基于随机过程的桥梁系统可靠性及其模糊综合评价研究
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摘要
桥梁健康监测系统可以分为在线测试、实时分析、损伤诊断、状态评估以及维修决策五个部分,桥梁系统的可靠性分析是状态评估中的关键部分。由于目前桥梁构件的可靠性研究比较成熟,相当一部分研究成果己经得到了应用。对于研究整个桥梁系统的可靠性,多是参照构件可靠性的研究方法,寻找桥梁系统的失效功能函数,由于桥梁系统是非常复杂的,失效功能函数的确定往往是相当困难的。基于目前的实际情况,本文欲在现有的比较成熟的构件可靠性研究的基础上,寻找评价桥梁结构系统可靠性的指标和方法,力求最大限度的利用构件可靠性分析的研究成果,使桥梁系统可靠性与构件的可靠性紧密的联系起来。
本文在随机过程相关理论的基础上,提出了采用Markov过程稳态概率作为桥梁系统可靠性的评价指标；提出了桥梁系统可靠性关联矩阵R的确定方法,建立了构件的可靠性指标β和Markov过程稳态概率之间的关系；桥梁构件的可靠度降低,即发生损伤时,是否会得到及时有效的维修,对桥梁系统的可靠性有着较大的影响,通过对桥梁系统可靠性关联矩阵R的变换,建立了桥梁的维修频率与Markov过程稳态概率之间的关系；桥梁系统在工作过程中各个构件的失效往往不是同时发生的,即不易出现同时失效的现象,通常是某些构件首先失效,使得剩余构件继续承担所有的外部载荷,在桥梁系统中产生内部应力的重新分配,造成其他构件可靠度的变化,本文推导出桥梁系统首次失效平均时间(Bridge System Mean Time To Failure,简称BSMTTF)的计算方法；通过对桥梁结构状况的分析可以得到桥梁系统可靠性评估的指标,即Markov过程稳态概率,而Markov过程稳态概率的数值在何种区间范围可认为桥梁结构系统是可靠的,在何种区间范围可认为是不可靠的,可靠与不可靠间还必定存在着过渡区间,并且该过渡区间是存在着一定的模糊性的,故本文研究了桥梁系统工作状态的模糊综合评价方法,首次将Markov过程稳态概率应用到桥梁系统的模糊综合评价上,降低了模糊综合评价方法的主观性和经验性。
本文各章的主要内容如下：
第1章是对现有的可靠性分析方法的综述和总结。重点总结了系统可靠性的理论及其在桥梁工程中的应用,并对可靠度的分析方法和结构系统可靠性分析方法进行了论述。
第2章研究了随机过程的相关理论,重点包括Markov过程及其特性,Markov过程状态方程及Markov过程稳态概率。在对桥梁系统进行工作状态划分的基础上,提出了采用Markov过程稳态概率作为桥梁系统可靠性的评价指标,并对Markov过程稳态概率计算方程中的Markov过程转换率矩阵进行了深入研究,提出了桥梁系统可靠性关联矩阵R的确定方法,建立了构件的可靠性指标β和Markov过程稳态概率之间的关系。借助算例分析了该方法的适用性和有效性,并通过系统可靠度的限界估计方法对该方法的正确性进行了验证。
第3章考虑了维修频率对桥梁系统可靠性的影响。通过对桥梁系统可靠性关联矩阵R的变换,建立了桥梁的维修频率与Markov过程稳态概率之间的关系,即进行了桥梁系统可靠性与维修性的分析,通过算例求出不同维修频率条件下的桥梁系统可靠性指标,得出了典型桥梁结构中可靠性指标和Markov过程稳态概率之间的关系。
第4章考虑桥梁结构系统中当出现首个失效构件后会发生荷载的转移,使应力重新分配,通过对Markov过程稳态概率计算方程及可靠度函数进行Laplace变换,求解变换后的系统状态方程,推导出桥梁系统首次失效平均时间(BSMTTF)的计算方法,并以此作为载荷共享条件下的桥梁系统可靠性评价指标。同时给出了采用桥梁系统首次失效平均时间(BSMTTF)进行桥梁系统时变可靠性分析的方法。
第5章针对目前桥梁系统状态评价的具体情况,在采用Markov过程稳态概率作为评价桥梁系统可靠性指标的基础上,根据行业标准及工程实际对桥梁系统进行部件及构件组成划分,选取了桥梁结构的模糊评价集,给出了典型桥梁的工作状态空间,研究了桥梁系统工作状态的模糊综合评价方法,首次将Markov过程稳态概率应用到桥梁系统的模糊综合评价上,得出桥梁系统处于可靠状态、过渡状态及不可靠状态的模糊概率数值。该评价体系未采用桥梁技术状况评价过程中的人为打分方法,避免了打分过程中可能产生的不确定性和随机性。
第6章通过全桥模型对顺次失效概率进行了模拟,计算了桥梁结构的Markov过程稳态概率、对桥梁系统首次失效平均时间(BSMTTF)进行了分析,并采用模糊综合评价的方法对桥梁部件及桥梁系统进行了模糊综合评价。结果表明,上述方法在全桥模型上的应用效果是可行并且有效的。
第7章总结了本文的主要研究成果,主要创新点,得出了如下结论：
