Abstract
Infrastructure monitoring is critical for safe operations and sustainability. Like many networked systems, water distribution networks (WDNs) exhibit both graph topological structure and complex embedded flow dynamics. The resulting networked cascade dynamics are difficult to predict without extensive sensor data. However, ubiquitous sensor monitoring in underground situations is expensive, and a key challenge is to infer the contaminant dynamics from partial sparse monitoring data. Existing approaches use multi-objective optimization to find the minimum set of essential monitoring points but lack performance guarantees and a theoretical framework. Here, we first develop a novel Graph Fourier Transform (GFT) operator to compress networked contamination dynamics to identify the essential principal data collection points with inference performance guarantees. As such, the GFT approach provides the theoretical sampling bound. We then achieve under-sampling performance by building auto-encoder (AE) neural networks (NN) to generalize the GFT sampling process and under-sample further from the initial sampling set, allowing a very small set of data points to largely reconstruct the contamination dynamics over real and artificial WDNs. Various sources of the contamination are tested, and we obtain high accuracy reconstruction using around 5%–10% of the network nodes for known contaminant sources, and 50%–75% for unknown source cases, which although larger than that of the schemes for contaminant detection and source identifications, is smaller than the current sampling schemes for contaminant data recovery. This general approach of compression and under-sampled recovery via NN can be applied to a wide range of networked infrastructures to enable efficient data sampling for digital twins.
- S. D. Guikema. 2009. Natural disaster risk analysis for critical infrastructure systems: An approach based on statistical learning theory. Reliab. Eng. Syst. Saf. 94, 4 (2009), 855–860. DOI:http://dx.doi.org/10.1016/j.ress.2008.09.003Google Scholar
Cross Ref
- V. I. Pye and R. Patrick. 1983. Ground water contamination in the united states. Science 221, 4612 (1983), 713–718. DOI:http://dx.doi.org/10.1126/science.6879171Google Scholar
- L. Mays. 2004. Water Supply Systems Security. McGraw-Hill Professional Engineering.Google Scholar
- T. Ping. 2010. Terrorism—A new perspective in the water management landscape. Int. J. Water Resour. Devel. 26, 1 (2010), 51–63. DOI:http://dx.doi.org/10.1080/07900620903392158Google Scholar
Cross Ref
- Robert Janke, Regan Murray, James Uber, and Tom Taxon. 2006. Comparison of physical sampling and real-time monitoring strategies for designing a contamination warning system in a drinking water distribution system. J. Water Resour. Plann. Manag. 132, 4 (2006), 310–313.Google Scholar
Cross Ref
- Oluwaseye S. Adedoja, Yskandar Hamam, Baset Khalaf, and Rotimi Sadiku. 2018. A state-of-the-art review of an optimal sensor placement for contaminant warning system in a water distribution network. Urb. Water J. 15, 10 (2018), 985–1000.Google Scholar
Cross Ref
- N. Chang, N. Prapinpongsanone, and A. Ernest. 2012. Optimal sensor deployment in a large-scale complex drinking water network: Comparisons between a rule-based decision support system and optimization models. Comput. Chem. Eng. 43 (2012).Google Scholar
- J. W. Berry, L. Fleischer, W. E. Hart, C. A. Phillips, and J. P. Watson. 2005. Sensor placement in municipal water networks. J. Water Resour. Plann. Manag. 131 (01 2005), 237–243.Google Scholar
- A. Kessler, A. Ostfeld, and G. Sinai. 1998. Detecting accidental contaminations in municipal water networks. J. Water Resour. Plann. Manag. 124 (1998), 192–198.Google Scholar
Cross Ref
- A. Ostfeld and E. Salomons. 2004. Optimal layout of early warning detection stations for water distribution systems security. J. Water Resour. Plann. Manag. 130 (09 2004). DOI:http://dx.doi.org/10.1061/(ASCE)0733-9496(2004)130:5(377)Google Scholar
