Optimal Sampling of Water Distribution Network Dynamics using Graph Fourier Transform

04/06/2019
by   Zhuangkun Wei, et al.
0

Water Distribution Networks (WDNs) are critical infrastructures that ensure safe drinking water. One of the major threats is the accidental or intentional injection of pollutants. Data collection remains challenging in underground WDNs and in order to quantify its threat to end users, modeling pollutant spread with minimal sensor data is can important open challenge. Existing approaches using numerical optimisation suffer from scalability issues and lack detailed insight and performance guarantees. Applying general data-driven approaches such as compressed sensing (CS) offer limited improvements in sample node reduction. Graph theoretic approaches link topology (e.g. Laplacian spectra) to optimal sensing locations, it neglects the complex dynamics. In this work, we introduce a novel Graph Fourier Transform (GFT) that exploits the low-rank property to optimally sample junction nodes in WDNs. The proposed GFT allows us to fully recover the full network dynamics using a subset of data sampled at the identified nodes. The proposed GFT technique offers attractive improvements over existing numerical optimisation, compressed sensing, and graph theoretic approaches. Our results show that, on average, with nearly 30-40% of the junctions monitored, we are able to fully recover the dynamics of the whole network. The framework is useful beyond the application of WDNs and can be applied to a variety of infrastructure sensing for digital twin modeling.

READ FULL TEXT
research
02/11/2020

Neural Network Approximation of Graph Fourier Transforms for Sparse Sampling of Networked Flow Dynamics

Infrastructure monitoring is critical for safe operations and sustainabi...
research
02/05/2018

Randomness and isometries in echo state networks and compressed sensing

Although largely different concepts, echo state networks and compressed ...
research
03/19/2019

Compressed Sensing: From Research to Clinical Practice with Data-Driven Learning

Compressed sensing in MRI enables high subsampling factors while maintai...
research
11/16/2018

Information Theoretic Limits for Standard and One-Bit Compressed Sensing with Graph-Structured Sparsity

In this paper, we analyze the information theoretic lower bound on the n...
research
04/20/2020

Sampling and Inference of Networked Dynamics using Log-Koopman Nonlinear Graph Fourier Transform

Networked nonlinear dynamics underpin the complex functionality of many ...
research
07/24/2021

Rheological and physical properties of a nanocomposite of graphene oxide nanoribbons with polyvinyl alcohol

In this work, the physicochemical and rheological properties of a nanoco...
research
05/29/2014

Deformation corrected compressed sensing (DC-CS): a novel framework for accelerated dynamic MRI

We propose a novel deformation corrected compressed sensing (DC-CS) fram...

Please sign up or login with your details

Forgot password? Click here to reset