1、提出了采用Markov过程稳态概率作为桥梁系统可靠性的评价指标。通过对Markov过程及其特性、Markov过程状态方程及Markov过程稳态概率的分析,结合桥梁可靠度的理论,提出了采用Markov过程稳态概率作为桥梁系统可靠性的评价指标,并通过界限估计法对该指标的正确性进行了验证。
2、提出了桥梁系统可靠性关联矩阵R的确定方法,建立了构件的可靠性指标β和Markov过程稳态概率之间的关系。结合桥梁中构件的可靠性指标β,通过修改桥梁系统工作状态的Markov过程转换率矩阵,建立了构件的可靠性指标β和Markov过程稳态概率之间的关系。
3、建立了桥梁的维修频率与Markov过程稳态概率之间的关系。通过对桥梁系统可靠性关联矩阵R的变换,考虑桥梁系统的维修频率对Markov过程稳态概率的影响,该方法可用来选定桥梁的检测维修频率。
4、推导出桥梁系统首次失效平均时间(BSMTTF)的计算方法,给出了实现桥梁系统时变可靠性分析的指标和方法。桥梁结构中由于部分构件失效,会产生内部应力的重分布,通过对桥梁系统状态方程进行Laplace变换,推导出桥梁系统首次失效平均时间(BSMTTF)的计算方法,并在算例上进行了应用。
5、首次将Markov过程稳态概率应用到桥梁系统的模糊综合评价上,降低了模糊综合评价方法的主观性和经验性。由于桥梁系统可靠性评估的结果是一个概率数值,而满足哪些概率数值时桥梁系统是可靠的,满足哪些概率数值时桥梁系统是不可靠的,可靠与不可靠间还必定存在着过渡区间。结合模糊综合评价的方法,将Markov过程稳态概率应用到了桥梁系统的模糊综合评价上
本文采用随机过程的方法对桥梁系统可靠性进行了深入的分析研究,提出了桥梁系统可靠性分析的评价指标；提出了桥梁系统可靠性关联矩阵R的确定方法；建立了构件的可靠性指标β和Markov过程稳态概率之间的关系；推导出桥梁系统首次失效平均时间的计算方法；结合Markov过程稳态概率对桥梁部件及桥梁系统进行了模糊综合评价,首次将Markov过程稳态概率应用到桥梁系统的模糊综合评价上。上述理论和方法为桥梁系统的可靠性评估提供了理论依据和方法,具有重要的理论价值和工程应用价值。
本文在研究和撰写过程中得到了教育部高等学校博士学科点专项科研基金项目(课题名称：多种失效模式下在役混凝土桥梁结构的时变可靠度分析；课题编号：20100061110051)的资助,在此表示感谢。
Bridge Health Monitoring System can be divided into five parts which contain onlinetesting, timely analysis, damage diagnosis, condition assessment and maintenance strategydecision. The bridge system reliability analysis is a key part in condition assessment.Because the bridge components reliability analysis is more mature now, even quite anumber of research results have been applied. The entire bridge system reliability mostlyrefer to component reliability research methods then look for the failure function of thebridge system. Since bridge system is very complex, the determination of the failurefunctions often is very difficult. Based on the above situation, this article will look forindexs and methods of bridge structural system reliability assesment on the basis of theexisting mature component reliability, study to make most use of the component reliabilityanalysis research, and to make the bridge system reliability closely linked with thecomponent reliability index, to find the relationship between them.
