The document discusses a methodology for evaluating the mechanical reliability of water distribution networks using a minimum cut set approach. The methodology involves computing the reliability at the component, segment, and network levels. Component reliability is based on failure rates calculated using regression models. Segment reliability is determined as the weighted sum of component reliabilities. Network reliability is evaluated using minimum cut sets, which are sets of network components whose simultaneous failure would cause network failure. The methodology is demonstrated through an example.
THEORETICAL STUDY ON PIPE OF TAPERED THICKNESS WITH AN INTERNAL FLOW TO ESTIM...IAEME Publication
This research study the effect of tapered thickness on the free transverse vibration of clamped – free pipe which have uniform circular cross section conveying water by using Raighly –Ritz method in the two case, the first involves the pipe have a constant wall thickness (t1) at clamped end equal to (1mm & 2mm) while the thickness (t2) at free end changes according to the ratio (t2/t1=0.2, 0.4, 0.6, 0.8, 1). In the second case the thickness at free end (t2) is constant (1mm & 2mm) whereas the thickness at clamped end (t1) changes at ratio (t1/t2=0.2, 0.4, 0.6, 0.8, 1). The pipe has a constant inner radius (Ri) of (1 cm or 2 cm) and different values of length (1m & 2m).
Analysis of Transformer Loadings and Failure Rate in Onitsha Electricity Dist...Dr. Hachimenum Amadi
This study analyzed transformer loadings and failure rates in the Onitsha electricity distribution network in Nigeria from 2011-2015. Electrical data from the network was simulated using ETAP software to determine transformer loadings, while questionnaires assessed failure rates. The findings showed an average transformer failure rate of 11.7% during the study period, higher than rates in developed countries. Major causes of failure included insulation issues (24.2%), overloading (22.5%), and inadequate maintenance (16.4%). The Army Barracks substation had the highest failure rate of 23.8%. The study recommends installing more transformers, using high quality transformers, balancing loads, and improving maintenance to increase reliability.
1. The document discusses representative hydraulic conductivities in saturated groundwater flow. It aims to synthesize and critically appraise results related to finding representative parameters that control average aquifer behavior at a given scale.
2. There are three related concepts defined - effective conductivity relates ensemble averages of flux and gradient, equivalent conductivity relates spatial averages within a volume, and interpreted conductivity is derived from field data interpretation.
3. Hydraulic conductivity is highly variable and heterogeneous, spanning over 12 orders of magnitude. Accounting for this heterogeneity is important for hydrologic analysis and flow modeling. The paper reviews works seeking representative parameters that can substitute heterogeneous distributions in groundwater flow equations.
This document summarizes a technical presentation on analyzing the effects of three variables - electrolyte (vanadium) flow rate, flow channel thickness, and current density - on the capital cost of a regenerative hydrogen-vanadium flow battery. It was found that flow rate and channel thickness had a small impact on cost and efficiency, while current density had the greatest effect. The optimal current density depends on the desired battery power capacity. A flow rate of at least 20 times the minimum, a channel thickness around 1-2cm, and a current density of 200-300mA/cm^2 for a 4-6MW battery were determined to be favorable design parameters based on the analysis.
This document describes a thesis analyzing natural convection in a vertical microchannel using computational fluid dynamics (CFD). The thesis examines:
1) Fully developed flow conditions in a vertical parallel-plate microchannel with asymmetric wall temperatures, considering both velocity slip and temperature jump at the walls.
2) A more general approach to analyze entrance region conditions, without assumptions of fully developed flow.
3) Governing equations of continuity, momentum and energy to model the natural convection problem using the boundary layer approximations.
IRJET- Study of Fluid Induced Vibrations using Simulation Means and their Eff...IRJET Journal
This document summarizes research on fluid-induced vibrations in pipes during internal flows. It discusses how turbulent and unsteady flows containing mixtures of water and soil can induce vibrations in dredging pipes and cause abrasion at bends and branches. Computational fluid dynamics (CFD) techniques are used to numerically analyze typical pipe lines and supporter designs under different flow conditions. The research also examines how pressure pulsations from flows can excite pipe vibrations at resonant frequencies, and studies fluid-structure interaction (FSI) phenomena between internal flows and vibrating pipes.
The document presents an integrated reliability assessment model for water distribution networks. It discusses developing a model that can identify crucial water mains and prioritize their renewal based on both mechanical and hydraulic reliability. The methodology includes collecting failure rate data, analyzing component and segment reliability, identifying minimum cut sets that could cause network failure, and using hydraulic modeling software to simulate normal and failure conditions. The overall goal is to semi-automate an integrated reliability assessment model that considers both mechanical and hydraulic aspects.
Implication of fractal dimension on properties of rivers and river basinsIAEME Publication
1) The document analyzes the fractal dimensions and scaling properties of river networks and catchment areas in Kerala, India.
2) It estimates the fractal dimensions of 17 individual river streams in Kerala based on their lengths measured from maps of different scales.
3) It also determines the scaling exponents of 3 river basins in Kerala by analyzing the relationship between catchment area and total network length from maps of different scales.
4) Additionally, it studies the effect of scaling on drainage networks within sub-watersheds of the Chaliyar river basin by analyzing relationships between sub-basin area, total network length, and main stream length.
THEORETICAL STUDY ON PIPE OF TAPERED THICKNESS WITH AN INTERNAL FLOW TO ESTIM...IAEME Publication
This research study the effect of tapered thickness on the free transverse vibration of clamped – free pipe which have uniform circular cross section conveying water by using Raighly –Ritz method in the two case, the first involves the pipe have a constant wall thickness (t1) at clamped end equal to (1mm & 2mm) while the thickness (t2) at free end changes according to the ratio (t2/t1=0.2, 0.4, 0.6, 0.8, 1). In the second case the thickness at free end (t2) is constant (1mm & 2mm) whereas the thickness at clamped end (t1) changes at ratio (t1/t2=0.2, 0.4, 0.6, 0.8, 1). The pipe has a constant inner radius (Ri) of (1 cm or 2 cm) and different values of length (1m & 2m).
Analysis of Transformer Loadings and Failure Rate in Onitsha Electricity Dist...Dr. Hachimenum Amadi
This study analyzed transformer loadings and failure rates in the Onitsha electricity distribution network in Nigeria from 2011-2015. Electrical data from the network was simulated using ETAP software to determine transformer loadings, while questionnaires assessed failure rates. The findings showed an average transformer failure rate of 11.7% during the study period, higher than rates in developed countries. Major causes of failure included insulation issues (24.2%), overloading (22.5%), and inadequate maintenance (16.4%). The Army Barracks substation had the highest failure rate of 23.8%. The study recommends installing more transformers, using high quality transformers, balancing loads, and improving maintenance to increase reliability.
