An improved cut-based recursive decomposition algorithm for reliability analysis of networks

In this paper,an improved cut-based recursive decomposition algorithm is proposed for lifeline networks.First,a complementary structural function is established and three theorems are presented as a pr...     

网络可靠度分析的最小路算法和最小割算法研究

网络可靠度分析是评价城市生命线工程系统整体抗震性能的主要手段。本文分别从最小路和最小割的角度介绍了网络可靠度分析算法,包括:经典不交最小路(割)算法、最小路(割)递推分解算法和改进最小路(割)递推分解算法。在此基础上,通过实例分析,着重进行了改进最小路递推分解算法和改进最小割递推分解算法的对比分析,分析结果表明两种算法在网络单元不同可靠度水平下具有不同的计算效率,并对引起以上区别的三个主要原因进行了分析。     

Seismic reliability assessment of lifeline networks using clustering‐based multi‐scale approach

Seismic reliability assessment of lifeline networks gives rise to various technical challenges, which are mostly caused by a large number of network components, complex network topology, and statistical dependence between component failures. For effective risk assessment and probabilistic inference based on post‐hazard observations, various non‐simulation‐based algorithms have been developed, including the selective recursive decomposition algorithm (S‐RDA). To facilitate the application of such an algorithm to large networks, a new multi‐scale approach is developed in this paper. Using spectral clustering algorithms, a network is first divided into an adequate number of clusters such that the number of inter‐cluster links is minimized while the number of the nodes in each cluster remains reasonably large. The connectivity around the identified clusters is represented by super‐links. The reduced size of the simplified network enables the S‐RDA algorithm to perform the network risk assessment efficiently. When the simplified network is still large even after a clustering, additional levels of clustering can be introduced to have a hierarchical modeling structure. The efficiency and effectiveness of the proposed multi‐scale approach are demonstrated successfully by numerical examples of a hypothetical network, a gas transmission pipeline network, and a water transmission network. Copyright © 2014 John Wiley & Sons, Ltd.     

生命线网络可靠度分析的改进最小路递推分解算法

在生命线网络最小路递推分解算法的基础上,充分利用分解过程中的信息,采用合并节点的方法,快速降低分解出来子网的复杂程度,从而达到大幅度减少分解出来的不交最小路(割)数量和提高计算效率的目的.计算实例分析表明,与最小路递推分解算法相比,改进算法能更为高效地给出网络可靠度,是一种有效的生命线工程网络抗震可靠性分析工具.     

An improved recursive decomposition algorithm for reliability evaluation of lifeline networks

The seismic reliability evaluation of lifeline networks has received considerable attention and been widely studied.In this paper,on the basis of an original recursive decomposition algorithm,an improved analytical approach to evaluate the seismic reliability of large lifeline systems is presented.The proposed algorithm takes the shortest path from the source to the sink of a network as decomposition policy.Using the Boolean laws of set operation and the probabilistic operation principal,a recursive deco...     

A disjoint algorithm for seismic reliability analysis of lifeline networks

The algorithm is based on constructing a disjoin kg t set of the minimal paths in a network system. In this paper, cubic notation was used to describe the logic function of a network in a well-balanced state, and then the sharp-product operation was used to construct the disjoint minimal path set of the network. A computer program has been developed, and when combined with decomposition technology, the reliability of a general lifeline network can be effectively and automatically calculated. Supported by: Key Project of Science and Technology from the State Plan Committee, No. 101-9914003     

Minimal cut-based recursive decomposition algorithm for seismic reliability evaluation of lifeline networks

In this paper, a new probabilistic analytical approach, the minimal cut-based recursive decomposition algorithm (MCRDA), is presented to evaluate the seismic reliability of large-scale lifeline systems. Based on the minimal cut searching algorithm, the approach calculates the disjoint minimal cuts one by one using the basic procedure of the recursive decomposition method. At the same time, the process obtains the disjoint minimal paths of the system. In order to improve the computation efficiency, probabilistic inequality is used to calculate a solution that satisfies the prescribed error bound. A series of case studies show that MCRDA converges rapidly when the edges of the systems have low reliabilities. Therefore, the approach can be used to evaluate large-scale lifeline systems subjected to strong seismic wave excitation.     

Multi‐scale system reliability analysis of lifeline networks under earthquake hazards

Recent earthquake events evidenced that damage of structural components in a lifeline network may cause prolonged disruption of lifeline services, which eventually results in significant socio‐economic losses in the affected area. Despite recent advances in network reliability analysis, the complexity of the problem and various uncertainties still make it a challenging task to evaluate the post‐hazard performance and connectivity of lifeline networks efficiently and accurately. In order to overcome such challenges and take advantage of merits of multi‐scale analysis, this paper develops a multi‐scale system reliability analysis method by integrating a network decomposition approach with the matrix‐based system reliability (MSR) method. In addition to facilitating system reliability analysis of large‐size networks, the multi‐scale approach enables optimizing the level of computational effort on subsystems; identifying the relative importance of components and subsystems at multiple scales; and providing a collaborative risk management framework. The MSR method is uniformly applied for system reliability analyses at both the lower‐scale (for link failure) and the higher‐scale (for system connectivity) to obtain the probability of general system events, various conditional probabilities, component importance measures, statistical correlation between subsystem failures and parameter sensitivities. The proposed multi‐scale analysis method is demonstrated by its application to a gas distribution network in Shelby County of Tennessee. A parametric study is performed to determine the number of segments during the lower‐scale MSR analysis of each pipeline based on the strength of the spatial correlation of seismic intensity. It is shown that the spatial correlation should be considered at both scales for accurate reliability evaluation. The proposed multi‐scale analysis approach provides an effective framework of risk assessment and decision support for lifeline networks under earthquake hazards. Copyright © 2009 John Wiley & Sons, Ltd.     

