基于贝叶斯网络的机械系统可靠性评估
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摘要
对于复杂系统进行可靠性评估,由于费用和试验组织等方面的原因,不可能进行大量的系统级可靠性试验,如何充分利用单元和系统的各种试验信息对系统可靠性进行精确的评估是一个复杂的问题。目前机械系统可靠性评估常用的方法有：可靠性框图法,故障树方法,Monte-Carlo仿真方法等。但由于这些方法都有一定的局限性,因此更合适的可靠性评估方法还有待进一步研究。
在传统的元件/系统可靠性研究中,一般是把研究对象看作只有两种状态,即失效和完好,仅用“是”与“否”二值逻辑来描述产品是否能完成规定功能的情况。但在实际应用中元件/系统可能存在多种状态,如阀门系统可能存在正常、堵、漏、开关不灵等多种状态,而且每种状态都存在一个失效渐近的问题。仅仅研究阀门的两态,由此建立的可靠性模型与实际情况存在较大差异。
“相关”是系统失效的普遍特征,忽略系统的相关性,简单地在各部分失效相互独立的假设条件下对系统可靠性进行定性分析和定量计算,常会导致较大的误差。
贝叶斯网络(Bayesian networks)提供了一种知识图解化的表示方法,可以对结点变量之间的因果概率关系进行有向图解描述,主要用于不确定性知识表达、因果推理和诊断推理等。贝叶斯网络的推理模式多样,可以有效地识别系统可靠性的薄弱环节。贝叶斯网络的图形化显示使得系统中元件间的关系更加直观、清晰,将贝叶斯网络技术应用于机械系统的可靠性评估,对系统的多状态和失效相关性进行分析,是本文的研究重点。
本文根据贝叶斯网络的特点,对其在机械系统可靠性评估中的应用进行了以下研究：
(1)在详细分析贝叶斯网络特点的基础上,将贝叶斯网络应用于机械系统尤其是复杂机械系统可靠性的评估,建立基于贝叶斯网络的系统可靠性评估模型。该模型能够监视系统中的任何不确定性变量,不仅可以求出系统正常工作概率,而且可以计算出系统条件失效概率,如可以方便地计算出某一个或某几个元件故障时系统故障的条件失效概率,进行推理诊断分析,找出系统的薄弱点。
(2)以贝叶斯网络在机械系统上的应用为基础,进一步探索研究贝叶斯网络在多状态机械系统中的应用,通过逐步的分析与算例验证,建立基于贝叶斯网络多状态系统可靠性模型。应用该模型进行多状态系统可靠性评估,使分析更加直观、灵活；并且该模型不限制元件的数量,使得模型的应用范围更广。
(3)建立了考虑失效相关性的系统可靠性贝叶斯网络模型,并应用该模型对考虑失效相关性的典型系统,如并联系统、串联系统和k/n(G)系统以及网络系统进行了可靠性评估,同时用蒙特卡罗仿真方法作了对比验证。
(4)研究了基于贝叶斯网络模型的系统可靠度分配。对一般可靠性工程中常用的几种重要度、系统可靠性评估的灵敏度分析和贝叶斯网络因果推理、诊断推理的条件概率的物理意义进行了对比分析,结果表明贝叶斯网络方法更适合于识别可靠性薄弱环节。
Doing a mass of system reliability experiments on complicated machinery system is impossible because of considerable expenses and experiment organization. How to make the best of components and system's experiment information to evaluate complicated machinery system accurately is a complicated problem. Now reliability block-diagram method, fault tree method and Monte-Carlo simulation method etc.are the usual methods of evaluating machinery system reliability.For the some limits of these methods, the more suitable reliability evaluation method needs to be researched.
The traditional models for reliability analysis are usually under the binary assumption for each element and the entire system, i.e. system and all elements are considered as being nothing but perfect functioning state and complete failure state, express the working states by means of two-value logic, less considering the multi-state and partly failures of all elements, which can lead to the partly failure of the entire system. Such as valve system, normal working,blocking up,seeping, switch failure etc.are all its states and also system can perform their tasks with various distinguished levels of efficiency usually referral to as performance rates. So only research system's two states to bulid a reliability model is not agree with the real case.