Based on random process related theory this article proposed the Markov processsteady-state probability as assessment index of bridge structural system reliability at thesame time proposed the confirming method of bridge system reliability relational matrixR. Establish the relationship between Markov process steady-state probabilities and thebridge components reliability index. Bridge components reliability is reduced, the damageoccurs. Whether it will be timely and effectively maintained, has a larger impact on thebridge system reliability. Through the transformation of reliability relational matrix R ofthe bridge system established the relationship between the bridge maintenance frequencyand Markov process steady-state probabilities. The failure of the respective members ofthe bridge system in the work process is often not occur simultaneously namely cannotappear the phenomenon of simultaneous failure. Some components are often fail firstly, sothat the remaining members continue to bear all the external load, and generatingre-distribution of internal stress in the bridge system to cause the changes of the othercomponent reliability. In this paper, the assessment methods ofBridge System Mean Tim e T o Failure BSMTTF in the bridge system have beenstudied Bridge system reliability assessment indicators, namely the Markov processstationary probability can be obtained through the analysis of the structural condition of the bridge. However, the value of the Markov process stationary probability is in what intervalrange we can consider that it is reliable and in what interval range it is unreliable.Transition interval must exist also between reliable and unreliable, and the transitioninterval must be vague, so this paper studies a fuzzy comprehensive evaluation methodabout the working condition of the bridge system, and for the first time the steady-stateprobability process is applied to fuzzy comprehensive evaluation of bridge system reducedthe subjective and experiential of fuzzy comprehensive evaluation. In this paper, the maincontent of the chapters are as follows.
Chapter1is a review and summary of existing reliability analysis methods. Focuson the summary of the system reliability theory and its application in bridge engineering,and the dissertation of reliability analysis method and structural system reliability analysis.
Chapter2study the random process related theory, mainly including the Markovprocess and its characteristics, equation of state of the Markov process and the Markovprocess steady-state probabilities. On the basis of division of the working condition in thebridge system, it put forward a way which using the Markov process steady-state probabilityas a bridge system reliability evaluation indicators additionally study the state transitionmatrix of Markov process steady-state probability calculation equation put forward themethod of determining the bridge system reliability relational matrix and derive therelationship between the reliability index of the bridge components with thesteady-state probability of the bridge system. With the applicability and effectiveness of theexample and the estimation methods of the reliability, verifyed the validity of the method.
Chapter3consider the effects on the bridge structure system reliability thatmaintenance rate generate. Through the transformation of the corresponding parameter inthe bridge system reliability relational matrix(R), establish the relationship betweenmaintenance rate and steady-state probability of the bridge system, namely analyze thebridge system reliability and maintainability, obtain the bridge system reliability indicesunder different maintenance rate conditions, draw the relationship between maintenancerate and matrix(R) steady-state probability of the bridge system in a typical bridgestructure.
