Redukcija dimenzije parametarski ovisnih nelinearnih sustava

master's thesis

• Author: Iva Manojlović
• Mentor: Zlatko Drmač (mentor)
• Committee member: Zlatko Drmač (predsjednik povjerenstva)
• Committee member: Eduard Marušić-Paloka (član povjerenstva)
• Committee member: Mladen Vuković (član povjerenstva)
• Committee member: Matija Kazalicki (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U današnje vrijeme mjerenja stanja nekog sustava od interesa su sve opširnija i sve točnija. Za opisivanje sustava koji ovise o različitim parametrima zato je sve popularniji pristup koji se upravo temelji na modeliranju ponašanja sustava pomoću već prikupljenih podataka. POD i DEIM pokazale su se kao dobre metode za redukciju dimenzionalnosti dinamičkih sustava i sustava nelinearnih jednadžbi. Pomoću reduciranih modela lako možemo opisati sustav za parametre za koje nismo napravili mjerenje. Pomoću DMDa i njegovih varijanti možemo opisati ponašanje sustava kao lokalno linearnog dinamičkog sustava, što nam omogućava procjenu budućih stanja temeljenoj samo na izmjerenim podacima, a ne na rješavanju sustava. U ovom radu opisani su navedeni algoritmi s primjenama na odabranim primjerima.

Abstract (english)

Nowadays measuring states of a system we are interested in can be done more accurately and in more detail than ever before. That's why there are different approaches which use collected data for describing systems which depend on different parameters. POD and DEIM proved to be good methods for reducing dimension of dynamical systems and systems of nonlinear equations. With reduced model we can easily describe system for parameters for which we don't have measured data or numerical solution. With DMD and its versions we can describe behaviour of system like a locally linear dynamical system, which provides an estimate of future state, which depend only on measured data and not on solving the system for that time. In this work, such algorithm were described with applications on selected examples.

• Keywords: mjerenje stanja sustava; parametarski ovisni sustavi; POD; DEIM; redukcija dimenzionalnosti; dinamički sustav; sustav nelinearnih jednadžbi; DMD
• Keywords (english): measuring states of a system; parameter-dependent systems; POD; DEIM; reducing dimension; dynamical system; system of nonlinear equations; DMD
• Language: croatian
• URN:NBN: urn:nbn:hr:217:155923
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-06-05 11:34:49