{"id":"https://openalex.org/W4415564678","doi":"https://doi.org/10.3390/sym17111802","title":"A Physics-Constrained Heterogeneous GNN Guided by Physical Symmetry for Heavy-Duty Vehicle Load Estimation","display_name":"A Physics-Constrained Heterogeneous GNN Guided by Physical Symmetry for Heavy-Duty Vehicle Load Estimation","publication_year":2025,"publication_date":"2025-10-26","ids":{"openalex":"https://openalex.org/W4415564678","doi":"https://doi.org/10.3390/sym17111802"},"language":"en","primary_location":{"id":"doi:10.3390/sym17111802","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17111802","pdf_url":"https://www.mdpi.com/2073-8994/17/11/1802/pdf?version=1761453588","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/11/1802/pdf?version=1761453588","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102685867","display_name":"Lizhuo Luo","orcid":"https://orcid.org/0009-0001-4531-923X"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]},{"id":"https://openalex.org/I204710742","display_name":"Ministry of Ecology and Environment","ror":"https://ror.org/04gwbew76","country_code":"CN","type":"government","lineage":["https://openalex.org/I204710742"]},{"id":"https://openalex.org/I4210156332","display_name":"Chinese Research Academy of Environmental Sciences","ror":"https://ror.org/05t8xvx87","country_code":"CN","type":"nonprofit","lineage":["https://openalex.org/I4210156332"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lizhuo Luo","raw_affiliation_strings":["Institute of Advanced Technology, University of Science and Technology of China, Hefei 230088, China","Key Laboratory for Vehicle Emission Control and Simulation of the Ministry of Ecology and Environment, Chinese Research Academy of Environmental Sciences, Beijing 100012, China","Vehicle Emission Control Center, Chinese Research Academy of Environmental Sciences, Beijing 100012, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Advanced Technology, University of Science and Technology of China, Hefei 230088, China","institution_ids":["https://openalex.org/I126520041"]},{"raw_affiliation_string":"Key Laboratory for Vehicle Emission Control and Simulation of the Ministry of Ecology and Environment, Chinese Research Academy of Environmental Sciences, Beijing 100012, China","institution_ids":["https://openalex.org/I204710742"]},{"raw_affiliation_string":"Vehicle Emission Control Center, Chinese Research Academy of Environmental Sciences, Beijing 100012, China","institution_ids":["https://openalex.org/I4210156332"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030240684","display_name":"Leqi Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I204710742","display_name":"Ministry of Ecology and Environment","ror":"https://ror.org/04gwbew76","country_code":"CN","type":"government","lineage":["https://openalex.org/I204710742"]},{"id":"https://openalex.org/I4210156332","display_name":"Chinese Research Academy of Environmental Sciences","ror":"https://ror.org/05t8xvx87","country_code":"CN","type":"nonprofit","lineage":["https://openalex.org/I4210156332"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Leqi Zhang","raw_affiliation_strings":["Key Laboratory for Vehicle Emission Control and Simulation of the Ministry of Ecology and Environment, Chinese Research Academy of Environmental Sciences, Beijing 100012, China","Vehicle Emission Control Center, Chinese Research Academy of Environmental Sciences, Beijing 100012, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory for Vehicle Emission Control and Simulation of the Ministry of Ecology and Environment, Chinese Research Academy of Environmental Sciences, Beijing 100012, China","institution_ids":["https://openalex.org/I204710742"]},{"raw_affiliation_string":"Vehicle Emission Control Center, Chinese Research Academy of Environmental Sciences, Beijing 100012, China","institution_ids":["https://openalex.org/I4210156332"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100367109","display_name":"Hongli Wang","orcid":"https://orcid.org/0000-0003-0655-3389"},"institutions":[{"id":"https://openalex.org/I204710742","display_name":"Ministry of Ecology and Environment","ror":"https://ror.org/04gwbew76","country_code":"CN","type":"government","lineage":["https://openalex.org/I204710742"]},{"id":"https://openalex.org/I4210156332","display_name":"Chinese Research Academy of Environmental Sciences","ror":"https://ror.org/05t8xvx87","country_code":"CN","type":"nonprofit","lineage":["https://openalex.org/I4210156332"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongli Wang","raw_affiliation_strings":["Key Laboratory for Vehicle Emission Control and Simulation of the Ministry of Ecology and Environment, Chinese Research Academy of Environmental Sciences, Beijing 100012, China","Vehicle Emission Control Center, Chinese Research Academy of Environmental Sciences, Beijing 100012, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory for Vehicle Emission Control and Simulation of the Ministry of Ecology and Environment, Chinese Research Academy of Environmental Sciences, Beijing 100012, China","institution_ids":["https://openalex.org/I204710742"]},{"raw_affiliation_string":"Vehicle Emission Control Center, Chinese Research Academy of Environmental Sciences, Beijing 100012, China","institution_ids":["https://openalex.org/I4210156332"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000336211","display_name":"Yunjing Wang","orcid":"https://orcid.org/0000-0003-4469-8538"},"institutions":[{"id":"https://openalex.org/I204710742","display_name":"Ministry