The never ending story of modeling control-devices in hydraulic systems analysis

Difficulties of simulation in existing hydraulic models arising from combinations of pressure and flow controlling devices in water distribution systems have been discussed in a number of previous papers. For instance, examples for non-convergence or wrong results of the hydraulic solver EPANET (version 2.00.10) were first published by Simpson in 1999. It may be shown that the problems were caused by a singularity of the equation system that appears if in an iteration two interacting control devices are active at the same time. In terms of graph theory the part of the network between the two active valves in this case is disconnected from the rest of the system leading to the singularity. In the new EPANET version 2.00.12 that has been released recently this problem is tackled by adding a virtual coefficient to all matrix columns and rows corresponding to nodes of active flow control valves. Mathematically this method is equivalent to adding a very small diameter pipe to the actual network in parallel to the FCV resulting in a nonsingular system. The examples of networks published by Simpson (1999) where EPANET 2.00.10 failed to converge or converged to wrong results now can be solved successfully. Nevertheless the latest release of EPANET still has difficulties in modeling of combinations of control devices. Whereas the former version of EPANET (version 2.00.10) often failed to calculate the correct valve states (active, closed, open) the problems of the new version consist of numerical inexactness that is caused by the addition of the virtual matrix terms for FCVs. In addition examples can be found where version 2.00.12 of EPANET still fails to converge. ©ASCE 2009.Jochen Deuerlein, Angus R. Simpson and Egbert Gros

Modeling the Behavior of Flow Regulating Devices in Water Distribution Systems Using Constrained Nonlinear Programming

Currently the modeling of check valves and flow control valves in water distribution systems is based on heuristics intermixed with solving the set of nonlinear equations governing flow in the network. At the beginning of a simulation, the operating status of these valves is not known and must be assumed. The system is then solved. The status of the check valves and flow control valves are then changed to try to determine their correct operating status, at times leading to incorrect solutions even for simple systems. This paper proposes an entirely different approach. Content and co-content theory is used to define conditions that guarantee the existence and uniqueness of the solution. The work here focuses solely on flow control devices with a defined head discharge versus head loss relationship. A new modeling approach for water distribution systems based on subdifferential analysis that deals with the nondifferentiable flow versus head relationships is proposed in this paper. The water distribution equations are solved as a constrained nonlinear programming problem based on the content model where the Lagrangian multipliers have important physical meanings. This new method gives correct solutions by dealing appropriately with inequality and equality constraints imposed by the presence of the flow regulating devices (check valves, flow control valves, and temporarily closed isolating valves). An example network is used to illustrate the concepts. © 2009 ASCE.Jochen W. Deuerlein, Angus R. Simpson and Stephan Demp

Elite Influence? Religion, Economics, and the Rise of the Nazis

Adolf Hitler's seizure of power was one of the most consequential events of the twentieth century. Yet, our understanding of which factors fueled the astonishing rise of the Nazis remains highly incomplete. This paper shows that religion played an important role in the Nazi party's electoral success -- dwarfing all available socioeconomic variables. To obtain the first causal estimates we exploit plausibly exogenous variation in the geographic distribution of Catholics and Protestants due to a peace treaty in the sixteenth century. Even after allowing for sizeable violations of the exclusion restriction, the evidence indicates that Catholics were significantly less likely to vote for the Nazi Party than Protestants. Consistent with the historical record, our results are most naturally rationalized by a model in which the Catholic Church leaned on believers to vote for the democratic Zentrum Party, whereas the Protestant Church remained politically neutral

A Greedy Scheduling of Post-Disaster Response and Restoration using Pressure-Driven Models and Graph Segment Analysis

In this manuscript, we consider the problem of optimally scheduling the restoration of a water distribution network with multiple failures after a disaster. The decisions made are the sequence of burst/broken pipes and leaks that need to be replaced or repaired, respectively, subject to constraints on workforce availability and physical hydraulic conditions. In order to sufficiently capture the objectives of the utility (e.g. service levels, resilience loss and customer minutes lost without service), which are all pressure dependent, pressure driven leakage and demand models (PDM) are employed.The restoration decisions are modelled as time-dependent closure and opening of links and are simulated using a PDM in EPANET, propagating decisions as pressure-driven hydraulic constraints and computing a posteriori their impact on the multiple desired restoration objectives, some of which have trade-offs. The combination of discrete decisions with time-dependent couplings, and the presence of objectives that are conditional functions of demands met and time indices make it difficult to pose this optimal task scheduling problem as a standard numerically tractable mixed-integer programming problem. To make the problem tractable for the given large-scale water distribution system, we propose greedy heuristics that use a hierarchical decomposition of the decision space using structural properties of the network graph and hydraulics. Firstly, PDM simulations are used to sort the breaks and leaks from the biggest losses to the smallest, or determine visibility of the damages. In addition to solving the multi-criteria scheduling problem, we also use engineering principles to derive metaheuristic that can prioritise water loss reductions. The greedy algorithm is employed to iteratively schedule isolation and repairs by first stabilizing the system with the isolation of the biggest breaks; an alternative approach considers all objectives ‘equally’. With these we explore the trade-offs in response between water loss and resilience indicators.To enable the scheduling, we use graph decomposition techniques to identify the valves that need to be closed to isolate a hydraulic segment (i.e. set of links sharing same closing valves) for replacement; this gives us a map (or look up table) that will be used in the scheduling. The map also includes information about the number of nodes isolated, unsatisfied demand when isolating each segment and the total pipe length of the segments. We also analyse the system flows, network pressures and how the depletion of tanks affects service levels. Using these, we make recommendations for improving the capacity of the system, including the improvement of pumping stations, installation of control valves and some pipe re-enforcement. The same greedy task scheduling algorithm is then used under these alternative network improvements, to show a much better response in all criteria.Water Resource

Pressure-Leak Duality for Leak Detection and Localization in Water Distribution Systems

Water utilities are challenged to reduce their water losses through detecting, localizing, and repairing leaks as quickly as possible in their aging distribution systems. In this work, we solve this challenging problem by detecting multiple leaks simultaneously in a water distribution network for the Battle of the Leak Detection and Isolation Methods. The performance of leak detection and localization depends on how well the system roughness and demand are calibrated. In addition, existing leaks affect the diagnosis performance unless they are identified and explicitly represented in the model. To circumvent this chicken-and-egg dilemma, we decompose the problem into multiple levels of decision-making (a hierarchical approach) where we iteratively improve the water distribution network model and so are able to solve the multileak diagnosis problem. First, a combination of time series and cluster analysis is used on smart meter data to build patterns for demand models. Second, point and interval estimates of pipe roughnesses are retrieved using least squares to calibrate the hydraulic model, utilizing the demand models from the first step. Finally, the calibrated primal model is transformed into a dual model that intrinsically combines sensor data and network hydraulics. This dual model automatically converts small pressure deviations caused by leaks into sharp and localized signals in the form of virtual leak flows. Analytical derivations of sensitivities with respect to these virtual leak flows are calculated and used to estimate the leakage impulse responses at candidate nodes. Subsequently, we use the dual network to (1) detect the start time of the leaks, and (2) compute the Pearson correlation of pressure residuals, which allows further localization of leaks. This novel dual modeling approach resulted in the highest true-positive rates for leak isolation among all participating teams in the competition.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Water Resource