{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/104953"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/104953","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Model order reduction in the frequency domain via spectral proper orthogonal decomposition","abstract":"In this thesis, we introduce a novel model order reduction framework for harmonically and randomly forced dynamical systems. Specifically, we emphasize the usage of spectral proper orthogonal decomposition (SPOD), recently revived by Towne et. al. (2018), which results in sets of orthogonal modes, each oscillating at a single frequency, that are said to optimally represent coherent-structures evolving in space and time. However, reduced-order models (ROMs) using SPOD modes have not yet been developed. Hence, in this study we investigate the potential of a novel approach utilizing SPOD modes to construct the lower-dimensional subspace for ROMs. Upon the discrete-time Fourier-transform (DFT) of the governing ordinary differential equation (ODE) system, an orthogonal projection onto the SPOD modes is performed, analogous to Proper Orthogonal Decomposition (POD) Galerkin ROMs, but compressing the system at each discrete frequency within the frequency domain. The ROM is solved at each frequency and after the inverse DFT of the spectral solution matrix we obtain the entire solution for a given timespan at once, with no time integration necessary. This new approach is illustrated using the example PDE of steady passive scalar transport in an inhomogenous, time-invariant flow field. Finally, we compare the performance of our ROM with the standard POD-Galerkin ROM in terms of accuracy and computational speedup.","abstract_html":"In this thesis, we introduce a novel model order reduction framework for harmonically and randomly forced dynamical systems. Specifically, we emphasize the usage of spectral proper orthogonal decomposition (SPOD), recently revived by Towne et. al. (2018), which results in sets of orthogonal modes, each oscillating at a single frequency, that are said to optimally represent coherent-structures evolving in space and time. However, reduced-order models (ROMs) using SPOD modes have not yet been developed. Hence, in this study we investigate the potential of a novel approach utilizing SPOD modes to construct the lower-dimensional subspace for ROMs. Upon the discrete-time Fourier-transform (DFT) of the governing ordinary differential equation (ODE) system, an orthogonal projection onto the SPOD modes is performed, analogous to Proper Orthogonal Decomposition (POD) Galerkin ROMs, but compressing the system at each discrete frequency within the frequency domain. The ROM is solved at each frequency and after the inverse DFT of the spectral solution matrix we obtain the entire solution for a given timespan at once, with no time integration necessary. This new approach is illustrated using the example PDE of steady passive scalar transport in an inhomogenous, time-invariant flow field. Finally, we compare the performance of our ROM with the standard POD-Galerkin ROM in terms of accuracy and computational speedup.","abstract_has_math":false,"creators":["Cong, Lin"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Aerospace Engineering","degree_department":null,"school":null,"contributors":["Balajewicz, Maciej"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-08-23T20:05:25Z","date_published":"2019-08-23T20:05:25Z","updated_at":"2026-07-22T22:24:44Z","subjects":["POD","SPOD","reduced-order modeling","reduced-order model","DMD"],"languages":["en"],"rights":["Copyright 2019 Cong Lin"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/104953","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Balajewicz, Maciej"]},{"key":"dc:creator","label":"Author","values":["Cong, Lin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-08-23T20:05:25Z","2019-04-26","2019-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Aerospace Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["POD","SPOD","reduced-order modeling","reduced-order model","DMD"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2019 Cong Lin"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/104953"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis, we introduce a novel model order reduction framework for harmonically and randomly forced dynamical systems. Specifically, we emphasize the usage of spectral proper orthogonal decomposition (SPOD), recently revived by Towne et. al. (2018), which results in sets of orthogonal modes, each oscillating at a single frequency, that are