1. The document discusses representative hydraulic conductivities in saturated groundwater flow. It aims to synthesize and critically appraise results related to finding representative parameters that control average aquifer behavior at a given scale.
2. There are three related concepts defined - effective conductivity relates ensemble averages of flux and gradient, equivalent conductivity relates spatial averages within a volume, and interpreted conductivity is derived from field data interpretation.
3. Hydraulic conductivity is highly variable and heterogeneous, spanning over 12 orders of magnitude. Accounting for this heterogeneity is important for hydrologic analysis and flow modeling. The paper reviews works seeking representative parameters that can substitute heterogeneous distributions in groundwater flow equations.
This document summarizes a technical presentation on analyzing the effects of three variables - electrolyte (vanadium) flow rate, flow channel thickness, and current density - on the capital cost of a regenerative hydrogen-vanadium flow battery. It was found that flow rate and channel thickness had a small impact on cost and efficiency, while current density had the greatest effect. The optimal current density depends on the desired battery power capacity. A flow rate of at least 20 times the minimum, a channel thickness around 1-2cm, and a current density of 200-300mA/cm^2 for a 4-6MW battery were determined to be favorable design parameters based on the analysis.
This document describes a thesis analyzing natural convection in a vertical microchannel using computational fluid dynamics (CFD). The thesis examines:
1) Fully developed flow conditions in a vertical parallel-plate microchannel with asymmetric wall temperatures, considering both velocity slip and temperature jump at the walls.
2) A more general approach to analyze entrance region conditions, without assumptions of fully developed flow.
3) Governing equations of continuity, momentum and energy to model the natural convection problem using the boundary layer approximations.
IRJET- Study of Fluid Induced Vibrations using Simulation Means and their Eff...IRJET Journal
This document summarizes research on fluid-induced vibrations in pipes during internal flows. It discusses how turbulent and unsteady flows containing mixtures of water and soil can induce vibrations in dredging pipes and cause abrasion at bends and branches. Computational fluid dynamics (CFD) techniques are used to numerically analyze typical pipe lines and supporter designs under different flow conditions. The research also examines how pressure pulsations from flows can excite pipe vibrations at resonant frequencies, and studies fluid-structure interaction (FSI) phenomena between internal flows and vibrating pipes.
The document presents an integrated reliability assessment model for water distribution networks. It discusses developing a model that can identify crucial water mains and prioritize their renewal based on both mechanical and hydraulic reliability. The methodology includes collecting failure rate data, analyzing component and segment reliability, identifying minimum cut sets that could cause network failure, and using hydraulic modeling software to simulate normal and failure conditions. The overall goal is to semi-automate an integrated reliability assessment model that considers both mechanical and hydraulic aspects.
Implication of fractal dimension on properties of rivers and river basinsIAEME Publication
1) The document analyzes the fractal dimensions and scaling properties of river networks and catchment areas in Kerala, India.
2) It estimates the fractal dimensions of 17 individual river streams in Kerala based on their lengths measured from maps of different scales.
3) It also determines the scaling exponents of 3 river basins in Kerala by analyzing the relationship between catchment area and total network length from maps of different scales.
4) Additionally, it studies the effect of scaling on drainage networks within sub-watersheds of the Chaliyar river basin by analyzing relationships between sub-basin area, total network length, and main stream length.
The document discusses various conspiracy theories including theories about moon landings being faked, the assassination of JFK involving a magic bullet, and Stanley Kubrick filming fake moon landings. It also mentions MTV VJ Kennedy and someone named Lillian putting forth their own theories on undisclosed topics.
The home, the workforce, and having it allmandywheadon
The document summarizes themes from "The Feminine Mystique" and "Why Women Still Can't Have It All" regarding women's roles in the home, workforce, and balancing the two. After WWII, women were expected to find fulfillment through domesticity and family, but Betty Friedan's book revealed many housewives' unhappiness. Second-wave feminism emerged and more women worked, yet faced lower pay and opportunity than men. While some balance career and family, others feel women unfairly must choose between the two or feel guilty for working. The struggle to have both a successful career and family life remains an issue for women.
Como realizar una presentación por Alejandro Toledoaltocu
La presentación ofrece consejos sobre cómo realizar una presentación efectiva, incluyendo evitar faltas de ortografía, usar colores chillones, sobrecargar la información o mostrar datos personales o profesionales. Se recomienda enfocarse en la sencillez, atraer la atención de manera adecuada, preparar bien la exposición y tener una buena postura sin tics.
BrandSlip is an influencer marketing agency that specializes in campaigns targeting African American, Latino, and Asian communities. It works with influencers across various social media platforms like YouTube, Instagram, Snapchat, and Vine who have a combined reach of over 400 million people. The agency develops custom content for brands and measures campaign performance with analytics on key metrics like views, likes, comments, and follower growth.
За прошедший год мы разработали и произвели множество вариантов, как традиционной, так и оригинальной полиграфической продукции. Смотрим, вдохновляемся!
This document provides an introduction to bulletproof glass and bullet resistant barriers. It discusses the three main types of bulletproof glass, the eight levels of bullet resistance, common component types of bullet resistant barriers, and the benefits of working with Total Security Solutions, who has over 30 years of experience in designing, manufacturing, and installing these security systems.
This thesis develops an integrated reliability assessment model for prioritizing rehabilitation of water distribution networks. The model assesses mechanical and hydraulic reliability at component, segment and network levels. Mechanical reliability is assessed using reliability theory and minimum cut sets. Hydraulic reliability is assessed by simulating pressure conditions and comparing required and actual pressures. The model was tested on two cities and prioritized rehabilitation for sub-networks in London, Ontario. The results help prioritize rehabilitation works and identify critical main segments for monitoring.
Horizontal trajectory based mobile multi-sink routing in underwater sensor ne...IJECEIAES
Scientific, commercial, exploration, and monitoring applications of underwater sensor networks have drawn the attention of researchers toward the investigation of routing protocols that are robust, scalable, and energy efficient. This has brought significant research in network layer routing protocols. Irrespective of the field of application it is desirable to increase network lifetime by reducing energy consumed by sensor nodes in the network or by balancing energy in the entire network. Energy balancing refers to the uniform distribution of the network’s residual energy such that all nodes remain alive for a long time. It requires uniform energy consumption by each sensor node in the network instead of the same node being involved in every transmission. In this paper, we discuss two routing methods for three-dimensional environments in which the water region under monitor is divided into subregions of equal height and each subregion has a sink. Nodes in the subregion send data to the sink designated for that subregion. The first method called static multi-sink routing uses static sinks and the second method called horizontal trajectory-based mobile multi-sink routing (HT-MMR) uses mobile sinks with a horizontal trajectory. Simulation results show that the proposed HT-MMR reduces average energy consumption and average energy tax by 16.69% and 16.44% respectively. HT-MMR is energy efficient as it enhances network lifetime by 11.11%.
