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Sampling of time-varying network signals from equation-driven to data-driven techniques
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Wei, Zhuangkun (2020) Sampling of time-varying network signals from equation-driven to data-driven techniques. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3717700~S15
Abstract
Sampling and recovering the time-varying network signals via the subset of network vertices is essential for a wide range of scientific and engineering purposes. Current studies on sampling a single (continuous) time-series or a static network data, are not suitable for time-varying network signals. This will be even more challenging when there is a lack of explicit dynamic models and signal-space that indicate the time-evolution and vertex dependency.
The work begins by bridging the time-domain sampling frequency and the network-domain sampling vertices, via the eigenvalues of the graph Fourier transform (GFT) operator composed by the combined dynamic equations and network topology. Then, for signals with hidden governing mechanisms, we propose a data-driven GFT sampling method using a prior signal-space. We characterize the signal dependency (among vertices) into the graph bandlimited frequency domain, and map such bandlimitedness into optimal sampling vertices.
Furthermore, to achieve dynamic model and signal-space independent sensor placement, a Koopman based nonlinear GFT sampling is proposed. A novel data-driven Log-Koopman operator is designed to extract a linearized evolution model using small (M = O(N)) and decoupled observables defined on N original vertices. Then, nonlinear GFT is proposed to derive sampling vertices, by exploiting the inherent nonlinear dependence between M observables (defined on N < M vertices), and the time-evolved information presented by Log-Koopman evolution model.
The work also informs the planned future work to formulate an easy-to-use and explainable neural network (NN) based sampling framework, for real-world industrial engineering and applications.
Item Type: | Thesis (PhD) | ||||
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Subjects: | T Technology > TK Electrical engineering. Electronics Nuclear engineering | ||||
Library of Congress Subject Headings (LCSH): | Signal processing -- Digital techniques, Wireless communication systems | ||||
Official Date: | December 2020 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | School of Engineering | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Guo, Weisi ; Chen, Yunfei, 1976- | ||||
Sponsors: | University of Warwick ; China Scholarship Council | ||||
Format of File: | |||||
Extent: | xiv, 129 leaves : colour illustrations | ||||
Language: | eng |
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