基于可能性Petri网的模糊系统建模与分析方法
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摘要
模糊系统是对确定性系统的推广。与确定性系统不同,模糊系统的输入和输出约束于某一模糊区间,令其状态和行为表现出一定的不确定性。对模糊系统不确定性的描述和分析,以及在信息不完备的情况下,能够准确地给出系统当前的状态是研究的重点。当系统的状态超过某一临界状态值时,可能会产生不可预料的影响,造成不同程度的经济损失。因此,对模糊系统的不确定性进行研究具有重要的应用价值。
针对模糊系统中的不确定性问题,特别是在存在不完备信息和存在差错数据的情况下,基于模糊集理论、混杂系统理论和Petri网理论及贝叶斯网络,提出一类可能性Petri网模型,并以此为基础定义了非确定性混杂Petri网模型和时间概率Petri网模型。本文所提出的非确定性混杂Petri网模型将模糊系统分为离散和连续两个部分,对其间的相互作用进行建模,从而分析系统的实时状态及其发展趋势,进而可依据分析结果采取相应的措施,使得系统高效安全的运行；时间概率Petri网模型则利用时间这二模糊系统中的重要属性,利用时序一致性判定函数判断系统中含有时间信息的状态是否相容,由推理演化并融合不同的状态信息而得到系统的最终状态。
本文运用非确定性混杂Petri网和时间概率Petri网分别对变压器系统和输电网系统进行了仿真实验。针对变压器系统故障分析的仿真实验表明,非确定性混杂Petri网是一种混杂系统状态检测和趋势分析的有效工具,运用该模型可为混杂系统的状态感知、预测、评估和实时控制提供有效方法；针对输电网系统进行的仿真实验表明,运用时间概率Petri网模型可综合分析系统元件中的时间延迟和概率因素,在信息不完备或存在数据差错的情况下,仍然能够给出较准确的诊断结果。对比试验表明,本文提出的方法提高了诊断的正确率。
The fuzzy system is an extension of deterministic system. Unlike the deterministic system, the value of its input and output is fuzzy. Therefore, there is uncertainty in fuzzy system state. It is the focus of study which describes and analyses the uncertainty of fuzzy system, and gives current state of system accurately in the case of incomplete information.
The probability Petri net is proposed based on fuzzy set theory, hybrid system theory, Petri net theory and Bayesian networks for uncertainty problems in fuzzy system. Two Petri nets which are uncertainty hybrid Petri net model and time probability Petri net are defined based on the probability Petri net. One is proposed a perceived trend analysis, method based on hybrid system power equipment which aims at predicting state and analyzing problems difficultly. This kind of systems is modeled by uncertain hybrid Petri net. It makes the tokens transfer through transitions triggering. So the states of system are changed. It can deduce the recent state of system by identify the state of system, and thus analyzes the tendency. The other model is time probability Petri net against the large amount of signal in the power system and difficult to model. Time interval in the model represents delay of alarm signal. And probability represents uncertainty of system which is component mal-operation and mis-operation of system component. The final state of the model is obtained by deduction of model. The possible failure system components are confirmed by calculating the final state probability. Using the timing consistency determination function determine whether system states are compatible, and reason out system state.
Using the example of transformers and electricity systems simulate two kinds of probability Petri net models which are non-deterministic hybrid Petri net and time probability Petri net. So, fault diagnosis of transformers in the power system as the background, a hybrid Petri net model is built which simulate state detection and process of trend analysis. The results verify the validity of the method. The model provides an effective method to predict the current status and predict, assess and real-time control future state. The time probability Petri net for power system takes the time delay and probability factor of the system components. In the case of incomplete fault information, the model is still able to give more accurate state results of system.