Reliability Indices Evaluation of a Real Time Rural Radial Distribution FeederIOSR Journals
This document summarizes a study that evaluates reliability indices for a real-time rural radial distribution feeder in India. The study calculates reliability before and after adding protective devices (isolators) to the feeder. It first inserts capacitors at weak voltage nodes to improve voltage profiles and reduce losses. Reliability indices are then determined for the existing feeder and after isolators are placed. Load diversity factor is used to analyze real-time load data. The methodology develops matrices to model relationships between bus currents, branch currents, and voltages to solve the load flow using a particle swarm optimization technique. Results are presented for an 11kV rural feeder case study in India.
The document discusses the development of an experimental setup for dynamic strain measurement. It describes different types of strain and methods for strain measurement, both static and dynamic. The aim is to study various static strain instruments, compare them to dynamic instruments, and develop structural models to measure strain under static and dynamic loads. Literature is reviewed on previous uses of strain gauges, accelerometers, and fiber optic sensors to monitor bridge responses and calculate modal parameters under traffic loading.
A laboratory based study of hydraulic simulation of leakage in water distribu...Alexander Decker
This document summarizes a laboratory study on hydraulic simulation of leakage in water distribution networks. The study used a small model network with pipes and instruments to measure pressure and flow at various points. Experiments were conducted with different initial water pressures, leakage volumes, and leakage locations. Pressure and flow data was collected and hydraulic modeling software was used to simulate the system and compare results. The goal was to validate an approach for detecting leakage location using pressure monitoring and hydraulic analysis.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Heuristic remedial actions in the reliability assessment of high voltage dire...IJECEIAES
Planning of high voltage direct current (HVDC) grids requires inclusion of reliability assessment of alternatives under study. This paper proposes a methodology to evaluate the adequacy of voltage source converter/VSCHVDC networks. The methodology analyses the performance of the system using N-1 and N-2 contingencies in order to detect weaknesses in the DC network and evaluates two types of remedial actions to keep the entire system under the acceptable operating limits . The remedial actions are applied when a violation of these limits on the DC system occurs; those include topology changes in the network and adjustments of power settings of VSC converter stations. The CIGRE B4 DC grid test system is used for evaluating the reliability/adequacy performance by means of the proposed methodology in this paper. The proposed remedial actions are effective for all contingencies; then, numerical results are as expected. This work is useful for planning and operation of grids based on VSC-HVDC technology.
The document discusses various conspiracy theories including theories about moon landings being faked, the assassination of JFK involving a magic bullet, and Stanley Kubrick filming fake moon landings. It also mentions MTV VJ Kennedy and someone named Lillian putting forth their own theories on undisclosed topics.
The home, the workforce, and having it allmandywheadon
The document summarizes themes from "The Feminine Mystique" and "Why Women Still Can't Have It All" regarding women's roles in the home, workforce, and balancing the two. After WWII, women were expected to find fulfillment through domesticity and family, but Betty Friedan's book revealed many housewives' unhappiness. Second-wave feminism emerged and more women worked, yet faced lower pay and opportunity than men. While some balance career and family, others feel women unfairly must choose between the two or feel guilty for working. The struggle to have both a successful career and family life remains an issue for women.
Como realizar una presentación por Alejandro Toledoaltocu
La presentación ofrece consejos sobre cómo realizar una presentación efectiva, incluyendo evitar faltas de ortografía, usar colores chillones, sobrecargar la información o mostrar datos personales o profesionales. Se recomienda enfocarse en la sencillez, atraer la atención de manera adecuada, preparar bien la exposición y tener una buena postura sin tics.
BrandSlip is an influencer marketing agency that specializes in campaigns targeting African American, Latino, and Asian communities. It works with influencers across various social media platforms like YouTube, Instagram, Snapchat, and Vine who have a combined reach of over 400 million people. The agency develops custom content for brands and measures campaign performance with analytics on key metrics like views, likes, comments, and follower growth.
За прошедший год мы разработали и произвели множество вариантов, как традиционной, так и оригинальной полиграфической продукции. Смотрим, вдохновляемся!
This document provides an introduction to bulletproof glass and bullet resistant barriers. It discusses the three main types of bulletproof glass, the eight levels of bullet resistance, common component types of bullet resistant barriers, and the benefits of working with Total Security Solutions, who has over 30 years of experience in designing, manufacturing, and installing these security systems.
This thesis develops an integrated reliability assessment model for prioritizing rehabilitation of water distribution networks. The model assesses mechanical and hydraulic reliability at component, segment and network levels. Mechanical reliability is assessed using reliability theory and minimum cut sets. Hydraulic reliability is assessed by simulating pressure conditions and comparing required and actual pressures. The model was tested on two cities and prioritized rehabilitation for sub-networks in London, Ontario. The results help prioritize rehabilitation works and identify critical main segments for monitoring.
Horizontal trajectory based mobile multi-sink routing in underwater sensor ne...IJECEIAES
Scientific, commercial, exploration, and monitoring applications of underwater sensor networks have drawn the attention of researchers toward the investigation of routing protocols that are robust, scalable, and energy efficient. This has brought significant research in network layer routing protocols. Irrespective of the field of application it is desirable to increase network lifetime by reducing energy consumed by sensor nodes in the network or by balancing energy in the entire network. Energy balancing refers to the uniform distribution of the network’s residual energy such that all nodes remain alive for a long time. It requires uniform energy consumption by each sensor node in the network instead of the same node being involved in every transmission. In this paper, we discuss two routing methods for three-dimensional environments in which the water region under monitor is divided into subregions of equal height and each subregion has a sink. Nodes in the subregion send data to the sink designated for that subregion. The first method called static multi-sink routing uses static sinks and the second method called horizontal trajectory-based mobile multi-sink routing (HT-MMR) uses mobile sinks with a horizontal trajectory. Simulation results show that the proposed HT-MMR reduces average energy consumption and average energy tax by 16.69% and 16.44% respectively. HT-MMR is energy efficient as it enhances network lifetime by 11.11%.
Reliability Indices Evaluation of a Real Time Rural Radial Distribution FeederIOSR Journals
This document summarizes a study that evaluates reliability indices for a real-time rural radial distribution feeder in India. The study calculates reliability before and after adding protective devices (isolators) to the feeder. It first inserts capacitors at weak voltage nodes to improve voltage profiles and reduce losses. Reliability indices are then determined for the existing feeder and after isolators are placed. Load diversity factor is used to analyze real-time load data. The methodology develops matrices to model relationships between bus currents, branch currents, and voltages to solve the load flow using a particle swarm optimization technique. Results are presented for an 11kV rural feeder case study in India.
