{"id":"https://openalex.org/W7136820356","doi":"https://doi.org/10.3390/e28030329","title":"Power Load Probabilistic Prediction Based on Multi-Value Quantile Regression and Timing Fusion Ensemble Learning Model","display_name":"Power Load Probabilistic Prediction Based on Multi-Value Quantile Regression and Timing Fusion Ensemble Learning Model","publication_year":2026,"publication_date":"2026-03-16","ids":{"openalex":"https://openalex.org/W7136820356","doi":"https://doi.org/10.3390/e28030329","pmid":"https://pubmed.ncbi.nlm.nih.gov/41899981"},"language":"en","primary_location":{"id":"doi:10.3390/e28030329","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28030329","pdf_url":"https://www.mdpi.com/1099-4300/28/3/329/pdf","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/28/3/329/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Yuhang Liu","orcid":"https://orcid.org/0009-0008-1613-5651"},"institutions":[{"id":"https://openalex.org/I163340411","display_name":"Hohai University","ror":"https://ror.org/01wd4xt90","country_code":"CN","type":"education","lineage":["https://openalex.org/I163340411"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuhang Liu","raw_affiliation_strings":["School of Electrical and Power Engineering, Hohai University, Nanjing 211100, China"],"raw_orcid":"https://orcid.org/0009-0008-1613-5651","affiliations":[{"raw_affiliation_string":"School of Electrical and Power Engineering, Hohai University, Nanjing 211100, China","institution_ids":["https://openalex.org/I163340411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029091114","display_name":"Fei Mei","orcid":"https://orcid.org/0000-0001-5379-6522"},"institutions":[{"id":"https://openalex.org/I163340411","display_name":"Hohai University","ror":"https://ror.org/01wd4xt90","country_code":"CN","type":"education","lineage":["https://openalex.org/I163340411"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fei Mei","raw_affiliation_strings":["School of Electrical and Power Engineering, Hohai University, Nanjing 211100, China"],"raw_orcid":"https://orcid.org/0000-0001-5379-6522","affiliations":[{"raw_affiliation_string":"School of Electrical and Power Engineering, Hohai University, Nanjing 211100, China","institution_ids":["https://openalex.org/I163340411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129560861","display_name":"Jun Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I163340411","display_name":"Hohai University","ror":"https://ror.org/01wd4xt90","country_code":"CN","type":"education","lineage":["https://openalex.org/I163340411"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Zhang","raw_affiliation_strings":["School of Electrical and Power Engineering, Hohai University, Nanjing 211100, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Power Engineering, Hohai University, Nanjing 211100, China","institution_ids":["https://openalex.org/I163340411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101585101","display_name":"Xiang Dai","orcid":"https://orcid.org/0000-0002-6020-9688"},"institutions":[{"id":"https://openalex.org/I163340411","display_name":"Hohai University","ror":"https://ror.org/01wd4xt90","country_code":"CN","type":"education","lineage":["https://openalex.org/I163340411"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiang Dai","raw_affiliation_strings":["School of Electrical and Power Engineering, Hohai University, Nanjing 211100, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Power Engineering, Hohai University, Nanjing 211100, China","institution_ids":["https://openalex.org/I163340411"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055304040","display_name":"Wei Li","orcid":"https://orcid.org/0000-0003-1444-5062"},"institutions":[{"id":"https://openalex.org/I163340411","display_name":"Hohai University","ror":"https://ror.org/01wd4xt90","country_code":"CN","type":"education","lineage":["https://openalex.org/I163340411"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wen Li","raw_affiliation_strings":["School of Electrical and Power Engineering, Hohai University, Nanjing 211100, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Power Engineering, Hohai University, Nanjing 211100, China","institution_ids":["https://openalex.org/I163340411"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I163340411"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.25242649,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"3","first_page":"329","last_page":"329"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11052","display_name":"Energy Load and Power Forecasting","score":0.7684000134468079,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T11052","display_name":"Energy Load and Power Forecasting","score":0.7684000134468079,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T11344","display_name":"Traffic