{"id":"https://openalex.org/W2909838422","doi":"https://doi.org/10.3390/e21010064","title":"Double Entropy Joint Distribution Function and Its Application in Calculation of Design Wave Height","display_name":"Double Entropy Joint Distribution Function and Its Application in Calculation of Design Wave Height","publication_year":2019,"publication_date":"2019-01-14","ids":{"openalex":"https://openalex.org/W2909838422","doi":"https://doi.org/10.3390/e21010064","mag":"2909838422","pmid":"https://pubmed.ncbi.nlm.nih.gov/33266780"},"language":"en","primary_location":{"id":"doi:10.3390/e21010064","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21010064","pdf_url":"https://www.mdpi.com/1099-4300/21/1/64/pdf?version=1547454676","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/1099-4300/21/1/64/pdf?version=1547454676","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100667299","display_name":"Guilin Liu","orcid":"https://orcid.org/0000-0002-4806-3591"},"institutions":[{"id":"https://openalex.org/I59028903","display_name":"Ocean University of China","ror":"https://ror.org/04rdtx186","country_code":"CN","type":"education","lineage":["https://openalex.org/I59028903"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guilin Liu","raw_affiliation_strings":["College of Engineering, Ocean University of China, Qingdao 266100, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Engineering, Ocean University of China, Qingdao 266100, China","institution_ids":["https://openalex.org/I59028903"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103276234","display_name":"Baiyu Chen","orcid":"https://orcid.org/0000-0002-5702-2169"},"institutions":[{"id":"https://openalex.org/I134446601","display_name":"Berkeley College","ror":"https://ror.org/02xewxa75","country_code":"US","type":"education","lineage":["https://openalex.org/I134446601"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Baiyu Chen","raw_affiliation_strings":["College of Engineering, University of California Berkeley, Berkeley, CA 94720, USA"],"raw_orcid":"https://orcid.org/0000-0002-5702-2169","affiliations":[{"raw_affiliation_string":"College of Engineering, University of California Berkeley, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I134446601","https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003578876","display_name":"Song Jiang","orcid":"https://orcid.org/0000-0003-2151-0977"},"institutions":[{"id":"https://openalex.org/I148099405","display_name":"Xi'an University of Architecture and Technology","ror":"https://ror.org/04v2j2k71","country_code":"CN","type":"education","lineage":["https://openalex.org/I148099405"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Song Jiang","raw_affiliation_strings":["School of Management, Xi\u2019an University of Architecture and Technology, Xi\u2019an 710055, China","School of Management, Xi'an University of Architecture and Technology, Xi'an 710055, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management, Xi\u2019an University of Architecture and Technology, Xi\u2019an 710055, China","institution_ids":["https://openalex.org/I148099405"]},{"raw_affiliation_string":"School of Management, Xi'an University of Architecture and Technology, Xi'an 710055, China","institution_ids":["https://openalex.org/I148099405"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058377107","display_name":"Hanliang Fu","orcid":"https://orcid.org/0000-0001-6817-374X"},"institutions":[{"id":"https://openalex.org/I148099405","display_name":"Xi'an University of Architecture and Technology","ror":"https://ror.org/04v2j2k71","country_code":"CN","type":"education","lineage":["https://openalex.org/I148099405"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hanliang Fu","raw_affiliation_strings":["School of Management, Xi\u2019an University of Architecture and Technology, Xi\u2019an 710055, China","School of Management, Xi'an University of Architecture and Technology, Xi'an 710055, China"],"raw_orcid":"https://orcid.org/0000-0001-6817-374X","affiliations":[{"raw_affiliation_string":"School of Management, Xi\u2019an University of Architecture and Technology, Xi\u2019an 710055, China","institution_ids":["https://openalex.org/I148099405"]},{"raw_affiliation_string":"School of Management, Xi'an University of Architecture and Technology, Xi'an 710055, China","institution_ids":["https://openalex.org/I148099405"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100605301","display_name":"Liping Wang","orcid":"https://orcid.org/0000-0002-4015-7788"},"institutions":[{"id":"https://openalex.org/I59028903","display_name":"Ocean University of China","ror":"https://ror.org/04rdtx186","country_code":"CN","type":"education","lineage":["https://openalex.org/I59028903"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liping Wang","raw_affiliation_strings":["School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China","institution_ids":["https://openalex.org/I59028903"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052753577","display_name":"Wei