Chapter4consider the transfer of load and stress re-distribution after appearingfirst fail component in the bridge structure system. Through the Laplace transform aboutthe process of steady-state probability calculation equation and reliability function, solving the system state equation after conversion, Bridge System Mean Tim e T o Failure
BSMTTF can be obtained then act it as the evaluation of bridge system reliabilityunder the condition of load sharing. At the same time, the method have been given thatusing the Bridge System Mean Tim e T o Failure BSMTTF to analyze the time-varyingreliability of bridge system.
In Chapter5, for the specific circumstances of the current state of the bridge systemevaluation, on the basis of using Markov process of steady-state probability as theevaluation of bridge system reliability index, divide bridge system parts and componentsaccording to standards and engineering practice, then select the set of fuzzy evaluation ofthe bridge structure, show the working state space of typical bridges and research fuzzycomprehensive evaluation of the state of the bridge system, for the first time the processsteady-state probability is applied to fuzzy comprehensive evaluation of the bridge system.The evaluation system does not adopt the human scoring method during bridge technicalcondition evaluation process to avoid generating uncertainty and randomness during thescoring process.
In Chapter6, sequential failure probability have been simulated through full-bridgemodel, the Markov process steady-state probability of bridge structure have beencalculated, Bridge System Mean Tim e T o Failure BSMTTF have been analyzed, andcarry on fuzzy comprehensive evaluation to the part of the bridge and bridge system byusing fuzzy comprehensive evaluation method. The results show that, the effect that theabove methods are applied in full-bridge model is feasible and effective.
Chapter7summarizees the main findings, the main innovations of this paper andreach the following conclusions:
1Propose a method of using steady-state probability as the evaluation index ofbridge system reliability. Through the analysis of the Markov process and itscharacteristics, the Markov process equation of state and the process of steady-stateprobability combining with the theory of bridge reliability analysis, put forward theevaluation of the bridge system reliability indicators by using the Markov process ofsteady-state probability and examine the correctness and validity of this evaluation throughboundary estimation method.
2Put forward a method of determining bridge system reliability relational matrixand establish the relationship between the reliability indicators of bridge component and the Markov process of steady-state probability. Combining reliability index of the bridgemembers, modify the transfer matrix of the bridge system working state, establish therelationship between the reliability indicators of bridge component and the Markovprocess of steady-state probability.
3Establish the relationship between maintenance rate and the Markov processsteady-state probability.Through the tranformation of the reliability relational matrix ofthe bridge system R, consider the effect to Markov process of steady-state probabilitywhich caused by the bridge system maintenance rate, this method can be used to select thefrequency of inspection and maintenance about a bridge.
4Deduce the calculation method of Bridge System Mean Tim e T o Failure
BSMTTF and put forward the indicators and methods of achieving reliability analysisof the bridge system.Because of the component failure in the bridge structure,there-distribution of the internal stress will occur, through the Laplace transform about thestate equation of the bridge system, deduce the calculation about calculatingBridge System Mean Tim e T o Failure BSMTTF and apply on the exmaples.
5Firstly apply this index on fuzzy comprehensive evaluation of the bridge system,reduce the subjectivity and the experience of human scoring process in the fuzzycomprehensive evaluation method. Since the results of bridge system reliabilityassessmentis a probability value, what bridge probabilities are satisfied when the bridgesystem is reliable and what bridge probabilities are satisfied when the bridge system isunreliable, meet what the probability of the bridge system is difficult to judge. Accordingto this problem, combine the fuzzy comprehensive evaluation method, on the basis ofusing Markov process of steady-state probability as bridge system reliability evaluation.
In this paper, the bridge system reliability has been analyzed deeply by using themethod of random process. Put forward the evaluation of bridge system reliabilityanalysis, Put forward a method of determining bridge system reliability relational matrixand establish the relationship between the reliability indicators of bridge component andthe Markov process of steady-state probability, derive the calculation method of theBridge System Mean Tim e T o Failure BSMTTF. Combining with Markov process ofsteady-state probability, the fuzzy comprehensive evaluation of bridge components andbridge system have been conducted, Markov process steady-state probability is firstlyused on fuzzy comprehensive evaluation of bridge system. The theory and methods that have been mentioned provide theoretical basis and method for the evaluation of bridgesystem reliability and have important theoretical value in the engineering applications.
