Assessment of reliability in water distribution networks using entropy based measures

Entropy based expressions for measurement of reliability and redundancy have recently been reported. These measures approach assessment of the reliability of the distribution network from the intrinsic redundancy of the network layout. The paper extends earlier work on entropy functions by including a more explicit statement of the alternate paths available in the network and by recognizing that under certain circumstances, e.g., failure of some part of the network work, an outflow link from a node under normal working condition may become an inflow link to the same node. The measures are assessed by comparison with parameters measuring Nodal Pair Reliability and percentage of flow supplied at adequate pressure for a range of networks and link failure conditions in this networks. The entropy measures are shown to reflect changes in the network reliability, as measured by these two comparative parameters, very well.     

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.     

Efficient risk assessment of lifeline networks under spatially correlated ground motions using selective recursive decomposition algorithm

For effective hazard mitigation planning and prompt-but-prudent post-disaster responses, it is essential to evaluate the reliability of infrastructure networks accurately and efficiently. A nonsimulation-based algorithm, termed as a recursive decomposition algorithm (RDA), was recently proposed to identify disjoint cut sets and link sets and to compute the network reliability. This paper introduces a ‘selective’ RDA, which preferentially identifies critical disjoint cut sets and link sets to calculate the probabilities of network disconnection events with a significantly reduced number of identified sets. To this end, the original RDA is improved by replacing the shortest path algorithm with an algorithm that identifies the most reliable path, and by using a graph decomposition scheme based on the probabilities associated with the subgraphs. The critical sets identified by the algorithm are also used to compute conditional probability-based importance measures that quantify the relative importance of network components by their contributions to network disconnection events. This paper also introduces a risk assessment framework for lifeline networks based on the use of the selective RDA, which can consider both interevent and intraevent uncertainties of spatially correlated ground motions. The risk assessment framework and the selective RDA are demonstrated by a hypothetical network example, and the gas and water transmission networks of Shelby County in Tennessee, USA. The examples show that the proposed framework and the selective RDA greatly improve efficiency of risk assessment of complex lifeline networks, which are characterized by a large number of components, complex network topology, and statistical dependence between component failures. Copyright © 2012 John Wiley & Sons, Ltd.     

Analytical approximation for stationary reliability of certain and uncertain linear dynamic systems with higher‐dimensional output

An analytical approximation for the calculation of the stationary reliability of linear dynamic systems with higher‐dimensional output under Gaussian excitation is presented. For systems with certain parameters theoretical and computational issues are discussed for two topics: (1) the correlation of failure events at different parts of the failure boundary and (2) the approximation of the conditional out‐crossing rate across the failure boundary by the unconditional one. The correlation in the first topic is approximated by a multivariate integral, which is evaluated numerically by an efficient algorithm. For the second topic some existing semi‐empirical approximations are discussed and a new one is introduced. The extension to systems with uncertain parameters requires the calculation of a multi‐dimensional reliability integral over the space of the uncertain parameters. An existing asymptotic approximation is used for this task and an efficient scheme for numerical calculation of the first‐ and second‐order derivatives of the integrand is presented. Stochastic simulation using an importance sampling approach is also considered as an alternative method, especially for cases where the dimension of the uncertain parameters is moderately large. Comparisons between the proposed approximations and Monte Carlo simulation for some examples related to earthquake excitation are made. It is suggested that the proposed analytical approximations are appropriate for problems that require a large number of consistent error estimates of the probability of failure, as occurs in reliability‐based design optimization. Numerical problems regarding computational efficiency may arise when the dimension of both the output and the uncertain parameters is large. Copyright © 2006 John Wiley & Sons, Ltd.     

基于DEA分析的生命线网络节点抗灾相对可靠度评估

对于生命线工程网络系统而言,合理分析和评估其带有网络特征的节点可靠度,比只研究单体可靠度更具实际意义。基于数据包络分析法（Data Envelopment Analysis,DEA）有效性分析的思想,提出了生命线网络节点抗灾相对可靠度的概念。从生命线工程在灾害环境下着重体现出的系统性和网络性出发,考察网络中的节点所能实现的资源供给功能与其所在网络中的空间结构重要性是否匹配,即功能性相对于结构性的可靠度。选择节点资源实际需求量和管内水压作为DEA有效性分析的输入参数,结构重要性作为输出参数,并用网络中介中心性评价结构重要性,获得相应参数。通过实例分析,得出实例工程网络中各节点相应的DEA有效性分析结果,即相对可靠度,并通过对参数的权系数调整,得到了使非有效单元变为有效单元的调整值。该调整值可供优化及改进工程网络的技术性调整方案参考,相对可靠度也可作为评价工程网络系统性能的有益补充。     