The document discusses the development of an experimental setup for dynamic strain measurement. It describes different types of strain and methods for strain measurement, both static and dynamic. The aim is to study various static strain instruments, compare them to dynamic instruments, and develop structural models to measure strain under static and dynamic loads. Literature is reviewed on previous uses of strain gauges, accelerometers, and fiber optic sensors to monitor bridge responses and calculate modal parameters under traffic loading.
A laboratory based study of hydraulic simulation of leakage in water distribu...Alexander Decker
This document summarizes a laboratory study on hydraulic simulation of leakage in water distribution networks. The study used a small model network with pipes and instruments to measure pressure and flow at various points. Experiments were conducted with different initial water pressures, leakage volumes, and leakage locations. Pressure and flow data was collected and hydraulic modeling software was used to simulate the system and compare results. The goal was to validate an approach for detecting leakage location using pressure monitoring and hydraulic analysis.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Heuristic remedial actions in the reliability assessment of high voltage dire...IJECEIAES
Planning of high voltage direct current (HVDC) grids requires inclusion of reliability assessment of alternatives under study. This paper proposes a methodology to evaluate the adequacy of voltage source converter/VSCHVDC networks. The methodology analyses the performance of the system using N-1 and N-2 contingencies in order to detect weaknesses in the DC network and evaluates two types of remedial actions to keep the entire system under the acceptable operating limits . The remedial actions are applied when a violation of these limits on the DC system occurs; those include topology changes in the network and adjustments of power settings of VSC converter stations. The CIGRE B4 DC grid test system is used for evaluating the reliability/adequacy performance by means of the proposed methodology in this paper. The proposed remedial actions are effective for all contingencies; then, numerical results are as expected. This work is useful for planning and operation of grids based on VSC-HVDC technology.
CASE STUDY OF HYDROMAGNETIC STABILITY OF A FLOW THROUGH A POROUS SUBSTANCEIRJET Journal
This document discusses the stability of fluids under various conditions such as the presence of magnetic fields, flow through porous media, and changes in temperature. It examines research on the hydromagnetic stability of flows, including how magnetic fields can induce stability. The stability of heterogeneous flows with shear forces and stratified layers of fluid are also analyzed. The interface stability between two immiscible fluids moving through porous media is investigated. In general, it is found that magnetic fields often have a stabilizing effect and can reduce instabilities, while variations in temperature, viscosity, or suspended particles can increase or decrease growth rates of instabilities.
Enhancing Resilience of Transportation Networks A Topological Analysis of Ext...ijtsrd
In light of the escalating frequency and intensity of extreme climatic events, evaluating and improving the resilience of transportation networks has become paramount for sustainable infrastructure development. This investigation presents a comprehensive methodology to assess network resilience and compare measures across different systems, considering both existing and upgraded infrastructure. The current prevailing uncertainty surrounding extreme climatic events often compels transportation agencies to resort to over engineered designs or, regrettably, to disregard necessary preparations due to the exorbitant costs associated with potential hazards. However, armed with pertinent data derived from this study, decision makers and legislators can make informed choices in allocating resources efficiently to critical locations, thereby enabling a more feasible and well considered response to climatic hazards. By leveraging hurricane storm surge simulation results, transportation agencies can accurately identify the most critical network components responsible for maintaining seamless network flow. Rather than undertaking a complete and expensive system overhaul, agencies can now prioritize targeted replacements and structural updates with ease. Furthermore, this approach facilitates the identification of network nodes that are most vulnerable to specific hazards, enabling planners to incorporate these vulnerabilities into long term planning strategies. The research underscores the effectiveness of utilizing topological graph properties to track network response, making it a valuable tool for investigations into the resilience of transportation networks. By examining the nodes most impacted by the envelope simulation, planners can develop strategies that integrate and mitigate these vulnerabilities, thereby enhancing the overall resilience of the transportation system. Ali Raza | Dr. Esar Ahmad "Enhancing Resilience of Transportation Networks: A Topological Analysis of Extreme Climatic Events" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-7 | Issue-4, August 2023, URL: https://www.ijtsrd.com/papers/ijtsrd59719.pdf Paper Url:https://www.ijtsrd.com/other-scientific-research-area/other/59719/enhancing-resilience-of-transportation-networks-a-topological-analysis-of-extreme-climatic-events/ali-raza
An energy aware scheme for layered chain in underwater wireless sensor networ...IJECEIAES
Extending the network lifetime is a very challenging problem that needs to be taken into account during routing data in wireless sensor networks in general and particularly in underwater wireless sensor networks (UWSN). For this purpose, the present paper proposes a multilayer chain based on genetic algorithm routing (MCGA) for routing data from nodes to the sink. This algorithm consists to create a limited number of local chains constructed by using genetic algorithm in order to obtain the shortest path between nodes; furthermore, a leader node (LN) is elected in each chain followed by constructing a global chain containing LNs. The selection of the LN in the closest chain to the sink is as follows: Initially, the closest node to sink is elected LN in this latter because all nodes have initially the same energy value; then the future selection of the LN is based on the residual energy of the nodes. LNs in the other chains are selected based on the proximity to the previous LNs. Data transmission is performed in two steps: intra-chain transmission and inter-chain transmission. Furthermore, MCGA is simulated for different scenarios of mobility and density of nodes in the networks. The performance evaluation of the proposed technique shows a considerable reduction in terms of energy consumption and network lifespan.
Fatigue Life Assessment for Power Cables in Floating Offshore Wind TurbinesFranco Bontempi
https://www.mdpi.com/journal/energies/special_issues/Wave_Tidal_Wind_Converters
Abstract: In this paper, a procedure is proposed to determine the fatigue life of the electrical cable connected to a 5MWfloating offshore wind turbine, supported by a spar-buoy at a water depth of 320 m, by using a numerical approach that takes into account site-specific wave and wind characteristics.
The efect of the intensity and the simultaneous actions of waves and wind are investigated and the outcomes for specific cable configurations are shown. Finally, the fatigue life of the cable is
evaluated. All analyses have been carried out using the Ansys AQWA computational code, which is a commercial code for the numerical investigation of the dynamic response of floating and fixed marine structures under the combined action of wind, waves and current. Furthermore, this paper applies the FAST NREL numerical code for comparison with the ANSYS AQWA results.
Keywords: wind energy; floating offshore wind turbine; dynamic analysis; fatigue life assessment; flexible power cables.