said to optimally represent coherent-structures evolving in space and time. However, reduced-order models (ROMs) using SPOD modes have not yet been developed. Hence, in this study we investigate the potential of a novel approach utilizing SPOD modes to construct the lower-dimensional subspace for ROMs. Upon the discrete-time Fourier-transform (DFT) of the governing ordinary differential equation (ODE) system, an orthogonal projection onto the SPOD modes is performed, analogous to Proper Orthogonal Decomposition (POD) Galerkin ROMs, but compressing the system at each discrete frequency within the frequency domain. The ROM is solved at each frequency and after the inverse DFT of the spectral solution matrix we obtain the entire solution for a given timespan at once, with no time integration necessary. This new approach is illustrated using the example PDE of steady passive scalar transport in an inhomogenous, time-invariant flow field. Finally, we compare the performance of our ROM with the standard POD-Galerkin ROM in terms of accuracy and computational speedup.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-08-22 without embargo terms","The student, Cong Lin, accepted the attached license on 2019-04-26 at 15:53.","The student, Cong Lin, submitted this Thesis for approval on 2019-04-26 at 16:51.","This Thesis was approved for publication on 2019-04-26 at 16:56.","DSpace SAF Submission Ingestion Package generated from Vireo submission #13956 on 2019-08-22 at 14:47:12","Made available in DSpace on 2019-08-23T20:05:25Z (GMT). No. of bitstreams: 2 LIN-THESIS-2019.pdf: 3377954 bytes, checksum: 5966e404048da3f1f81d09ca1c6b6a48 (MD5) LICENSE.txt: 4205 bytes, checksum: a93f1c8fb5ba4418550af66ce3d140ed (MD5) Previous issue date: 2019-04-26"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Model order reduction in the frequency domain via spectral proper orthogonal decomposition"]}]}],"canonical_facts":{"dc:contributor":["Balajewicz, Maciej"],"dc:creator":["Cong, Lin"],"dc:date":["2019-08-23T20:05:25Z","2019-04-26","2019-05"],"dc:description":["In this thesis, we introduce a novel model order reduction framework for harmonically and randomly forced dynamical systems. Specifically, we emphasize the usage of spectral proper orthogonal decomposition (SPOD), recently revived by Towne et. al. (2018), which results in sets of orthogonal modes, each oscillating at a single frequency, that are said to optimally represent coherent-structures evolving in space and time. However, reduced-order models (ROMs) using SPOD modes have not yet been developed. Hence, in this study we investigate the potential of a novel approach utilizing SPOD modes to construct the lower-dimensional subspace for ROMs. Upon the discrete-time Fourier-transform (DFT) of the governing ordinary differential equation (ODE) system, an orthogonal projection onto the SPOD modes is performed, analogous to Proper Orthogonal Decomposition (POD) Galerkin ROMs, but compressing the system at each discrete frequency within the frequency domain. The ROM is solved at each frequency and after the inverse DFT of the spectral solution matrix we obtain the entire solution for a given timespan at once, with no time integration necessary. This new approach is illustrated using the example PDE of steady passive scalar transport in an inhomogenous, time-invariant flow field. Finally, we compare the performance of our ROM with the standard POD-Galerkin ROM in terms of accuracy and computational speedup.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-08-22 without embargo terms","The student, Cong Lin, accepted the attached license on 2019-04-26 at 15:53.","The student, Cong Lin, submitted this Thesis for approval on 2019-04-26 at 16:51.","This Thesis was approved for publication on 2019-04-26 at 16:56.","DSpace SAF Submission Ingestion Package generated from Vireo submission #13956 on 2019-08-22 at 14:47:12","Made available in DSpace on 2019-08-23T20:05:25Z (GMT). No. of bitstreams: 2 LIN-THESIS-2019.pdf: 3377954 bytes, checksum: 5966e404048da3f1f81d09ca1c6b6a48 (MD5) LICENSE.txt: 4205 bytes, checksum: a93f1c8fb5ba4418550af66ce3d140ed (MD5) Previous issue date: 2019-04-26"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/104953"],"dc:language":["en"],"dc:rights":["Copyright 2019 Cong Lin"],"dc:subject":["POD","SPOD","reduced-order modeling","reduced-order model","DMD"],"dc:title":["Model order reduction in the frequency domain via spectral proper orthogonal decomposition"],"dc:type":["text"],"thesis:degree_discipline":["Aerospace Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:44Z"}