12 results found
Pecci F, Parpas P, Stoianov I, 2020, Sequential Convex Optimization for Detecting and Locating Blockages in Water Distribution Networks, Journal of Water Resources Planning and Management, Vol: 146, Pages: 04020057-04020057, ISSN: 0733-9496
Blocher C, Pecci F, Stoianov I, 2020, Localizing leakage hotspots in water distribution networks via the regularization of an inverse problem, Journal of Hydraulic Engineering, Vol: 146, Pages: 04020025-1-04020025-13, ISSN: 0733-9429
The ill-posed inverse problem for detecting and localizing leakage hotspots is solved using a novel optimization-based method which aims to minimize the difference between hydraulic measurement data and simulated steady states of a water distribution network. Regularization constrains the set of leak candidate nodes obtained from a solution to the optimization problem. Hydraulic conservation laws are enforced as nonlinear constraints. The resulting nonconvex optimization problem is solved using smooth mathematical optimization techniques. The solution identifies leakage hotspot areas, which can then be further investigated with alternative methods for precise leak localization. A metric is proposed to quantitatively assess the performance of the developed leak localization approach in comparison with a method that uses the sensitivity matrix. In addition, we propose a strategy to select the regularization parameter when large-scale operational networks are considered. Using two numerical case studies, we demonstrate that the proposed approach outperforms the sensitivity matrix method, with regards to leak isolation, in most single leak scenarios. Moreover, the developed method enables the localization of multiple simultaneous leaks.
Waldron A, Pecci F, Stoianov I, The regularisation of an inverse problem for parameter estimation in water distribution networks, Journal of Water Resources Planning and Management, ISSN: 0733-9496
An accurate hydraulic model of a water distribution network (WDN) is a critical prerequisite for a multitude of operational, optimisation and planning tasks. The accuracy of a hydraulic model can only be maintained through its periodic calibration and validation with acquired pressure and flow data from a WDN. It is important that this process is robust and computationally efficient. This paper describes the regularisation of an inverse problem to deal with data uncertainties and ill-posedness of parameter estimation problems in WDNs. A novel data driven strategy is presented for tuning the regularisation hyper-parameter for the inverse problem and also for validating the results on an independent set of operational hydraulic data. A limited-memory quasi-Newton method (L-BFGS19 B) is implemented for solving the resulting regularised nonlinear inverse problem. Furthermore, the implemented method utilises either the Darcy-Weisbach or Hazen-Williams head loss formulae, and is investigated both with and without pipe grouping. An extensive experimental programmewas carried out to acquire unique hydraulic data from an operational WDN in order to investigate the robustness of the proposed parameter estimation method. The hydraulic model of the operational WDN and the acquired hydraulic data are provided as supplementary data to enable the comparisonof hydraulic model calibration methods with operational data and encourage reproducible research
Ulusoy A-J, Pecci F, Stoianov I, 2020, A MINLP-based approach for the design-for-control of resilient water supply systems, IEEE Systems Journal, ISSN: 1932-8184
The improvement in resilience of water supplysystems by increasing their redundancy, either in energyor in connectivity, is a common priority when doing rehabilitation and expansion. This however can come at thecost of other aspects of network performance, such asleakage management. In this work, we consider the designfor-control problem of adding new connections (from a predefined set of candidate pipes) to water supply systems toimprove their resilience to failure events while minimizingthe impact on leakage management under normal operatingconditions. We present a mixed-integer non-linear programming formulation of the problem of optimal link additionfor the minimization of average zone pressure, a surrogatemeasure of pressure dependent leakage. We implement amethod based on spatial branch-and-bound to solve theproblem on a case study network from the literature andan operational network part of an urban water system inthe UK. Finally, we validate the improvement in networkresilience resulting from the addition of new connectionsby performing an a posteriori critical link analysis, usingthe hydraulic resilience measure of reserve capacity.