Analysis of Water Quality Characteristics in Distribution NetworksAI Publications
In this study, a model was developed by Epanet2.0 software to analyze water quality for parameters of hydraulic and water quality model (chlorine concentration and water age model) for a segment of Erbil city WDS by using observed and documented data. Controlling free residual chlorine properly is important to ensure meeting regulatory requirements and satisfying customer needs. For the calibration process and collecting field data digital pressure loggers for recording pressure in a WDS was installed. For discharge measurements, ultrasonic flow meters were used. To assure the reliability of the model a calibration process was carried out for extended period analysis and several alternatives had been studied as a solution to overcome negative pressure zones by the calculated Hazen William C-factor. This kind of study can be used to predict so many infrastructure projects.
This document describes research using an artificial neural network (ANN) model to predict the length of hydraulic jumps on rough beds. The ANN model takes the Froude number and relative roughness as inputs and predicts the non-dimensional jump length as the output. Experimental data from previous studies was used to train, validate and test the ANN model. The ANN model was found to predict jump length with higher accuracy than an existing empirical equation, with a coefficient of determination of 0.9596, mean absolute percentage error of 6.9231, and root mean square error of 3.2438. A sensitivity analysis showed that the Froude number has a greater influence on jump length prediction than relative roughness.
This paper elaborates the hydraulic characteristics of the water supply network of the town of Puerto Ayora. First, it intends to replicate the household individual storage by simulating nodal tanks with the use of the EPANET software. Later, it uses the Pressure-Driven Approach (PDA) to develop a methodology that estimates the overflow of storage facilities, one of the main sources of wastage in Puerto Ayora. Finally, it uses the Demand-Driven Approach (DDA), with the aim of assessing the network in the future, under four population growth scenarios. With the chosen moderate growth scenario, two options are suggested in order to tackle the water supply issues at the end of the planning horizon.
A Revisit To Forchheimer Equation Applied In Porous Media FlowIJRES Journal
This document presents an experimental study that revisits the Forchheimer equation for modeling flow through porous media. The study aims to express the coefficients in the Forchheimer equation in terms of measurable media properties. Experiments were conducted using different sizes of coarse materials and glass spheres in a specially designed permeameter. For Reynolds numbers below 10, the results agreed with Darcy's linear law. For higher Reynolds numbers, the inverse of hydraulic gradient varied linearly with velocity, supporting the Forchheimer equation. The coefficients decreased with increasing media size. Equations were proposed relating the coefficients to media properties.
Optimization techniques for water supply network a critical reviewIAEME Publication
This document provides a critical review of optimization techniques that have been used for water supply network design. It discusses various methods that have been developed over the past few decades to analyze and optimize pipe networks, including Newton Raphson, linear theory, genetic algorithms, particle swarm optimization, and ant colony optimization. The review examines literature on applying these techniques to optimize network design factors like cost, reliability, and water quality. Overall, the document surveys extensive research on using mathematical and computational optimization methods to develop more efficient and cost-effective water distribution systems.
Analysis of the Use of Universal Distribution Factors in SEC Power Gridresearchinventy
Distribution factors have been extensively used in many power system analysis and planning studies. In recent power system studies, the AC distribution factors are insensitive to the operating point and relatively sensitive at certain degree to changes in network topology. These factors are linear approximations of sensitivities of variables with various inputs. This paper presents the calculation of the universal distribution factors (UDF’s) applies them on several practical scenarios of Saudi Electricity Company (SEC) power grid. The results are analyzed and evaluated considering various system conditions of SEC load. The results show that the accuracy of the used approach is acceptable compared with exact method. This is practically beneficial to SEC in computing its grid complex power flows using UDF's at the base case without the need to recalculate UDF’s which save efforts and time.
The Underwater Sensor Network (UWSN) is main interesting area due to its most valuable
applications like: disaster preventions, distributed tactical surveillance, undersea exploration, seismic
monitoring, environmental monitoring and many more. The design of energy efficient routing protocol
however is a challenging issue because in underwater environment the batteries of the sensor nodes
cannot be recharged easily. Majority of the researchers have adapted the terrestrial WSN methodologies
to overcome this problem but in underwater environment the terrestrial WSN approach is not feasible due
to the acoustic signaling and water current. This research paper focuses the key limitation of the current
energy efficient routing protocols. The simulation results with comparative analysis for energy efficient
routing protocols are also presented in this research article; which helps the researchers to find the further
research gap in the field of energy efficient routing protocols.
Fredrick Ishengoma - A Novel Design of IEEE 802.15.4 and Solar Based Autonomo...Fredrick Ishengoma
The document proposes a novel Autonomous Water Quality Monitoring Prototype (AWQMP) using IEEE 802.15.4 and solar energy. The prototype uses sensor nodes dispersed in water bodies to gather data on parameters like pH, temperature, and conductivity. The sensor nodes transmit the real-time data to a base station via a wireless sensor network. The prototype is designed to use an ECHERP routing protocol and solar power to allow autonomous monitoring and reduce costs compared to manual monitoring. It aims to help study the behavior of aquatic animals in the deployed water bodies.
This paper suggests the theory of distance protection criteria in power distribution systems for power plant generation. Multi-developed countries have energy power plants that placed in remote areas which are far from the grid line. Hence, they should be coupled to the low power transportation systems necessarily. While higher-rating relays are adopted to preserve feeders at power substations, fuses are merely obtainable outside on feeder channel. The safe system process, space protection is dispatched to save feeders. In this review, feeders with distance relays are equipped, together with over-current protection relays and fuses. Energy power plant having distance protection system is designed the implemented system was a 6-MW unit of compressed power energy reproduction. The sample feeder was shortened to be equal four-bus experiment feeder for transmitting resolution. The fault currents have chances adopted to form protecting regions of distance relays. Protection of the power line through the designed power plants for distance relaying can decrease problem in relay location because of the impedance-based location of the distance relay.
Similar to Mohammed_A_et_al_ICSC2015_263_Reliability_of_Water (20)
1. 5th
International/11th
Construction Specialty Conference
5e
International/11e
Conférence spécialisée sur la construction
Vancouver, British Columbia
June 8 to June 10, 2015 / 8 juin au 10 juin 2015
RELIABILITY ANALYSIS OF WATER DISTRIBUTION NETWORKS
USING MINIMUM CUT SET APPROACH
Azhar Uddin Mohammed1,4, Tarek Zayed2, Osama Moselhi2 and Alaa Alhawari3
1 Graduate Student, Building, Civil and Environmental Engineering, Concordia University, Canada
2 Professor, Building, Civil and Environmental Engineering, Concordia University, Canada
3 Assistant Professor, Department of Civil Engineering, Qatar University, Qatar
4 m_fnu@live.concordia.ca
Abstract: Canadian Water and Wastewater Association (CWWA) estimated the cost to replace 112,000
km of water mains in Canada to be 34 billion Canadian Dollars. Reliability analysis of water distribution
networks (WDNs) is an important aspect in planning and operation of a WDN and hence plays an important
role in the efficient use of allocated budget. In general, reliability analysis is classified into mechanical
reliability and hydraulic reliability. Mechanical reliability is defined as the ability to function even when some
components are out of service or there is any mechanical break. Hydraulic reliability is concerned with
delivery of the specified quantity of water to a specific location at the required time under the desired
pressure. This paper introduces a methodology for evaluating mechanical reliability of WDNs using the
minimum cut set approach. The methodology involves the computation of mechanical reliability at the
component (pipe, hydrant etc.), segment (collection of pipes and components) and network levels. An
illustrative example is worked out to demonstrate the use of the developed methodology.