of Ecology and Environment","ror":"https://ror.org/04gwbew76","country_code":"CN","type":"government","lineage":["https://openalex.org/I204710742"]},{"id":"https://openalex.org/I4210156332","display_name":"Chinese Research Academy of Environmental Sciences","ror":"https://ror.org/05t8xvx87","country_code":"CN","type":"nonprofit","lineage":["https://openalex.org/I4210156332"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunjing Wang","raw_affiliation_strings":["Key Laboratory for Vehicle Emission Control and Simulation of the Ministry of Ecology and Environment, Chinese Research Academy of Environmental Sciences, Beijing 100012, China","Vehicle Emission Control Center, Chinese Research Academy of Environmental Sciences, Beijing 100012, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory for Vehicle Emission Control and Simulation of the Ministry of Ecology and Environment, Chinese Research Academy of Environmental Sciences, Beijing 100012, China","institution_ids":["https://openalex.org/I204710742"]},{"raw_affiliation_string":"Vehicle Emission Control Center, Chinese Research Academy of Environmental Sciences, Beijing 100012, China","institution_ids":["https://openalex.org/I4210156332"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075738106","display_name":"Hang Yin","orcid":"https://orcid.org/0009-0009-2635-1769"},"institutions":[{"id":"https://openalex.org/I204710742","display_name":"Ministry of Ecology and Environment","ror":"https://ror.org/04gwbew76","country_code":"CN","type":"government","lineage":["https://openalex.org/I204710742"]},{"id":"https://openalex.org/I4210156332","display_name":"Chinese Research Academy of Environmental Sciences","ror":"https://ror.org/05t8xvx87","country_code":"CN","type":"nonprofit","lineage":["https://openalex.org/I4210156332"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hang Yin","raw_affiliation_strings":["Key Laboratory for Vehicle Emission Control and Simulation of the Ministry of Ecology and Environment, Chinese Research Academy of Environmental Sciences, Beijing 100012, China","Vehicle Emission Control Center, Chinese Research Academy of Environmental Sciences, Beijing 100012, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory for Vehicle Emission Control and Simulation of the Ministry of Ecology and Environment, Chinese Research Academy of Environmental Sciences, Beijing 100012, China","institution_ids":["https://openalex.org/I204710742"]},{"raw_affiliation_string":"Vehicle Emission Control Center, Chinese Research Academy of Environmental Sciences, Beijing 100012, China","institution_ids":["https://openalex.org/I4210156332"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030240684","https://openalex.org/A5075738106"],"corresponding_institution_ids":["https://openalex.org/I204710742","https://openalex.org/I4210156332"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.24606829,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"11","first_page":"1802","last_page":"1802"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10534","display_name":"Structural Health Monitoring Techniques","score":0.996399998664856,"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/T10534","display_name":"Structural Health Monitoring Techniques","score":0.996399998664856,"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/T10220","display_name":"Machine Fault Diagnosis Techniques","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11372","display_name":"Hydraulic and Pneumatic Systems","score":0.9936000108718872,"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/adaptability","display_name":"Adaptability","score":0.7181000113487244},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6086999773979187},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.4645000100135803},{"id":"https://openalex.org/keywords/kinematics","display_name":"Kinematics","score":0.40939998626708984},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.39629998803138733},{"id":"https://openalex.org/keywords/test-data","display_name":"Test data","score":0.35600000619888306},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.3314000070095062},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.30169999599456787}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7580000162124634},{"id":"https://openalex.org/C177606310","wikidata":"https://www.wikidata.org/wiki/Q5674297","display_name":"Adaptability","level":2,"score":0.7181000113487244},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6086999773979187},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.4645000100135803},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.43959999084472656},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.40939998626708984},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.39629998803138733},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38359999656677246},{"id":"https://openalex.org/C16910744","wikidata":"https://www.wikidata.org/wiki/Q7705759","display_name":"Test data","level":2,"score":0.35600000619888306},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3314000070095062},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.30169999599456787},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28999999165534973},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2847000062465668},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.2800999879837036},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.2775000035762787},{"id":"https://openalex.org/C169903167","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Test