针对模糊系统中的不确定性问题,特别是在存在不完备信息和存在差错数据的情况下,基于模糊集理论、混杂系统理论和Petri网理论及贝叶斯网络,提出一类可能性Petri网模型,并以此为基础定义了非确定性混杂Petri网模型和时间概率Petri网模型。本文所提出的非确定性混杂Petri网模型将模糊系统分为离散和连续两个部分,对其间的相互作用进行建模,从而分析系统的实时状态及其发展趋势,进而可依据分析结果采取相应的措施,使得系统高效安全的运行；时间概率Petri网模型则利用时间这二模糊系统中的重要属性,利用时序一致性判定函数判断系统中含有时间信息的状态是否相容,由推理演化并融合不同的状态信息而得到系统的最终状态。
本文运用非确定性混杂Petri网和时间概率Petri网分别对变压器系统和输电网系统进行了仿真实验。针对变压器系统故障分析的仿真实验表明,非确定性混杂Petri网是一种混杂系统状态检测和趋势分析的有效工具,运用该模型可为混杂系统的状态感知、预测、评估和实时控制提供有效方法；针对输电网系统进行的仿真实验表明,运用时间概率Petri网模型可综合分析系统元件中的时间延迟和概率因素,在信息不完备或存在数据差错的情况下,仍然能够给出较准确的诊断结果。对比试验表明,本文提出的方法提高了诊断的正确率。
The fuzzy system is an extension of deterministic system. Unlike the deterministic system, the value of its input and output is fuzzy. Therefore, there is uncertainty in fuzzy system state. It is the focus of study which describes and analyses the uncertainty of fuzzy system, and gives current state of system accurately in the case of incomplete information.
The probability Petri net is proposed based on fuzzy set theory, hybrid system theory, Petri net theory and Bayesian networks for uncertainty problems in fuzzy system. Two Petri nets which are uncertainty hybrid Petri net model and time probability Petri net are defined based on the probability Petri net. One is proposed a perceived trend analysis, method based on hybrid system power equipment which aims at predicting state and analyzing problems difficultly. This kind of systems is modeled by uncertain hybrid Petri net. It makes the tokens transfer through transitions triggering. So the states of system are changed. It can deduce the recent state of system by identify the state of system, and thus analyzes the tendency. The other model is time probability Petri net against the large amount of signal in the power system and difficult to model. Time interval in the model represents delay of alarm signal. And probability represents uncertainty of system which is component mal-operation and mis-operation of system component. The final state of the model is obtained by deduction of model. The possible failure system components are confirmed by calculating the final state probability. Using the timing consistency determination function determine whether system states are compatible, and reason out system state.
Using the example of transformers and electricity systems simulate two kinds of probability Petri net models which are non-deterministic hybrid Petri net and time probability Petri net. So, fault diagnosis of transformers in the power system as the background, a hybrid Petri net model is built which simulate state detection and process of trend analysis. The results verify the validity of the method. The model provides an effective method to predict the current status and predict, assess and real-time control future state. The time probability Petri net for power system takes the time delay and probability factor of the system components. In the case of incomplete fault information, the model is still able to give more accurate state results of system.
引文
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[2]Yuanguo Zhu. Fuzzy optimal control for multistage fuzzy systems[C]. In:IEEE Transactions on Systems Man and Cybernetics, Part B,2011,964-975
[3]Wierman, Mark J. Cloud sets as a measure theoretic basis for fuzzy set theory[C]. In:2010 Annual Meeting of the North American Fuzzy Information Processing Society,2010,1-5
[4]Xiaoshuang Cui, Bin Chen. PS-convergence theory of nets of fuzzy sets[C]. In:2010 International Conference on Environmental Science and Information Application Technology,2010,443-446
[5]Yuanhua Liang, Bingcheng Yuan. Method for generating fuzzy Petri nets fault diagnosis model based rough set theory[C]. In:2010 2nd International Conference on Future Computer and Communication,2010,411-414
[6]马德仲,周真,于晓洋等.基于模糊概率的多状态贝叶斯网络可靠性分析[J].系统工程与电子技术,2012,34(12)：2607～2611
[7]宋功益,郭清滔,涂福荣等.模糊贝叶斯网的变压器故障诊断[J].输电网系统及其自动化学报,2012,24(2)：102～106
[8]兰华,孙传蒙,王韵然.基于贝叶斯网络的分布式输电网故障诊断[J].电测与仪表,2012,49(11)：1～5
[9]袁崇义.Petri网原理[M].北京：电子工业出版,1998.
[10]吴哲辉.Petri网导论[M].北京：机械工业出版社,2006.