1 INTRODUCTION
Water distribution networks (WDN) are complex interconnected networks consisting of sources, pipes, and
other hydraulic control elements such as pumps, valves, regulators, tanks etc., that require extensive
planning and maintenance to ensure good quality water is delivered to all customers (Shinstine et al., 2002).
These networks are often described in terms of a graph, with links representing the pipes, and nodes
representing connections between pipes, hydraulic control elements, consumers, and sources (Ostfeld et
al., 2002). They are vital part of urban infrastructure and require high investment, operation and
maintenance costs. The main task of WDN is to provide consumers with a minimum acceptable level of
supply (in terms of pressure, availability, and water quality) at all times under a range of operating
conditions. The degree to which the network is able to achieve this, under both normal and abnormal
conditions, is termed its reliability. (Atkinson et al., 2014). Hence, reliability is considered as an integral part
in making decisions regarding the planning, design, and operation phases of WDNs.
Many researchers defined reliability based on different conditions. Al-Zahrani and Syed (2005) defined
reliability of WDN as its ability to deliver water to individual consumers in the required quantity and quality
and under a satisfactory pressure head. Kalungi and Tanyimboh (2003) defined reliability as the extent to
which the network can meet customer demands at adequate pressure under normal and abnormal
operating conditions. In general reliability of any network refers to its ability of performing a mission placed
on it, adequately under stated environmental conditions and for a prescribed time interval.
No network is entirely reliable. In every network, undesirable events, i.e. failures, can cause decline or
interruptions in the network performance (Ostfeld 2004). Reliability of WDNs relates to two types of failure,
2. (1) mechanical failure of network components and (2) hydraulic failure caused by changes in demand and
pressure head. Mechanical reliability reflects the degree to which the network can continue to provide
adequate levels of service during unplanned events such as mechanical failure (e.g., pipe bursts, pump
malfunction). Hydraulic reliability reflects how well the network can cope with changes over time, such as
deterioration of components or demand variations (Atkinson et al., 2014). Some authors (Islam et al., 2014;
Gupta et al., 2012) have also argued about water quality reliability which is assessed with respect to a
predefined level or range of selected water quality parameters (e.g., residual chlorine concentration). If the
water quality parameter is within the prescribed range, the WDN is considered reliable, otherwise it is
considered unreliable for water quality. However, the scope of this paper is limited to the evaluation of
mechanical reliability of WDN and its components.
According to Su et al. (1987), reliability of components in a WDN such as valves, hydrants, controls etc.
has an effect upon, and must be used to determine, the overall network reliability. However, no model has
been found in the literature evaluating reliability of components. In this paper, a methodology is developed
to assess the reliability of components in a WDN, and using reliabilities of these components, segment
reliability is evaluated. Then the overall network reliability is assessed using minimum cut set method.
2 BACKGROUND
A review of the literature reveals that there is no universally acceptable measure for the reliability of water
distribution networks. It gained considerable research attention over the last few decades. This research
has concentrated on methodologies for reliability assessment and for reliability inclusion in optimal design
and operation of WDNs. This section provides a summary of these efforts.
As reliability is not a network property that can be measured directly, it should be assessed based on other
characteristics of the network that can be directly measured or calculated. Ostfeld (2004) categorized
reliability assessment methods into (1) connectivity/topological, (2) hydraulic and (3) entropy as a reliability
surrogate. The reliability which is based on the concept of connectivity refers to measures associated with
the probability that a given network remains physically connected by taking into account the topology of the
network. This type of measure mainly serves the purpose of evaluating mechanical reliability. Shamsi
(1990) and Quimpo & Shamsi (1991) incorporated the use of node pair reliability (NPR) as the network
reliability measure. The NPR is defined as the probability that a specific source and demand nodes are
connected. This definition corresponds to the probability that at least one path is functional between the
source node and the demand node considered. Yannopoulos and Spiliotis (2013) focused on topology of
network as a measure for analyzing mechanical reliability. They developed a methodology based on
adjacent matrix of graph theory in order to determine connectivity among different nodes. Measures used
within this category do not consider the level of service provided to the consumers during a failure. The
existence of a path between a consumer and a node is only a necessary condition for supplying its required
demands (Ostfeld, 2004).
The second category of reliability assessment i.e., hydraulic measure is concerned with the conveyance of
desired quantities and qualities of water at required pressures to the appropriate locations at the appropriate
times. Xu and Goulter (1999) used a probabilistic hydraulic approach, based on the concept of the first-
order reliability method (FORM), to determine the capacity reliability of the water distribution network, which
is related to the hydraulic and demand variation failures, and is defined as the probability that the nodal
demand is met at or over the prescribed minimum pressure for a fixed network configuration under random
nodal demands and random pipe roughnesses. Shinstine et al. (2002), coupled a cut-set method with a
hydraulic steady state simulation model that implicitly solves the continuity and energy equations for two
large scale municipal water distribution networks in the Tucson Metropolitan Area. The measure of reliability
was defined as the probability of satisfying nodal demands and pressure heads for various possible pipe
breaks in the water distribution network at any given time. Zhuang et al. (2011) presented a methodology
for reliability and availability assessment of a WDN based on an adaptive pump operation. In response to
a pipe break, pump operations were adapted using various sizes of pump combinations. In their method,
they evaluate hydraulic reliability in terms of available water to fulfill desired demand.
3. Entropy, as a surrogate measure for reliability is the third category which has been used by several
researchers for reliability assessment during recent years. The fundamental idea is to use Shannon’s (1948)
entropy measure of uncertainty that quantifies the amount of information contained in a finite probability
distribution, to measure the inherent redundancy of a network. In this regard, entropy is more related to the
category of connectivity/topological analysis than to that of hydraulic reliability. It is assumed that distribution
networks, which are designed to carry maximum entropy flows, are generally reliable (Ostfeld, 2004). A
WDN with higher entropy is expected to cope better with simultaneous multi-pipe failure (Gheisi and Naser,
2014). Prasad and Tanyimboh (2008) used Flow Entropy, a statistical entropy measure for WDNs to show
that surrogate reliability measure can be used effectively to improve reliability of multi-source networks.
