摘要
在工程管理实践中,不同工序的工时变量之间存在非常普遍的相依性,各种客观因素的影响和人为的控制都是工时变量相依的可能根源。当前,人们对工程项目管理的要求越来越高,对工程进度控制的要求也越来越苛刻。在实际工程的进度管理中,合理考虑工时变量之间的相依性,能充分估计工期计划的不确定性,更加准确地预测和评估工期风险,并对进度计划进行动态更新,从而更有效地控制工程进度。
本文旨在通过对工时变量之间相依关系的调查分析,构建能描述工时变量之间相依结构的图形模型,建立合理的相依性测度指标体系,并在工时相依的情形下研究工期问题及进度计划的动态更新。主要内容包括以下几个方面:
首先,回顾经典的CPM/PERT网络计划模型的基本结构及工时的随机性,了解其工时变量的独立性假设。然后通过对多个实际工程项目的调查,用相依性指标对项目的工时数据进行统计分析,结果表明所调查项目的并行工序、序列工序之间存在较强的工时相依性。结合调查内容和专家问卷,分析工时相依性产生的原因主要在于受共同因素的影响和项目的组织与控制,并对工时的相依性进行了系统分类。
其次,通过对两种有向无环图模型——AON网络计划及贝叶斯网的分析,以AON网络计划为背景层,考虑工时变量之间的序列相依及并行相依关系,建立了能合理描述工时变量之间相依关系的贝叶斯网络计划(BNP)模型结构,讨论了BNP模型中的图分隔与条件独立性质。另外,介绍了BNP模型中工时变量概率分布的确定方法,研究了变量间条件概率的确定、模型中减少参数以及缺值数据下参数学习的方法。
第三,基于Copula函数的优良性质,在分析线性相关系数在工时相依性度量时的优缺点的基础上,建立了基于Copula函数的工时相依性度量指标,并给出了这些相依性指标在具体工程项目中的估计方法。另外,分析了常用的Copula函数描述工时相依性的性质与模式,建立了混合Copula函数来描述具有各种相依模式的工时变量之间的相依关系。
第四,介绍了Monte Carlo模拟应用于工时相依的工期问题模拟的基本步骤。结合前述理论模型及相依性度量指标,研究了相依的工时变量随机数的产生以及概率分布的确定,对BNP网络的工期、完工概率及工序关键度进行了模拟,最后以一个简单实例演示了模拟过程,并与其他模型的计算结果进行了对比分析。
第五,结合贝叶斯定理及贝叶斯网推理原理,介绍了BNP模型中工时变量的动态更新方法。在变量为离散的情形下,给出了变量消元算法、团树传播算法以及马尔科夫链蒙特卡洛算法;在变量为连续或混合的情形下,分别研究了连续BNP模型、混合BNP模型中工时变量的动态更新方法,并给出了计算实例。
最后,给出了研究成果在实际工程项目进度管理中的应用框架,介绍了考虑工时相依性的工程进度计划制定以及动态更新方法与流程,并以某工程项目为例进行了分析。结果表明,本文研究的方法能更合理地估计进度计划的不确定性,并能根据工时之间的相依性对进度计划进行动态更新,在实践中有广泛的应用前景和较好的应用价值。
In the practice of construction management, dependence between the duration variables of activities becomes very common, which may be caused by various objective or man-made factors. Currently, the requirement of construction project management becomes increasingly high, and demands for construction progress control also get more and more harsh. In the progress management of real construction projects, it is very important to consider the dependence between duration variables reasonably, which can be very helpful to estimate the uncertainty of construction period more adequately,forecast and assess risk more accurately, update the project schedule, and thus to control construction progress more efficiently. This dissertation, based on survey and analysis of dependence between duration variables, aims to construct graph models describing the dependence structure between duration variables, set up reasonable index system for dependence measurement, and study the problems of construction period and project schedule updating in view of dependence between activity durations. Main contents and details are listed below:
Firstly, basic structure, randomness of activity durations and the independence assumption in classical CPM/PERT network models have been reviewed. Then based on the survey of multiple real construction projects, statistical analysis has been made on durations using dependence index, which indicated that there exists strong dependence between durations of parallel or serial activities. With surveying matters and questionnaires for experts, dependence between activity durations has been categorized systematically. The cause for such dependence has been analyzed, which turns out to be common factors and project organization and control.
Secondly, through analyzing AON network plan and Bayesian network, a Bayesian Network Plan (BNP) model structure has been presented laying the AON network plan as background layer and considering parallel/serial dependence between duration variables, which can reasonably describe the dependence between duration variables. The separate and conditional independence in the model has also been discussed. In addition, methods for determining probability distribution of duration variables in BNP model has been introduced, and approaches for determining conditional probability between variables and parameter learning with reduced parameters and incomplete data has been studied.
Thirdly, based on unique advantages of Copula function, Copula-function-based indexes for measuring dependence between durations and the methods to estimate such index in real projects have been presented, which has been done through analyzing advantages and disadvantages of liner correlation in measuring dependence between durations. Moreover, the properties and modes of general Copula functions when describing dependence between durations have been analyzed, and a mixed Copula function has been constructed to describe the dependence between duration variables with various dependence modes.
Fourthly, basic steps of Monte Carlo simulation applied in construction period with dependent durations have been introduced. According to theoretical models and dependence measuring indexes mentioned above, approaches to generate random numbers and determine probability distribution of duration variables have been studied. A simple example has been given to demonstrate the simulating process, with the results compared with those from other models.
Fifthly, methods for updating duration variables in BNP model have been introduced according to Bayesian Theorem and Bayesian Network Reasoning Theorem. Several methods including variable elimination, clique tree propagation and Markov chain Monte Carlo algorithm have been presented for the case that duration variables are discrete. In the situation with continuous or mixed variables, approaches for updating duration variables in BNP models and mixed BNP models have been studied and a numerical example has been given.
At last, the application framework for applying the research results to the practice of construction project schedule management has been proposed, methods for determining and updating project schedule plan have been introduced when considering dependence between durations, and a real construction project has been taken as an example to illustrate the application. The results indicated that the approaches proposed in the dissertation have wide application prospect and fairly good value, because they can give more reasonable estimation to the uncertainty of schedule plan and update schedule plan dynamically according to the dependence between activity durations.
引文
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