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Grey-box modelling of distributed parameter systems
KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
2018 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Hybridmodellering av distribuerade parametersystem (Swedish)
Abstract [en]

Grey-box models are constructed by combining model components that are derived from first principles with components that are identified empirically from data. In this thesis a grey-box modelling method for describing distributed parameter systems is presented. The method combines partial differential equations with a multi-layer perceptron network in order to incorporate prior knowledge about the system while identifying unknown dynamics from data. A gradient-based optimization scheme which relies on the reverse mode of automatic differentiation is used to train the network. The method is presented in the context of modelling the dynamics of a chemical reaction in a fluid. Lastly, the grey-box modelling method is evaluated on a one-dimensional and two-dimensional instance of the reaction system. The results indicate that the grey-box model was able to accurately capture the dynamics of the reaction system and identify the underlying reaction.

Abstract [sv]

Hybridmodeller konstrueras genom att kombinera modellkomponenter som härleds från grundläggande principer med modelkomponenter som bestäms empiriskt från data. I den här uppsatsen presenteras en metod för att beskriva distribuerade parametersystem genom hybridmodellering. Metoden kombinerar partiella differentialekvationer med ett neuronnätverk för att inkorporera tidigare känd kunskap om systemet samt identifiera okänd dynamik från data. Neuronnätverket tränas genom en gradientbaserad optimeringsmetod som använder sig av bakåt-läget av automatisk differentiering. För att demonstrera metoden används den för att modellera kemiska reaktioner i en fluid. Metoden appliceras slutligen på ett en-dimensionellt och ett två-dimensionellt exempel av reaktions-systemet. Resultaten indikerar att hybridmodellen lyckades återskapa beteendet hos systemet med god precision samt identifiera den underliggande reaktionen.

Place, publisher, year, edition, pages
2018.
Series
TRITA-EECS-EX ; 2018:749
Keywords [en]
grey-box, distributed parameter system, partial differential equations, chemical reactions, finite element method, FEM, machine learning, neural networks
Keywords [sv]
hybridmodell, distribuerade parametersystem, partiella differentialekvationer, kemiska reaktioner, finita elementmetoden, FEM, maskininlärning, neuronnätverk
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:kth:diva-240677OAI: oai:DiVA.org:kth-240677DiVA, id: diva2:1274745
Educational program
Master of Science in Engineering -Engineering Physics
Supervisors
Examiners
Available from: 2019-01-09 Created: 2019-01-02 Last updated: 2019-01-09Bibliographically approved

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Citation style
  • apa
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