- Jonathan Berry, Robert D. Carr, William E. Hart, Vitus J. Leung, Cynthia A. Phillips, and Jean-Paul Watson. 2009. Designing contamination warning systems for municipal water networks using imperfect sensors. J. Water Resour. Plann. Manag. 135, 4 (2009), 253–263.Google Scholar
Cross Ref
- Mohammad Reza Bazargan-Lari. 2014. An evidential reasoning approach to optimal monitoring of drinking water distribution systems for detecting deliberate contamination events. J. Clean. Product. 78 (2014), 1–14.Google Scholar
Cross Ref
- Hervé Ung, Olivier Piller, Denis Gilbert, and Iraj Mortazavi. 2017. Accurate and optimal sensor placement for source identification of water distribution networks. J. Water Resour. Plann. Manag. 143, 8 (2017), 04017032.Google Scholar
Cross Ref
- C. Giudicianni, M. Herrera, A. Di Nardo, R. Greco, E. Creaco, and A. Scala. 2020. Topological placement of quality sensors in water-distribution networks without the recourse to hydraulic modeling. J. Water Resour. Plann. Manag. 146, 6 (2020), 04020030.Google Scholar
Cross Ref
- J. Chu, C. Zhang, G. Fu, Y. Li, and H. Zhou. 2015. Improving multi-objective reservoir operation optimization with sensitivity-informed dimension reduction. Hydrol. Earth Syst. Sci. 19, 8 (2015).Google Scholar
- N. Sankary and A. Ostfeld. 2017. Incorporating operational uncertainty in early warning system design optimization for water distribution system security. Procedia Eng. 186 (2017), 160–167. DOI:http://dx.doi.org/10.1016/j.proeng.2017.03.222Google Scholar
Cross Ref
- M. M. Aral, J. Guan, and M. L. Maslia. 2010. Optimal design of sensor placement in water distribution networks. J. Water Resour. Plann. Manag. 136, 1 (2010), 5–18. DOI:http://dx.doi.org/10.1061/(ASCE)WR.1943-5452.0000001Google Scholar
Cross Ref
- A. Krause, J. Leskovec, C. Guestrin, and J. Van Briesen. 2008. Efficient sensor placement optimization for securing large water distribution networks. J. Water Resour. Plann. Manag. 134 (2008).Google Scholar
- F. Archetti, A. Candelieri, and D. Soldi. 2015. Network analysis for resilience evaluation in water distribution networks. Environ. Eng. Manag. J. 14 (2015).Google Scholar
- C. Giudicianni, A. Nardo, M. Natale, R. Greco, G. Santonastaso, and A. Scala. 2018. Topological taxonomy of water distribution systems. Water 10 (2018).Google Scholar
- A. Simone, L. Ridolfi, D. Laucelli, L. Berardi, and O. Giustolisi. 2018. Centrality metrics for water distribution networks. EPiC Series Eng. 3 (2018).Google Scholar
- A. Di Nardo, C. Giudicianni, R. Greco, M. Herrera, G. Santonastaso, and A. Scala. 2018. Sensor placement in water distribution networks based on spectral algorithms. In 13th International Conference on Hydroinformatics (HIC’18). DOI:http://dx.doi.org/10.29007/whzrGoogle Scholar
- K. Diao, R. Farmani, G. Fu, and D. Butler. 2014. Vulnerability assessment of water distribution systems using directed and undirected graph theory. In International Conference on Hydroinformatics.Google Scholar
- J. Hart, I. Guymer, F. Sonnenwald, and V. Stovin. 2016. Residence time distributions for turbulent, critical, and laminar pipe flow. J. Hydraul. Eng. 142 (2016).Google Scholar
- R. Du, L. Gkatzikis, C. Fischione, and M. Xiao. 2015. Energy efficient sensor activation for water distribution networks based on compressive sensing,. IEEE J. Select. Areas Commun. 33 (2015).Google Scholar
- S. Kartakis, G. Tzagkarakis, and J. McCann. 2019. Adaptive compressive sensing in smart water networks. MDPI 2nd Int. Ele. Conf. Sens. Applic. 6 (2019).Google Scholar
- X. Xie, Q. Zhou, D. Hou, and H. Zhang. 2017. Compressed sensing based optimal sensor placement for leak localization in water distribution networks. J. Hydroinform. 20 (2017).Google Scholar
- E. J. Candes and Y. Plan. 2011. Tight oracle inequalities for low-rank matrix recovery from a minimal number of noisy random measurements. IEEE Trans. Inf. Theor. 57, 4 (2011), 2342–2359. Google Scholar
Digital Library
