Reduced Order Modelling using Dynamic Mode Decomposition and Koopman Spectral Analysis with Deep Learning
(2020) In Master's Theses in Mathematical Sciences FMNM01 20201Mathematics (Faculty of Engineering)
- Abstract
- In the industry simulation models are commonly used in system development. These models can become complicated in order to capture the physical behaviour of the underlying dynamical system. A high-fidelity representation, which can result in long simulation times, is in some settings not strictly required. A method for overall model fidelity reduction is therefore of interest.
In this thesis, two data-driven methods for model order reduction based on modal decomposition of data have been investigated. More specifically, we explore dynamic mode decomposition (DMD) and Koopman spectral analysis with deep learning. We validated this approach by extracting dominant dynamical characteristics from data for reduced order modelling. This was... (More) - In the industry simulation models are commonly used in system development. These models can become complicated in order to capture the physical behaviour of the underlying dynamical system. A high-fidelity representation, which can result in long simulation times, is in some settings not strictly required. A method for overall model fidelity reduction is therefore of interest.
In this thesis, two data-driven methods for model order reduction based on modal decomposition of data have been investigated. More specifically, we explore dynamic mode decomposition (DMD) and Koopman spectral analysis with deep learning. We validated this approach by extracting dominant dynamical characteristics from data for reduced order modelling. This was achieved by applying the methods to both linear and non-linear dynamical systems.
A reduced order model of a large highly non-linear dynamical system with meaningful fidelity was produced using the DMD method. Additionally, this reduced order model can be simulated significantly faster than the original high-fidelity model. The Koopman method was successfully applied to smaller non-linear systems, but did not capture the dynamics of the large highly non-linear system. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9022444
- author
- Krantz, David LU and Månsson, Olof LU
- supervisor
-
- Philipp Birken LU
- Pontus Fyhr LU
- organization
- course
- FMNM01 20201
- year
- 2020
- type
- H2 - Master's Degree (Two Years)
- subject
- keywords
- non-linear dynamical systems, modal decomposition, Koopman operator theory, machine learning, data-driven analysis
- publication/series
- Master's Theses in Mathematical Sciences
- report number
- LUTFNA-3048-2020
- ISSN
- 1404-6342
- other publication id
- 2020:E45
- language
- English
- id
- 9022444
- date added to LUP
- 2020-07-07 14:51:35
- date last changed
- 2020-07-07 14:51:35
@misc{9022444,
abstract = {{In the industry simulation models are commonly used in system development. These models can become complicated in order to capture the physical behaviour of the underlying dynamical system. A high-fidelity representation, which can result in long simulation times, is in some settings not strictly required. A method for overall model fidelity reduction is therefore of interest.
In this thesis, two data-driven methods for model order reduction based on modal decomposition of data have been investigated. More specifically, we explore dynamic mode decomposition (DMD) and Koopman spectral analysis with deep learning. We validated this approach by extracting dominant dynamical characteristics from data for reduced order modelling. This was achieved by applying the methods to both linear and non-linear dynamical systems.
A reduced order model of a large highly non-linear dynamical system with meaningful fidelity was produced using the DMD method. Additionally, this reduced order model can be simulated significantly faster than the original high-fidelity model. The Koopman method was successfully applied to smaller non-linear systems, but did not capture the dynamics of the large highly non-linear system.}},
author = {{Krantz, David and Månsson, Olof}},
issn = {{1404-6342}},
language = {{eng}},
note = {{Student Paper}},
series = {{Master's Theses in Mathematical Sciences}},
title = {{Reduced Order Modelling using Dynamic Mode Decomposition and Koopman Spectral Analysis with Deep Learning}},
year = {{2020}},
}