复杂系统动态故障树分析的新方法及其应用研究
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摘要
随着现代工程系统的大型化、复杂化以及高新技术的引入，系统可靠性已经成为制约复杂系统发展的关键所在。可靠性分析技术作为实施系统可靠性工程的关键基础技术，目前正面临着复杂系统所带来的若干技术难点和应用挑战。针对复杂系统的可靠性分析技术已经成为可靠性工程领域的研究热点及难点问题之一。系统可靠性分析常规方法主要包括：可靠性框图法、故障模式影响及危害性分析法、故障树分析法、Petri网方法以及蒙特卡洛数值仿真方法等。常规方法通常不考虑系统的动态失效特性，且多数建立在零部件故障相互独立和故障数据完备的基础之上。在实际复杂工程系统中，零部件失效之间通常并不是相互独立的，往往存在着多种复杂的关联关系和动态特性，比如部件失效的顺序关系。另一方面，由于成本、时间、管理和人因等多方面的原因导致零部件失效数据存在模糊不确定性。目前，在考虑动态失效特性的故障树分析方面已取得了一定成果。然而，在同时考虑模糊不确定性以及动态失效特性等情况下的故障树分析方面的研究工作还很缺乏，以致用常规方法分析所得结果与实际情况不符甚至相差甚远。因此，迫切需要开展考虑零部件动态失效特性和模糊不确定性的系统可靠性分析方法的研究。
针对上述问题，本文主要开展了以下研究工作：
（1）基于模糊马尔科夫模型的动态故障树分析方法。马尔科夫模型方法是一种状态空间分析方法，用该模型能够准确地描述失效分布与维修分布都服从指数分布的系统的失效及维修过程。本文在基于马尔科夫模型的基础上，考虑了零部件失效信息的模糊不确定性，研究了在模糊失效率下的动态故障树分析方法。通过建立系统的动态故障树模型，并运用三角模糊数来描述零部件和系统的失效率，通过已经得到的动态故障树模型建立系统失效过程的模糊马尔科夫模型。运用模糊理论中扩展原理的思想和Laplace-Stieltjes变换求解该模型，得到系统在给定时刻下的模糊失效概率和给定隶属度下的模糊可靠度曲线。最后应用该模糊马尔科夫模型对某数控加工中心液压系统进行可靠性建模与分析。研究结果表明，该方法能够有效地对具有动态失效特性和模糊不确定性的系统进行可靠性建模及定量评估。
（2）基于离散时间贝叶斯网络的动态故障树可靠性评估模型。研究了基于贝叶斯网络和动态故障树的系统可靠性建模和评估方法。通过把系统失效的动态故障树模型转化为贝叶斯网络模型，并运用贝叶斯网络的拓扑结构来表达系统中部件失效之间的逻辑关系。针对基于马尔科夫模型的动态故障树求解方法中存在的状态爆炸问题，借助贝叶斯网络的条件独立性来降低模型求解的复杂度。在此基础上，建立了静态和动态故障树中各种逻辑门的条件概率分布的公式，以实现对系统失效过程及其动态特性进行建模和分析。以卫星太阳翼驱动机构为对象，建立了动态故障树模型和相应的贝叶斯网络模型，并运用联合树推理算法对该模型进行了双向概率推理。实例分析结果表明：该方法能够有效地解决具有动态失效特性的复杂系统的可靠性分析和评估问题。
（3）模糊数据下基于连续时间贝叶斯网络的动态故障树分析方法。研究了考虑模糊不确定性的基于连续时间贝叶斯网络的系统可靠性建模与分析方法。基于连续时间贝叶斯网络模型的方法能够直接得到系统的可靠度和失效概率的解析表达式。本文用三角模糊数描述零部件的失效率，并用其来构造零部件的模糊边缘失效密度函数及模糊失效分布函数。用单位阶跃函数和冲激函数来构造贝叶斯网络中非根节点失效事件的条件概率密度函数和分布函数。在此基础上，推导了在模糊失效率下的几种典型的故障树逻辑门输出事件发生的模糊边缘失效密度函数和模糊失效分布函数的表达式。最后，运用算例验证了该方法的正确性和有效性，并通过对大型矿用挖掘机电气系统整流回馈子系统的建模与分析阐述了该方法在实际工程系统中的应用。
（4）考虑共因失效的动态故障树分析方法。运用故障树分析方法对具有共因失效的系统进行了可靠性分析。阐述了当前共因失效研究中的一些经典模型和建模方法，运用显式建模方法与平方根模型对某动车组追尾事故进行了故障树分析。分别计算了考虑共因失效和假设部件失效独立两种情况下的系统失效概率。结果表明：不考虑共因失效因素的影响会对可靠性分析结果带来较大的误差，说明了共因失效对于交通工具这种重要设施的安全性影响非常重大，同时也表明了考虑共因失效的动态故障树分析方法可为列车安全性及可靠性评估提供基础。同时，本文还提出了各种备份条件下考虑共因失效的动态故障树及贝叶斯网络可靠性建模及评估方法。建立了考虑共因失效条件下，确定贝叶斯网络中各种备件门输出事件对应节点的条件概率分布表的方法。通过算例验证了该方法的有效性，并通过与蒙特卡洛数值仿真方法对比，验证表明该方法的计算精度能够满足实际要求。
Reliability and safety analysis and evaluation of complex systems have becomeone of the hot issues in reliability engineering. Reliability block diagram (RBD), failuremodes, effects and criticality analysis (FMECA), fault tree analysis (FTA), petri netsmethod and Monte Carlo Simulation (MCS) method are the most commonly used toolsfor system reliability analysis. The traditional methods frequently do not consider thedynamic characteristics of system failure, such as the sequential dependency ofcomponent failure. However, in actual complex engineering systems, component failureevents are mostly not independent to each other, but there are many interacting dynamiccharacteristics. On the other hand, due to the lack of data, the factors such as the updateof product design, human factors, et al. will cause the uncertainty of components failuredata. At present, the fault tree analysis considering the dynamic characteristics of failurehas achieved fruitful results. However, the research of fault tree analysis whichconsidering the influence in combination of fuzzy uncertainty and dynamic failurecharacters is still insufficient. Therefore, it is necessary to do some further exploratoryresearches on system reliability analysis on condition that component failures are notindependent and considering fuzzy uncertainty of systems.
To solve the above problems, the following works are carried out in thisdissertation:
(1) Dynamic fault tree analysis method based on fuzzy Markov model. Markovmodel is a state space method, which can be used for system failure and maintenancemodeling where the failure and maintenance time is exponentially distributed. On thebasis of Markov model and considering the influence of the fuzzy uncertainty ofcomponent failure parameters to system, a research on dynamic fault tree analysismethod in the case of fuzzy failure rate is carried out in this dissertation. A dynamicfault tree model has been built. The triangular fuzzy numbers are used to express thefailure rate of the components and system, after which the fuzzy Markov model hasbeen established based on the dynamic fault tree model obtained before. The fuzzyMarkov model can be solved using the expansion principle of fuzzy theory andLaplace-Stieltjes transformation. The fuzzy failure probability or fuzzy reliability curveon given degree of membership could be obtained. Finally, the fuzzy Markov model based DFTA method is used for reliability modeling and analysis of hydraulic system ofCNC machining center. The results show that this method can conduct reliabilitymodeling and quantitative assessment effectively for systems which have dynamicfailure characteristics and uncertainty of failure rate.
(2) Dynamic fault tree analysis method based on Discrete-Time Bayesian Network.The system reliability modeling and evaluation method based on Bayesian Network anddynamic fault tree is studied in this dissertation. In the Discrete-Time Bayesian Networkmodel, the fault tree model of system failure in transformed into a Bayesian Networkmodel, and the logical relationship between the failure components of system isexpressed by the use of Bayesian Network topological structure. Taking advantage ofthe conditional independence of Bayesian Networks, the state space explosion problemfor solving the Markov model corresponding to the dynamic fault tree model can bealleviated. Conditional probability distribution tables for various kinds of logic gates inboth static and dynamic fault trees are created. A solar array drive assembly of satelliteis used for case study. The dynamic fault tree model and corresponding BayesianNetwork model is established, and the junction tree inference algorithm is used forbidirectional probabilistic reasoning for this model. The result shows that this methodcan solve the problem of dynamic complex system reliability analysis and evaluationeffectively.
(3) Dynamic fault tree analysis under fuzzy data based on the Continuous-TimeBayesian Network. A system reliability modeling and analysis method based oncontinuous-time Bayesian network is introduced and the fuzzy uncertainty of the systemis also taken into account. The analytical expression of reliability and failure probabilitycan be obtained directly on the basis of Continuous-Time Bayesian Network. Triangularfuzzy number is used to describe the failure rate and construct the fuzzy marginaldensity function and fuzzy distribution function of failure distribution of components.The conditional probability density function and distribution function of non-root nodesfailure events in Bayesian Networks are jointly constructed by the unit step function andimpulse function. Expressions of fuzzy marginal density function and fuzzy distributionfunction for several typical logical gates of fault tree under the fuzzy failure rate dataare derived. The results of a case study verified the feasibility and correctness of thismethod.