Prediction and Management Techniques","score":0.02590000070631504,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"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/T13429","display_name":"Electricity Theft Detection Techniques","score":0.02459999918937683,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/interpretability","display_name":"Interpretability","score":0.7213000059127808},{"id":"https://openalex.org/keywords/quantile","display_name":"Quantile","score":0.6442999839782715},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6243000030517578},{"id":"https://openalex.org/keywords/quantile-regression","display_name":"Quantile regression","score":0.5680999755859375},{"id":"https://openalex.org/keywords/probabilistic-forecasting","display_name":"Probabilistic forecasting","score":0.4564000070095062},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.41370001435279846},{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.3846000134944916},{"id":"https://openalex.org/keywords/ensemble-learning","display_name":"Ensemble learning","score":0.37700000405311584},{"id":"https://openalex.org/keywords/ensemble-forecasting","display_name":"Ensemble forecasting","score":0.3668000102043152},{"id":"https://openalex.org/keywords/prediction-interval","display_name":"Prediction interval","score":0.36329999566078186}],"concepts":[{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.7213000059127808},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.644599974155426},{"id":"https://openalex.org/C118671147","wikidata":"https://www.wikidata.org/wiki/Q578714","display_name":"Quantile","level":2,"score":0.6442999839782715},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6243000030517578},{"id":"https://openalex.org/C63817138","wikidata":"https://www.wikidata.org/wiki/Q3455889","display_name":"Quantile regression","level":2,"score":0.5680999755859375},{"id":"https://openalex.org/C122282355","wikidata":"https://www.wikidata.org/wiki/Q7246855","display_name":"Probabilistic forecasting","level":3,"score":0.4564000070095062},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.41370001435279846},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3937999904155731},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.3846000134944916},{"id":"https://openalex.org/C45942800","wikidata":"https://www.wikidata.org/wiki/Q245652","display_name":"Ensemble learning","level":2,"score":0.37700000405311584},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.36970001459121704},{"id":"https://openalex.org/C119898033","wikidata":"https://www.wikidata.org/wiki/Q3433888","display_name":"Ensemble forecasting","level":2,"score":0.3668000102043152},{"id":"https://openalex.org/C103402496","wikidata":"https://www.wikidata.org/wiki/Q1106171","display_name":"Prediction interval","level":2,"score":0.36329999566078186},{"id":"https://openalex.org/C47121976","wikidata":"https://www.wikidata.org/wiki/Q3489473","display_name":"Quantile function","level":4,"score":0.3614000082015991},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.3474000096321106},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.34209999442100525},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.3409999907016754},{"id":"https://openalex.org/C81692654","wikidata":"https://www.wikidata.org/wiki/Q225926","display_name":"Kriging","level":2,"score":0.3352000117301941},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.29809999465942383},{"id":"https://openalex.org/C158525013","wikidata":"https://www.wikidata.org/wiki/Q2593739","display_name":"Fusion","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.288100004196167},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.2793000042438507},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.2653000056743622},{"id":"https://openalex.org/C52622490","wikidata":"https://www.wikidata.org/wiki/Q1026626","display_name":"Feature extraction","level":2,"score":0.26499998569488525},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.263700008392334},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.25929999351501465},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.25690001249313354},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.25360000133514404},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e28030329","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28030329","pdf_url":"https://www.mdpi.com/1099-4300/28/3/329/pdf","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:41899981","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41899981","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:13025978","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13025978/","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13025978/pdf/entropy-28-00329.