基于微粒群算法的供水管网抗震优化设计

以管网年费用折算值为优化目标、管网拓扑结构与管径为优化参数、管网节点最低可靠度为约束条件,建立了供水管网抗震优化设计模型。利用微粒群算法对这一模型进行了求解,该算法以管网作为微粒个体,通过不断地更新微粒的位置来搜索最优的管网结构,直到最后给出优化的管网结构。利用上述方法对一典型供水管网进行了抗震优化设计分析,给出了3种不同节点最低可靠度约束条件下的优化改造方案。     

运用地震活动时间扫描分析方法的综合预测信度预测地震时间的研究

认为地震活动度5、P(b)值、A(b)值、b值、小震调制比Rm、地震时间熵Q^l、算法复杂性AC、地震非均匀度GL、多分维均值Dq、地震集中度C值、地震演化指数YH、地震强度熵Q^E、G-R关系偏离度η、缺震和等效震级M^*等15种地震活动时间扫描分析方法对东南沿海地震带西段4．8级以上地震的发震时间具有一定的预测能力,并将这些方法在震前所显示的异常同步性引伸为地震时间预测信度同步性,初步确定了各种地震活动参数首次出现异常后4．8级以上地震发生在不同时段上的信度,证实了震前预测地震时间信度的同步性要远好于异常同步性,进而计算出这15种分析方法的综合预测信度。研究发现,运用综合预测信度可以较为明确地预测出M≥4．8级地震的发生时段,如果在所预测时段内同步发生了地震活动度．S、P(b)、A(b)和b值异常(并非都要全部发生),则有可能做出6个月内发震的短期预报。     

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。     

Reliability upgrading of lifeline networks for post-earthquake serviceability

Efficient procedures for reliability upgrading of existing lifeline networks for post-earthquake serviceability are presented. A simple method is developed to determine critical components of the network whose strengthening improves the network reliability for specified serviceability criteria. Measures of effectiveness of strengthening each component are also introduced. Based on critical components and measures of effectiveness, step-by-step upgrading procedures are proposed. Both connectivity and minimum-flow serviceability criteria may be specified. Two upgrading objectives considered are achieving a specified target reliability and reducing the total costs of upgrading plus expected losses due to failure of the lifeline. A hypothetical application to a water-distribution system in the San Francisco Bay Area illustrates the proposed method.     

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 urban water networks

We present a framework for the seismic risk assessment of water supply networks, operating in either normal or abnormal conditions. We propose a methodology for assessing the reliability of water pipe networks combining data of past non‐seismic damage and the vulnerability of the network components against seismic loading. Historical data are obtained using records of damages that occur on a daily basis throughout the network and are processed to produce‘survival curves’, depicting their estimated survival rate over time. The fragility of the network components is assessed using the approach suggested in the American Lifelines Alliance guidelines. The network reliability is assessed using graph theory, whereas the system network reliability is calculated using Monte Carlo simulation. The methodology proposed is demonstrated both on a simple, small‐scale, network and also on a real‐scale district metered area from the water network of the city of Limassol, Cyprus. The proposed approach allows the estimation of the probability that the network fails to provide the desired level of service and allows the prioritization of retrofit interventions and of capacity‐upgrade actions pertaining to existing water pipe networks. Copyright © 2013 John Wiley & Sons, Ltd.     

钢框架结构的非线性静力抗震可靠性分析 II:可靠度指标及其灵敏度

将有限元反应及其灵敏度分析与结构可靠度分析的近似解析方法结合起来,可以进行具有隐式功能函数的大型复杂结构的可靠性分析。在基于位移的非线性纤维梁柱单元及其灵敏度直接微分表达式的基础上,通过力学变换、概率变换和反应灵敏度,将结构可靠度计算方法FORM和SORM与有限元方法有机地集成在一起。依据现行抗震设计规范,建立了钢框架结构典型构件承载能力和结构层间变形能力的抗震极限状态方程,利用地震作用的等效随机静力模型,采用非线性有限元静力可靠度方法,对一实际工程结构的抗震可靠度及其灵敏度进行了概率分析和评价,结果表明:尽管在大震作用下该结构的层间弹塑性变形可靠度较高,但是构件极限承载能力的可靠度指标较低,仍然存在失效的可能性。因此,仅验算"小震"作用下结构的承载能力可靠度和"大震"作用下结构的变形能力可靠度是不够的,还需要验算在"中震"和"大震"作用下结构的极限承载能力可靠度。     