Jiang","orcid":"https://orcid.org/0000-0001-5402-2203"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wei Jiang","raw_affiliation_strings":["School of Forest Resources and Conservation, University of Florida, Gainesville, FL 32611, USA"],"raw_orcid":"https://orcid.org/0000-0001-5402-2203","affiliations":[{"raw_affiliation_string":"School of Forest Resources and Conservation, University of Florida, Gainesville, FL 32611, USA","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5103276234"],"corresponding_institution_ids":["https://openalex.org/I134446601","https://openalex.org/I95457486"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":2.8373,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.8933247,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"21","issue":"1","first_page":"64","last_page":"64"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13804","display_name":"Physical Activity and Education Research","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2312","display_name":"Water Science and Technology"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13804","display_name":"Physical Activity and Education Research","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2312","display_name":"Water Science and Technology"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13955","display_name":"Evaluation Methods in Various Fields","score":0.9376999735832214,"subfield":{"id":"https://openalex.org/subfields/2302","display_name":"Ecological Modeling"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.6662936806678772},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6082913875579834},{"id":"https://openalex.org/keywords/maximum-entropy-probability-distribution","display_name":"Maximum entropy probability distribution","score":0.566066324710846},{"id":"https://openalex.org/keywords/significant-wave-height","display_name":"Significant wave height","score":0.5653615593910217},{"id":"https://openalex.org/keywords/joint-probability-distribution","display_name":"Joint probability distribution","score":0.5557582974433899},{"id":"https://openalex.org/keywords/maximum-entropy-spectral-estimation","display_name":"Maximum entropy spectral estimation","score":0.5280025005340576},{"id":"https://openalex.org/keywords/wave-height","display_name":"Wave height","score":0.5207086205482483},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.5178976058959961},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.502112627029419},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.428016722202301},{"id":"https://openalex.org/keywords/distribution-function","display_name":"Distribution function","score":0.41404736042022705},{"id":"https://openalex.org/keywords/wave-packet","display_name":"Wave packet","score":0.41353359818458557},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.41044723987579346},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3450494706630707},{"id":"https://openalex.org/keywords/wind-wave","display_name":"Wind wave","score":0.28881996870040894},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.26926684379577637},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19134652614593506},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10900115966796875}],"concepts":[{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.6662936806678772},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6082913875579834},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.566066324710846},{"id":"https://openalex.org/C85910571","wikidata":"https://www.wikidata.org/wiki/Q2674049","display_name":"Significant wave height","level":3,"score":0.5653615593910217},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.5557582974433899},{"id":"https://openalex.org/C89735579","wikidata":"https://www.wikidata.org/wiki/Q6795894","display_name":"Maximum entropy spectral estimation","level":3,"score":0.5280025005340576},{"id":"https://openalex.org/C70620910","wikidata":"https://www.wikidata.org/wiki/Q821563","display_name":"Wave height","level":2,"score":0.5207086205482483},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.5178976058959961},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.502112627029419},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.428016722202301},{"id":"https://openalex.org/C186603090","wikidata":"https://www.wikidata.org/wiki/Q55505926","display_name":"Distribution function","level":2,"score":0.41404736042022705},{"id":"https://openalex.org/C106978608","wikidata":"https://www.wikidata.org/wiki/Q1412691","display_name":"Wave packet","level":2,"score":0.41353359818458557},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.41044723987579346},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3450494706630707},{"id":"https://openalex.org/C165082838","wikidata":"https://www.wikidata.org/wiki/Q165848","display_name":"Wind