(4) Dynamic Fault tree analysis method considering common cause failure. The reliability analysis of the instance system with common cause failure is carried out byusing fault tree analysis method. Some classic models and modeling methods forcommon cause failure are introduced. The explicit modeling approach and the squareroot model are used for the fault tree analysis of train rear-end accident. The failureprobabilities of the system with and without considering common cause failure arecalculated, respectively. The result shows that, a large error will exists in reliabilityanalysis result without considering the effect of common cause failure on system. Thisillustrates that common cause failure has very significant impact on the facility securityof transport, and this also provide the foundation of train safety and reliabilityassessment. The dynamic fault tree and Bayesian Network reliability modeling andassessment method considering common cause failure are proposed. The equations fordetermining the conditional probability distribution of spare gate nodes under CCF areestablished. Finally, an example is given to validate the correctness of this method. Thecomparison with MCS shows that the result can meet the requirement of precision.
针对上述问题，本文主要开展了以下研究工作：
（1）基于模糊马尔科夫模型的动态故障树分析方法。马尔科夫模型方法是一种状态空间分析方法，用该模型能够准确地描述失效分布与维修分布都服从指数分布的系统的失效及维修过程。本文在基于马尔科夫模型的基础上，考虑了零部件失效信息的模糊不确定性，研究了在模糊失效率下的动态故障树分析方法。通过建立系统的动态故障树模型，并运用三角模糊数来描述零部件和系统的失效率，通过已经得到的动态故障树模型建立系统失效过程的模糊马尔科夫模型。运用模糊理论中扩展原理的思想和Laplace-Stieltjes变换求解该模型，得到系统在给定时刻下的模糊失效概率和给定隶属度下的模糊可靠度曲线。最后应用该模糊马尔科夫模型对某数控加工中心液压系统进行可靠性建模与分析。研究结果表明，该方法能够有效地对具有动态失效特性和模糊不确定性的系统进行可靠性建模及定量评估。
（2）基于离散时间贝叶斯网络的动态故障树可靠性评估模型。研究了基于贝叶斯网络和动态故障树的系统可靠性建模和评估方法。通过把系统失效的动态故障树模型转化为贝叶斯网络模型，并运用贝叶斯网络的拓扑结构来表达系统中部件失效之间的逻辑关系。针对基于马尔科夫模型的动态故障树求解方法中存在的状态爆炸问题，借助贝叶斯网络的条件独立性来降低模型求解的复杂度。在此基础上，建立了静态和动态故障树中各种逻辑门的条件概率分布的公式，以实现对系统失效过程及其动态特性进行建模和分析。以卫星太阳翼驱动机构为对象，建立了动态故障树模型和相应的贝叶斯网络模型，并运用联合树推理算法对该模型进行了双向概率推理。实例分析结果表明：该方法能够有效地解决具有动态失效特性的复杂系统的可靠性分析和评估问题。
（3）模糊数据下基于连续时间贝叶斯网络的动态故障树分析方法。研究了考虑模糊不确定性的基于连续时间贝叶斯网络的系统可靠性建模与分析方法。基于连续时间贝叶斯网络模型的方法能够直接得到系统的可靠度和失效概率的解析表达式。本文用三角模糊数描述零部件的失效率，并用其来构造零部件的模糊边缘失效密度函数及模糊失效分布函数。用单位阶跃函数和冲激函数来构造贝叶斯网络中非根节点失效事件的条件概率密度函数和分布函数。在此基础上，推导了在模糊失效率下的几种典型的故障树逻辑门输出事件发生的模糊边缘失效密度函数和模糊失效分布函数的表达式。最后，运用算例验证了该方法的正确性和有效性，并通过对大型矿用挖掘机电气系统整流回馈子系统的建模与分析阐述了该方法在实际工程系统中的应用。
（4）考虑共因失效的动态故障树分析方法。运用故障树分析方法对具有共因失效的系统进行了可靠性分析。阐述了当前共因失效研究中的一些经典模型和建模方法，运用显式建模方法与平方根模型对某动车组追尾事故进行了故障树分析。分别计算了考虑共因失效和假设部件失效独立两种情况下的系统失效概率。结果表明：不考虑共因失效因素的影响会对可靠性分析结果带来较大的误差，说明了共因失效对于交通工具这种重要设施的安全性影响非常重大，同时也表明了考虑共因失效的动态故障树分析方法可为列车安全性及可靠性评估提供基础。同时，本文还提出了各种备份条件下考虑共因失效的动态故障树及贝叶斯网络可靠性建模及评估方法。建立了考虑共因失效条件下，确定贝叶斯网络中各种备件门输出事件对应节点的条件概率分布表的方法。通过算例验证了该方法的有效性，并通过与蒙特卡洛数值仿真方法对比，验证表明该方法的计算精度能够满足实际要求。
Reliability and safety analysis and evaluation of complex systems have becomeone of the hot issues in reliability engineering. Reliability block diagram (RBD), failuremodes, effects and criticality analysis (FMECA), fault tree analysis (FTA), petri netsmethod and Monte Carlo Simulation (MCS) method are the most commonly used toolsfor system reliability analysis. The traditional methods frequently do not consider thedynamic characteristics of system failure, such as the sequential dependency ofcomponent failure. However, in actual complex engineering systems, component failureevents are mostly not independent to each other, but there are many interacting dynamiccharacteristics. On the other hand, due to the lack of data, the factors such as the updateof product design, human factors, et al. will cause the uncertainty of components failuredata. At present, the fault tree analysis considering the dynamic characteristics of failurehas achieved fruitful results. However, the research of fault tree analysis whichconsidering the influence in combination of fuzzy uncertainty and dynamic failurecharacters is still insufficient. Therefore, it is necessary to do some further exploratoryresearches on system reliability analysis on condition that component failures are notindependent and considering fuzzy uncertainty of systems.
