{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/90965"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/90965","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Noniterative construction of optimal quadratically-nonlinear ODE models from time series","abstract":"We consider the problem of constructing a quadratically nonlinear ordinary differential equation (ODE) system from time series, with the latter obtained either from experiment, or from computational simulation using a higher-dimensional mathematical model (e.g., one or more partial differential equations). Previous approaches iteratively seek a solution of the nonlinear problem of finding a set of coefficients for the quadratically nonlinear right-hand side providing the best agreement between the time series and numerical solutions of the ODE system. The present approach has several advantages compare to these iterative approaches. First, our approach involves solution only of linear algebraic equations, and avoids the problems associated with the iterative solution of a nonlinear algebraic equation system, namely the possibility of multiple solutions and failure of the iteration to converge. Second, our approach finds the ODE system which is best satisfied (in a least-square sense) by the time series, rather than attempting to find the ODE system whose solution best matches the time series. Among other advantages, this avoids the sensitive dependence on initial conditions encountered for ODE systems having solutions that exhibit chaotic behavior. The approach is illustrated with numerical examples demonstrating its utility for a variety of nonchaotic and chaotic time series, including systems where the time series is corrupted by multiplicative noise, and for cases where a given ODE system has two qualitatively different solutions for different initial conditions.","abstract_html":"We consider the problem of constructing a quadratically nonlinear ordinary differential equation (ODE) system from time series, with the latter obtained either from experiment, or from computational simulation using a higher-dimensional mathematical model (e.g., one or more partial differential equations). Previous approaches iteratively seek a solution of the nonlinear problem of finding a set of coefficients for the quadratically nonlinear right-hand side providing the best agreement between the time series and numerical solutions of the ODE system. The present approach has several advantages compare to these iterative approaches. First, our approach involves solution only of linear algebraic equations, and avoids the problems associated with the iterative solution of a nonlinear algebraic equation system, namely the possibility of multiple solutions and failure of the iteration to converge. Second, our approach finds the ODE system which is best satisfied (in a least-square sense) by the time series, rather than attempting to find the ODE system whose solution best matches the time series. Among other advantages, this avoids the sensitive dependence on initial conditions encountered for ODE systems having solutions that exhibit chaotic behavior. The approach is illustrated with numerical examples demonstrating its utility for a variety of nonchaotic and chaotic time series, including systems where the time series is corrupted by multiplicative noise, and for cases where a given ODE system has two qualitatively different solutions for different initial conditions.","abstract_has_math":false,"creators":["Ding, Ke"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Pearlstein, Arne J."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-07-07T21:18:07Z","date_published":"2016-07-07T21:18:07Z","updated_at":"2026-07-22T22:26:34Z","subjects":["ODE System Identification"],"languages":["en"],"rights":["Copyright 2016 Ke Ding"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/90965","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Pearlstein, Arne J."]},{"key":"dc:creator","label":"Author","values":["Ding, Ke"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2016-07-07T21:18:07Z","2018-07-08T09:15:16Z","2016-04-27","2016-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical 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":["ODE System Identification"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2016 Ke Ding"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/90965"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We consider the problem of constructing a quadratically nonlinear ordinary differential equation (ODE) system from time series, with the latter obtained either from experiment, or from computational simulation using a higher-dimensional mathematical model (e.g., one or more partial differential equations). Previous approaches iteratively seek a solution of the nonlinear problem of finding a set of coefficients for the quadratically nonlinear right-hand side providing the best agreement between the time series and numerical solutions of the ODE system. The