arXiv subjects

Lina Sela

Publications and source records attributed to Lina Sela.

7 recordsLinked to original sources

arXiv2023

Comprehensive Framework for Controlling Nonlinear Multi-Species Water Quality Dynamics

Tracing disinfectant (e.g., chlorine) and contaminants evolution in water networks requires the solution of 1- D advection-reaction (AR) partial differential equations (PDEs). With the absence of analytical solutions in many scenarios, numerical solutions require high-resolution time- and spacediscretizations resulting in large model dimensions. This adds complexity to the water quality control problem. In addition, considering multi-species water quality dynamics rather than the single-species dynamics produces a more accurate description of the reaction dynamics under abnormal hazardous conditions (e.g., contamination events). Yet, these dynamics introduces nonlinear reaction formulation to the model. To that end, solving nonlinear 1-D AR PDEs in real time is critical in achieving monitoring and control goals for various scaled networks with a high computational burden. In this work, we propose a novel comprehensive framework to overcome the large-dimensionality issue by introducing different approaches for applying model order reduction (MOR) algorithms to the nonlinear system followed by applying real-time water quality regulation algorithm that is based on an advanced model to maintain desirable disinfectant levels in water networks under multi-species dynamics. The performance of this framework is validated using rigorous numerical case studies under a wide range of scenarios demonstrating the challenges associated with regulating water quality under such conditions.

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arXiv2022

Control-Theoretic Modeling of Multi-Species Water Quality Dynamics in Drinking Water Networks: Survey, Methods, and Test Cases

Chlorine is a widely used disinfectant and proxy for water quality (WQ) monitoring in water distribution networks (WDN). Chlorine-based WQ regulation and control aims to maintain pathogen-free water. Chlorine residual evolution within WDN is commonly modeled using the typical single-species decay and reaction dynamics that account for network-wide, spatiotemporal chlorine concentrations only. Prior studies have proposed more advanced and accurate descriptions via multi-species dynamics. This paper presents a host of novel state-space, control-theoretic representations of multi-species water quality dynamics. These representations describe decay, reaction, and transport of chlorine and a fictitious reactive substance to reflect realistic complex scenarios in WDN. Such dynamics are simulated over space- and time-discretized grids of the transport partial differential equation and the nonlinear reaction ordinary differential equation. To that end, this paper (i) provides a full description on how to formulate a high fidelity model-driven state-space representation of the multi-species water quality dynamics and (ii) investigates the applicability and performance of different Eulerian-based schemes (Lax-Wendroff, backward Euler, and Crank- Nicolson) and Lagrangian-based schemes (method of characteristics) in contrast with EPANET and its EPANET-MSX extension. Numerical case studies reveal that the Lax-Wendroff scheme and method of characteristics outperform other schemes with reliable results under reasonable assumptions and limitations.

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arXiv2022

Model Order Reduction for Water Quality Dynamics

A state-space representation of water quality dynamics describing disinfectant (e.g., chlorine) transport dynamics in drinking water distribution networks has been recently proposed. Such representation is a byproduct of space- and time-discretization of the PDE modeling transport dynamics. This results in a large state-space dimension even for small networks with tens of nodes. Although such a state-space model provides a model-driven approach to predict water quality dynamics, incorporating it into model-based control algorithms or state estimators for large networks is challenging and at times intractable. To that end, this paper investigates model order reduction (MOR) methods for water quality dynamics with the objective of performing post-reduction feedback control. The presented investigation focuses on reducing state-dimension by orders of magnitude, the stability of the MOR methods, and the application of these methods to model predictive control.

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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.

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arXiv2020

Network Inspection for Detecting Strategic Attacks

This article studies a problem of strategic network inspection, in which a defender (agency) is tasked with detecting the presence of multiple attacks in the network. An inspection strategy entails monitoring the network components, possibly in a randomized manner, using a given number of detectors. We formulate the network inspection problem $(\mathcal{P})$ as a large-scale bilevel optimization problem, in which the defender seeks to determine an inspection strategy with minimum number of detectors that ensures a target expected detection rate under worst-case attacks. We show that optimal solutions of $(\mathcal{P})$ can be obtained from the equilibria of a large-scale zero-sum game. Our equilibrium analysis involves both game-theoretic and combinatorial arguments, and leads to a computationally tractable approach to solve $(\mathcal{P})$. Firstly, we construct an approximate solution by utilizing solutions of minimum set cover (MSC) and maximum set packing (MSP) problems, and evaluate its detection performance. In fact, this construction generalizes some of the known results in network security games. Secondly, we leverage properties of the optimal detection rate to iteratively refine our MSC/MSP-based solution through a column generation procedure. Computational results on benchmark water networks demonstrate the scalability, performance, and operational feasibility of our approach. The results indicate that utilities can achieve a high level of protection in large-scale networks by strategically positioning a small number of detectors.

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arXiv2020

State Estimation in Water Distribution Networks through a New Successive Linear Approximation

State estimation (SE) of water distribution networks (WDNs) is difficult to solve due to nonlinearity/nonconvexity of water flow models, uncertainties from parameters and demands, lack of redundancy of measurements, and inaccurate flow and pressure measurements. This paper proposes a new, scalable successive linear approximation to solve the SE problem in WDNs. The approach amounts to solving either a sequence of linear or quadratic programs---depending on the operators' objectives. The proposed successive linear approximation offers a seamless way of dealing with valve/pump model nonconvexities, is different than a first order Taylor series linearization, and can incorporate with robust uncertainty modeling. Two simple testcases are adopted to illustrate the effectiveness of proposed approach using head measurements at select nodes.

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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.

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