skip to main content
research-article

Neural Network Approximation of Graph Fourier Transform for Sparse Sampling of Networked Dynamics

Authors Info & Claims
Published:14 September 2021Publication History
Skip Abstract Section

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.

References

  1. 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 ScholarGoogle ScholarCross RefCross Ref
  2. 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 ScholarGoogle Scholar
  3. L. Mays. 2004. Water Supply Systems Security. McGraw-Hill Professional Engineering.Google ScholarGoogle Scholar
  4. 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 ScholarGoogle ScholarCross RefCross Ref
  5. 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 ScholarGoogle ScholarCross RefCross Ref
  6. 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 ScholarGoogle ScholarCross RefCross Ref
  7. 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 ScholarGoogle Scholar
  8. 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 ScholarGoogle Scholar
  9. 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 ScholarGoogle ScholarCross RefCross Ref
  10. 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 ScholarGoogle Scholar
  11. 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 ScholarGoogle ScholarCross RefCross Ref
  12. 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 ScholarGoogle ScholarCross RefCross Ref
  13. 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 ScholarGoogle ScholarCross RefCross Ref
  14. 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 ScholarGoogle ScholarCross RefCross Ref
  15. 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 ScholarGoogle Scholar
  16. 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 ScholarGoogle ScholarCross RefCross Ref
  17. 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 ScholarGoogle ScholarCross RefCross Ref
  18. 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 ScholarGoogle Scholar
  19. F. Archetti, A. Candelieri, and D. Soldi. 2015. Network analysis for resilience evaluation in water distribution networks. Environ. Eng. Manag. J. 14 (2015).Google ScholarGoogle Scholar
  20. C. Giudicianni, A. Nardo, M. Natale, R. Greco, G. Santonastaso, and A. Scala. 2018. Topological taxonomy of water distribution systems. Water 10 (2018).Google ScholarGoogle Scholar
  21. A. Simone, L. Ridolfi, D. Laucelli, L. Berardi, and O. Giustolisi. 2018. Centrality metrics for water distribution networks. EPiC Series Eng. 3 (2018).Google ScholarGoogle Scholar
  22. 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 ScholarGoogle Scholar
  23. 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 ScholarGoogle Scholar
  24. 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 ScholarGoogle Scholar
  25. 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 ScholarGoogle Scholar
  26. 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 ScholarGoogle Scholar
  27. 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 ScholarGoogle Scholar
  28. 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 ScholarGoogle ScholarDigital LibraryDigital Library
  29. 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 ScholarGoogle ScholarCross RefCross Ref
  30. 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 ScholarGoogle ScholarCross RefCross Ref
  31. 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 ScholarGoogle Scholar
  32. 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 ScholarGoogle ScholarDigital LibraryDigital Library
  33. 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 ScholarGoogle Scholar
  34. Mikael Henaff, Joan Bruna, and Yann LeCun. 2015. Deep Convolutional Networks on Graph-Structured Data. arXiv preprint arXiv:1506.05163 (2015).Google ScholarGoogle Scholar
  35. 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 ScholarGoogle ScholarDigital LibraryDigital Library
  36. Thomas Kipf and Max Welling. 2016. Semi-supervised classification with graph convolutional networks. In the International Conference on Learning Representations.Google ScholarGoogle Scholar
  37. 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 ScholarGoogle ScholarDigital LibraryDigital Library
  38. 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 ScholarGoogle Scholar
  39. 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 ScholarGoogle ScholarCross RefCross Ref
  40. 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 ScholarGoogle Scholar
  41. 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 ScholarGoogle Scholar
  42. 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 ScholarGoogle ScholarCross RefCross Ref
  43. 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 ScholarGoogle ScholarCross RefCross Ref
  44. 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 ScholarGoogle ScholarCross RefCross Ref
  45. 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 ScholarGoogle ScholarDigital LibraryDigital Library
  46. Isaac Pesenson. 2008. Sampling in Paley-Wiener spaces on combinatorial graphs. Trans. Amer. Math. Soc. 360, 10 (2008), 5603–5627.Google ScholarGoogle ScholarCross RefCross Ref
  47. A. Sandryhaila and J. Moura. 2014. Discrete signal processing on graphs: Frequency analysis. IEEE Trans. Sig. Process. 62 (2014). Google ScholarGoogle ScholarDigital LibraryDigital Library
  48. 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 ScholarGoogle ScholarCross RefCross Ref
  49. S. Chen, R. Varma, A. Sandryhaila, and J. Kovacevic. 2015. Discrete signal processing on graphs: Sampling theory. IEEE Trans. Sig. Process. 63 (2015).Google ScholarGoogle Scholar
  50. 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 ScholarGoogle ScholarCross RefCross Ref
  51. 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 ScholarGoogle ScholarDigital LibraryDigital Library
  52. 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 ScholarGoogle Scholar
  53. 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 ScholarGoogle Scholar
  54. Luiz F. O. Chamon and Alejandro Ribeiro. 2018. Greedy sampling of graph signals. IEEE Trans. Sig. Process. 66, 1 (2018), 34–47.Google ScholarGoogle ScholarDigital LibraryDigital Library
  55. 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 ScholarGoogle ScholarCross RefCross Ref
  56. 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 ScholarGoogle ScholarCross RefCross Ref
  57. 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 ScholarGoogle Scholar
  58. L. A. Rossman. 2000. EPANET 2 Users Manual. U.S. Environmental Protection Agency, Washington, D.C., EPA/600/R-00/057.Google ScholarGoogle Scholar
  59. 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 ScholarGoogle ScholarDigital LibraryDigital Library
  60. 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 ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Neural Network Approximation of Graph Fourier Transform for Sparse Sampling of Networked Dynamics

        Recommendations

        Comments

        Login options

        Check if you have access through your login credentials or your institution to get full access on this article.

        Sign in

        Full Access

        • Published in

          cover image ACM Transactions on Internet Technology
          ACM Transactions on Internet Technology  Volume 22, Issue 1
          February 2022
          717 pages
          ISSN:1533-5399
          EISSN:1557-6051
          DOI:10.1145/3483347
          • Editor:
          • Ling Liu
          Issue’s Table of Contents

          Copyright © 2021 Association for Computing Machinery.

          Publisher

          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 14 September 2021
          • Accepted: 1 April 2021
          • Revised: 1 March 2021
          • Received: 1 March 2020
          Published in toit Volume 22, Issue 1

          Permissions

          Request permissions about this article.

          Request Permissions

          Check for updates

          Qualifiers

          • research-article
          • Refereed
        • Article Metrics

          • Downloads (Last 12 months)56
          • Downloads (Last 6 weeks)1

          Other Metrics

        PDF Format

        View or Download as a PDF file.

        PDF

        eReader

        View online with eReader.

        eReader

        HTML Format

        View this article in HTML Format .

        View HTML Format
        About Cookies On This Site

        We use cookies to ensure that we give you the best experience on our website.

        Learn more

        Got it!