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Article(id=1243896234579181719, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243896229885751465, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2025.08.007, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1740153600000, receivedDateStr=2025-02-22, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774497572798, onlineDateStr=2026-03-26, pubDate=1755619200000, pubDateStr=2025-08-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774497572798, onlineIssueDateStr=2026-03-26, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774497572798, creator=13701087609, updateTime=1774497572798, updator=13701087609, issue=Issue{id=1243896229885751465, tenantId=1146029695717560320, journalId=1240685776644648972, year='2025', volume='29', issue='8', pageStart='1181', pageEnd='1342', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774497571678, creator=13701087609, updateTime=1774501555614, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1243912939799949656, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243896229885751465, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1243912939799949657, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243896229885751465, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1250, endPage=1260, ext={EN=ArticleExt(id=1243896234902143133, articleId=1243896234579181719, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Probability characteristics of ice loads on polar ships based on the Monte Carlo method, columnId=1242129251223274417, journalTitle=Journal of Ship Mechanics, columnName=Structural Mechanics, runingTitle=null, highlight=null, articleAbstract=

The study of probability characteristics of ice loads can offer more precise input loads for the assessment of ship structural safety, taking into account the uncertainties involved in the interaction between polar ships and sea ice. By integrating the ice load estimation formula with a statistical characteristic analysis method, a Monte Carlo-based approach was proposed to investigate the probabilistic characteristics of ice loads on polar ships. According to the typical sea area and route, the scenarios of interaction between the midship and bow of the vessel with sea ice were considered separately. Based on the study of the probability distribution types and statistical parameters of the relevant variables, the ice loads at different positions was calculated by the method presented in this paper, and the corresponding probability density function was obtained. It can be found that the probability characteristics of ice force in the midship can be accurately modeled by a normal distribution, and the Weibull distribution can be used to describe the probability characteristics of both horizontal and vertical ice forces at the bow. Moreover, the horizontal force exerted on the ship due to ice crushing is significantly greater than that resulting from its bending failure.

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考虑极地船舶与海冰作用过程中的不确定性因素，开展冰载荷的概率特性研究。通过将冰载荷估算公式和统计特性分析方法相结合，给出一种基于蒙特卡罗法的极地船舶冰载荷概率特性研究方法。针对典型海域和航线，分别考虑船舯、船艏与海冰作用的场景，在研究相关变量概率分布类型和统计参数基础上，采用本文方法计算不同位置的冰载荷，获得对应的概率密度函数。研究表明，舯部的冰作用力可使用正态分布来描述其概率特性；艏部的水平冰作用力和垂直冰作用力均可使用威布尔分布来描述其概率特性；海冰压溃破坏时，船舶受到的水平冰作用力远大于其弯曲破坏时对应的冰作用力。研究结果可为船舶结构安全性评估提供更为精确的输入载荷。

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通讯作者，E-mail：
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董海波（1985-），男，博士研究生，高级工程师，通讯作者，E-mail：。

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董海波（1985-），男，博士研究生，高级工程师，通讯作者，E-mail：。

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董海波（1985-），男，博士研究生，高级工程师，通讯作者，E-mail：。