Dependence is the common characteristic of system failure, it is an important cause leading to the system failure dependence. Omitting the failure dependence, qualitative analysis and quantitative calculating simply under independence hypothesis condition will lead to a large error. Probability hazard analysis shows that failure dependence is one of the main reasons to make the system and equipment failure, such as it is the main reason to make the nuclear power plant failure. So it is quite important to pay much more importance to failure denpendence.
Bayesian networks provide a method to represent knowledge in a graphical mode and can be used to do directed graphical description for causal probability relation between random variables. They are mainly used for uncertainty knowledge representation, casual inference and diagnosis inference. By means of various inference modes, the weak elements of system can be readily identified. Bayesian networks makes the relations of components in system more direct and clear.Applying Bayesian networks on reliability evaluation of machinery system and analyzing the multi-state system and common cause system are the keypoints in the thesis.
Taking the advantages of Bayesian networks, the author makes a deep study on applying Bayesian networks to machinery system reliability assessment. The main contributions are:
Applying Bayesian networks on machinery system, eapecially complicated machinery system and building machinery system reliability model based on bayesian networks after analyzing the characters of Bayesian networks. The model can monitor the uncertainty variables, calculate the work probability and conditional failure probability, such as one or more components' conditional failure probability as the system fails, inference and diagonosis the system, find out the weak elements of the sytem.
Applying bayesian networks on multi-state machinery system based on the application of Bayesian networks on machinery system.and building multi-state machinery system reliability model based on Bayesian networks through analyzing and confirming Bayesian networks. It is direct and simple to apply the model on multi-state machinery system evaluation which escaping the calculation of Minimal route-set and cut-set. The multi-state machinery system reliability model don't limit the numbers of components in system that makes the more widely application.
Building a failure dependence model of machinery system reliability based on Bayesian networks and applying it on the evaluation of the typical system considering dependence of elements, such as series system, parallel system, k/n(G) system and network system. At the end confirm the validity of the model using Monte-Carlo simulation method.
System reliability distribution based on Bayesian networks model is researched.By analyzing and comparing the implication of several kinds of importance approaches used in the reliability analysis of general engineering, the implication of the sensitivity analysis approach for system reliability assessment and the implication of various conditional probabilities inferred from Bayesian networks, it can be concluded that Bayesian networks based approach is more suitable to identify the weak components in a machinery system.
在传统的元件/系统可靠性研究中,一般是把研究对象看作只有两种状态,即失效和完好,仅用“是”与“否”二值逻辑来描述产品是否能完成规定功能的情况。但在实际应用中元件/系统可能存在多种状态,如阀门系统可能存在正常、堵、漏、开关不灵等多种状态,而且每种状态都存在一个失效渐近的问题。仅仅研究阀门的两态,由此建立的可靠性模型与实际情况存在较大差异。
“相关”是系统失效的普遍特征,忽略系统的相关性,简单地在各部分失效相互独立的假设条件下对系统可靠性进行定性分析和定量计算,常会导致较大的误差。
贝叶斯网络(Bayesian networks)提供了一种知识图解化的表示方法,可以对结点变量之间的因果概率关系进行有向图解描述,主要用于不确定性知识表达、因果推理和诊断推理等。贝叶斯网络的推理模式多样,可以有效地识别系统可靠性的薄弱环节。贝叶斯网络的图形化显示使得系统中元件间的关系更加直观、清晰,将贝叶斯网络技术应用于机械系统的可靠性评估,对系统的多状态和失效相关性进行分析,是本文的研究重点。
本文根据贝叶斯网络的特点,对其在机械系统可靠性评估中的应用进行了以下研究：
(1)在详细分析贝叶斯网络特点的基础上,将贝叶斯网络应用于机械系统尤其是复杂机械系统可靠性的评估,建立基于贝叶斯网络的系统可靠性评估模型。该模型能够监视系统中的任何不确定性变量,不仅可以求出系统正常工作概率,而且可以计算出系统条件失效概率,如可以方便地计算出某一个或某几个元件故障时系统故障的条件失效概率,进行推理诊断分析,找出系统的薄弱点。
(2)以贝叶斯网络在机械系统上的应用为基础,进一步探索研究贝叶斯网络在多状态机械系统中的应用,通过逐步的分析与算例验证,建立基于贝叶斯网络多状态系统可靠性模型。应用该模型进行多状态系统可靠性评估,使分析更加直观、灵活；并且该模型不限制元件的数量,使得模型的应用范围更广。
(3)建立了考虑失效相关性的系统可靠性贝叶斯网络模型,并应用该模型对考虑失效相关性的典型系统,如并联系统、串联系统和k/n(G)系统以及网络系统进行了可靠性评估,同时用蒙特卡罗仿真方法作了对比验证。
(4)研究了基于贝叶斯网络模型的系统可靠度分配。对一般可靠性工程中常用的几种重要度、系统可靠性评估的灵敏度分析和贝叶斯网络因果推理、诊断推理的条件概率的物理意义进行了对比分析,结果表明贝叶斯网络方法更适合于识别可靠性薄弱环节。