present approach has several advantages compare to these iterative approaches. First, our approach involves solution only of linear algebraic equations, and avoids the problems associated with the iterative solution of a nonlinear algebraic equation system, namely the possibility of multiple solutions and failure of the iteration to converge. Second, our approach finds the ODE system which is best satisfied (in a least-square sense) by the time series, rather than attempting to find the ODE system whose solution best matches the time series. Among other advantages, this avoids the sensitive dependence on initial conditions encountered for ODE systems having solutions that exhibit chaotic behavior. The approach is illustrated with numerical examples demonstrating its utility for a variety of nonchaotic and chaotic time series, including systems where the time series is corrupted by multiplicative noise, and for cases where a given ODE system has two qualitatively different solutions for different initial conditions.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2018-05-01","The student, Ke Ding, accepted the attached license on 2016-04-27 at 12:39.","The student, Ke Ding, submitted this Thesis for approval on 2016-04-27 at 12:43.","This Thesis was approved for publication on 2016-04-27 at 15:15.","DSpace SAF Submission Ingestion Package generated from Vireo submission #9520 on 2016-07-07 at 14:18:05","Made available in DSpace on 2016-07-07T21:18:07Z (GMT). No. of bitstreams: 2 DING-THESIS-2016.pdf: 1769672 bytes, checksum: 149319a2facdae11bc8ffcd8055263e8 (MD5) LICENSE.txt: 4204 bytes, checksum: aeb0d28d98158b819ece76d392be12e0 (MD5) Previous issue date: 2016-04-27","Embargo set by: Seth Robbins for item 93320 Lift date: 2018-07-07T21:18:16Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Limited Restriction Lifted for Item 93320 on 2018-07-08T09:15:16Z."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Noniterative construction of optimal quadratically-nonlinear ODE models from time series"]}]}],"canonical_facts":{"dc:contributor":["Pearlstein, Arne J."],"dc:creator":["Ding, Ke"],"dc:date":["2016-07-07T21:18:07Z","2018-07-08T09:15:16Z","2016-04-27","2016-05"],"dc:description":["We consider the problem of constructing a quadratically nonlinear ordinary differential equation (ODE) system from time series, with the latter obtained either from experiment, or from computational simulation using a higher-dimensional mathematical model (e.g., one or more partial differential equations). Previous approaches iteratively seek a solution of the nonlinear problem of finding a set of coefficients for the quadratically nonlinear right-hand side providing the best agreement between the time series and numerical solutions of the ODE system. The present approach has several advantages compare to these iterative approaches. First, our approach involves solution only of linear algebraic equations, and avoids the problems associated with the iterative solution of a nonlinear algebraic equation system, namely the possibility of multiple solutions and failure of the iteration to converge. Second, our approach finds the ODE system which is best satisfied (in a least-square sense) by the time series, rather than attempting to find the ODE system whose solution best matches the time series. Among other advantages, this avoids the sensitive dependence on initial conditions encountered for ODE systems having solutions that exhibit chaotic behavior. The approach is illustrated with numerical examples demonstrating its utility for a variety of nonchaotic and chaotic time series, including systems where the time series is corrupted by multiplicative noise, and for cases where a given ODE system has two qualitatively different solutions for different initial conditions.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2018-05-01","The student, Ke Ding, accepted the attached license on 2016-04-27 at 12:39.","The student, Ke Ding, submitted this Thesis for approval on 2016-04-27 at 12:43.","This Thesis was approved for publication on 2016-04-27 at 15:15.","DSpace SAF Submission Ingestion Package generated from Vireo submission #9520 on 2016-07-07 at 14:18:05","Made available in DSpace on 2016-07-07T21:18:07Z (GMT). No. of bitstreams: 2 DING-THESIS-2016.pdf: 1769672 bytes, checksum: 149319a2facdae11bc8ffcd8055263e8 (MD5) LICENSE.txt: 4204 bytes, checksum: aeb0d28d98158b819ece76d392be12e0 (MD5) Previous issue date: 2016-04-27","Embargo set by: Seth Robbins for item 93320 Lift date: 2018-07-07T21:18:16Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Limited Restriction Lifted for Item 93320 on 2018-07-08T09:15:16Z."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/90965"],"dc:language":["en"],"dc:rights":["Copyright 2016 Ke Ding"],"dc:subject":["ODE System Identification"],"dc:title":["Noniterative construction of optimal quadratically-nonlinear ODE models from time series"],"dc:type":["text"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:34Z"}