{"id":"https://openalex.org/W2897085391","doi":"https://doi.org/10.1177/0142331218798893","title":"Time-limited Gramians-based model order reduction for second-order form systems","display_name":"Time-limited Gramians-based model order reduction for second-order form systems","publication_year":2018,"publication_date":"2018-10-15","ids":{"openalex":"https://openalex.org/W2897085391","doi":"https://doi.org/10.1177/0142331218798893","mag":"2897085391"},"language":"en","primary_location":{"id":"doi:10.1177/0142331218798893","is_oa":false,"landing_page_url":"https://doi.org/10.1177/0142331218798893","pdf_url":null,"source":{"id":"https://openalex.org/S24148485","display_name":"Transactions of the Institute of Measurement and Control","issn_l":"0142-3312","issn":["0142-3312","1477-0369"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the Institute of Measurement and Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054478213","display_name":"Shafiq Haider","orcid":"https://orcid.org/0000-0002-6732-4945"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shafiq Haider","raw_affiliation_strings":["Department of Electrical Engineering, National University of Science and Technology, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, National University of Science and Technology, Pakistan","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064268028","display_name":"Abdul Ghafoor","orcid":"https://orcid.org/0000-0002-6117-3656"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Abdul Ghafoor","raw_affiliation_strings":["Department of Electrical Engineering, National University of Science and Technology, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, National University of Science and Technology, Pakistan","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080309684","display_name":"Muhammad Imran","orcid":"https://orcid.org/0000-0003-1001-9648"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Muhammad Imran","raw_affiliation_strings":["Department of Electrical Engineering, National University of Science and Technology, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, National University of Science and Technology, Pakistan","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074734756","display_name":"Fahad Mumtaz Malik","orcid":"https://orcid.org/0000-0002-3998-5850"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fahad Mumtaz Malik","raw_affiliation_strings":["Department of Electrical Engineering, National University of Science and Technology, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, National University of Science and Technology, Pakistan","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5064268028"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5366,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.83325743,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"41","issue":"8","first_page":"2310","last_page":"2318"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9749000072479248,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.678309440612793},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6581703424453735},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5945549011230469},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5817379951477051},{"id":"https://openalex.org/keywords/model-order-reduction","display_name":"Model order reduction","score":0.5422263145446777},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5155513286590576},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43387627601623535},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.42878293991088867},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3960551619529724},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26589927077293396},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17563539743423462},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.11033949255943298},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10182163119316101},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.0709821879863739}],"concepts":[{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.678309440612793},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6581703424453735},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5945549011230469},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5817379951477051},{"id":"https://openalex.org/C2779277453","wikidata":"https://www.wikidata.org/wiki/Q12202921","display_name":"Model order reduction","level":3,"score":0.5422263145446777},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5155513286590576},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43387627601623535},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.42878293991088867},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3960551619529724},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26589927077293396},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17563539743423462},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.11033949255943298},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10182163119316101},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.0709821879863739},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1177/0142331218798893","is_oa":false,"landing_page_url":"https://doi.org/10.1177/0142331218798893","pdf_url":null,"source":{"id":"https://openalex.org/S24148485","display_name":"Transactions of the Institute of Measurement and Control","issn_l":"0142-3312","issn":["0142-3312","1477-0369"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the Institute of Measurement and Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W131468270","https://openalex.org/W747309577","https://openalex.org/W1648161269","https://openalex.org/W1762060417","https://openalex.org/W1969325212","https://openalex.org/W1984714339","https://openalex.org/W2007101284","https://openalex.org/W2009762405","https://openalex.org/W2028703352","https://openalex.org/W2052005273","https://openalex.org/W2064733273","https://openalex.org/W2070727619","https://openalex.org/W2099180896","https://openalex.org/W2140440476","https://openalex.org/W2338979487","https://openalex.org/W2514357593"],"related_works":["https://openalex.org/W2765250005","https://openalex.org/W2110312969","https://openalex.org/W2182451763","https://openalex.org/W2153566364","https://openalex.org/W1991018216","https://openalex.org/W2118904547","https://openalex.org/W3127703504","https://openalex.org/W2015479478","https://openalex.org/W1964286429","https://openalex.org/W2800915648"],"abstract_inverted_index":{"A":[0],"new":[1],"scheme":[2,75],"for":[3,26,49,82],"model":[4],"order":[5],"reduction":[6],"of":[7,21,39,72],"large-scale":[8],"second-order":[9,27,33],"systems":[10,29],"in":[11,59],"time-limited":[12,83],"intervals":[13],"is":[14],"presented.":[15],"Time-limited":[16,32],"Gramians":[17,44,80],"that":[18,56],"are":[19,30,45,52,62,66],"solutions":[20],"continuous-time":[22],"algebraic":[23],"Lyapunov":[24],"equations":[25],"form":[28],"introduced.":[31],"balanced":[34],"truncation":[35],"procedures":[36],"with":[37,77],"provision":[38],"balancing":[40],"position":[41],"and":[42,54],"velocity":[43],"formulated.":[46],"Stability":[47],"conditions":[48],"reduced-order":[50,60],"models":[51,61],"stated":[53],"algorithms":[55],"preserve":[57],"stability":[58],"discussed.":[63],"Numerical":[64],"examples":[65],"presented":[67],"to":[68],"validate":[69],"the":[70,73,78],"superiority":[71],"proposed":[74],"compared":[76],"infinite-time":[79],"technique":[81],"applications.":[84]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}