Nerantzis D, Pecci F, Stoianov I, 2019, Optimal control of water distribution networks without storage, European Journal of Operational Research, ISSN: 0377-2217
The paper investigates the problem of optimal control of water distribution networks without storage capacity. Using mathematical optimization, we formulate and solve the problem as a non-convex NLP, in order to obtain optimal control curves for both variable speed pumps and pressure reducing valves of the network and thus propose a methodology for the automated control of real operational networks. We consider both single-objective and multi-objective problems with average zonal pressure, pump energy consumption and water treatment cost as objectives. Furthermore, we investigate global optimality bounds for the calculated solutions using global optimization techniques. The proposed approach is shown to outperform state-of-the-art global optimization solvers. The described procedure is demonstrated in a case study using a large size operational network.
Pecci F, Abraham E, Stoianov I, 2019, Global optimality bounds for the placement of control valves in water supply networks, Optimization and Engineering, Vol: 20, Pages: 457-495, ISSN: 1389-4420
© 2018, The Author(s). This manuscript investigates the problem of optimal placement of control valves in water supply networks, where the objective is to minimize average zone pressure. The problem formulation results in a nonconvex mixed integer nonlinear program (MINLP). Due to its complex mathematical structure, previous literature has solved this nonconvex MINLP using heuristics or local optimization methods, which do not provide guarantees on the global optimality of the computed valve configurations. In our approach, we implement a branch and bound method to obtain certified bounds on the optimality gap of the solutions. The algorithm relies on the solution of mixed integer linear programs, whose formulations include linear relaxations of the nonconvex hydraulic constraints. We investigate the implementation and performance of different linear relaxation schemes. In addition, a tailored domain reduction procedure is implemented to tighten the relaxations. The developed methods are evaluated using two benchmark water supply networks and an operational water supply network from the UK. The proposed approaches are shown to outperform state-of-the-art global optimization solvers for the considered benchmark water supply networks. The branch and bound algorithm converges to good quality feasible solutions in most instances, with bounds on the optimality gap that are comparable to the level of parameter uncertainty usually experienced in water supply network models.
Pecci F, Abraham E, Stoianov I, 2019, Model Reduction and Outer Approximation for Optimizing the Placement of Control Valves in Complex Water Networks, Journal of Water Resources Planning and Management, Vol: 145, ISSN: 0733-9496
© 2019 American Society of Civil Engineers. The optimal placement and operation of pressure control valves in water distribution networks is a challenging engineering problem. When formulated in a mathematical optimization framework, this problem results in a nonconvex mixed integer nonlinear program (MINLP), which has combinatorial computational complexity. As a result, the considered MINLP becomes particularly difficult to solve for large-scale looped operational networks. We extend and combine network model reduction techniques with the proposed optimization framework in order to lower the computational burden and enable the optimal placement and operation of control valves in these complex water distribution networks. An outer approximation algorithm is used to solve the considered MINLPs on reduced hydraulic models. We demonstrate that the restriction of the considered optimization problem on a reduced hydraulic model is not equivalent to solving the original larger MINLP, and its solution is therefore sub-optimal. Consequently, we investigate the trade-off between reducing computational complexity and the potential sub-optimality of the solutions that can be controlled with a parameter of the model reduction routine. The efficacy of the proposed method is evaluated using two large scale water distribution network models.
Pecci F, Abraham E, Stoianov I, 2017, Outer approximation methods for the solution of co-design optimisation problems in water distribution networks, 20th IFAC World Congress, Publisher: Elsevier, Pages: 5373-5379, ISSN: 1474-6670
In the present manuscript, we investigate and demonstrate the use of outer approximation methods for simultaneously optimising the placement and operation of control valves in water distribution networks. The problem definition results in a mixed-integer nonlinear program with nonconvex constraints. We simplify the formulation, compared to previous literature, in order to reduce the degree of nonlinearity in the constraints and decrease the total problem size. We then formulate the application of outer approximation based methods for the generation of good quality local optimal solutions for the considered co-design problem. Finally, we present the results of applying the developed techniques to two case studies, and also comparing the performances of the outer approximation approaches with those of other local mixed integer nonlinear programming solution methods.