[11]于枫,罗军舟,李伟等.一种基于进程验证的Petri网可达性判定方法[J].计算机学报,2010,33(2)：288～299
[12]宋春跃,王慧,李平.线性混杂系统优化控制的Monte Carlo统计预测方法[J].自动化学报,2008,34(8)：1028～1032
[13]Jean T, dier D, Jean B. Predictive control of hybrid systems under a multi MLD formalism with status space polyhedral partition [C].In:Proc of American Control Conf. Boston, 2004:2516-1512
[14]郑刚,谭民,宋永华.混杂系统的研究进展[J].控制与决策,2004,19(1)：7～11
[15]邹媛媛,贾廷纲,牛玉刚.一类混杂系统的预测控制设计[J].电气自动化,2011,33(3)：1-2
[16]李继方,汤天浩,姚刚.基于混杂Petri网的共直流母线交流传动系统建模与节能控制[J].输电网系统保护与控制,2011,39(6)：1～6
[17]张聚,陈圆,丁靖.输电网系统电压崩溃的显式模型预测控制[J].输电网系统保护与控制,2012,40(16)：8-14
[18]Giua A, Seatzu C. Modelingand supervisorycontrol of railwaynetworks using Petri nets [J]. In:IEEE Transactions on Automation Science and Engineering,2008,5(3):431-445
[19]Lesire C, Tessier C. Particle Petri netsfor aircraft procedure monitoring under uncertainty. In: Applications and Theoryof Petri Nets 26th[C]. Miami, FL, USA:Springer,2005,329-348
[20]Navarro-Lopez, E.M., Barajas-Ramirez, J.G Bringing order to chaos:Hybrid modelling of a discontinuous chaotic system[C]. In:2010 11th International Workshop on Variable Structure Systems (VSS),2010:325-330
[21]佘维,叶阳东.基于时间贝叶斯Petri网的溯因故障诊断[J].计算机应用与软件,2012,29(10)：52～57
[22]DL/T722-2000《变压器油中溶解气体分析和判断导则》
[23]周媛媛,刘功能,周力行,曾玉清.基于DGA的变压器故障可视化诊断[J].电力科学与技术学报,2010,25(3)：87～91
[24]叶阳东,王娟,贾利民.基于模糊时间Petri网的列车运行时间不确定性问题的处理[J].铁道学报,2005,27(1)：6-13
[25]佘维,叶阳东.一种基于贝叶斯Petri网的故障诊断方法[J].小型微型计算机系统,2011,32(11)：2303～2308
[26]ORCHARD M, VACHTSEVANOS G J. A particle-filtering approach for on-line fault diagnosis and failure prognosis[J]. In:Transactions of the Institute of Measurement and Control,2009,31(3):221-246
[27]LI B, LIU P Y, HU R X, MI S S, FU J P. Fuzzy lattice classifier and its application to bearing fault diagnosis [J]. Applied Soft Computing Journal,2012,12(6):1708-1719
[28]CHRISSANTHI A. Online expert systems for fault diagnosis in technical processes. Expert Systems [J],2008,25(2):115-132
[29]Yongbao Liu, Yanping Wang, Shuhong Huang. A Fault Diagnosis Model Based on Extended Fuzzy Timed Petri Nets Applying to Gas Turbine[C]. In:2nd International Conference on Power Electronics and Intelligent Transportation System. Shenzhen,2009,132-135
[30]Jiangping Shi, Weiguang Tong, Daling Wang. Design of the Transformer fault diagnosis expert system Based on Fuzzy reasoning[C]. In:International Forum on Computer Science-Technology and Applications,2009,110-114
[31]李林,万志聪.基于模糊三比值法的电力变压器绝缘故障诊断研究[J].浙江电力,2011,30(2)：12～14
[32]Wenqing Zhao, Shenglong Zhang,Dongxiao Niu. Multi-agent and bayesian network applied in transformer faults diagnosis[C]. In:2010 International Conference on Machine Learning and Cybernetics (ICMLC),,2010,43-46
[33]项文强,张华,王姮等.基于L-M算法的BP网络在变压器故障诊断中的应用.输电网系统保护与控制,2011,39(8)100～103
[34]曹谢东.模糊信息处理及应用[M].北京：科学出版社,2003
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