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Probabilistic analysis of local ice pressures[J]. Journal of Offshore Mechanics and Arctic Engineering, 1993, 115(1): 83-89., articleTitle=Probabilistic analysis of local ice pressures, refAbstract=null), Reference(id=1243896247078208252, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=2010, volume=61, issue=2-3, pageStart=97, pageEnd=106, url=null, language=null, rfNumber=[2], rfOrder=1, authorNames=Jordaan I, Bruce J, Masterson D, journalName=Cold Regions Science and Technology, refType=null, unstructuredReference=Jordaan I, Bruce J, Masterson D, et al. Local ice pressures for multi-year ice accounting for exposure[J]. Cold Regions Science and Technology, 2010, 61(2-3): 97-106., articleTitle=Local ice pressures for multi-year ice accounting for exposure, refAbstract=null), Reference(id=1243896247174677246, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=2017, volume=52, issue=null, pageStart=153, pageEnd=172, url=null, language=null, rfNumber=[3], rfOrder=2, authorNames=Suominen M, Kujala P, Romanoff J, journalName=Marine Structures, refType=null, unstructuredReference=Suominen M, Kujala P, Romanoff J, et al. Influence of load length on short-term ice load statistics in full-scale[J]. Marine Structures, 2017, 52:153-172., articleTitle=Influence of load length on short-term ice load statistics in full-scale, refAbstract=null), Reference(id=1243896247262757634, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[4], rfOrder=3, authorNames=Kujala P, Suominen M, Riska K, journalName=null, refType=null, unstructuredReference=Kujala P, Suominen M, Riska K. Statistics of ice loads measured on MT Uikku in the Baltic[C]//Proceedings of the 20th International Conference on Port and Ocean Engineering under Arctic Conditions, Luleå, Sweden, June 8-12, 2009., articleTitle=Statistics of ice loads measured on MT Uikku in the Baltic, refAbstract=null), Reference(id=1243896247346643720, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=2014, volume=97, issue=null, pageStart=7, pageEnd=20, url=null, language=null, rfNumber=[5], rfOrder=4, authorNames=Suyuthi A, Leira B J, Riska K, journalName=Cold Regions Science and Technology, refType=null, unstructuredReference=Suyuthi A, Leira B J, Riska K. A generalized probabilistic model of ice load peaks on ship hulls in broken-ice fields[J]. Cold Regions Science and Technology, 2014, 97:7-20., articleTitle=A generalized probabilistic model of ice load peaks on ship hulls in broken-ice fields, refAbstract=null), Reference(id=1243896247468278541, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=2021, volume=80, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[6], rfOrder=5, authorNames=Li F, Lu L, Suominen M, journalName=Marine Structures, refType=null, unstructuredReference=Li F, Lu L, Suominen M, et al. Short-term statistics of ice loads on ship bow frames in floe ice fields: Full-scale measurements in the Antarctic ocean[J]. Marine Structures, 2021, 80:103049., articleTitle=Short-term statistics of ice loads on ship bow frames in floe ice fields: Full-scale measurements in the Antarctic ocean, refAbstract=null), Reference(id=1243896247535387409, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=2023, volume=27, issue=7, pageStart=1109, pageEnd=1117, url=null, language=null, rfNumber=[7], rfOrder=6, authorNames=何林, 柴威, 余象鹏, journalName=船舶力学, refType=null, unstructuredReference=何林，柴威，余象鹏，等. 极地船舶冰载荷随机特性研究综述[J]. 船舶力学，2023, 27(7):1109-1117., articleTitle=极地船舶冰载荷随机特性研究综述, refAbstract=null), Reference(id=1243896247619273495, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=2023, volume=27, issue=7, pageStart=1109, pageEnd=1117, url=null, language=null, rfNumber=[7], rfOrder=7, authorNames=He L, Chai W, Yu X P, journalName=Journal of Ship Mechanics, refType=null, unstructuredReference=He L, Chai W, Yu X P, et al. Review on random nature of ice loads for Arctic ships[J]. Journal of Ship Mechanics, 2023, 27(7): 1109-1117. (in Chinese), articleTitle=Review on random nature of ice loads for Arctic ships, refAbstract=null), Reference(id=1243896247724131097, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=2018, volume=146, issue=null, pageStart=87, pageEnd=97, url=null, language=null, rfNumber=[8], rfOrder=8, authorNames=Chai W, Leira B J, Naess A, journalName=Cold Regions Science and Technology, refType=null, unstructuredReference=Chai W, Leira B J, Naess A. Probabilistic methods for estimation of the extreme value statistics of ship ice loads[J]. Cold Regions Science and Technology, 2018, 146:87-97., articleTitle=Probabilistic methods for estimation of the extreme value statistics of ship ice loads, refAbstract=null), Reference(id=1243896247808017178, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=1996, volume=9, issue=9, pageStart=849, pageEnd=871, url=null, language=null, rfNumber=[9], rfOrder=9, authorNames=Kujala P, journalName=Marine Structures, refType=null, unstructuredReference=Kujala P. Semi-empirical evaluation of long term ice loads on a ship hull[J]. Marine Structures, 1996, 9(9): 849-871., articleTitle=Semi-empirical evaluation of long term ice loads on a ship hull, refAbstract=null), Reference(id=1243896247896097566, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=2013, volume=17, issue=1-2, pageStart=112, pageEnd=117, url=null, language=null, rfNumber=[10], rfOrder=10, authorNames=张大勇, 李刚, 岳前进, journalName=船舶力学, refType=null, unstructuredReference=张大勇，李刚，岳前进，等. 冰区海洋平台结构整体抗力及极值响应的概率统计特性[J]. 