Data Driven System Identification of Water Distribution Systems via Kernel-Based Interpolation
Publication: World Environmental and Water Resources Congress 2024
ABSTRACT
Water distribution systems (WDSs) are critical infrastructure demanding effective control for optimal pressure and flow. Existing control algorithms rely on accurate system models, a challenging task for large-scale WDSs due to complex, nonlinear hydraulics. This work proposes a data-driven system identification using kernel-based interpolation, assuming general WDS dynamics without prior knowledge of the true basis functions. Leveraging WDSs’ automation, such as water level and flow sensors, this method constructs a regularized interpolated kernel-based model based on input-output pairs. Compared to state-of-the-art system identification, the predicted model offers deterministic bounds on the approximation error to enhance the accuracy. Given that WDSs are changing over time, this approach is useful to ensure that the controller is adept with the changing dynamics of WDS. The proposed method is validated on four interconnected water tanks, representing simplified WDSs yet equipped with WDSs’ nonlinearities. The results demonstrate high accuracy with errors varying from 0.02% to 3%.
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REFERENCES
Alizadeh, Z., Yazdi, J., Mohammadiun, S., Hewage, K., and Sadiq, R. (2019). “Eval- uation of data driven models for pipe burst prediction in urban water distribution systems.” Urban Water Journal, 16(2), 136–145.
Aronszajn, N. (1950). “Theory of reproducing kernels.” Transactions of the American mathematical society, 68(3), 337–404.
Balla, K. M., Jensen, T. N., Bendtsen, J. D., and Kallesøe, C. S. (2019). “Model predic- tive control using linearized radial basis function neural models for water distribution networks.” 2019 IEEE Conference on Control Technology and Applications (CCTA), IEEE, 368–373.
Cembrano, G., Wells, G., Quevedo, J., Pérez, R., and Argelaguet, R. (2000). “Optimal control of a water distribution network in a supervisory control system.” Control engineering practice, 8(10), 1177–1188.
Chapra, S. C., and Canale, R. P. (2020). Numerical methods for engineers. Mcgraw-hill.
Cristianini, N., and Shawe-Taylor, J. (2000). An introduction to support vector machines and other kernel-based learning methods. Cambridge university press.
De Persis, C., Rotulo, M., and Tesi, P. (2023). “Learning controllers from data via approximate nonlinearity cancellation.” IEEE Transactions on Automatic Control.
Hu, Z., De Persis, C., and Tesi, P. (2023). “Learning controllers from data via kernel- based interpolation.” arXiv preprint arXiv:2304.09577.
Iwakin, O. M., and Moazeni, F. (2023). “Short-term water demand prediction using machine learning techniques—a case study of telford borough in pennsylvania.” World Environmental and Water Resources Congress 2023, 1027–1036.
Johansson, K. H. (2000). “The quadruple-tank process: A multivariable laboratory process with an adjustable zero.” IEEE Transactions on control systems technology, 8(3), 456–465.
Jung, M., da Costa Mendes, P. R., Önnheim, M., and Gustavsson, E. (2023). “Model predictive control when utilizing lstm as dynamic models.” Engineering Applications of Artificial Intelligence, 123, 106226.
Kanagawa, M., Hennig, P., Sejdinovic, D., and Sriperumbudur, B. K. (2018). “Gaussian processes and kernel methods: A review on connections and equivalences.” arXiv preprint arXiv:1807.02582.
Maalouf, M., Homouz, D., and Abutayeh, M. (2016). “Accurate prediction of preheat temperature in solar flash desalination systems using kernel ridge regression.” Journal of Energy Engineering, 142(2), E4015017.
Martin, T., Schön, T. B., and Allgöwer, F. (2023). “Guarantees for data-driven control of nonlinear systems using semidefinite programming: A survey.” Annual Reviews in Control, 100911.
NRC, N. R. C. (2007). Drinking water distribution systems: Assessing and reducing risks. National Academies Press.
Pillonetto, G., Dinuzzo, F., Chen, T., De Nicolao, G., and Ljung, L. (2014). “Ker- nel methods in system identification, machine learning and function estimation: A survey.” Automatica, 50(3), 657–682.
Safari, M. J. S., and Rahimzadeh Arashloo, S. (2021). “Kernel ridge regression model for sediment transport in open channel flow.” Neural Computing and Applications, 33(17), 11255–11271.
Saleem, F., Ali, A., Shaikh, I.-U.-H., and Wasim, M. (2023). “Application and comparison of kernel functions for linear parameter varying model approximation of nonlinear systems.” Applied Mathematics-A Journal of Chinese Universities, 38(1), 58–77.
Scharnhorst, P., Maddalena, E. T., Jiang, Y., and Jones, C. N. (2022). “Robust uncertainty bounds in reproducing kernel hilbert spaces: A convex optimization approach.” IEEE Transactions on Automatic Control.
Thiele, G., Fey, A., Sommer, D., and Krüger, J. (2020). “System identification of a hysteresis-controlled pump system using sindy.” 2020 24th International Conference on System Theory, Control and Computing (ICSTCC), IEEE, 457–464.
van Waarde, H. J., De Persis, C., Camlibel, M. K., and Tesi, P. (2020). “Willems’ fundamental lemma for state-space systems and its extension to multiple datasets.” IEEE Control Systems Letters, 4(3), 602–607.
Wang, S., Chakrabarty, A., and Taha, A. F. (2023). “Data-driven identification of dynamic quality models in drinking water networks.” Journal of Water Resources Planning and Management, 149(4), 04023008.
Wendland, H. (2004). Scattered data approximation, Vol. 17. Cambridge university press.
Willems, J. C., Rapisarda, P., Markovsky, I., and De Moor, B. L. (2005). “A note on persistency of excitation.” Systems & Control Letters, 54(4), 325–32.
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Published online: May 16, 2024
ASCE Technical Topics:
- Continuum mechanics
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Equipment and machinery
- Errors (statistics)
- Hydraulic models
- Infrastructure
- Lifeline systems
- Mathematics
- Model accuracy
- Models (by type)
- Pressure (type)
- Solid mechanics
- Statistics
- Tanks (by type)
- Water and water resources
- Water management
- Water pressure
- Water supply
- Water supply systems
- Water tanks
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