wave","level":2,"score":0.28881996870040894},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26926684379577637},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19134652614593506},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10900115966796875},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e21010064","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21010064","pdf_url":"https://www.mdpi.com/1099-4300/21/1/64/pdf?version=1547454676","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:33266780","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33266780","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:mdpi.com:/1099-4300/21/1/64/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e21010064","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7514171","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7514171","pdf_url":null,"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"}],"best_oa_location":{"id":"doi:10.3390/e21010064","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21010064","pdf_url":"https://www.mdpi.com/1099-4300/21/1/64/pdf?version=1547454676","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":[{"display_name":"Life below water","score":0.8799999952316284,"id":"https://metadata.un.org/sdg/14"}],"awards":[{"id":"https://openalex.org/G4512301423","display_name":null,"funder_award_id":"U1706226","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"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2909838422.pdf"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1964948030","https://openalex.org/W1973055373","https://openalex.org/W1986926488","https://openalex.org/W1991347244","https://openalex.org/W2031298242","https://openalex.org/W2032712317","https://openalex.org/W2061165361","https://openalex.org/W2082033753","https://openalex.org/W2105290563","https://openalex.org/W2291350157","https://openalex.org/W2343132017","https://openalex.org/W2344211156","https://openalex.org/W2527430838","https://openalex.org/W2563167163","https://openalex.org/W2754291201","https://openalex.org/W2772222285","https://openalex.org/W2778809741","https://openalex.org/W2783525110","https://openalex.org/W2791052411","https://openalex.org/W2794208501","https://openalex.org/W2799501716","https://openalex.org/W2809236353","https://openalex.org/W2885468577","https://openalex.org/W2885801264","https://openalex.org/W2886614520","https://openalex.org/W2888347392","https://openalex.org/W2890126157","https://openalex.org/W2890970224","https://openalex.org/W2895501952","https://openalex.org/W2899690110","https://openalex.org/W2901415036","https://openalex.org/W2902575637","https://openalex.org/W2904599941","https://openalex.org/W2914672265","https://openalex.org/W6746504834","https://openalex.org/W6753369622","https://openalex.org/W6759577795"],"related_works":["https://openalex.org/W2324808582","https://openalex.org/W4399682427","https://openalex.org/W2042390733","https://openalex.org/W2999761183","https://openalex.org/W3150600118","https://openalex.org/W2392597884","https://openalex.org/W2058448586","https://openalex.org/W2183162320","https://openalex.org/W4390590419","https://openalex.org/W2922317433"],"abstract_inverted_index":{"Wave":[0],"height":[1,31,69,85,110,187,205],"and":[2,56,70,87,111,125,137,206],"wave":[3,30,68,71,84,109,112,186,189,204,207],"period":[4,72,113],"are":[5,11],"important":[6],"oceanic":[7],"environmental":[8],"factors":[9],"that":[10,160,175,196],"used":[12],"to":[13,142,149],"describe":[14],"the":[15,21,26,81,88,94,99,132,150,161,166,177,182,198],"randomness":[16],"of":[17,23,28,33,53,67,96,98,108,185,203],"a":[18,39],"wave.":[19],"Within":[20],"field":[22],"ocean":[24],"engineering,":[25],"calculation":[27],"design":[29],"is":[32,49,73,78,114,172,192],"great":[34],"significance.":[35],"In":[36],"this":[37],"paper,":[38],"periodic":[40,91],"maximum":[41,82,89],"entropy":[42,63,83,90,104,168],"distribution":[43,65,106,170,180,201],"function":[44,66,77,86,107,171,202],"with":[45,93],"four":[46],"undetermined":[47,152],"parameters":[48,153],"derived":[50,79,164],"by":[51,117,121],"means":[52],"coordinate":[54],"transformation":[55],"solving":[57],"conditional":[58],"variational":[59],"problems.":[60],"A":[61],"double":[62,103,167],"joint":[64,105,169,200],"also":[74,193],"derived.":[75],"The":[76,102,156],"from":[80,165,176,197],"function,":[92],"help":[95],"structures":[97],"Copula":[100],"function.":[101],"not":[115],"limited":[116],"weak":[118],"nonlinearity,":[119],"nor":[120],"normal":[122],"stochastic":[123],"process":[124],"narrow":[126],"spectrum.":[127],"Besides,":[128],"it":[129,154],"can":[130],"fit":[131],"observed":[133],"data":[134],"more":[135,139],"carefully":[136],"be":[138],"widely":[140],"applicable":[141],"nonlinear":[143],"waves":[144],"in":[145],"various":[146],"cases,":[147],"owing":[148],"many":[151],"contains.":[155],"engineering":[157],"cases":[158],"show":[159],"recurrence":[162],"level":[163],"higher":[173,194],"than":[174,195],"extreme":[178],"value":[179],"using":[181],"single":[183],"variables":[184],"or":[188],"period.":[190,208],"It":[191],"traditional":[199]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":15}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