船舶力学，2013, 17(1-2):112-117., articleTitle=冰区海洋平台结构整体抗力及极值响应的概率统计特性, refAbstract=null), Reference(id=1243896248013538083, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=2013, volume=17, issue=1-2, pageStart=112, pageEnd=117, url=null, language=null, rfNumber=[10], rfOrder=11, authorNames=Zhang D Y, Li G, Yue Q J, journalName=Journal of Ship Mechanics, refType=null, unstructuredReference=Zhang D Y, Li G, Yue Q J, et al. Statistical properties of structural global resistance and extreme response of offshore platform in ice zone[J]. Journal of Ship Mechanics, 2013, 17(1-2): 112-117. (in Chinese), articleTitle=Statistical properties of structural global resistance and extreme response of offshore platform in ice zone, refAbstract=null), Reference(id=1243896248135172902, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=2020, volume=198, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[11], rfOrder=12, authorNames=Sinsabvarodom C, Chai W, Leira B J, journalName=Ocean Engineering, refType=null, unstructuredReference=Sinsabvarodom C, Chai W, Leira B J, et al. Uncertainty assessments of structural loading due to first year ice based on the ISO standard by using Monte-Carlo simulation[J]. Ocean Engineering, 2020, 198:106935., articleTitle=Uncertainty assessments of structural loading due to first year ice based on the ISO standard by using Monte-Carlo simulation, refAbstract=null), Reference(id=1243896248298750764, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=2019, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[12], rfOrder=13, authorNames=null, journalName=null, refType=null, unstructuredReference=ISO 19906, Petroleum and natural gas industries-arctic offshore structures[S]. Switzerland: International Organization for Standardization, 2019., articleTitle=null, refAbstract=null), Reference(id=1243896248432968497, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=2002, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[13], rfOrder=14, authorNames=null, journalName=null, refType=null, unstructuredReference=QQ/HSn 3000-2002，中国海海冰条件及应用规定[S]. 北京：中国海洋石油总公司，2002., articleTitle=null, refAbstract=null), Reference(id=1243896248525243187, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=2002, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[13], rfOrder=15, authorNames=null, journalName=null, refType=null, unstructuredReference=QQ/HSn 3000-2002, Regulations for offshore ice condition & application in China Sea[S]. Beijing: China National Offshore Oil Corporation, 2002. (in Chinese), articleTitle=null, refAbstract=null), Reference(id=1243896248613323575, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=2018, volume=39, issue=4, pageStart=629, pageEnd=634, url=null, language=null, rfNumber=[14], rfOrder=16, authorNames=屈衍, 张大勇, 许宁, journalName=哈尔滨工程大学学报, refType=null, unstructuredReference=屈衍，张大勇，许宁，等. 《中国海冰条件及应用》与ISO 19906冰载荷规定比较[J]. 哈尔滨工程大学学报，2018, 39(4):629-634., articleTitle=《中国海冰条件及应用》与ISO 19906冰载荷规定比较, refAbstract=null), Reference(id=1243896248718181179, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=2018, volume=39, issue=4, pageStart=629, pageEnd=634, url=null, language=null, rfNumber=[14], rfOrder=17, authorNames=Qu Y, Zhang D Y, Xu N, journalName=Journal of Harbin Engineering University, refType=null, unstructuredReference=Qu Y, Zhang D Y, Xu N, et al. Comparison of ice load regulations in ISO 19906 and “The sea ice conditions and its application in China”[J]. Journal of Harbin Engineering University, 2018, 39(4): 629-634. (in Chinese), articleTitle=Comparison of ice load regulations in ISO 19906 and “The sea ice conditions and its application in China”, refAbstract=null), Reference(id=1243896248818844478, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=1943, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[15], rfOrder=18, authorNames=Zubov N N, journalName=Arctic ice, refType=null, unstructuredReference=Zubov N N. Arctic ice[M]. Moscow: Izdatel’stvo Glavsevmorputi, 1943., articleTitle=null, refAbstract=null), Reference(id=1243896248919507776, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[16], rfOrder=19, authorNames=Li H T, Bjerkås M, V Høyland K, journalName=null, refType=null, unstructuredReference=Li H T, Bjerkås M, V Høyland K, et al. Panel loads and weather conditions at Norströmsgrund lighthouse 2000-2003[C]//23rd IAHR International Symposium on Ice, Ann Arbor, Michigan USA, May 31 to June 3, 2016., articleTitle=Panel loads and weather conditions at Norströmsgrund lighthouse 2000-2003, refAbstract=null), Reference(id=1243896249011782467, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=2020, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[17], rfOrder=20, authorNames=梅浩, journalName=null, refType=null, unstructuredReference=梅浩. 基于船基图像分析的北极夏季海冰分布的时空变化研究[D]. 大连：大连理工大学，2020., articleTitle=基于船基图像分析的北极夏季海冰分布的时空变化研究, refAbstract=null), Reference(id=1243896249120834377, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=2020, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[17], rfOrder=21, authorNames=Mei H, journalName=null, refType=null, unstructuredReference=Mei H. Study on distribution and variation of sea ice in Arctic summer based on shipboard image analysis[D]. Dalian: Dalian University of Technology, 2020. (in Chinese), articleTitle=Study on distribution and variation of sea ice in Arctic summer based on shipboard image analysis, refAbstract=null), Reference(id=1243896249263440712, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, doi=null, pmid=null, pmcid=null, year=1994, volume=22, issue=3, pageStart=285, pageEnd=298, url=null, language=null, rfNumber=[18], rfOrder=22, authorNames=Timco G W, O Brien S, journalName=Cold Regions Science and Technology, refType=null, unstructuredReference=Timco G W, O Brien S. Flexural strength equation for sea ice[J]. Cold Regions Science and Technology, 1994, 22(3): 285-298., articleTitle=Flexural strength equation for sea ice, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1243896240493150626, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, xref=1., ext=[AuthorCompanyExt(id=1243896240501539235, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, companyId=1243896240493150626, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.College of Shipbullding Engineering, Harbin Engineering University, Harbin I5000l, China), AuthorCompanyExt(id=1243896240505733540, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, companyId=1243896240493150626, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.哈尔滨工程大学　船舶工程学院，哈尔滨　150001)]), 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the vertical ice force, figureFileSmall=gCz9bZsriaxvwFAh9d/ADQ==, figureFileBig=S9yKqPg7tm8T3QTOaDqMxA==, tableContent=null), ArticleFig(id=1243896244800701075, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=CN, label=图8, caption=垂直冰作用力概率密度函数, figureFileSmall=gCz9bZsriaxvwFAh9d/ADQ==, figureFileBig=S9yKqPg7tm8T3QTOaDqMxA==, tableContent=null), ArticleFig(id=1243896244918141594, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=EN, label=Tab.1, caption=