This research has been supported by grants from Specialized Research Fund for theDoctoral Program of Higher Education (project name: Time-varying reliability analysis ofexisting concrete bridge structures under a variety of failure modes project number:20100061110051) during the process of research and writing, thanks very much.
本文在随机过程相关理论的基础上,提出了采用Markov过程稳态概率作为桥梁系统可靠性的评价指标；提出了桥梁系统可靠性关联矩阵R的确定方法,建立了构件的可靠性指标β和Markov过程稳态概率之间的关系；桥梁构件的可靠度降低,即发生损伤时,是否会得到及时有效的维修,对桥梁系统的可靠性有着较大的影响,通过对桥梁系统可靠性关联矩阵R的变换,建立了桥梁的维修频率与Markov过程稳态概率之间的关系；桥梁系统在工作过程中各个构件的失效往往不是同时发生的,即不易出现同时失效的现象,通常是某些构件首先失效,使得剩余构件继续承担所有的外部载荷,在桥梁系统中产生内部应力的重新分配,造成其他构件可靠度的变化,本文推导出桥梁系统首次失效平均时间(Bridge System Mean Time To Failure,简称BSMTTF)的计算方法；通过对桥梁结构状况的分析可以得到桥梁系统可靠性评估的指标,即Markov过程稳态概率,而Markov过程稳态概率的数值在何种区间范围可认为桥梁结构系统是可靠的,在何种区间范围可认为是不可靠的,可靠与不可靠间还必定存在着过渡区间,并且该过渡区间是存在着一定的模糊性的,故本文研究了桥梁系统工作状态的模糊综合评价方法,首次将Markov过程稳态概率应用到桥梁系统的模糊综合评价上,降低了模糊综合评价方法的主观性和经验性。
本文各章的主要内容如下：
第1章是对现有的可靠性分析方法的综述和总结。重点总结了系统可靠性的理论及其在桥梁工程中的应用,并对可靠度的分析方法和结构系统可靠性分析方法进行了论述。
第2章研究了随机过程的相关理论,重点包括Markov过程及其特性,Markov过程状态方程及Markov过程稳态概率。在对桥梁系统进行工作状态划分的基础上,提出了采用Markov过程稳态概率作为桥梁系统可靠性的评价指标,并对Markov过程稳态概率计算方程中的Markov过程转换率矩阵进行了深入研究,提出了桥梁系统可靠性关联矩阵R的确定方法,建立了构件的可靠性指标β和Markov过程稳态概率之间的关系。借助算例分析了该方法的适用性和有效性,并通过系统可靠度的限界估计方法对该方法的正确性进行了验证。
第3章考虑了维修频率对桥梁系统可靠性的影响。通过对桥梁系统可靠性关联矩阵R的变换,建立了桥梁的维修频率与Markov过程稳态概率之间的关系,即进行了桥梁系统可靠性与维修性的分析,通过算例求出不同维修频率条件下的桥梁系统可靠性指标,得出了典型桥梁结构中可靠性指标和Markov过程稳态概率之间的关系。
第4章考虑桥梁结构系统中当出现首个失效构件后会发生荷载的转移,使应力重新分配,通过对Markov过程稳态概率计算方程及可靠度函数进行Laplace变换,求解变换后的系统状态方程,推导出桥梁系统首次失效平均时间(BSMTTF)的计算方法,并以此作为载荷共享条件下的桥梁系统可靠性评价指标。同时给出了采用桥梁系统首次失效平均时间(BSMTTF)进行桥梁系统时变可靠性分析的方法。
第5章针对目前桥梁系统状态评价的具体情况,在采用Markov过程稳态概率作为评价桥梁系统可靠性指标的基础上,根据行业标准及工程实际对桥梁系统进行部件及构件组成划分,选取了桥梁结构的模糊评价集,给出了典型桥梁的工作状态空间,研究了桥梁系统工作状态的模糊综合评价方法,首次将Markov过程稳态概率应用到桥梁系统的模糊综合评价上,得出桥梁系统处于可靠状态、过渡状态及不可靠状态的模糊概率数值。该评价体系未采用桥梁技术状况评价过程中的人为打分方法,避免了打分过程中可能产生的不确定性和随机性。
第6章通过全桥模型对顺次失效概率进行了模拟,计算了桥梁结构的Markov过程稳态概率、对桥梁系统首次失效平均时间(BSMTTF)进行了分析,并采用模糊综合评价的方法对桥梁部件及桥梁系统进行了模糊综合评价。结果表明,上述方法在全桥模型上的应用效果是可行并且有效的。
第7章总结了本文的主要研究成果,主要创新点,得出了如下结论：