生命线网络可靠性分析的类分法

本文应用点集拓扑分类原理，提出一个计算大型复杂网络可靠度上界的类分法，该算法简单实用，并可利用对偶理论求得网络可靠度下界，通过郑州、许昌等城市给水管网的工程实践，验证了算法的有效性。     

钢框架结构的非线性静力抗震可靠性分析Ⅱ:可靠度指标及其灵敏度

将有限元反应及其灵敏度分析与结构可靠度分析的近似解析方法结合起来,可以进行具有隐式功能函数的大型复杂结构的可靠性分析。在基于位移的非线性纤维梁柱单元及其灵敏度直接微分表达式的基础上,通过力学变换、概率变换和反应灵敏度,将结构可靠度计算方法FORM和SORM与有限元方法有机地集成在一起。依据现行抗震设计规范,建立了钢框架结构典型构件承载能力和结构层间变形能力的抗震极限状态方程,利用地震作用的等效随机静力模型,采用非线性有限元静力可靠度方法,对一实际工程结构的抗震可靠度及其灵敏度进行了概率分析和评价,结果表明：尽管在大震作用下该结构的层间弹塑性变形可靠度较高,但是构件极限承载能力的可靠度指标较低,仍然存在失效的可能性。因此,仅验算“小震”作用下结构的承载能力可靠度和“大震”作用下结构的变形能力可靠度是不够的,还需要验算在“中震”和“大震”作用下结构的极限承载能力可靠度。     

大震下被动与智能隔震结构动力可靠度的对比

对被动及智能隔震结构在“大震”条件下的动力可靠度进行探讨。将被动及智能隔震体系均取作弹塑性模型,并用退化Bouc-W en滞变模型描述上部结构的恢复力,用非退化Bouc-W en模型描述隔震层的恢复力。采用虚拟激励法计算结构的随机响应,根据我国抗震规范中“大震不倒”的设防目标,采用各层最大层间位移峰值响应和累积滞变耗能构造双参数的随机疲劳累积损伤指数,作为功能状态指标。假定各层失效相关,用串联系统计算体系动力可靠度。通过数值算例,对比了被动隔震、智能隔震与非隔震体系的条件失效概率,从动力可靠度角度显示了智能隔震体系的减震优势。     

Cost-effective network design for groundwater flow monitoring

The extensive use of groundwater resources has increased the need for developing cost-effective monitoring networks to provide an indication of the degree to which the subsurface environment has been affected by human activities. This study presents a cost-effective approach to the design of groundwater flow monitoring networks. The groundwater network design is formulated with two problem formats: maximizing the statistical monitoring power for specified budget constraint and minimizing monitoring cost for statistical power requirement. The statistical monitoring power constraint is introduced with an information reliability threshold value. A branch and bound technique is employed to select the optimal solution from a discrete set of possible network alternatives. The method is tested to the design of groundwater flow monitoring problem in the Pomona County, California.     

Seismic reliability analysis of urban water distribution network

An approach to analyze the seismic reliability of water distribution networks by combining a hydraulic analysis with a first-order reliability method （FORM）, is proposed in this paper. The hydraulic analysis method for normal conditions is modified to accommodate the special conditions necessary to perform a seismic hydraulic analysis. In order to calculate the leakage area and leaking flow of the pipelines in the hydraulic analysis method, a new leakage model established from the seismic response analysis of buried pipelines is presented. To validate the proposed approach, a network with 17 nodes and 24 pipelines is investigated in detail. The approach is also applied to an actual project consisting of 463 nodes and 767 pipelines. The results show that the proposed approach achieves satisfactory results in analyzing the seismic reliability of large-scale water distribution networks.     

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...     

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。     

基于响应面法的连续刚构地震可靠度分析

地震可靠度是桥梁抗震研究中的重要问题。基于随机分析的响应面理论和规范反应谱法,提出了一种分析具有随机结构参数的桥梁地震可靠度的方法,研究了结构的破坏准则及其极限状态方程,计算了高墩大跨连续刚构桥在地震激励下设计基准期内的动力可靠度。分析时考虑了结构参数和场地土的随机性,分别计算了连续刚构在多遇地震、设防地震和罕遇地震作用下的失效概率,得到了结构在设计基准期内,"三水准设防标准"条件下的地震可靠度。结果表明,该桥设计满足抗震规范要求。