Values for ice strength coefficient in different areas

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冰强度系数CR/MPa区域
2.8北极当年冰和多年冰区域（如波弗特海）
2.4靠近北极区域（如鄂霍次克海-库页岛东北海域）
1.8温带地区（鄂霍次克海-阿尼瓦湾、北里海、库克海湾、波罗的海、渤海）
), ArticleFig(id=1243896245035582111, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=CN, label=表1, caption=

不同区域的冰强度系数[12]

, figureFileSmall=null, figureFileBig=null, tableContent=
冰强度系数CR/MPa区域
2.8北极当年冰和多年冰区域（如波弗特海）
2.4靠近北极区域（如鄂霍次克海-库页岛东北海域）
1.8温带地区（鄂霍次克海-阿尼瓦湾、北里海、库克海湾、波罗的海、渤海）
), ArticleFig(id=1243896245132051107, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=EN, label=Tab.2, caption=

Distribution types and statistical parameters of different variables for the midship

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变量分布类型均值变异系数
正态分布30.020
正态分布100.020
接触区域宽度w/m正态分布170.020
正态分布240.020
正态分布310.020
冰厚h/m对数正态1.5480.071
冰强度系数CR/MPa威布尔分布2.80.252
), ArticleFig(id=1243896245220131497, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=CN, label=表2, caption=

船舯区域变量的分布类型和统计参数

, figureFileSmall=null, figureFileBig=null, tableContent=
变量分布类型均值变异系数
正态分布30.020
正态分布100.020
接触区域宽度w/m正态分布170.020
正态分布240.020
正态分布310.020
冰厚h/m对数正态1.5480.071
冰强度系数CR/MPa威布尔分布2.80.252
), ArticleFig(id=1243896245366932141, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=EN, label=Tab.3, caption=

Cases of interaction between the midship and sea ice

, figureFileSmall=null, figureFileBig=null, tableContent=
工况序号名称w均值/mh均值/mCR均值/MPa
1M0131.5482.8
2M02101.5482.8
3M03171.5482.8
4M04241.5482.8
5M05311.5482.8
), ArticleFig(id=1243896245505344184, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=CN, label=表3, caption=

船舯与海冰作用的工况

, figureFileSmall=null, figureFileBig=null, tableContent=
工况序号名称w均值/mh均值/mCR均值/MPa
1M0131.5482.8
2M02101.5482.8
3M03171.5482.8
4M04241.5482.8
5M05311.5482.8
), ArticleFig(id=1243896245610201789, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=EN, label=Tab.4, caption=

Distribution types and statistical parameters of different variables for the bow

, figureFileSmall=null, figureFileBig=null, tableContent=
变量分布类型均值变异系数
斜面宽度B/m正态分布30.020
冰弯曲强度λ/kPa威布尔分布4800.542
冰厚h/m正态分布0.870.287
正态分布40.580.020
夹角φ/°正态分布64.490.020
正态分布72.550.020
), ArticleFig(id=1243896245715059394, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=CN, label=表4, caption=

船艏区域变量的分布类型和统计参数

, figureFileSmall=null, figureFileBig=null, tableContent=
变量分布类型均值变异系数
斜面宽度B/m正态分布30.020
冰弯曲强度λ/kPa威布尔分布4800.542
冰厚h/m正态分布0.870.287
正态分布40.580.020
夹角φ/°正态分布64.490.020
正态分布72.550.020
), ArticleFig(id=1243896245824111303, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=EN, label=Tab.5, caption=

Cases of interaction between the bow and sea ice

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工况序号工况名称φ均值/°B均值/mλ均值/kPah均值/m
1S0140.5834800.87
2S0264.4934800.87
3S0372.5534800.87
), ArticleFig(id=1243896245899608781, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=CN, label=表5, caption=

船艏与海冰作用的工况

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工况序号工况名称φ均值/°B均值/mλ均值/kPah均值/m
1S0140.5834800.87
2S0264.4934800.87
3S0372.5534800.87
), ArticleFig(id=1243896245975106258, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=EN, label=Tab.6, caption=

Distribution types of ice loads for different cases

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工况序号名称分布类型
1M01正态分布
2M02正态分布
3M03正态分布
4M04正态分布
5M05正态分布
), ArticleFig(id=1243896246096741077, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=CN, label=表6, caption=

不同工况下冰载荷的分布类型

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工况序号名称分布类型
1M01正态分布
2M02正态分布
3M03正态分布
4M04正态分布
5M05正态分布
), ArticleFig(id=1243896246193210074, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=EN, label=Tab.7, caption=