A recursive decomposition algorithm for network seismic reliability evaluation

A new probabilistic analytical approach to evaluate seismic system reliability of large lifeline systems is presented in this paper. The algorithm takes the shortest path from the source to the terminal of a node weight or edge weight network as decomposition policy, using the Boolean laws of set operation and probabilistic operation principal, a recursive decomposition process then could be constructed. For a general weight network, the modified Torrieri method (NTR/T method) is introduced to combine with the suggested algorithm. Therefore, the recursive decomposition algorithm may be applied to evaluate the seismic reliability of general lifeline systems. A series of case studies, including a practical district electric power network system and a large urban water supply system, show that the suggested algorithm supplies a useful probabilistic analysis means for the seismic reliability evaluation of large lifeline systems. Copyright © 2002 John Wiley & Sons, Ltd.     

基于改进的风险矩阵法的生命线网络地震脆弱性分析

生命线网络的脆弱性不单单只表示地震发生后对网络作用而产生的后果,还应该包括网络的连通情况。本文在重新确定生命线网络脆弱性定义的基础上,运用风险评估理论中的风险矩阵方法综合考虑生命线网络的连通性能和失效后果两个方面来评价生命线网络的脆弱性,并以一个供气管网为例说明改进的风险矩阵法评价生命线网络脆弱性的有效性和合理性,找出供气管网中脆弱性等级最高的节点,分析其脆弱性等级最高的原因,以便于重点保护,并降低网络的脆弱性。     

生命线工程网络抗震可靠性算法研究

现代城市的迅速发展对生命线工程系统依赖性逐渐增强。地震后生命线工程系统的性能直接决定了灾后生活和生产的恢复以及抢险工作的进行,因此对生命线工程系统进行地震作用下的可靠性分析具有十分重要的意义。本文中主要介绍2种求解大型网络抗震可靠度算法———最小路递推分解算法和最小割递推分解算法。在此基础上,利用这2种算法对沈阳市供气系统进行了分析。研究结果表明,合理选择使用这2种算法可以有效的进行不同地震烈度条件下的大型生命线工程系统的可靠性分析。     

Efficient sampling and data reduction techniques for probabilistic seismic lifeline risk assessment

Probabilistic seismic risk assessment for spatially distributed lifelines is less straightforward than for individual structures. While procedures such as the ‘PEER framework’ have been developed for risk assessment of individual structures, these are not easily applicable to distributed lifeline systems, due to difficulties in describing ground‐motion intensity (e.g. spectral acceleration) over a region (in contrast to ground‐motion intensity at a single site, which is easily quantified using Probabilistic Seismic Hazard Analysis), and since the link between the ground‐motion intensities and lifeline performance is usually not available in closed form. As a result, Monte Carlo simulation (MCS) and its variants are well suited for characterizing ground motions and computing resulting losses to lifelines. This paper proposes a simulation‐based framework for developing a small but stochastically representative catalog of earthquake ground‐motion intensity maps that can be used for lifeline risk assessment. In this framework, Importance Sampling is used to preferentially sample ‘important’ ground‐motion intensity maps, and K‐Means Clustering is used to identify and combine redundant maps in order to obtain a small catalog. The effects of sampling and clustering are accounted for through a weighting on each remaining map, so that the resulting catalog is still a probabilistically correct representation. The feasibility of the proposed simulation framework is illustrated by using it to assess the seismic risk of a simplified model of the San Francisco Bay Area transportation network. A catalog of just 150 intensity maps is generated to represent hazard at 1038 sites from 10 regional fault segments causing earthquakes with magnitudes between five and eight. The risk estimates obtained using these maps are consistent with those obtained using conventional MCS utilizing many orders of magnitudes more ground‐motion intensity maps. Therefore, the proposed technique can be used to drastically reduce the computational expense of a simulation‐based risk assessment, without compromising the accuracy of the risk estimates. This will facilitate computationally intensive risk analysis of systems such as transportation networks. Finally, the study shows that the uncertainties in the ground‐motion intensities and the spatial correlations between ground‐motion intensities at various sites must be modeled in order to obtain unbiased estimates of lifeline risk. Copyright © 2010 John Wiley & Sons, Ltd.     

