Abstract
This paper firstly introduces the development of Monte-Carlo method in connectivity reliability and its advantages and disadvantages in the study of road connectivity reliability. Secondly, introduce the traditional Monte Carlo method to calculate the reliability of the connection, and improve the accuracy and speed of the traditional Monte Carlo method, that is, replace the pseudo-random number with Sobol sequence, which overcomes the The shortcomings make the result more accurate and increase the calculation speed from the side. Finally, by comparing the results of the Monte Carlo method and Monte Carlo method for calculating the reliability of road connectivity, the advantages of the improved Monte Carlo method in this respect are obtained. It shows that this method has certain correctness and superiority, and has a positive reference value for the evaluation of the reliability of the road connectivity. The research on the reliability of road connectivity, this paper improves the accuracy and speed of the traditional Monte Carlo method, that is, replacing the pseudo-random numbers with Sobol sequences, which overcomes the shortcomings caused by pseudo-random sequence sampling and makes the results It is more accurate and speeds up calculations from the side. Finally, by comparing the results of improved Monte Carlo method and Monte Carlo method for the seismic reliability calculation of roads, the advantages of improved Monte Carlo method in this respect are obtained. It shows that the method has certain correctness and superiority, and has a positive reference value for road reliability assessment.
Highlights
This paper firstly introduces the development of Monte-Carlo method in connectivity reliability and its advantages and disadvantages in the study of road connectivity reliability
本文通过改进蒙特卡洛法,将蒙特卡洛模拟法存在的 收敛速度慢、误差具有概率性等不足的地方进行部分优化 改进,提出一种改进的蒙特卡洛法,即改进蒙特卡洛法。 模拟计算表明,利用Sobol序列代替伪随机序列对路网的 连通可靠性进行计算,更加贴近实际数值,更加适合于精 度要求较高的大型道路网络分析。该方法在研究道路连通 可靠性上,较传统蒙特卡洛法提高了精确度和速度,是一 次较好的尝试。本文目前只涉及到道路可靠性的研究上, 并未涉及到其他路网连通可靠性的研究,将在后续的工作 中做更加深入的研究。
Summary
This paper firstly introduces the development of Monte-Carlo method in connectivity reliability and its advantages and disadvantages in the study of road connectivity reliability. 众所周知,生命线对于抗震救灾和重建家园非常重 要,而其中道路抗震可靠性又是重中之重,连通可靠性是 生命线网络如道路网络分析的关键环节,较好的处理道路 的连通可靠性对道路抗震可靠性计算具有重要意义。 随 着电子计算机以及计算方法的进步,人们对于道路抗震可 靠性的评估越来越精确。道路抗震可靠性考虑因素众多, 蒙特卡洛法作为一种能够轻松处理复杂情况的方法而应 用广泛。文献[1]采用蒙特卡洛法,先对城市交通路网的单 元进行可靠性分析,然后纵观全局进行分析,从而得到网 络连通概率。文献[2]对于节点进行了不同烈度下的分析, 采用蒙特卡络法算出了网络节点的可靠度。文献[3]系统阐 述了基于蒙特卡络方法的网络连通可靠性,为道路抗震可 靠性研究提供了一个基本理论依据。文献[4]在采用蒙特卡 洛模拟法对山区路网连通可靠度进行分析和计算中,通过 概率解析法来检验蒙特卡罗模拟法的计算精度,并在文献 [2]的基础上加入了边坡和隧道的因素。文献[5]在震后通 行可靠度出发,用蒙特卡洛法得到了最优化疏散路径。文 献[6]在文献[4]增加了震后各种道路上的各种因素,如道 路与沿街建筑的距离。文献[7]提出了解决路网问题的一种 可靠方法,首次提出路段概率重要度。文献[8]应用蒙特卡 洛法时,加上了道路单元、桥梁单元、边坡单元、隧道单 元的通行概率。文献[9]在采用蒙特卡络法分析路网抗震可 靠性时,增加了单体的易损性分析。但是随着研究的深入, 蒙特卡洛法的弊端也暴露出来,文献[10]提出了蒙特卡洛 模拟法也存在收敛速度慢、误差具有概率性等不足的地 方。针对传统蒙特卡洛法的弊端,本文从精确度和速度两 方面进行优化,提出一种改进的蒙特卡洛法,即改进蒙特 卡洛法。在研究道路连通可靠性上,此法较以往的蒙特卡 洛法提高了精确度和速度。 相关节点间的可靠性数,其中自身节点(i=j)连通可靠性 的数值设为1,不相关则为0; 2然后用计算机生成随机数矩阵:X=[i][j]; 3接着建立布尔矩阵并计算: B[i][j]=R[i][j]-X[i][j]; 如果B[i][j]>0,则B[i][j]=1; 如果B[i][j]≤0,则B[i][j]=0; 4道路的网络存在二元传递关系,可用Warshall算法 [11]的传递闭包(设W是一个二元关系,若W’是包含W的最 小的传递关系,则称 W’为W的传递闭包)进行计算,可以 得到道路网络的可达矩阵BL[i][j]; 5若BL[i][j]=1,则表示节点i与节点j能保持连通;若 BL[i][j]=0,则表示节点i与节点j不连通; 最后将步骤2~5重复N次,其中若有n次连通,则节 点间的连通可靠度为: Q≈n/N
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