To solve the above problems, the following works are carried out in thisdissertation:
(1) Dynamic fault tree analysis method based on fuzzy Markov model. Markovmodel is a state space method, which can be used for system failure and maintenancemodeling where the failure and maintenance time is exponentially distributed. On thebasis of Markov model and considering the influence of the fuzzy uncertainty ofcomponent failure parameters to system, a research on dynamic fault tree analysismethod in the case of fuzzy failure rate is carried out in this dissertation. A dynamicfault tree model has been built. The triangular fuzzy numbers are used to express thefailure rate of the components and system, after which the fuzzy Markov model hasbeen established based on the dynamic fault tree model obtained before. The fuzzyMarkov model can be solved using the expansion principle of fuzzy theory andLaplace-Stieltjes transformation. The fuzzy failure probability or fuzzy reliability curveon given degree of membership could be obtained. Finally, the fuzzy Markov model based DFTA method is used for reliability modeling and analysis of hydraulic system ofCNC machining center. The results show that this method can conduct reliabilitymodeling and quantitative assessment effectively for systems which have dynamicfailure characteristics and uncertainty of failure rate.
(2) Dynamic fault tree analysis method based on Discrete-Time Bayesian Network.The system reliability modeling and evaluation method based on Bayesian Network anddynamic fault tree is studied in this dissertation. In the Discrete-Time Bayesian Networkmodel, the fault tree model of system failure in transformed into a Bayesian Networkmodel, and the logical relationship between the failure components of system isexpressed by the use of Bayesian Network topological structure. Taking advantage ofthe conditional independence of Bayesian Networks, the state space explosion problemfor solving the Markov model corresponding to the dynamic fault tree model can bealleviated. Conditional probability distribution tables for various kinds of logic gates inboth static and dynamic fault trees are created. A solar array drive assembly of satelliteis used for case study. The dynamic fault tree model and corresponding BayesianNetwork model is established, and the junction tree inference algorithm is used forbidirectional probabilistic reasoning for this model. The result shows that this methodcan solve the problem of dynamic complex system reliability analysis and evaluationeffectively.
(3) Dynamic fault tree analysis under fuzzy data based on the Continuous-TimeBayesian Network. A system reliability modeling and analysis method based oncontinuous-time Bayesian network is introduced and the fuzzy uncertainty of the systemis also taken into account. The analytical expression of reliability and failure probabilitycan be obtained directly on the basis of Continuous-Time Bayesian Network. Triangularfuzzy number is used to describe the failure rate and construct the fuzzy marginaldensity function and fuzzy distribution function of failure distribution of components.The conditional probability density function and distribution function of non-root nodesfailure events in Bayesian Networks are jointly constructed by the unit step function andimpulse function. Expressions of fuzzy marginal density function and fuzzy distributionfunction for several typical logical gates of fault tree under the fuzzy failure rate dataare derived. The results of a case study verified the feasibility and correctness of thismethod.
(4) Dynamic Fault tree analysis method considering common cause failure. The reliability analysis of the instance system with common cause failure is carried out byusing fault tree analysis method. Some classic models and modeling methods forcommon cause failure are introduced. The explicit modeling approach and the squareroot model are used for the fault tree analysis of train rear-end accident. The failureprobabilities of the system with and without considering common cause failure arecalculated, respectively. The result shows that, a large error will exists in reliabilityanalysis result without considering the effect of common cause failure on system. Thisillustrates that common cause failure has very significant impact on the facility securityof transport, and this also provide the foundation of train safety and reliabilityassessment. The dynamic fault tree and Bayesian Network reliability modeling andassessment method considering common cause failure are proposed. The equations fordetermining the conditional probability distribution of spare gate nodes under CCF areestablished. Finally, an example is given to validate the correctness of this method. Thecomparison with MCS shows that the result can meet the requirement of precision.
引文
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