naa a22 4500 510774105 CHVBK 20180411083224.0 cr unu---uuuuu 180411e20131201xx s 000 0 eng 10.1007/s40295-015-0064-y doi (NATIONALLICENCE)springer-10.1007/s40295-015-0064-y An Iterative Proper Orthogonal Decomposition (I-POD) Technique with Application to the Filtering of Partial Differential Equations [Elektronische Daten] [Dan Yu, Suman Chakravorty] In this paper, we consider the filtering of systems governed by partial differential equations (PDE). We adopt a reduced order model (ROM) based strategy to solve the problem. We propose an iterative version of the snapshot proper orthogonal decomposition (POD) technique, termed I-POD, to sequentially construct a single ROM for PDEs that is capable of capturing their behavior over the entire state space of the system, and not just around the snapshot trajectory. Further, the technique is entirely data based, and is applicable to forced as well as unforced systems. The I-POD is compared to two other ROM techniques: the Balanced POD (BPOD) and the dynamic mode decomposition (DMD). We apply the ROM generated using the I-POD technique to construct reduced order Kalman filters to solve the filtering problem. The methodology is tested on several 1-dimensional PDEs of interest including the heat equation, the wave equation and 2-dimensional pollutant transport equation. American Astronautical Society, 2015 Model reduction nationallicence Proper orthogonal decomposition nationallicence Kalman filtering nationallicence Yu Dan Department of Aerospace Engineering, Texas A&M University, 301A RDMC, TAMU, 77840, College Station, TX, USA aut Chakravorty Suman Department of Aerospace Engineering, Texas A&M University, 741A HRBB, 77840, College Station, TX, USA aut The Journal of the Astronautical Sciences Springer US; http://www.springer-ny.com 60/3-4(2013-12-01), 468-493 0021-9142 60:3-4<468 2013 60 40295 https://doi.org/10.1007/s40295-015-0064-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s40295-015-0064-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Yu Dan Department of Aerospace Engineering, Texas A&M University, 301A RDMC, TAMU, 77840, College Station, TX, USA aut NATIONALLICENCE 700 1- Chakravorty Suman Department of Aerospace Engineering, Texas A&M University, 741A HRBB, 77840, College Station, TX, USA aut NATIONALLICENCE 773 0- The Journal of the Astronautical Sciences Springer US; http://www.springer-ny.com 60/3-4(2013-12-01), 468-493 0021-9142 60:3-4<468 2013 60 40295 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer