based on Petri nets and moment generating function[J].Transactions of Beijing Institute of Technology,2010,30(9):1121-1125.
[25]SNDOR Z,WEDEL M.Heterogeneous conjoint choice designs[J].Journal of Marketing Research,2005,42(2):210-218.
[26]苏春.基于GSPN模型的系统动态可靠性仿真研究[J].中国机械工程,2008,19(1):1-5.SU C.Simulation research on system dynamic reliability based on general stochastic Petri nets[J].China Mechanical Engineering,2008,19(1):1-5.
[27]JIANG Z B,ZUO M J,FUNG Y K,et al.Performance modeling of complex dynamic production system by temporized object oriented Petri nets with changeable structure(TOPNsCS)[J].International Journal of Advanced Manufacturing Technology,2000,11(2):24-31.