1、提出了采用Markov过程稳态概率作为桥梁系统可靠性的评价指标。通过对Markov过程及其特性、Markov过程状态方程及Markov过程稳态概率的分析,结合桥梁可靠度的理论,提出了采用Markov过程稳态概率作为桥梁系统可靠性的评价指标,并通过界限估计法对该指标的正确性进行了验证。
2、提出了桥梁系统可靠性关联矩阵R的确定方法,建立了构件的可靠性指标β和Markov过程稳态概率之间的关系。结合桥梁中构件的可靠性指标β,通过修改桥梁系统工作状态的Markov过程转换率矩阵,建立了构件的可靠性指标β和Markov过程稳态概率之间的关系。
3、建立了桥梁的维修频率与Markov过程稳态概率之间的关系。通过对桥梁系统可靠性关联矩阵R的变换,考虑桥梁系统的维修频率对Markov过程稳态概率的影响,该方法可用来选定桥梁的检测维修频率。
4、推导出桥梁系统首次失效平均时间(BSMTTF)的计算方法,给出了实现桥梁系统时变可靠性分析的指标和方法。桥梁结构中由于部分构件失效,会产生内部应力的重分布,通过对桥梁系统状态方程进行Laplace变换,推导出桥梁系统首次失效平均时间(BSMTTF)的计算方法,并在算例上进行了应用。
5、首次将Markov过程稳态概率应用到桥梁系统的模糊综合评价上,降低了模糊综合评价方法的主观性和经验性。由于桥梁系统可靠性评估的结果是一个概率数值,而满足哪些概率数值时桥梁系统是可靠的,满足哪些概率数值时桥梁系统是不可靠的,可靠与不可靠间还必定存在着过渡区间。结合模糊综合评价的方法,将Markov过程稳态概率应用到了桥梁系统的模糊综合评价上
本文采用随机过程的方法对桥梁系统可靠性进行了深入的分析研究,提出了桥梁系统可靠性分析的评价指标；提出了桥梁系统可靠性关联矩阵R的确定方法；建立了构件的可靠性指标β和Markov过程稳态概率之间的关系；推导出桥梁系统首次失效平均时间的计算方法；结合Markov过程稳态概率对桥梁部件及桥梁系统进行了模糊综合评价,首次将Markov过程稳态概率应用到桥梁系统的模糊综合评价上。上述理论和方法为桥梁系统的可靠性评估提供了理论依据和方法,具有重要的理论价值和工程应用价值。
本文在研究和撰写过程中得到了教育部高等学校博士学科点专项科研基金项目(课题名称：多种失效模式下在役混凝土桥梁结构的时变可靠度分析；课题编号：20100061110051)的资助,在此表示感谢。
Bridge Health Monitoring System can be divided into five parts which contain onlinetesting, timely analysis, damage diagnosis, condition assessment and maintenance strategydecision. The bridge system reliability analysis is a key part in condition assessment.Because the bridge components reliability analysis is more mature now, even quite anumber of research results have been applied. The entire bridge system reliability mostlyrefer to component reliability research methods then look for the failure function of thebridge system. Since bridge system is very complex, the determination of the failurefunctions often is very difficult. Based on the above situation, this article will look forindexs and methods of bridge structural system reliability assesment on the basis of theexisting mature component reliability, study to make most use of the component reliabilityanalysis research, and to make the bridge system reliability closely linked with thecomponent reliability index, to find the relationship between them.
