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Parameter and State Estimation of Infiltration Processes
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- Author / Creator
- Bo, Song
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Open-loop irrigation is a common practice in agriculture which leads to excessive consumption of water resources. Closed-loop is a promising alternative to reduce water consumption and to better maintain the health of crops, which requires soil moisture information of the investigated fields. An agro-hydrological system describes the water movements between soil, crop and atmosphere. Richards equation plays an important role in the study of agro-hydrological systems. It models the water movement in soil in the vadose zone, which is driven by capillary and gravitational forces. Its states (capillary potential) and parameters (hydraulic conductivity, saturated and residual soil moistures, and van Genuchten-Mualem parameters) are essential for the accuracy of mathematical modeling, yet difficult to obtain experimentally. In this thesis, methods are developed to estimate the parameters and states of Richards equation simultaneously.
First, the estimation problem is studied on one-dimensional Richards equation with spatially and temporally homogeneous parameters. The finite difference model and augmented model of Richards equation are constructed for simultaneous estimation. In the proposed estimation approach, parameter identifiability is tested to determine the identifiable parameter sets and sensitivity analysis is used to determine the most important parameter set for estimation purpose. The minimum number of sensors to ensure the identifiability of parameters is determined by conducting maximum multiplicity method. Three common estimation schemes (extended Kalman filter, ensemble Kalman filter and moving horizon estimation) are investigated. The estimation performance is compared and analyzed based on extensive simulations.
The estimation problem is extended to estimate the parameters and states of three-dimensional Richards equation with spatially heterogeneous and temporally homogeneous parameters. The finite difference model and augmented model of three-dimensional Richards equation are developed which include parameters of multiple types of soil. In the proposed approach, decentralized or distributed estimation scheme is proposed since the increasing number of states presented in the system. Before subsystem decomposition, observability of the original augmented system is ensured. In other words, parameter identifiability and sensitivity analysis are used to determine the significant parameter set for estimation purpose. Then, the guidelines for subsystem decomposition are introduced, which is followed by observability test on subsystems. A study of interaction between subsystems is conducted which further motivates the decentralized estimation framework. The decentralized moving horizon estimation is studied and its performance is extensively discussed.
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- Graduation date
- Spring 2020
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- Type of Item
- Thesis
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- Degree
- Master of Science
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- License
- Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.