Doing a mass of system reliability experiments on complicated machinery system is impossible because of considerable expenses and experiment organization. How to make the best of components and system's experiment information to evaluate complicated machinery system accurately is a complicated problem. Now reliability block-diagram method, fault tree method and Monte-Carlo simulation method etc.are the usual methods of evaluating machinery system reliability.For the some limits of these methods, the more suitable reliability evaluation method needs to be researched.
The traditional models for reliability analysis are usually under the binary assumption for each element and the entire system, i.e. system and all elements are considered as being nothing but perfect functioning state and complete failure state, express the working states by means of two-value logic, less considering the multi-state and partly failures of all elements, which can lead to the partly failure of the entire system. Such as valve system, normal working,blocking up,seeping, switch failure etc.are all its states and also system can perform their tasks with various distinguished levels of efficiency usually referral to as performance rates. So only research system's two states to bulid a reliability model is not agree with the real case.
Dependence is the common characteristic of system failure, it is an important cause leading to the system failure dependence. Omitting the failure dependence, qualitative analysis and quantitative calculating simply under independence hypothesis condition will lead to a large error. Probability hazard analysis shows that failure dependence is one of the main reasons to make the system and equipment failure, such as it is the main reason to make the nuclear power plant failure. So it is quite important to pay much more importance to failure denpendence.
Bayesian networks provide a method to represent knowledge in a graphical mode and can be used to do directed graphical description for causal probability relation between random variables. They are mainly used for uncertainty knowledge representation, casual inference and diagnosis inference. By means of various inference modes, the weak elements of system can be readily identified. Bayesian networks makes the relations of components in system more direct and clear.Applying Bayesian networks on reliability evaluation of machinery system and analyzing the multi-state system and common cause system are the keypoints in the thesis.
Taking the advantages of Bayesian networks, the author makes a deep study on applying Bayesian networks to machinery system reliability assessment. The main contributions are:
Applying Bayesian networks on machinery system, eapecially complicated machinery system and building machinery system reliability model based on bayesian networks after analyzing the characters of Bayesian networks. The model can monitor the uncertainty variables, calculate the work probability and conditional failure probability, such as one or more components' conditional failure probability as the system fails, inference and diagonosis the system, find out the weak elements of the sytem.
Applying bayesian networks on multi-state machinery system based on the application of Bayesian networks on machinery system.and building multi-state machinery system reliability model based on Bayesian networks through analyzing and confirming Bayesian networks. It is direct and simple to apply the model on multi-state machinery system evaluation which escaping the calculation of Minimal route-set and cut-set. The multi-state machinery system reliability model don't limit the numbers of components in system that makes the more widely application.
Building a failure dependence model of machinery system reliability based on Bayesian networks and applying it on the evaluation of the typical system considering dependence of elements, such as series system, parallel system, k/n(G) system and network system. At the end confirm the validity of the model using Monte-Carlo simulation method.
System reliability distribution based on Bayesian networks model is researched.By analyzing and comparing the implication of several kinds of importance approaches used in the reliability analysis of general engineering, the implication of the sensitivity analysis approach for system reliability assessment and the implication of various conditional probabilities inferred from Bayesian networks, it can be concluded that Bayesian networks based approach is more suitable to identify the weak components in a machinery system.
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