{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/36921"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/36921","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Parameter Identification of Nonlinear Systems Using Perturbation Methods and Higher-Order Statistics","abstract":"A parametric identification procedure is proposed that combines the method of multiple scales and higher-order statistics to efficiently and accurately model nonlinear systems. A theoretical background for the method of multiple scales and higher-order statistics is given. Validation of the procedure is performed through applying it to numerical simulations of two nonlinear systems. The results show how the procedure can successfully characterize the system damping and nonlinearities and determine the corresponding parameters. The procedure is then applied to experimental measurements from two structural systems, a cantilevered beam and a three-beam frame. The results show that quadratic damping should be accounted for in both systems. Moreover, for the three-beam frame, the parametric excitation is much more important than the direct excitation. To show the flexibility of the procedure, numerical simulations of ship motion under parametric excitation are used to determine nonlinear parameters govening the relation between pitch, heave, and roll motions. The results show a high level of agreement between the numerical simulation and the mathematical model with the identified parameters.","abstract_html":"A parametric identification procedure is proposed that combines the method of multiple scales and higher-order statistics to efficiently and accurately model nonlinear systems. A theoretical background for the method of multiple scales and higher-order statistics is given. Validation of the procedure is performed through applying it to numerical simulations of two nonlinear systems. The results show how the procedure can successfully characterize the system damping and nonlinearities and determine the corresponding parameters. The procedure is then applied to experimental measurements from two structural systems, a cantilevered beam and a three-beam frame. The results show that quadratic damping should be accounted for in both systems. Moreover, for the three-beam frame, the parametric excitation is much more important than the direct excitation. To show the flexibility of the procedure, numerical simulations of ship motion under parametric excitation are used to determine nonlinear parameters govening the relation between pitch, heave, and roll motions. The results show a high level of agreement between the numerical simulation and the mathematical model with the identified parameters.","abstract_has_math":false,"creators":["Fung, Jimmy"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Engineering Mechanics","degree_department":"Engineering Mechanics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Hajj, Muhammad R."],"committee_members":["Mook, Dean T."],"year":1998,"date_issued":"1998-08-03","date_published":"1998-08-03","updated_at":"2026-07-24T05:56:18Z","subjects":["Nonlinear systems","system identification","parametric identification","higher-order statistics","bispectra","perturbation methods","method of multiple scales."],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-72098-173139"],"render_values":[{"text":"etd-72098-173139","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/36921","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Hajj, Muhammad R."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Mook, Dean T."]},{"key":"dc:contributor.department","label":"Department","values":["Engineering Mechanics"]},{"key":"dc:creator","label":"Author","values":["Fung, Jimmy"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:52:13Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:52:13Z","1999-08-21"]},{"key":"dc:date.issued","label":"Date","values":["1998-08-03"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Engineering Mechanics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Nonlinear systems","system identification","parametric identification","higher-order statistics","bispectra","perturbation methods","method of multiple scales."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-72098-173139"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/36921"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A parametric identification procedure is proposed that combines the method of multiple scales and higher-order statistics to efficiently and accurately model nonlinear systems. A theoretical background for the method of multiple scales and higher-order statistics is given. Validation of the procedure is performed through applying it to numerical simulations of two nonlinear systems. The results show how the procedure can successfully characterize the system damping and nonlinearities and determine the corresponding parameters. The procedure is then applied to experimental measurements from two structural systems, a cantilevered beam and a three-beam frame. The results show that quadratic damping should be accounted for in both systems. Moreover, for the three-beam frame, the parametric excitation is much more important than the direct excitation. To show the flexibility of the procedure, numerical simulations of ship motion under parametric excitation are used to determine nonlinear parameters govening the relation between pitch, heave, and roll motions. The results show a high level of agreement between the numerical simulation and the mathematical model with the identified parameters."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["Parameter Identification of Nonlinear Systems Using Perturbation Methods and Higher-Order Statistics"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Hajj, Muhammad R."],"dc:contributor.committeemember":["Mook, Dean T."],"dc:contributor.department":["Engineering Mechanics"],"dc:creator":["Fung, Jimmy"],"dc:date.accessioned":["2014-03-14T20:52:13Z"],"dc:date.available":["2014-03-14T20:52:13Z","1999-08-21"],"dc:date.issued":["1998-08-03"],"dc:description.abstract":["A parametric identification procedure is proposed that combines the method of multiple scales and higher-order statistics to efficiently and accurately model nonlinear systems. A theoretical background for the method of multiple scales and higher-order statistics is given. Validation of the procedure is performed through applying it to numerical simulations of two nonlinear systems. The results show how the procedure can successfully characterize the system damping and nonlinearities and determine the corresponding parameters. The procedure is then applied to experimental measurements from two structural systems, a cantilevered beam and a three-beam frame. The results show that quadratic damping should be accounted for in both systems. Moreover, for the three-beam frame, the parametric excitation is much more important than the direct excitation. To show the flexibility of the procedure, numerical simulations of ship motion under parametric excitation are used to determine nonlinear parameters govening the relation between pitch, heave, and roll motions. 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