Ian C. Goulter

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.

Reliability Improvements in Design of Water Distribution Networks Recognizing Valve Location

Water distribution networks can fail either by the actual demand at one or more nodes exceeding the design demands, or by a pipe between two nodes failing. The implications of each type of failure can be assessed by the shortfall in supply caused by a failure event together with the probability of occurrence of the event, and can be represented by the expected volume of deficit. Converting the implications of the two failure types into these commensurate units permits them to be added directly to give a single consistent measure of reliability. The assessment of shortfall for the pipe failure mode is derived from the observation that when a pipe breaks, a section of pipe must be isolated by valves to permit the repair to be made. Isolating the pipe also isolates the customers who withdraw water from that section of pipe. Thus the shortfall in supply in this case is based on the amount of supply (number of customers) cut off by isolating the pipe for repair. The measure extends previous reliability parameters by recognizing that in reality demand occurs along links rather than being concentrated solely at nodes at the ends of the links which is the normal assumption for both simulation and optimization models. If reliability of the network is found to be unsatisfactory, it can be improved in two ways. One is to increase the design demand at nodes so that the probability of actual demands exceeding the design value is reduced. The other is to add more valves so that the length of pipe which has to be isolated in order to repair a pipe is reduced, thereby, reducing the number of customers who must have their supply cut off during a repair. Use of the two methods to determine and, if necessary, to improve reliability is demonstrated by their application to an example network.

OPTIMIZATION OF REDUNDANCY IN WATER DISTRIBUTION NETWORKS USING GRAPH THEORETIC PRINCIPLES

Abstract An integer goal programming based approach to maximize reliability in water distribution networks is developed. Previous work has shown that graphs which are inherently the most invulnerable to failure have the same number of links incident at each node, i.e. they are regular in degree. The converse of this statement is not true. Regular graphs can contain weaknesses such as bridges, articulation nodes, and even total disconnections. The integer goal programming formulation in this paper is combined with a procedure which recognizes both explicit and implicit articulation points within the water distribution network to ensure that such weaknesses are excluded from the final solution. The integer program component of the approach attempts to maximize regularity within the network. In the goal programming context this is achieved by minimizing the sum of the deviations, at each node, in terms of the number of links incident upon it, from the average number of links incident on a node over the whole...

An approach to the rationalization of streamflow data collection networks

A new procedure for rationalizing a streamflow data collection network is developed. The procedure is a two-phase approach in which in the first phase, a hierarchical clustering technique is used to identify groups of similar gauging stations. In the second phase, a single station from each identified group of gauging stations is selected to be retained in the rationalized network. The station selection phase is an inherently heuristic process that incorporates information about the characteristics of the individual stations in the network. The methodology allows the direct inclusion of user judgement into the station selection process in that it is possible to select more than one station from a group, if conditions warrant. The technique is demonstrated using streamflow gauging stations in and near the Pembina River basin, southern Manitoba, Canada.

AN INTEGER PROGRAMMING MODEL FOR LAYOUT DESIGN OF WATER DISTRIBUTION NETWORKS

Abstract A model for the layout optimization of water distribution networks under single loadings is presented. The model uses zero-one integer programming to select the links that should form the network, while still satisfying looping, redundancy, and hydraulic requirements. This solution constitutes a starting solution to any network component optimization model. A network component optimization step, using well established design models, is then applied to this solution to refine the pipe sizes and pressure heads, thus giving a layout and component optimal solution. The model is demonstrated by application to an example.

MIXED INTEGER MODEL FOR RESOURCE ALLOCATION IN PROJECT MANAGEMENT

Abstract A mixed integer formulation has been developed for resource levelling within project scheduling. The starting point for the model is the result of a critical path analysis of the project. The project is then rescheduled by the resource levelling model within the constraints of the free float of the activities. {0-1} integer variables are used to ensure the allocation of integer resource requirements in each time period. Besides meeting the resource requirements of the activities, the model can also constrain the activities to be scheduled on consecutive days. The model itself has three global objectives (1) the overall resource levelling on the project, (2) the resource levelling of individual activities (internal levelling), and (3) the minimization of the total duration of the individual activities, i.e. to try to make each activity occur on consecutive days. These objectives are placed within the formulation in a weighted multi-objective framework. The model is demonstrated by application to a...

Multi‐objective analysis of boating and fishlife interests in Lake Sommen, Sweden

The conflicts between boating and fishlife interests in Lake Sommen and hydroelectric, irrigation and urban water supply uses in the Svarta river downstream of Lake Sommen are examined using a goal programming model. The desired water levels corresponding to boating and fishlife interests in Lake Sommen are specified as minimum goals. The hydroelectric, irrigation and water supply needs in the Svarta river are specified as minimum levels within the constraint set for the model. The model was applied for a range of levels of the hydroelectric, irrigation and urban water supply uses. During the winter periods the lake level goals for fishing and boating are always fulfilled. However, in the dry periods, in which fishing and boating interests are critical, the goals are not met during the summer. Furthermore there appears to be very little flexibility within the present operating system to improve boating and fishing conditions during these dry summer periods.

Watershed Land-Use Planning under Uncertainty

A model of watershed land-use planning is formulated that improves on existing models by recognizing that land-use decisions have uncertain outcomes and that land uses change over time. Implications of recognizing the distinction between land-use decisions and their uncertain outcomes are discussed. The land-use changes are modelled using a Markov process. Because of the computational difficulties in determining the return associated with the complete range of possible decision sets, a heuristic technique is required. A heuristic search procedure based on stochastic dynamic programming is described.

Application of multi‐objective analysis to water storage

A multi‐objective analysis was applied to allocation of water storage for food control and irrigation water supply in the Bili‐Bili reservoir in South Sulawesi, Indonesia. In order to recognize the stochastic nature of floods and irrigation demands, the two objectives were measured in terms of expected annual flood damage and expected annual irrigation‐water deficit respectively. The multi‐objective analysis was performed by developing the line of non‐inferior solutions for these two objectives to show how each objective is changed with variation in the allocation of storage.

MIXED INTEGER PROGRAMMING FOR THE OPTIMAL (LEAST COST) DESIGN OF ECCENTRICALLY LOADED MASONRY BEARING WALLS:Part II. High Eccentricities

A mixed integer approach for the least cost design of structural masonry walls with high eccentricities is developed. The integer variables in the approach are used to select the optimum values from a range of discrete block sizes, discrete grouting conditions, and discrete reinforcement levels. The structural constraints in the model are based upon the requirements of the Transformed Section type of analysis for masonry walls. The non-linear functions representing the relationships for determining the resisting capacities of the masonry element are approximated by linear functions which come very close in form and results to the original curves. Application of the model to an example problem demonstrates that in spite of the integer requirements, the approach is easily and efficiently solved using a standard software package.