{"id":"https://openalex.org/W7165001663","doi":"https://doi.org/10.3390/act15060344","title":"Physics-Informed Modeling of Electrohydraulic Semi-Active Dampers Using LSTM, Transformer and Extended Hyperbolic Tangent Model","display_name":"Physics-Informed Modeling of Electrohydraulic Semi-Active Dampers Using LSTM, Transformer and Extended Hyperbolic Tangent Model","publication_year":2026,"publication_date":"2026-06-17","ids":{"openalex":"https://openalex.org/W7165001663","doi":"https://doi.org/10.3390/act15060344"},"language":"en","primary_location":{"id":"doi:10.3390/act15060344","doi":"https://doi.org/10.3390/act15060344","is_oa":true,"landing_page_url":"https://doi.org/10.3390/act15060344","pdf_url":"https://www.mdpi.com/2076-0825/15/6/344/pdf?version=1781712757","source":{"id":"https://openalex.org/S2736557103","display_name":"Actuators","issn_l":"2076-0825","issn":["2076-0825"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Actuators","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2076-0825/15/6/344/pdf?version=1781712757","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018153440","display_name":"Mert B\u00fcy\u00fckk\u00f6pr\u00fc","orcid":"https://orcid.org/0000-0003-3493-8323","observed_orcids":["https://orcid.org/0000-0003-3493-8323"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mert B\u00fcy\u00fckk\u00f6pr\u00fc","raw_affiliation_strings":["Groupe Renault, 16225 Bursa, T\u00fcrkiye"],"raw_orcid":"https://orcid.org/0000-0003-3493-8323","affiliations":[{"raw_affiliation_string":"Groupe Renault, 16225 Bursa, T\u00fcrkiye","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138805348","display_name":"Muhammet G\u00fcven","orcid":"https://orcid.org/0009-0000-0797-4535","observed_orcids":["https://orcid.org/0009-0000-0797-4535"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Muhammet G\u00fcven","raw_affiliation_strings":["Groupe Renault, 16225 Bursa, T\u00fcrkiye"],"raw_orcid":"https://orcid.org/0009-0000-0797-4535","affiliations":[{"raw_affiliation_string":"Groupe Renault, 16225 Bursa, T\u00fcrkiye","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047486928","display_name":"Erdem Uzunsoy","orcid":"https://orcid.org/0000-0002-6449-552X","observed_orcids":["https://orcid.org/0000-0002-6449-552X"]},"institutions":[{"id":"https://openalex.org/I192257213","display_name":"Bursa Technical University","ror":"https://ror.org/03rdpn141","country_code":"TR","type":"education","lineage":["https://openalex.org/I192257213"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Erdem Uzunsoy","raw_affiliation_strings":["Department of Mechanical Engineering, Bursa Technical University, 16310 Bursa, T\u00fcrkiye"],"raw_orcid":"https://orcid.org/0000-0002-6449-552X","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Bursa Technical University, 16310 Bursa, T\u00fcrkiye","institution_ids":["https://openalex.org/I192257213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035511403","display_name":"Xavier Mouton","orcid":"https://orcid.org/0000-0003-1676-477X","observed_orcids":["https://orcid.org/0000-0003-1676-477X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xavier Mouton","raw_affiliation_strings":["Ampere Software Technology, 92100 Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ampere Software Technology, 92100 Paris, France","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5018153440"],"corresponding_institution_ids":[],"apc_list":{"value":2400,"currency":"CHF","value_usd":2896},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2896},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.38367125,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"6","first_page":"344","last_page":"344"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10690","display_name":"Vibration Control and Rheological Fluids","score":0.8784000277519226,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10690","display_name":"Vibration Control and Rheological Fluids","score":0.8784000277519226,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.09279999881982803,"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/T11372","display_name":"Hydraulic and Pneumatic Systems","score":0.012199999764561653,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"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/physics-informed-neural-networks","display_name":"physics-informed