Tanyimboh et al. (2011) used statistical entropy and other surrogate measures such as network resilience,
resilience index and modified resilience index, for the reliability assessment of WDN to assess the
effectiveness of surrogate reliability measures in relation to more rigorous and accurate hydraulic reliability
measures.
Among the most well-defined processes to determine the topological/ mechanical reliability of a network is
the process of minimum cut-set (Yannopoulos and Spiliotis, 2013). Tung (1985) discussed six techniques
for WDN reliability evaluation and concluded that the cut-set method is the most efficient technique in
evaluating the network reliability. The minimum cut-set approach is usually applied in order to investigate
the topology of a WDN and the detection of its critical elements the failure of which will affect the network
operation. The minimum cut-set is a set of network components which, when failed, causes failure of the
network; but if just one component of the set has not failed, no failure of network occurs. Following the cut-
set method, an estimation of mechanical reliability of the WDN can be achieved.
2.1 Identification of minimum cut sets
To identify the minimum cut sets of a network in a reduced computational time, a method generally used in
power transmission networks for the same purpose has been adopted (Zhou et al., 2012). It involves 1)
finding all possible paths from the source node to the demand node, 2) Constructing a path matrix and 3)
getting minimum cut sets from the path matrix.
A path is a connection between a source node and a demand node. This model considers a node to be
adequately supplied as long as there is at least one link connecting it to the rest of the network which means
that the network is not considered as failed even if there is a single path from the source node to the demand
node. After finding all possible paths, a path matrix is constructed in which, number of rows is equivalent to
the number of paths from source node to demand node under consideration, and number of columns is
equivalent to the number of segments (or combinations of segments) in a network. This matrix is a zero-
one matrix with 1 as its entry if the segment is present in the path to the demand node, and 0 as its entry if
it is not. For example, there are 3 segments A, B and C in a network and the possible paths from the source
node to the demand node are AB and AC. Then the path matrix is expressed as
[1] P = [
A B C
1 1 0
1 0 1
]
Once the path matrix is constructed for the demand node under consideration, the network is analyzed for
minimum cut sets. First order cut set is a single segment which when fails, causes the failure of entire
network. Similarly, second order cut set is the combination of two segments, the combined failure of which
causes the failure of entire network. If any column in a path matrix contains all elements as 1, then the
segment corresponding to that column is recorded as a first order cut set. For example, all the elements of
the first column are 1 in the matrix 1. Hence segment {A} is recorded as a first order cut set. To find the
second order cut sets, create all combinations of 2 segments and construct a new path matrix by merging
the elements as per the combinations. For example, combination of 2 segments for the above example
network are {A, B}, {B, C} and {C, A}. New path matrix would be
[2] P = [
A+B B+C C+A
1 1 1
1 1 1
]
4. From the matrix 2, combination of B and C results in a column with all elements as 1. Hence {B, C} is
recorded as second order cut set. Note that, any combination with A is neglected because A is already a
minimum cut set. The same procedure is followed for finding third and higher order cut sets with
combinations of corresponding segments.
3 METHODOLOGY
This section discusses the various computing measures adopted to develop the methodology.
Start
Compute failure rate of
all components
Compute component
reliability
Compute segment reliability and failure
probability of all segments
Compute network
reliability based on
cut sets
Stop
Perform cut set analysis for all nodes
Find all possible paths from source to
demand node under consideration
Construct path matrix.
Is the segment present in the
path to demand node?
Enter element
as 0
Enter element
as 1
Is there any column
with no zero element
No Yes
Record cut
set
Repeat for combination of 2 segments
Yes
No
Repeat for combination of 3 segments
Figure 1: Network reliability flowchart
3.1 Failure rate
Most researchers have chosen failure rate as the primary indicator of reliability. Quantitatively, it is defined
as the number of breaks per year per unit length. Breaks are considered one of the significant factors
contributing to water losses and require substantial human effort and cost to repair such failures. As the
number of breaks increases, the reliability of a WDN decreases. The most often applied formulae for
estimating the pipe failure rate have been obtained using simple regression models on the available pipe
failure data from a limited time period. In this paper, the pipe failure rate or breakage rate is computed using
a regression model based on age of pipe, being developed in an ongoing research work at Concordia
University. According to this model, the failure rate can be expressed as
5. [1] λpipe = 6×10-6
X2
+ 0.0004X + 0.0026
Where X is the age of pipe in years and λpipe is the failure rate of pipe expressed in number of breaks per
year per unit length of pipe.
The failure rate of other components (hydrants, valves, controls) can be expressed as
[2] λcomponent =
Nf
Length of segment
Where Nf is the number of failures per year and λcomponent is the failure rate of component expressed in
number of failures per year per unit length of segment.
3.2 Component reliability
After determining the failure rates of pipes and other components, the reliability is assumed to follow
negative exponential distribution which would mean that reliability decreases exponentially as the failure
rate increases with time, and can be computed as
[3] Rc = e-λt
Where Rc is the reliability of a component or pipe and λt is the failure rate of a component or pipe.
3.3 Segment reliability
A segment is a single water main pipe or a group of connected pipes (along with all the associated
components) which are usually located between two nearest intersections at which isolation valves may
exist (Salman A., 2011). According to the definition, the segment reliability can be expressed as
[4] Rseg= ∑ Rc
The above equation represents segment reliability where components have the same weight which is not
true. Each component has its relative importance in a segment. To be more specific in determining segment
reliability, a relative weight component (wi) is included in equation 4 to adjust it.
[5] Rseg = ∑ Rcwi
n
i=1
Where i is the water main component, n is total number of water main components and wi is the relative
weight of component.
The relative weight of component (wi) is the ratio of weight of component under consideration to the total
weight of components in that particular segment. The weights of components are obtained from Salman A.
(2011).
[6] Relative Weight (wi) =
Weight of component
Sum of weights of all components
Table 1 Component Weights (Salman A., 2011)
Pipe 38%
Hydrant 31%
Isolation Valve 28%
Control Valve 3%
3.4 Network reliability
The procedure for determining the network reliability of a WDN based on the minimum cut-set method is
as follows.
6. 3.4.1 Probability of failure of segments
Quantitatively, the probability of failure of a segment is the complement of the reliability of a segment. It can
be expressed as
[7] Q = 1 - e-λt
These segment failure probabilities are computed so that they can be used later for determining network
reliability using minimum cut set method.
3.4.2 Identification of minimum cut sets
As described earlier in the literature review, all the minimum cut sets have to be identified to serve the
purpose of evaluating network reliability.
Find all possible paths
from source node to
destination node.
Create path matrix.
From the path matrix,
check if any column is
non zero.
Any non zero column is
a first order cut set.
Combine any two columns
representing segments in a
path matrix and check if their
addition creates a non zero
column.