Based on random process related theory this article proposed the Markov processsteady-state probability as assessment index of bridge structural system reliability at thesame time proposed the confirming method of bridge system reliability relational matrixR. Establish the relationship between Markov process steady-state probabilities and thebridge components reliability index. Bridge components reliability is reduced, the damageoccurs. Whether it will be timely and effectively maintained, has a larger impact on thebridge system reliability. Through the transformation of reliability relational matrix R ofthe bridge system established the relationship between the bridge maintenance frequencyand Markov process steady-state probabilities. The failure of the respective members ofthe bridge system in the work process is often not occur simultaneously namely cannotappear the phenomenon of simultaneous failure. Some components are often fail firstly, sothat the remaining members continue to bear all the external load, and generatingre-distribution of internal stress in the bridge system to cause the changes of the othercomponent reliability. In this paper, the assessment methods ofBridge System Mean Tim e T o Failure BSMTTF in the bridge system have beenstudied Bridge system reliability assessment indicators, namely the Markov processstationary probability can be obtained through the analysis of the structural condition of the bridge. However, the value of the Markov process stationary probability is in what intervalrange we can consider that it is reliable and in what interval range it is unreliable.Transition interval must exist also between reliable and unreliable, and the transitioninterval must be vague, so this paper studies a fuzzy comprehensive evaluation methodabout the working condition of the bridge system, and for the first time the steady-stateprobability process is applied to fuzzy comprehensive evaluation of bridge system reducedthe subjective and experiential of fuzzy comprehensive evaluation. In this paper, the maincontent of the chapters are as follows.
Chapter1is a review and summary of existing reliability analysis methods. Focuson the summary of the system reliability theory and its application in bridge engineering,and the dissertation of reliability analysis method and structural system reliability analysis.
Chapter2study the random process related theory, mainly including the Markovprocess and its characteristics, equation of state of the Markov process and the Markovprocess steady-state probabilities. On the basis of division of the working condition in thebridge system, it put forward a way which using the Markov process steady-state probabilityas a bridge system reliability evaluation indicators additionally study the state transitionmatrix of Markov process steady-state probability calculation equation put forward themethod of determining the bridge system reliability relational matrix and derive therelationship between the reliability index of the bridge components with thesteady-state probability of the bridge system. With the applicability and effectiveness of theexample and the estimation methods of the reliability, verifyed the validity of the method.
Chapter3consider the effects on the bridge structure system reliability thatmaintenance rate generate. Through the transformation of the corresponding parameter inthe bridge system reliability relational matrix(R), establish the relationship betweenmaintenance rate and steady-state probability of the bridge system, namely analyze thebridge system reliability and maintainability, obtain the bridge system reliability indicesunder different maintenance rate conditions, draw the relationship between maintenancerate and matrix(R) steady-state probability of the bridge system in a typical bridgestructure.
Chapter4consider the transfer of load and stress re-distribution after appearingfirst fail component in the bridge structure system. Through the Laplace transform aboutthe process of steady-state probability calculation equation and reliability function, solving the system state equation after conversion, Bridge System Mean Tim e T o Failure
BSMTTF can be obtained then act it as the evaluation of bridge system reliabilityunder the condition of load sharing. At the same time, the method have been given thatusing the Bridge System Mean Tim e T o Failure BSMTTF to analyze the time-varyingreliability of bridge system.