neural networks","score":0.953000009059906},{"id":"https://openalex.org/keywords/hysteresis-modeling","display_name":"hysteresis modeling","score":0.7990000247955322},{"id":"https://openalex.org/keywords/lstm","display_name":"LSTM","score":0.5910000205039978},{"id":"https://openalex.org/keywords/transformer","display_name":"transformer models","score":0.6650000214576721},{"id":"https://openalex.org/keywords/hybrid-physics-data-driven-modeling","display_name":"hybrid physics-data models","score":0.8199999928474426},{"id":"https://openalex.org/keywords/valve-control","display_name":"valve control","score":0.7670000195503235},{"id":"https://openalex.org/keywords/vehicle-suspension","display_name":"vehicle suspension","score":0.7070000171661377},{"id":"https://openalex.org/keywords/nonlinear-damping","display_name":"nonlinear damping","score":0.36800000071525574}],"concepts":[{"id":"https://openalex.org/C140096630","wikidata":"https://www.wikidata.org/wiki/Q3423628","display_name":"Damper","level":2,"score":0.635200023651123},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6294999718666077},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.613099992275238},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.550599992275238},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5307999849319458},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5115000009536743},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5020999908447266},{"id":"https://openalex.org/C108619579","wikidata":"https://www.wikidata.org/wiki/Q902419","display_name":"Magnetorheological fluid","level":3,"score":0.41909998655319214},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.4165000021457672},{"id":"https://openalex.org/C66322947","wikidata":"https://www.wikidata.org/wiki/Q11658","display_name":"Transformer","level":3,"score":0.41600000858306885},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.3968000113964081},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.3905999958515167},{"id":"https://openalex.org/C526921623","wikidata":"https://www.wikidata.org/wiki/Q190117","display_name":"Automotive industry","level":2,"score":0.3855000138282776},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.3677999973297119},{"id":"https://openalex.org/C28704281","wikidata":"https://www.wikidata.org/wiki/Q180165","display_name":"Mechatronics","level":2,"score":0.3528999984264374},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.3407999873161316},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.325300008058548},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28049999475479126},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.2786000072956085},{"id":"https://openalex.org/C47890412","wikidata":"https://www.wikidata.org/wiki/Q1179296","display_name":"Tangent vector","level":3,"score":0.2782000005245209},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C125884559","wikidata":"https://www.wikidata.org/wiki/Q369791","display_name":"Linear variable differential transformer","level":5,"score":0.2603999972343445},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.26019999384880066},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.2590000033378601},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2574999928474426},{"id":"https://openalex.org/C178295079","wikidata":"https://www.wikidata.org/wiki/Q919765","display_name":"Tangent stiffness matrix","level":4,"score":0.2565999925136566}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/act15060344","doi":"https://doi.org/10.3390/act15060344","is_oa":true,"landing_page_url":"https://doi.org/10.3390/act15060344","pdf_url":"https://www.mdpi.com/2076-0825/15/6/344/pdf?version=1781712757","source":{"id":"https://openalex.org/S2736557103","display_name":"Actuators","issn_l":"2076-0825","issn":["2076-0825"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Actuators","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:86babba5d56847fda57654c0f72028ee","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/86babba5d56847fda57654c0f72028ee","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Actuators, Vol 15, Iss 6, p 344 