The resultant non zero
column of combination of
segments is second order cut
set.
Path Matrix
First order cut
sets
Second order cut
sets
Figure 2: Identification of minimum cut sets
3.4.3 Mechanical reliability of WDN based on Minimum Cut Set
According to Shinstine et al. (2002), for n components (segments) in the ith minimum cut set of a WDN, the
failure probability of the jth component (segment) is Qj, which can be obtained by Eq. 7. The failure
probability of the ith minimum cut set is
[8] Q(MCi) = ∏ Qj
n
j=1
Where n is the number of segments in corresponding minimum cut set.
Assuming that the occurrence of the failure of the components within a minimum cut set are statistically
independent. For example, if a water distribution network has four minimum cut sets, MC1, MC2, MC3, and
MC4, for the network reliability, the failure probability of the network QN, is then defined as follows (Billinton
and Allan 1983):
[9] QN=Q(MC1∩MC2∩MC3∩MC4)
By applying the principle of inclusion and exclusion, equation 9 can be reduced to:
[10] QN=Q(MC1)+Q(MC2)+Q(MC3)+Q(MC4) = ∑ Q(MCi)M
i=1
Where M is the number of minimum cut-sets in the network.
Finally, the mechanical reliability of the network can be expressed as:
[11] RN = 1 - QN = 1 - ∑ Q(MCi)M
i=1
7. 4 CASE EXAMPLE
The hypothetical network shown in figure 3 is utilized for the demonstration of the developed methodology.
The network consists of 8 segments named alphabetically and 7 nodes named numerically. Node 7 is a
source node while the other nodes are demand nodes. Assuming the repair data for the network as shown
in table 2, reliability of each component, each segment and whole network can be calculated. To calculate
the reliability of presented hypothetical network using minimum cut sets method, network should be
analyzed for the identification of minimum cut sets.
1 2 3
456
7
A
B
C
D
E
F G
H
Demand Nodes
Segments
Source Node
Figure 3: Network model of case study
Let us consider node 3 as the demand node. The possible paths for the water to reach demand node 3
from source node 7 are found to be ABD, ACFED, ACFGH, and ABEGH and there are 8 segments.
Therefore the path matrix can be constructed as
[3] P =
[
A B C D E F G H
1 1 0 1 0 0 0 0
1 0 1 1 1 1 0 0
1 0 1 0 0 1 1 1
1 1 0 0 1 0 1 1]
The elements in column A of matrix 3 are all 1. Hence {A} is recorded as a first order cut set. Note that,
while finding second order cut sets, combination of segment A with other segments is not needed. Because
the failure of A, alone causes the failure of network. It does not need combination of any other segment to
cause failure of network.
To find second order cut sets, combinations list of 2 segments out of 8 segments is generated using
WOLFRAM MATHEMATICA 10.1. Total number of combinations are found to be 28 and are listed in table
3. Hence the new path matrix contains 5 rows (No. of paths) and 28 columns (No. of combinations of
segments) and can be constructed as
[4] P =
[
A+B . B+C . B+F . C+D . D+E . D+G D+H E+F . G+H
1 . 1 . 1 . 1 . 1 . 1 1 0 . 0
1 . 1 . 1 . 1 . 1 . 1 1 1 . 0
1 . 1 . 1 . 1 . 0 . 1 1 1 . 1
1 . 1 . 1 . 0 . 1 . 1 1 1 . 1 ]
(All the combinations with segment A are not needed and hence they are neglected. Dotted columns
represent that there are few combinations that are not shown here because it’s a large matrix and could
not be fit to page.)
It can be observed that the elements in columns of matrix 4, representing combinations of {B, C}, {B, F},
{D, G} and {D, H} are all 1. It means that combined failure of these segments can cause failure of network
and hence {B, C}, {B, F}, {D, G} and {D, H} are recorded as second order cut sets. Note that, while finding
9. Same procedure is repeated for finding third order cut sets with combinations list of 3 segments. Total
number of combinations are found to be 56 as listed in table 3. Hence the new path matrix contains 5 rows
(No. of paths) and 56 columns (No. of combinations of segments) and can be constructed as
[5] P =
[
A+B+C . B+C+D . B+D+F . B+D+G . B+E+G B+E+H . C+D+E . D+E+F .
1 . 1 . 1 . 1 . 1 1 . 1 . 1 .
1 . 1 . 1 . 1 . 1 1 . 1 . 1 .
1 . 1 . 1 . 1 . 1 1 . 1 . 1 .
1 . 1 . 1 . 1 . 1 1 . 1 . 1 .]
As we can see, elements in columns of matrix 5, representing combinations of {B, E, G}, {B, E, H}, {C, D,
E} and {D, E, F} are all 1, which means that the combined failure of these segments can cause failure of
network and these are recorded as third order cut sets. The same procedure is repeated for each and every
demand node in the network and all the cut sets are recorded. Note that any cut set is recorded only once.
If the same cut set is identified while performing network analysis considering another demand node, it is
not recorded as a cut set again.
Finally, the minimum cut sets after analyzing the network for all demand nodes are listed in table below.
Table 4 Minimum Cut Sets
Order of cut sets List of cut sets
1 {A}
2 {B, C}, {B, F}, {D, G}, {D, H}, {C, F} and {G, H}
3 {B, D, E}, {B, E, G}, {B, E, H}, {C, D, E}, {C, E, H}, {C, F, G}, {D, E, F}, {E, F, H}, and {E, F, G}
Hence the reliability of the presented hypothetical network can be calculated as
RN = 1 - QN = 1 - ∑ Q(MCi)
M
i=1
QN = Q(MC1)+Q(MC2)+Q(MC3) = 0.0107
∴RN = 1 - QN = 0.9893
5 CONCLUSIONS:
Mechanical failure of pipes in water distribution networks has been studied by numerous statistical models
in the past. But none of these models focused on mechanical failure of other components of water
distribution networks which may also affect the reliability of the whole network. This paper presents a
methodology to evaluate mechanical reliability of water distribution networks along with its components,
using minimum cut set method. The accuracy of a developed model depends on the accuracy of the data
used to build it. The proposed model requires very detailed historic break data of all the components
including pipes. But many municipalities are not equipped to collect such detailed data. In this paper, the
failure rate of pipes is based only on a single parameter i.e., age of the pipe and the failure rate of other
components is obtained using a more general formula. Consideration of as much parameters should lead
to more realistic failure rate predictions. Research should be extended to also predict the failure rate of
components other than pipe. Municipalities are required to collect detailed break data of all the components
of water distribution networks. The availability of such data would assist in evaluating reliability more
accurately.
Acknowledgements
The authors would like to acknowledge the financial support of Qatar Fund under project NPRP 5-165-2-
005.
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