Genetic algorithm for seismic topology optimization of lifeline network systems

Lifeline systems, such as water distribution and gas supply networks, usually cover large areas. For these systems, seismic design is always a difficult problem because of the complexity of large‐scale networks. In this paper, a topology optimization technology for lifeline networks is established. Firstly, in order to speed up the convergence of optimization process, an element investment importance analysis is carried out to evaluate the importance of components to the lifeline network. Then a topology optimization model is established. The aim of the model is to find the least‐cost network topology while the seismic reliability between the sources and each terminal satisfies prescribed reliability constraints. For this optimization problem, a genetic algorithm, which takes network topologies as the individuals of its population, is used to search for the optimal solutions by suitable operators, including selection, crossover and mutation operators. The capacity of the proposed algorithm is illustrated by its applications to a simple example network consisting of 10 nodes and an actual network with 391 nodes located in a large city of China. Copyright © 2008 John Wiley & Sons, Ltd.     

网络可靠度分析的最小割递推分解算法

基于不交最小割求解系统失效概率的思想,提出了求解网络系统失效概率的最小割递推分解算法。在此基础上,利用概率不等式给出了失效概率的上、下界,从而可以通过控制上、下界之间的误差来获得计算精度和计算时间之间的平衡。计算实例分析表明,该算法能计算给出中、小型网络失效概率的精确值,并能够高效、高精度地求解出大型复杂网络系统的失效概率。     

单一震源下生命线系统失效概率分析的新方法(一)--系统可靠路径与失效路径的识别

本文第一部分提出一类识别生命线系统可靠路径与失效路径的新方法，该方法从系统发生概率最大的可靠路径出发，采用递推分解的思路，识别出系统的互斥可靠路径和互斥失效路径，并给出系统失效概率的表达式和失效概率上下界表达式。实例分析表明，该识别方法的计算复杂性较小并具有较高的运算效率。     

迭代优化的网络最短路径射线追踪方法研究

网络最短路径射线追踪算法,用预先设置的网格节点的连线表示地震波传播路径,当网格节点稀疏时,获得的射线路径呈Z字形,计算的走时比实际走时偏差大.本文在网络最短路径射线追踪算法的基础上,提出了迭代法与网络最短路径相结合的射线追踪算法,运用迭代法优化计算由网络最短路径算法得到的射线路径,并对迭代法进行修正,从而克服了最短路径射线追踪算法的缺陷,大大提高了最小走时和射线路径的计算精度.     

供电网络系统的可靠性分析

研究了生命线工程系统中供电网络系统的可靠性分析方法。在元件可靠性分析的基础上,进行供电网络系统工程地震可靠性分析,提出了供电网络系统功能失效分级及失效等级的判定方法,并建立了功能失效系数的概念,给出了供电网络系统功能失效系数的计算方法,从而实现了供电网络系统功能失效分析的定量化。     

Decomposition algorithms for system reliability estimation with applications to interdependent lifeline networks

Reliability and risk assessment of lifeline systems call for efficient methods that integrate hazard and interdependencies. Such methods are computationally challenged when the probabilistic response of systems is tied to multiple events, as performance quantification requires a large catalog of ground motions. Available methods to address this issue use catalog reductions and importance sampling. However, besides comparisons against baseline Monte Carlo trials in select cases, there is no guarantee that such methods will perform or scale well in practice. This paper proposes a new efficient method for reliability assessment of interdependent lifeline systems, termed RAILS, that considers systemic performance and is particularly effective when dealing with large catalogs of events. RAILS uses the state‐space partition method to estimate systemic reliability with theoretical bounds and, for the first time, supports cyclic interdependencies among lifeline systems. Recycling computations across an entire seismic catalog with RAILS considerably reduces the number of system performance evaluations in seismic performance studies. Also, when performance estimate bounds are not tight, we adopt an importance and stratified sampling method that in our computational experiments is various orders of magnitude more efficient than crude Monte Carlo. We assess the efficiency of RAILS using synthetic networks and illustrate its application to quantify the seismic risk of realistic yet streamlined systems hypothetically located in the San Francisco Bay Region.     

基于模拟退火算法的供水管网抗震优化设计

本文以管网造价为优化目标,管网拓扑结构为优化参数,管网节点最低可靠度为约束条件,建立了供水管网抗震拓扑优化模型。在供水管网功能可靠性分析方法的基础上,结合单元概率重要度分析方法,利用模拟退火算法提出了供水管网的抗震拓扑优化方法,并对一典型供水管网进行了拓扑优化分析。分析表明,对于管网抗震拓扑优化这样一个组合优化问题,模拟退火算法提供了一类很好的途径,以此为基础进行供水管网抗震可靠性优化设计具有很好的效果。     

大型城市管网抗震可靠性分析与优化

本文提出了地震作用下供水系统的渗漏模型,发展了地震后带渗漏管网的流分析技术,结合一次二阶矩方法获得了地震后供水管网的功能可靠度。针对供燃气管网系统则提出了一类高效精确的大型网络抗震连通可靠度分析的概率解析算法———递推分解算法。以上述管网抗震可靠性分析理论为基础,分别发展了基于模拟退火算法的供水系统网络拓扑优化分析理论和基于遗传算法的供燃气网络系统拓扑优化理论。