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/act15060344","doi":"https://doi.org/10.3390/act15060344","is_oa":true,"landing_page_url":"https://doi.org/10.3390/act15060344","pdf_url":"https://www.mdpi.com/2076-0825/15/6/344/pdf?version=1781712757","source":{"id":"https://openalex.org/S2736557103","display_name":"Actuators","issn_l":"2076-0825","issn":["2076-0825"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Actuators","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5378999710083008,"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9"}],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7165001663.pdf","grobid_xml":"https://content.openalex.org/works/W7165001663.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1623335607","https://openalex.org/W2001237288","https://openalex.org/W2034682809","https://openalex.org/W2064675550","https://openalex.org/W2091110674","https://openalex.org/W2136848157","https://openalex.org/W2576983082","https://openalex.org/W2899283552","https://openalex.org/W2948230027","https://openalex.org/W3126289201","https://openalex.org/W3153200540","https://openalex.org/W3157684034","https://openalex.org/W3163993681","https://openalex.org/W4223897975","https://openalex.org/W4389820087","https://openalex.org/W4394948009","https://openalex.org/W4403470503","https://openalex.org/W7123351496","https://openalex.org/W7124713640"],"related_works":[],"abstract_inverted_index":{"This":[0],"study":[1],"investigates":[2],"physics-informed":[3,91,176,204],"and":[4,29,45,66,72,101,183,193],"data-driven":[5,37,102,157,188],"hybrid":[6],"modeling":[7,210],"strategies":[8,93,206],"for":[9,57,207],"an":[10],"automotive-grade":[11],"electrohydraulic":[12],"(EH)":[13],"semi-active":[14],"damper":[15,215],"system.":[16],"Although":[17],"deep":[18],"sequence":[19,158],"learning":[20,150,205],"architectures":[21,177],"such":[22],"as":[23,142],"Long":[24],"Short-Term":[25],"Memory":[26],"(LSTM)":[27],"networks":[28],"Transformers":[30],"can":[31],"provide":[32],"high":[33],"predictive":[34],"accuracy,":[35],"purely":[36,187],"approaches":[38],"may":[39],"struggle":[40],"to":[41],"preserve":[42],"physical":[43,100,139,181],"consistency":[44],"maintain":[46],"robustness":[47,184],"under":[48,69,165],"unseen":[49],"operating":[50,168],"conditions.":[51,169],"These":[52],"limitations":[53],"become":[54],"more":[55,77],"pronounced":[56],"EH":[58,214],"dampers,":[59],"whose":[60],"hysteretic":[61],"characteristics":[62],"exhibit":[63],"highly":[64],"nonlinear":[65,212],"non-proportional":[67],"variations":[68],"different":[70],"current":[71],"frequency":[73],"excitations,":[74],"unlike":[75],"the":[76,119,122,131,138,149,154,174,201],"scalable":[78],"behavior":[79],"commonly":[80],"observed":[81],"in":[82,117,191],"magnetorheological":[83],"(MR)":[84],"dampers.":[85],"To":[86],"address":[87],"these":[88],"challenges,":[89],"two":[90],"integration":[92],"are":[94,127,163],"investigated.":[95],"The":[96,108,160,196],"first":[97],"strategy":[98,110],"combines":[99],"models":[103,162],"through":[104],"parallel":[105],"loss-function":[106],"synthesis.":[107],"second":[109],"introduces":[111],"a":[112,143],"learnable":[113],"physics":[114],"layer":[115],"(PINN-Hybrid),":[116],"which":[118],"coefficients":[120],"of":[121,156,203,211],"extended":[123],"hyperbolic":[124],"tangent":[125],"formulation":[126],"adaptively":[128],"learned":[129],"within":[130],"neural":[132],"network":[133],"architecture.":[134],"In":[135],"this":[136],"framework,":[137],"model":[140],"acts":[141],"structural":[144],"regularization":[145],"mechanism":[146],"that":[147,173],"guides":[148],"process":[151],"while":[152],"preserving":[153],"flexibility":[155],"modeling.":[159],"proposed":[161,175,197],"evaluated":[164],"abrupt":[166],"valve-control":[167],"Comparative":[170],"results":[171],"indicate":[172],"improve":[178],"hysteresis":[179],"continuity,":[180],"plausibility,":[182],"compared":[185],"with":[186],"approaches,":[189],"particularly":[190],"low-velocity":[192],"transition":[194],"regions.":[195],"framework":[198],"therefore":[199],"demonstrates":[200],"potential":[202],"reliable":[208],"real-time":[209],"automotive":[213],"systems.":[216]},"counts_by_year":[],"updated_date":"2026-09-21T07:43:02.447757","created_date":"2026-06-18T00:00:00"}