Results of parameter estimation for the probability density function

, figureFileSmall=null, figureFileBig=null, tableContent=
工况序号名称未知参数估计结果变异系数δu
均值μu/MN标准差σu/MN
1M0123.3746.3920.273
2M0228.4357.4210.261
3M0344.21411.4130.258
4M0459.32615.0500.254
5M0573.49919.3280.263
), ArticleFig(id=1243896246319039199, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=CN, label=表7, caption=

概率密度函数未知参数的估计结果

, figureFileSmall=null, figureFileBig=null, tableContent=
工况序号名称未知参数估计结果变异系数δu
均值μu/MN标准差σu/MN
1M0123.3746.3920.273
2M0228.4357.4210.261
3M0344.21411.4130.258
4M0459.32615.0500.254
5M0573.49919.3280.263
), ArticleFig(id=1243896246407119585, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=EN, label=Tab.8, caption=

Distribution types of ice loads for different cases

, figureFileSmall=null, figureFileBig=null, tableContent=
工况序号名称水平冰作用力分布类型垂直冰作用力分布类型
1S01威布尔分布威布尔分布
2S02威布尔分布威布尔分布
3S03威布尔分布威布尔分布
), ArticleFig(id=1243896246495199972, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=CN, label=表8, caption=

不同工况冰载荷的分布类型

, figureFileSmall=null, figureFileBig=null, tableContent=
工况序号名称水平冰作用力分布类型垂直冰作用力分布类型
1S01威布尔分布威布尔分布
2S02威布尔分布威布尔分布
3S03威布尔分布威布尔分布
), ArticleFig(id=1243896246579086056, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=EN, label=Tab.9, caption=

Results of parameter estimation for the probability density function

, figureFileSmall=null, figureFileBig=null, tableContent=
工况序号名称水平冰作用力概率密度函数垂直冰作用力概率密度函数
尺度参数βu形状参数αu尺度参数βu形状参数αu
1S01109.9361.294126.3951.263
2S02267.7101.295123.9641.303
3S03406.8611.271127.6491.293
), ArticleFig(id=1243896246658777834, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=CN, label=表9, caption=

概率密度函数未知参数的估计结果

, figureFileSmall=null, figureFileBig=null, tableContent=
工况序号名称水平冰作用力概率密度函数垂直冰作用力概率密度函数
尺度参数βu形状参数αu尺度参数βu形状参数αu
1S01109.9361.294126.3951.263
2S02267.7101.295123.9641.303
3S03406.8611.271127.6491.293
), ArticleFig(id=1243896246755246829, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=EN, label=Tab.10, caption=

Probability characteristics of ice forces

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工况序号名称水平冰作用力垂直冰作用力
均值μu/kN标准差σu/kN变异系数δu均值μu/kN标准差σu/kN变异系数δu
1S01101.63079.1800.779117.44993.6250.797
2S02247.444192.6450.779114.43888.5790.774
3S03377.543299.1670.792118.02392.0200.780
), ArticleFig(id=1243896246843327218, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243896234579181719, language=CN, label=表10, caption=

冰作用力的概率特性

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工况序号名称水平冰作用力垂直冰作用力
均值μu/kN标准差σu/kN变异系数δu均值μu/kN标准差σu/kN变异系数δu
1S01101.63079.1800.779117.44993.6250.797
2S02247.444192.6450.779114.43888.5790.774
3S03377.543299.1670.792118.02392.0200.780
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基于蒙特卡罗法的极地船舶冰载荷概率特性研究
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董海波 1, 2, 3 , 冯士超 2, 3 , 刘俊杰 2, 3 , 夏劲松 2, 3
船舶力学 | 结构力学 2025,29(8): 1250-1260
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船舶力学 | 结构力学 2025, 29(8): 1250-1260
基于蒙特卡罗法的极地船舶冰载荷概率特性研究
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董海波1, 2, 3 , 冯士超2, 3, 刘俊杰2, 3, 夏劲松2, 3
作者信息
  • 1.哈尔滨工程大学　船舶工程学院，哈尔滨　150001
  • 2.中国船舶科学研究中心，江苏　无锡　214082
  • 3.船舶结构安全全国重点实验室，江苏　无锡　214082

    • 董海波（1985-），男，博士研究生，高级工程师，通讯作者，E-mail：。

通讯作者:

通讯作者，E-mail：
Probability characteristics of ice loads on polar ships based on the Monte Carlo method
Hai-bo DONG1, 2, 3 , Shi-chao FENG2, 3, Jun-jie LIU2, 3, Jin-song XIA2, 3
Affiliations
  • 1.College of Shipbullding Engineering, Harbin Engineering University, Harbin I5000l, China
  • 2.China Ship Scientific Research Center, Wuxi 214082, China
  • 3.National Key Laboratory of Ship Structural Safety, Wuxi 214082, China
出版时间: 2025-08-20 doi: 10.3969/j.issn.1007-7294.2025.08.007
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摘要
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考虑极地船舶与海冰作用过程中的不确定性因素，开展冰载荷的概率特性研究。通过将冰载荷估算公式和统计特性分析方法相结合，给出一种基于蒙特卡罗法的极地船舶冰载荷概率特性研究方法。针对典型海域和航线，分别考虑船舯、船艏与海冰作用的场景，在研究相关变量概率分布类型和统计参数基础上，采用本文方法计算不同位置的冰载荷，获得对应的概率密度函数。研究表明，舯部的冰作用力可使用正态分布来描述其概率特性；艏部的水平冰作用力和垂直冰作用力均可使用威布尔分布来描述其概率特性；海冰压溃破坏时，船舶受到的水平冰作用力远大于其弯曲破坏时对应的冰作用力。研究结果可为船舶结构安全性评估提供更为精确的输入载荷。

冰载荷概率特性  /  蒙特卡罗法  /  概率密度函数  /  概率图纸  /  极大似然估计

The study of probability characteristics of ice loads can offer more precise input loads for the assessment of ship structural safety, taking into account the uncertainties involved in the interaction between polar ships and sea ice. By integrating the ice load estimation formula with a statistical characteristic analysis method, a Monte Carlo-based approach was proposed to investigate the probabilistic characteristics of ice loads on polar ships. According to the typical sea area and route, the scenarios of interaction between the midship and bow of the vessel with sea ice were considered separately. Based on the study of the probability distribution types and statistical parameters of the relevant variables, the ice loads at different positions was calculated by the method presented in this paper, and the corresponding probability density function was obtained. It can be found that the probability characteristics of ice force in the midship can be accurately modeled by a normal distribution, and the Weibull distribution can be used to describe the probability characteristics of both horizontal and vertical ice forces at the bow. Moreover, the horizontal force exerted on the ship due to ice crushing is significantly greater than that resulting from its bending failure.