- Z. Wei, A. Pagani, G. Fu, I. Guymer, W. Chen, J. McCann, and W. Guo. 2020. Optimal sampling of water distribution network dynamics using graph Fourier transform. IEEE Trans. Netw. Sci. Eng. 7, 3 (2020), 1570–1582. DOI:http://dx.doi.org/10.1109/TNSE.2019.2941834Google Scholar
Cross Ref
- Z. Wei, B. Li, C. Sun, and W. Guo. 2020. Sampling and inference of networked dynamics using Log-Koopman nonlinear graph Fourier transform. IEEE Trans. Sig. Process. 68 (2020), 6187–6197.Google Scholar
Cross Ref
- M. Gori, G. Monfardini, and F. Scarselli. 2005. A new model for learning in graph domains. In the IEEE International Joint Conference on Neural Networks.729–734.Google Scholar
- F. Scarselli, M. Gori, A. C. Tsoi, M. Hagenbuchner, and G. Monfardini. 2009. The graph neural network model. IEEE Trans. Neural Netw. 20, 1 (2009), 61–80. Google Scholar
Digital Library
- Joan Bruna, Wojciech Zaremba, Arthur Szlam, and Yann LeCun. 2014. Spectral networks and locally connected networks on graphs. In the 2nd International Conference on Learning Representations.Google Scholar
- Mikael Henaff, Joan Bruna, and Yann LeCun. 2015. Deep Convolutional Networks on Graph-Structured Data. arXiv preprint arXiv:1506.05163 (2015).Google Scholar
- R. Levie, F. Monti, X. Bresson, and M. M. Bronstein. 2019. CayleyNets: Graph convolutional neural networks with complex rational spectral filters. IEEE Trans. Sig. Process. 67, 1 (2019), 97–109.Google Scholar
Digital Library
- Thomas Kipf and Max Welling. 2016. Semi-supervised classification with graph convolutional networks. In the International Conference on Learning Representations.Google Scholar
- Michaël Defferrard, Xavier Bresson, and Pierre Vandergheynst. 2016. Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering. Advances in Neural Information Processing Systems 29 (2016), 3844–3852. Google Scholar
Digital Library
- Zonghan Wu, Shirui Pan, Fengwen Chen, Guodong Long, Chengqi Zhang, and Philip S. Yu. 2019. A Comprehensive Survey on Graph Neural Networks. arxiv:1901.00596.Google Scholar
- Thapelo Mosetlhe, Yskandar Hamam, Shengzhi Du, and Yasser Alayli. 2018. Artificial neural networks in water distribution systems: A literature synopsis. In the International Conference on Intelligent and Innovative Computing Applications (ICONIC’18). DOI:http://dx.doi.org/10.1109/ICONIC.2018.8601090Google Scholar
Cross Ref
- Andrzej Czapczuk, Jacek Dawidowicz, and Jacek Piekarski. 2017. Application of multilayer perceptron for the calculation of pressure losses in water supply lines. Rocznik Ochrona Srodowiska 19 (11 2017).Google Scholar
- J. Dawidowicz, A. Czapczuk, and J. Piekarski. 2018. The application of artificial neural networks in the assessment of pressure losses in water pipes in the design of water distribution systems. Rocznik Ochrona Srodowiska 20 (10 2018), 292–308.Google Scholar
- G. A. Cuesta Cordoba, L. Tuhovčák, and M. Tauš. 2014. Using artificial neural network models to assess water quality in water distribution networks. Procedia Eng. 70 (2014), 399-408. DOI:http://dx.doi.org/10.1016/j.proeng.2014.02.045Google Scholar
Cross Ref
- Manuel A. Andrade, Doosun Kang, Christopher Y. Choi, and Kevin Lansey. 2013. Heuristic postoptimization approaches for design of water distribution systems. J. Water Resour. Plann. Manag. 139, 4 (2013), 387–395. DOI:http://dx.doi.org/10.1061/(ASCE)WR.1943-5452.0000265Google Scholar
Cross Ref
- Z. Wei, B. Li, and W. Guo. 2019. Optimal sampling for dynamic complex networks with graph-bandlimited initialization. IEEE Access 7 (2019), 150294–150305.Google Scholar
Cross Ref
- Siheng Chen, Rohan Varma, Aliaksei Sandryhaila, and Jelena Kovacevic. 2015. Discrete signal processing on graphs: Sampling theory.IEEE Trans. Sig. Process. 63, 24 (2015), 6510–6523.Google Scholar
Digital Library
- Isaac Pesenson. 2008. Sampling in Paley-Wiener spaces on combinatorial graphs. Trans. Amer. Math. Soc. 360, 10 (2008), 5603–5627.Google Scholar
Cross Ref
- A. Sandryhaila and J. Moura. 2014. Discrete signal processing on graphs: Frequency analysis. IEEE Trans. Sig. Process. 62 (2014). Google Scholar
Digital Library