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:00697788684549a89d598fae097cb14a","is_oa":true,"landing_page_url":"https://doaj.org/article/00697788684549a89d598fae097cb14a","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,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 28, Iss 3, p 329 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e28030329","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28030329","pdf_url":"https://www.mdpi.com/1099-4300/28/3/329/pdf","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5539801261","display_name":null,"funder_award_id":"2022YFE0140600","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G6711486644","display_name":null,"funder_award_id":"U24A20149","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8132380206","display_name":null,"funder_award_id":"52277089","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7136820356.pdf","grobid_xml":"https://content.openalex.org/works/W7136820356.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W2091158010","https://openalex.org/W2327401273","https://openalex.org/W2752082601","https://openalex.org/W2879959793","https://openalex.org/W2884414452","https://openalex.org/W2898515673","https://openalex.org/W2951882118","https://openalex.org/W2953233651","https://openalex.org/W2963188571","https://openalex.org/W2996876695","https://openalex.org/W3095582408","https://openalex.org/W3115188337","https://openalex.org/W3140526156","https://openalex.org/W3171884590","https://openalex.org/W3194355893","https://openalex.org/W3200726017","https://openalex.org/W3211177584","https://openalex.org/W4229033585","https://openalex.org/W4313043344","https://openalex.org/W4385519390","https://openalex.org/W4388378214","https://openalex.org/W4392697897","https://openalex.org/W4392901584","https://openalex.org/W4401634380","https://openalex.org/W4402082898","https://openalex.org/W4402742702","https://openalex.org/W4405310453","https://openalex.org/W4406064024","https://openalex.org/W4406756322","https://openalex.org/W4407151755","https://openalex.org/W7126429681"],"related_works":[],"abstract_inverted_index":{"The":[0,162],"core":[1,113,210],"component":[2],"to":[3,89,116,178,215],"ensure":[4],"the":[5,112,125,150,157,166,179,218],"refined":[6],"and":[7,32,60,155,199],"safe":[8],"operation":[9],"of":[10,95,152,159,175,183,190,196,217],"distribution":[11],"network":[12,82],"scheduling":[13],"is":[14,75,109,139],"10":[15,48],"kV":[16,49],"bus":[17,50],"load":[18,51,105,120,126],"probabilistic":[19,23,52],"prediction.":[20],"However,":[21],"existing":[22],"prediction":[24,34,53],"methods":[25],"suffer":[26],"from":[27],"insufficient":[28],"dynamic":[29],"feature":[30,100],"extraction":[31],"compromised":[33],"reliability":[35],"caused":[36],"by":[37],"quantile":[38,57,143,153],"crossing.":[39],"To":[40],"address":[41],"these":[42],"issues,":[43],"this":[44],"paper":[45],"proposes":[46],"a":[47,61,69,86,130,170,185,192,200],"method":[54],"integrating":[55],"multi-value":[56],"regression":[58],"(MQR)":[59],"temporal":[62,70,80,93],"fusion":[63,71,81],"ensemble":[64,72],"learning":[65,73],"model":[66,74],"(ELM).":[67],"Firstly,":[68],"constructed,":[76],"which":[77,141],"integrates":[78],"multiple":[79],"(TFN)":[83],"sub-models":[84],"through":[85,145],"stacking":[87],"framework":[88],"parallel":[90],"extract":[91],"multi-dimensional":[92],"features":[94],"loads,":[96],"effectively":[97],"enhancing":[98],"its":[99],"capture":[101],"capability":[102],"for":[103],"complex":[104],"data.":[106],"Secondly,":[107],"MQR":[108],"introduced":[110],"as":[111,205,207],"objective":[114],"function":[115],"synchronously":[117],"generate":[118],"multi-quantile":[119],"forecasting":[121,160],"results,":[122],"comprehensively":[123],"depicting":[124],"probability":[127],"distribution.":[128],"Finally,":[129],"Listwise":[131],"Maximum":[132],"Likelihood":[133],"Estimation":[134],"(ListMLE)":[135],"ranking":[136],"constraint":[137],"mechanism":[138],"embedded,":[140],"optimizes":[142],"ordering":[144],"monotonicity":[146],"constraints,":[147],"significantly":[148,213],"reducing":[149],"degree":[151],"crossing":[154],"improving":[156],"interpretability":[158],"results.":[161],"results":[163],"show":[164],"that":[165],"MQR-ELM":[167],"algorithm":[168],"achieves":[169],"Prediction":[171,186],"Interval":[172,187],"Coverage":[173],"Probability":[174,203],"94.624%":[176],"(close":[177],"nominal":[180],"coverage":[181],"rate":[182],"95%),":[184],"Averaged":[188],"Width":[189],"588.526,":[191],"Crossing":[193],"Degree":[194],"Index":[195],"only":[197],"0.0476,":[198],"Continuous":[201],"Ranked":[202],"Score":[204],"low":[206],"84.931.":[208],"All":[209],"indicators":[211],"are":[212],"superior":[214],"those":[216],"comparative":[219],"algorithms.":[220]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2026-03-17T00:00:00"}