probability characteristics of ice loads  /  Monte Carlo method  /  probability density function  /  probability paper  /  maximum likelihood estimate
董海波, 冯士超, 刘俊杰, 夏劲松. 基于蒙特卡罗法的极地船舶冰载荷概率特性研究. 船舶力学, 2025 , 29 (8) : 1250 -1260 . DOI: 10.3969/j.issn.1007-7294.2025.08.007
Hai-bo DONG, Shi-chao FENG, Jun-jie LIU, Jin-song XIA. Probability characteristics of ice loads on polar ships based on the Monte Carlo method[J]. Journal of Ship Mechanics, 2025 , 29 (8) : 1250 -1260 . DOI: 10.3969/j.issn.1007-7294.2025.08.007
正文
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0　引言
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船舶在极地航行过程中，船体承受的冰载荷是影响结构安全性的主要环境载荷。冰载荷的大小与船体结构型式、海冰尺度参数、海冰力学特性及船-冰作用模式等密切相关。由于海冰的冰厚、大小、压缩强度、剪切强度、弯曲强度等参数均为随机变化的量，加上海冰破坏失效的不确定性，船-冰作用过程为典型的随机过程，导致船体所受的冰载荷具有一定的概率特性。
采用传统的确定性方法计算冰载荷时，认为关键参数为常量，获得的冰载荷为确定性结果，无法精确反映冰载荷的不确定性特征。因此，开展冰载荷的概率统计特性研究是非常必要的。在考虑船-冰作用过程中的随机性基础上，结合抽样分布、参数估计等统计分析方法，研究获得冰载荷的不确定性特征，为极地船舶结构安全性评估提供更为精确的输入载荷。
考虑典型的冰区航行场景，可基于实船测试数据研究冰载荷的不确定性特征。实船测试主要获得结构响应，然后通过识别和反演转化为结构典型位置的冰载荷，包括冰压力和线载荷。针对冰压力，Jordaan等[1]首先提出了概率分布模型，认为在船舶典型测试区域实测获得的冰压力载荷呈指数分布。在此基础上，Jordaan等[2]发展了事件最大法（Event-Maximum Method），可预报冰载荷的极值。针对线载荷实测数据，为了准确描述冰载荷幅值，一些学者分别使用了指数分布、对数正态分布、威布尔分布、三参数指数分布和混合指数分布等概率分布模型[3-6]。在此基础上，可通过渐进极值法[7]、序列极值法[7]、平均条件超越率（Average Conditional Exceedance Rate，ACER）法[8]开展冰载荷的短期预报，以及通过Kujula等[9]提出的方法开展长期极值预报。另一方面，通过将关键参数视为服从某一分布的变量，结合冰载荷估算公式和模拟技术，可研究获得冰载荷的不确定性特征。张大勇等[10]考虑海洋平台结构抗冰设计的各种不确定性，结合蒙特卡罗（Monte-Carlo）方法和平台结构简化力学模型，研究了结构整体抗力及极值冰力响应的概率统计特性。Sinsabvarodom等[11]考虑海冰参数的统计分布特征，结合ISO 19906[12]中的公式，基于不确定性方法对结构-冰作用过程中的冰载荷进行研究。
上述研究中，基于实测数据的方法，对实测方案、数据规模、反演方法等具有很高的依赖性；数据拟合时，分布函数与实际工况、作用环境等因素密切相关；同时，极值预报过程中，典型参数的取值较难确定。基于冰载荷估算公式的方法，目前主要应用于海洋工程领域，考虑到其简便性、适用性，加上模拟技术的发展日趋成熟，该方法可发展应用于极地航行船舶。鉴于此，本文针对典型目标船，考虑船舯与海冰、船艏与海冰作用的两种典型场景，结合冰载荷估算公式和统计特性分析方法，对船舶冰载荷概率特性进行研究，获得对应的概率密度函数、均值、变异系数等。
1　冰载荷理论方法
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冰载荷理论方法主要包括冰载荷估算公式和统计特性分析方法。
1.1　冰载荷估算公式
结构-海冰作用过程中，受冰层厚度、冰形状、相互作用速度及结构形状等关键参数的影响，海冰会形成不同的破坏模式。垂直结构与海冰碰撞或挤压作用时，海冰主要破坏模式为压溃失效；斜面结构与海冰碰撞或挤压作用时，海冰对应的破坏模式主要为弯曲破坏。图1给出了海冰与不同结构作用时的破坏模式。
不同的破坏模式直接决定了冰载荷的大小，对应有不同的冰载荷估算公式。
（1）海冰与垂直结构作用
结合ISO19906规定[12]，当海冰和垂直结构作用时，冰作用力UG垂直于作用截面，其大小可通过下式计算：
式中，UG为冰作用力，单位为MN；A为名义接触面积，单位为m2；pG为名义接触面积上的平均冰压力，单位为MPa。
对于层冰或浮冰来说，名义接触面积为
式中，w为结构与冰接触区域的宽度，单位为m；h为冰厚，单位为m。
平均冰压力受名义接触面积、接触区域形状、结构-海冰的相对速度及结构柔度等影响。根据库克湾、波弗特海、波罗的海和渤海的实尺度试验测量数据，针对当年冰或多年冰与垂直结构作用的场景，平均冰压力为
式中，CR为冰强度系数，单位为MPa，不同区域的冰强度系数取值如表1所示；h1为参考冰厚，取1 m；n为冰厚效应的经验系数，当冰厚小于1 m时，取−0.5+h/5，当冰厚大于等于1 m时，取−0.3；m为接触区域宽度效应的经验系数，取值为−0.16；vAR为经验项，可表示为
式（3）和式（4）适用于接触区域宽高比w/h大于1的情况；特别地，当宽高比大于5时，式（3）中可忽略vAR项。
（2）海冰与斜面结构作用
针对海冰与斜面结构作用，考虑使用Q/HSn规定[13-14]中的相关公式进行简化计算，水平冰作用力和垂直冰作用力分别为
式中，UH为水平冰作用力，单位为kN；UV为垂直冰作用力，单位为kN；K为系数，可取0.1B，B为倾斜面的宽度，单位为m；λ为冰的弯曲强度，单位为kPa，应结合极地区域海冰数据确定；φ为倾斜面与水平面的夹角，一般小于75°。
（3）冰厚估算