- Aamir Anis, Akshay Gadde, and Antonio Ortega. 2014. Towards a sampling theorem for signals on arbitrary graphs. In the International Conference on Acoustics, Speech, & Signal Processing. 3864–3868.Google Scholar
Cross Ref
- S. Chen, R. Varma, A. Sandryhaila, and J. Kovacevic. 2015. Discrete signal processing on graphs: Sampling theory. IEEE Trans. Sig. Process. 63 (2015).Google Scholar
- Xiaohan Wang, Jiaxuan Chen, and Yuantao Gu. 2015. Generalized graph signal sampling and reconstruction. In the IEEE Global Conference on Signal and Information Processing (GlobalSIP’15). IEEE, 567–571.Google Scholar
Cross Ref
- Aamir Anis, Akshay Gadde, and Antonio Ortega. 2016. Efficient sampling set selection for bandlimited graph signals using graph spectral proxies. IEEE Trans. Sig. Process. 64, 14 (2016), 3775–3789.Google Scholar
Digital Library
- S. Chen, R. Varma, A. Sandryhaila, and J. Kovacevic. 2016. Signal recovery on graphs: Fundamental limits of sampling strategies. IEEE Trans. Sig. Inf. Process. Netw. 4 (2016).Google Scholar
- Fen Wang, Yongchao Wang, and Gene Cheung. 2018. A optimal sampling and robust reconstruction for graph signals via truncated Neumann series. arXiv preprint arXiv:1803.03353 (2018).Google Scholar
- Luiz F. O. Chamon and Alejandro Ribeiro. 2018. Greedy sampling of graph signals. IEEE Trans. Sig. Process. 66, 1 (2018), 34–47.Google Scholar
Digital Library
- Antonio Ortega, Pascal Frossard, Jelena Kovačević, José M. F. Moura, and Pierre Vandergheynst. 2018. Graph signal processing: Overview, challenges, and applications. Proc. IEEE 106, 5 (2018), 808–828.Google Scholar
Cross Ref
- Mark A. Kramer. 1991. Nonlinear principal component analysis using autoassociative neural networks. AIChE J. 37, 2 (1991), 233–243. DOI:http://dx.doi.org/10.1002/aic.690370209Google Scholar
Cross Ref
- K. Klise, R. Murray, and T. Haxton.2018. An overview of the water network tool for resilience (WNTR). In Proc., 1st Int. WDSA/CCWI Joint Conf., 8. Albuquerque, Sandia National Lab.Google Scholar
- L. A. Rossman. 2000. EPANET 2 Users Manual. U.S. Environmental Protection Agency, Washington, D.C., EPA/600/R-00/057.Google Scholar
- R. Du, L. Gkatzikis, C. Fischione, and M. Xiao. 2015. Energy efficient sensor activation for water distribution networks based on compressive sensing. IEEE J. Select. Areas Commun. 33, 12 (2015), 2997–3010.Google Scholar
Digital Library
- B. O’Flynn, R. Martinez-Catala, S. Harte, C. O’Mathuna, J. Cleary, C. Slater, F. Regan, D. Diamond, and H. Murphy. 2007. SmartCoast: A wireless sensor network for water quality monitoring. In the 32nd IEEE Conference on Local Computer Networks (LCN’07). 815–816. Google Scholar
Digital Library
Index Terms
Neural Network Approximation of Graph Fourier Transform for Sparse Sampling of Networked Dynamics
Recommendations
Complex Dynamics of 4D Hopfield-Type Neural Network with Two Parameters
IWCFTA '09: Proceedings of the 2009 International Workshop on Chaos-Fractals Theories and ApplicationsIn this paper, a novel four-dimensional (4D) autonomous continuous time Hopfield-type neural network with two parameters is investigated. Computer simulations show that the 4D Hopfield neural network has rich and funny dynamics, and it can display ...
Stability of quasi-periodic orbit in discrete recurrent neural network
CONTROL'05: Proceedings of the 2005 WSEAS international conference on Dynamical systems and controlA simple discrete recurrent neural network model is considered. The local stability is analyzed with the associated characteristic model. In order to study the quasi-periodic orbit dynamic behavior, it is necessary to determinate the Neimark-Sacker ...
Compressive Sensing of Multichannel EEG Signals Based on Graph Fourier Transform and Cosparsity
AbstractCosparsity as a useful prior has been extensively applied in accurate compressive sensing (CS) recovery of multichannel electroencephalogram (EEG) signals from only a few measurements. Latest studies proved that exploiting cosparsity and channel ...






Comments