arXiv subjects

Marcio Giacomoni

Publications and source records attributed to Marcio Giacomoni.

5 recordsLinked to original sources

arXiv2021

Probabilistic State Estimation in Water Networks

State estimation in water distribution networks (WDN), the problem of estimating all unknown network heads and flows given select measurements, is challenging due to the nonconvexity of hydraulic models and significant uncertainty from water demands, network parameters, and measurements. To this end, a probabilistic modeling for state estimation (PSE) in WDNs is proposed. After linearizing the nonlinear hydraulic WDN model, the proposed PSE shows that the covariance matrix of unknown system states (unmeasured heads and flows) can be linearly expressed by the covariance matrix of three uncertainty sources (i.e., measurement noise, network parameters, and water demands). Instead of providing deterministic results for unknown states, the proposed PSE approach (i) regards the system states and uncertainty sources as random variables and yields variances of individual unknown states, (ii) considers thorough modeling of various types of valves and measurement scenarios in WDNs, and (iii) is also useful for uncertainty quantification, extended period simulations, and confidence limit analysis. The effectiveness and scalability of the proposed approach is tested using several WDN case studies.

math.OC↗

arXiv2020

A New Derivative-Free Linear Approximation for Solving the Network Water Flow Problem with Convergence Guarantees

Addressing challenges in urban water infrastructure systems including aging infrastructure, supply uncertainty, extreme events, and security threats, depend highly on water distribution networks modeling emphasizing the importance of realistic assumptions, modeling complexities, and scalable solutions. In this study, we propose a derivative-free, linear approximation for solving the network water flow problem (WFP). The proposed approach takes advantage of the special form of the nonlinear head loss equations and, after the transformation of variables and constraints, the WFP reduces to a linear optimization problem that can be efficiently solved by modern linear solvers. Ultimately, the proposed approach amounts to solving a series of linear optimization problems. We demonstrate the proposed approach through several case studies and show that the approach can model arbitrary network topologies and various types of valves and pumps, thus providing modeling flexibility. Under mild conditions, we show that the proposed linear approximation converges. We provide sensitivity analysis and discuss in detail the current limitations of our approach and suggest solutions to overcome these. All the codes, tested networks, and results are freely available on Github for research reproducibility.

math.OC↗

arXiv2019

Receding Horizon Control for Drinking Water Networks: The Case for Geometric Programming

Optimal, network-driven control of Water Distribution Networks (WDN) is very difficult: valve and pump models form non-trivial, combinatorial logic; hydraulic models are nonconvex; water demand patterns are uncertain; and WDN are naturally large-scale. Prior research on control of WDN addressed major research challenges, yet either (i) adopted simplified hydraulic models, WDN topologies, and rudimentary valve/pump modeling or (ii) used mixed-integer, nonconvex optimization to solve WDN control problems. The objective of this paper is to develop tractable computational algorithms to manage WDN operation, while considering arbitrary topology, flow direction, an abundance of valve types, control objectives, hydraulic models, and operational constraints---all while only using convex, continuous optimization. Specifically, we propose new Geometric Programming (GP)-based Model Predictive Control (MPC) algorithms, designed to solve the water flow equations and obtain WDN controls, i.e., pump/valve schedules alongside heads and flows. The proposed approach amounts to solving a series of convex optimization problems that graciously scale to large networks. The proposed approach is tested using a 126-node network with many valves and pumps and shown to outperform traditional, rule-based control. The developed GP-based MPC algorithms, as well as the numerical test results are all included on Github.

eess.SY↗

arXiv2019

Geometric Programming-Based Control for Nonlinear, DAE-Constrained Water Distribution Networks

Control of water distribution networks (WDNs) can be represented by an optimization problem with hydraulic models describing the nonlinear relationship between head loss, water flow, and demand. The problem is difficult to solve due to the non-convexity in the equations governing water flow. Previous methods used to obtain WDN controls (i.e., operational schedules for pumps and valves) have adopted simplified hydraulic models. One common assumption found in the literature is the modification of WDN topology to exclude loops and assume a known water flow direction. In this paper, we present a new geometric programming-based model predictive control approach, designed to solve the water flow equations and obtain WDN controls. The paper considers the nonlinear difference algebraic equation (DAE) form of the WDN dynamics, and the GP approach amounts to solving a series of convex optimization problems and requires neither the knowledge of water flow direction nor does it restrict the water network topology. A case study is presented to illustrate the performance of the proposed method.

math.OC↗

arXiv2018

A Fixed-Point Iteration for Steady-State Analysis of Water Distribution Networks

This paper develops a fixed-point iteration to solve the steady-state water flow equations in an urban water distribution network. The fixed-point iteration is derived upon the assumption of turbulent flow solutions and the validity of the Hazen-Williams head loss formula for water flow. Local convergence is ensured if the spectral radius of the Jacobian at the solution is smaller than one. The implication is that the solution is at least locally unique and that the spectral radius of the Jacobian provides an estimate of the convergence speed. A sample water network is provided to assert the application of the proposed method.

eess.SY↗