set","level":2,"score":0.2705000042915344},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C104122410","wikidata":"https://www.wikidata.org/wiki/Q1416406","display_name":"Network model","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C193415008","wikidata":"https://www.wikidata.org/wiki/Q639681","display_name":"Network architecture","level":2,"score":0.25949999690055847},{"id":"https://openalex.org/C80519477","wikidata":"https://www.wikidata.org/wiki/Q3532236","display_name":"Scenario testing","level":3,"score":0.25699999928474426},{"id":"https://openalex.org/C134727501","wikidata":"https://www.wikidata.org/wiki/Q5597073","display_name":"Graph bandwidth","level":5,"score":0.25369998812675476},{"id":"https://openalex.org/C150217764","wikidata":"https://www.wikidata.org/wiki/Q6803607","display_name":"Mean absolute percentage error","level":3,"score":0.2524000108242035}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17111802","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17111802","pdf_url":"https://www.mdpi.com/2073-8994/17/11/1802/pdf?version=1761453588","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"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":"Symmetry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/sym17111802","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17111802","pdf_url":"https://www.mdpi.com/2073-8994/17/11/1802/pdf?version=1761453588","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6966914631","display_name":null,"funder_award_id":"2022YFC3701802","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320326956","display_name":"Chinese Research Academy of Environmental Sciences","ror":"https://ror.org/05t8xvx87"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415564678.pdf"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W2100495367","https://openalex.org/W2981587994","https://openalex.org/W3086566408","https://openalex.org/W3102498159","https://openalex.org/W3146765912","https://openalex.org/W3168924565","https://openalex.org/W4320495994","https://openalex.org/W4389298155","https://openalex.org/W4390467883","https://openalex.org/W4399797252"],"related_works":[],"abstract_inverted_index":{"Accurate":[0],"heavy-duty":[1,159,224],"vehicle":[2,52,160,225],"load":[3,36,226],"estimation":[4,37],"is":[5],"crucial":[6],"for":[7,22,35,149,210,223,239],"transportation":[8],"and":[9,20,55,65,99,132,144,185,201,236],"environmental":[10,240],"regulation,":[11],"yet":[12],"current":[13],"methods":[14],"lack":[15],"precision":[16],"in":[17,183,187,231],"data":[18,129],"accuracy":[19],"practicality":[21],"field":[23],"implementation.":[24],"We":[25],"propose":[26],"a":[27,78,93,111,134,154],"Self-Supervised":[28],"Reconstruction":[29],"Heterogeneous":[30],"Graph":[31],"Convolutional":[32],"Network":[33],"(SSR-HGCN)":[34],"using":[38],"On-Board":[39],"Diagnostics":[40],"(OBD)":[41],"data.":[42,71],"The":[43,72],"method":[44,73,217],"integrates":[45],"physics-constrained":[46,79],"heterogeneous":[47,80],"graph":[48,59,81,140,145,194],"construction":[49],"based":[50],"on":[51],"speed,":[53],"acceleration,":[54],"engine":[56],"parameters,":[57],"leveraging":[58],"neural":[60],"networks\u2019":[61],"information":[62],"propagation":[63],"mechanisms":[64],"self-supervised":[66,112],"learning\u2019s":[67],"adaptability":[68,127],"to":[69,106,128],"low-quality":[70],"comprises":[74],"three":[75],"modules:":[76],"(1)":[77],"structure":[82],"that,":[83],"guided":[84],"by":[85,96,199,203],"the":[86,172,192],"symmetry":[87],"(invariance)":[88],"of":[89,157,181,213],"physical":[90],"laws,":[91],"introduces":[92],"structural":[94],"asymmetry":[95],"treating":[97],"kinematic":[98],"dynamic":[100],"features":[101],"as":[102],"distinct":[103],"node":[104],"types":[105],"enhance":[107],"model":[108,175,195],"interpretability;":[109],"(2)":[110],"reconstruction":[113],"module":[114],"that":[115],"learns":[116],"robust":[117],"representations":[118],"from":[119],"noisy":[120],"OBD":[121],"streams":[122],"without":[123],"extensive":[124],"labeling,":[125],"improving":[126],"quality":[130],"variations;":[131],"(3)":[133],"multi-layer":[135],"feature":[136,151],"extraction":[137],"architecture":[138],"combining":[139],"convolutional":[141],"networks":[142,147],"(GCNs)":[143],"attention":[146],"(GATs)":[148],"hierarchical":[150],"aggregation.":[152],"On":[153],"test":[155,214],"set":[156],"800":[158],"trips,":[161],"SSR-HGCN":[162],"demonstrated":[163],"superior":[164],"performance":[165],"over":[166,211],"key":[167],"baseline":[168],"models.":[169],"Compared":[170],"with":[171,228],"classical":[173],"time-series":[174],"LSTM,":[176],"it":[177],"achieved":[178],"average":[179],"improvements":[180],"20.76%":[182],"RMSE":[184,198],"41.23%":[186],"MAPE.":[188],"It":[189],"also":[190],"outperformed":[191],"standard":[193],"GraphSAGE,":[196],"reducing":[197],"21.98%":[200],"MAPE":[202],"7.15%,":[204],"ultimately":[205],"achieving":[206],"&lt;":[207],"15%":[208],"error":[209],"90%":[212],"samples.":[215],"This":[216],"provides":[218],"an":[219],"effective":[220],"technical":[221],"solution":[222],"monitoring,":[227],"immediate":[229],"applications":[230],"fleet":[232],"supervision,":[233],"overloading":[234],"detection,":[235],"regulatory":[237],"enforcement":[238],"compliance.":[241]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-28T00:00:00"}
