Dinamička modalna dekompozicija u realnom vremenu

master's thesis

• Author: Matej Poletar
• Mentor: Zlatko Drmač (mentor)
• Committee member: Zlatko Drmač (predsjednik povjerenstva)
• Committee member: Eduard Marušić-Paloka (član povjerenstva)
• Committee member: Saša Singer (član povjerenstva)
• Committee member: Boris Muha (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-07-18, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Dinamička modalna dekompozicija (textit{Dynamic Mode Decomposition, DMD) je metoda originalno razvijena za numeričke simulacije u dinamici fluida i pokazala se uspješnom u analizi tzv. koherentnih struktura. U praktičnoj realizaciji je često kombinirana s Proper Orthogonal Decomposition (POD). DMD je posebno prikladna u tzv. data driven scenarijima, kada se iz niza dobivenih podataka empirijski gradi model kojeg se može koristiti za kontrolu i/ili predviđanje budućih vrijednosti. U slučaju simulacija u realnom vremenu i s vremenski promjenjivim koeficijentima nužno je koristiti podatke iz klizećeg vremenskog prozora ograničene širine koji uključuje najnovije podatke. Pri tome se DMD mora u svakom koraku obnavljati, što zahtijeva nove efikasne algoritme. U ovoj radnji su proučeni takvi algoritmi s primjenama na odabranim primjerima.

Abstract (english)

Dynamic Mode Decomposition (DMD) is method originally developed for numerical simulations in fluid dynamics and it has been well used in analysis of coherent structures. In practice, it often goes with Proper Orthogonal Decomposition. DMD is especially suitable for analysis of data-driven scenarios, where model is empirically built from sequence of input data and can be used for control and/or anticipation of future states. For real-time simulations and with variable coefficients in time, usage of data from sliding width-limited time window which includes most recent data is mandatory. In that case DMD has to be renewed in each step, which requires new efficient algorithms. In this work, such algorithms have been studied in selected examples.

• Keywords: dinamička modalna dekompozicija; numeričke simulacije; simulacija u realnom vremenu; DMD; POD
• Keywords (english): Dynamic Mode Decomposition; numerical simulations; real-time simulation; Proper Orthogonal Decomposition; DMD; POD
• Language: croatian
• URN:NBN: urn:nbn:hr:217:503989
• 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: 2019-06-10 12:26:12