Pecci F, Abraham E, Stoianov I, 2017, Quadratic head loss approximations for optimisation problems in water supply networks, Journal of Hydroinformatics, Vol: 19, Pages: 493-506, ISSN: 1464-7141
© 2017 The Authors. This paper presents a novel analysis of the accuracy of quadratic approximations for the Hazen-Williams (HW) head loss formula, which enables the control of constraint violations in optimisation problems for water supply networks. The two smooth polynomial approximations considered here minimise the absolute and relative errors, respectively, from the original non-smooth HW head loss function over a range of flows. Since quadratic approximations are used to formulate head loss constraints for different optimisation problems, we are interested in quantifying and controlling their absolute errors, which affect the degree of constraint violations of feasible candidate solutions. We derive new exact analytical formulae for the absolute errors as a function of the approximation domain, pipe roughness and relative error tolerance. We investigate the efficacy of the proposed quadratic approximations in mathematical optimisation problems for advanced pressure control in an operational water supply network. We propose a strategy on how to choose the approximation domain for each pipe such that the optimisation results are sufficiently close to the exact hydraulically feasible solution space. By using simulations with multiple parameters, the approximation errors are shown to be consistent with our analytical predictions.
Pecci F, Abraham E, Stoianov I, 2017, Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks, Computational Optimization and Applications, Vol: 67, Pages: 201-223, ISSN: 0926-6003
© 2016, The Author(s). In this paper, we investigate the application of penalty and relaxation methods to the problem of optimal placement and operation of control valves in water supply networks, where the minimization of average zone pressure is the objective. The optimization framework considers both the location and settings of control valves as decision variables. Hydraulic conservation laws are enforced as nonlinear constraints and binary variables are used to model the placement of control valves, resulting in a mixed-integer nonlinear program. We review and discuss theoretical and algorithmic properties of two solution approaches. These include penalty and relaxation methods that solve a sequence of nonlinear programs whose stationary points converge to a stationary point of the original mixed-integer program. We implement and evaluate the algorithms using a benchmarking water supply network. In addition, the performance of different update strategies for the penalty and relaxation parameters are investigated under multiple initial conditions. Practical recommendations on the numerical implementation are provided.
Pecci F, Abraham E, Stoianov I, 2017, Scalable Pareto set generation for multiobjective co-design problems in water distribution networks: a continuous relaxation approach, Structural and Multidisciplinary Optimization, Vol: 55, Pages: 857-869, ISSN: 1615-147X
© 2016, The Author(s). In this paper, we study the multiobjective co-design problem of optimal valve placement and operation in water distribution networks, addressing the minimization of average pressure and pressure variability indices. The presented formulation considers nodal pressures, pipe flows and valve locations as decision variables, where binary variables are used to model the placement of control valves. The resulting optimization problem is a multiobjective mixed integer nonlinear optimization problem. As conflicting objectives, average zone pressure and pressure variability can not be simultaneously optimized. Therefore, we present the concept of Pareto optima sets to investigate the trade-offs between the two conflicting objectives and evaluate the best compromise. We focus on the approximation of the Pareto front, the image of the Pareto optima set through the objective functions, using the weighted sum, normal boundary intersection and normalized normal constraint scalarization techniques. Each of the three methods relies on the solution of a series of single-objective optimization problems, which are mixed integer nonlinear programs (MINLPs) in our case. For the solution of each single-objective optimization problem, we implement a relaxation method that solves a sequence of nonlinear programs (NLPs) whose stationary points converge to a stationary point of the original MINLP. The relaxed NLPs have a sparse structure that come from the sparse water network graph constraints. In solving the large number of relaxed NLPs, sparsity is exploited by tailored techniques to improve the performance of the algorithms further and render the approaches scalable for large scale networks. The features of the proposed scalarization approaches are evaluated using a published benchmarking network model.
Pecci F, Abraham E, Stoianov I, 2015, Mathematical programming methods for pressure management in water distribution systems, Pages: 937-946
© 2015 Published by Elsevier Ltd. In this paper, we survey mathematical programming methods for the management of pressure in water distribution systems through optimal placement and operation of control valves. The optimization framework addresses the minimization of average zone pressure under multiple demand scenarios, enforcing hydraulic equations as nonlinear constraints. Binary variables are used to model the placement of valves. The derived nonlinear optimization problem is a non-convex MINLP. We implement and evaluate a direct MINLP solver and two different reformulation methods for MINLPs that solve sequences of regular NLPs. Moreover, we investigate the solutions under different design and operation loading conditions.
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