In Chapter5, for the specific circumstances of the current state of the bridge systemevaluation, on the basis of using Markov process of steady-state probability as theevaluation of bridge system reliability index, divide bridge system parts and componentsaccording to standards and engineering practice, then select the set of fuzzy evaluation ofthe bridge structure, show the working state space of typical bridges and research fuzzycomprehensive evaluation of the state of the bridge system, for the first time the processsteady-state probability is applied to fuzzy comprehensive evaluation of the bridge system.The evaluation system does not adopt the human scoring method during bridge technicalcondition evaluation process to avoid generating uncertainty and randomness during thescoring process.
In Chapter6, sequential failure probability have been simulated through full-bridgemodel, the Markov process steady-state probability of bridge structure have beencalculated, Bridge System Mean Tim e T o Failure BSMTTF have been analyzed, andcarry on fuzzy comprehensive evaluation to the part of the bridge and bridge system byusing fuzzy comprehensive evaluation method. The results show that, the effect that theabove methods are applied in full-bridge model is feasible and effective.
Chapter7summarizees the main findings, the main innovations of this paper andreach the following conclusions:
1Propose a method of using steady-state probability as the evaluation index ofbridge system reliability. Through the analysis of the Markov process and itscharacteristics, the Markov process equation of state and the process of steady-stateprobability combining with the theory of bridge reliability analysis, put forward theevaluation of the bridge system reliability indicators by using the Markov process ofsteady-state probability and examine the correctness and validity of this evaluation throughboundary estimation method.
2Put forward a method of determining bridge system reliability relational matrixand establish the relationship between the reliability indicators of bridge component and the Markov process of steady-state probability. Combining reliability index of the bridgemembers, modify the transfer matrix of the bridge system working state, establish therelationship between the reliability indicators of bridge component and the Markovprocess of steady-state probability.
3Establish the relationship between maintenance rate and the Markov processsteady-state probability.Through the tranformation of the reliability relational matrix ofthe bridge system R, consider the effect to Markov process of steady-state probabilitywhich caused by the bridge system maintenance rate, this method can be used to select thefrequency of inspection and maintenance about a bridge.
4Deduce the calculation method of Bridge System Mean Tim e T o Failure
BSMTTF and put forward the indicators and methods of achieving reliability analysisof the bridge system.Because of the component failure in the bridge structure,there-distribution of the internal stress will occur, through the Laplace transform about thestate equation of the bridge system, deduce the calculation about calculatingBridge System Mean Tim e T o Failure BSMTTF and apply on the exmaples.
5Firstly apply this index on fuzzy comprehensive evaluation of the bridge system,reduce the subjectivity and the experience of human scoring process in the fuzzycomprehensive evaluation method. Since the results of bridge system reliabilityassessmentis a probability value, what bridge probabilities are satisfied when the bridgesystem is reliable and what bridge probabilities are satisfied when the bridge system isunreliable, meet what the probability of the bridge system is difficult to judge. Accordingto this problem, combine the fuzzy comprehensive evaluation method, on the basis ofusing Markov process of steady-state probability as bridge system reliability evaluation.
In this paper, the bridge system reliability has been analyzed deeply by using themethod of random process. Put forward the evaluation of bridge system reliabilityanalysis, Put forward a method of determining bridge system reliability relational matrixand establish the relationship between the reliability indicators of bridge component andthe Markov process of steady-state probability, derive the calculation method of theBridge System Mean Tim e T o Failure BSMTTF. Combining with Markov process ofsteady-state probability, the fuzzy comprehensive evaluation of bridge components andbridge system have been conducted, Markov process steady-state probability is firstlyused on fuzzy comprehensive evaluation of bridge system. The theory and methods that have been mentioned provide theoretical basis and method for the evaluation of bridgesystem reliability and have important theoretical value in the engineering applications.
This research has been supported by grants from Specialized Research Fund for theDoctoral Program of Higher Education (project name: Time-varying reliability analysis ofexisting concrete bridge structures under a variety of failure modes project number:20100061110051) during the process of research and writing, thanks very much.
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