根据冰生长模型[15-16]计算典型海域的海冰厚度，公式如下：
式中，CFDD为与冰点天数（Freezing Degree Days，FDD）相关的系数，表示冰冻温度的累积参数，可表述如下：
式中，T0为海水的冻结温度，单位为℃，在北极地区一般取为−1.8；Td为日平均气温，单位为℃；求和的天数为气温低于海水冻结温度的天数。
1.2　统计特性分析方法
在获得相关变量概率分布类型和统计参数基础上，利用蒙特卡罗法、概率图纸（Probability Paper）及极大似然估计（Maximum Likelihood Estimate，MLE）研究冰载荷的统计特性。
（1）变量分布类型和统计参数
针对接触区域宽度w、冰厚h、冰强度系数CR、斜面宽度B、冰弯曲强度λ及夹角φ等参数，考虑其随机性特征，确定变量的分布类型，以及对应的均值μ、标准差σ和变异系数δ。
船舶与海洋工程领域常用分布类型主要有正态分布、对数正态分布和威布尔分布等，假定随机变量X分别服从上述3种不同的分布，则对应的概率密度函数分别为
式中，μx为变量X的均值，σx为变量X标准差，αx为形状参数，βx为尺度参数。
当变量的统计资料较少，较难确定其概率分布类型时，可以比照其他具有类似变异性质基本变量的概率分布类型予以近似选定。
（2）冰载荷计算
利用蒙特卡罗方法解决不确定性问题，进行冰载荷计算。对影响冰载荷的各变量进行大量随机抽样，然后将抽样值以不同组合形式分别代入冰作用力公式，计算获得一定数量的冰载荷样本值。
（3）冰载荷概率分布类型
针对足够数量的冰载荷样本值，初步确定其所符合的分布类型，采用概率图纸法判断分布类型是否合适。如果载荷样本值在概率图纸上呈直线或近似呈直线分布，可初步判断该分布用以描述抽样结果是合适的；否则，需选取其他的分布类型并继续进行验证。
（4）概率密度函数中未知参数的值
在确定分布类型基础上，结合式（9）~（11）获得对应的概率密度函数。运用极大似然估计法确定函数中未知参数的值。
2　变量的统计特性
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2.1　目标作用场景
本文针对一艘极地航行船开展冰载荷概率统计特性研究。该船适于在中厚当年冰（冰厚0.7~1.2 m）及更薄的海冰冰况下航行。舯部区域局部位置相对于冰面为垂直结构（两者夹角大于75°），如图2（a）所示，舯部与海冰作用时，可借鉴使用式（1）计算冰作用力。
艏部或船肩区域局部位置相对于冰面为斜面结构，如图2（b）所示，直航或转弯艏部与海冰作用时，为简化分析，可借鉴使用式（5）和式（6）计算冰作用力。
针对该极地航行船，在研究冰载荷时主要考虑两种冰况场景：“区域型”和“航线型”，前者选取典型海域的极值冰况条件作为计算的输入，后者是基于我国科考船的典型路线，以其所遭遇的冰况特征作为计算的输入。
考虑到极地船舶穿过白令海峡后，无论是直接驶向北极，还是沿西北航线或东北航线航行，首先进入楚科奇海（Chukchi Sea），因此本文选取楚科奇海作为“区域型”的目标场景，其地理位置如图3（a）所示。
“航线型”考虑选取2018年我国北极科考对应的航线作为目标场景，假定本文研究的船舶和科考船航行路线一致，结合相关的冰况统计数据进行冰载荷的研究。科考船的航行线路如图3（b）所示。
2.2　变量的分布类型和统计参数
（1）船舯与海冰作用
以“区域型”作为目标场景，考虑的作用工况为船舶转弯时舯部与冰层挤压作用，或海冰运动直接碰撞、挤压舯部区域。基于上述条件，确定以下变量的分布类型和统计参数。
i）接触区域宽度w。根据目标船舶水线平行于中纵剖面那部分的长度，选取典型的值，分别取为3 m、10 m、17 m、24 m及31 m，根据构件几何尺寸的统计特性[10]，宽度的概率分布类型选为正态分布。
ii）冰厚h。考虑到目标场景为“区域型”，将基于典型海域楚科奇海的CFDD来计算冰厚。根据ISO19906[12]的数据，CFDD的年平均值为4000，观测到的最大值和最小值分别为3500和4500，按式（7）计算得到冰厚的均值为1.548 m，此处的冰厚为“区域型”的极值冰厚，其符合对数正态分布。
iii）冰强度系数CR。根据表1，冰强度系数取为2.8 MPa，其分布类型选为威布尔分布[11]。
变量的概率分布类型和统计参数结果如表2所示。
结合表2，针对舯部与海冰作用，可设置的工况如表3所示。
（2）船艏与海冰作用
以“航线型”作为目标场景，结合具体的航行路线，研究航行时间周期内冰载荷的规律特征。
i）斜面宽度B和夹角φ。根据本文所述船舶的艏部线型和尺度参数，B取为3 m，φ选取3个典型值，为40.58°、64.49°和72.55°。
ii）冰弯曲强度λ。结合极地区域海冰特性相关测量统计结果[18]，均值取480 kPa，变异系数取为0.542。
iii）冰厚h。考虑到“航线型”的目标场景，参考科考船2018年北极航行相关数据的统计结果[17]，获得冰厚的统计特征，均值为0.87 m，变异系数为0.287。
变量的概率分布类型和统计参数结果如表4所示。
结合表4，针对艏部与海冰作用，可设置的工况如表5所示。
3　冰载荷概率特性计算结果
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3.1　船舯与海冰作用
（1）冰载荷分布类型
针对舯部与海冰作用，结合表2给出的变量分布类型和统计参数，以及式（1）~（4）的冰作用力计算公式，按照本文所述的基于蒙特卡罗的冰载荷计算方法，可获得表3中不同工况的冰作用力。对于每种工况来说，计算结果为包含多个样本值的变量，记为u1，u2，u3，…，uz，其中，z为样本值的数量。然后通过概率图纸判断样本值所符合的分布类型。
以M02工况为例，示意说明分布类型确定过程。
针对该工况，考虑接触区域宽度w、冰厚h和冰强度系数CR等变量所对应的均值、标准差和变异系数等，每个变量运算产生2000个随机数，按组分别代入式（1），计算获得冰作用力值2000个。将2000个样本值绘制于不同的概率图纸上，判断其所符合的分布类型。可以发现，当样本值在正态概率图纸上时，大部分数据值位于拟合直线上或附近区域，认为M02工况的冰载荷值符合正态分布。M02工况的正态概率图纸如图4所示。
按照上述方法，依次确定其他工况下冰载荷值的分布类型，结果如表6所示。
（2）未知参数的确定
在确定冰载荷分布类型的基础上，采用极大似然估计方法确定概率密度函数中未知参数的值。冰载荷样本值对应的分布类型为正态分布，需确定的未知参数为均值μu和标准差σu。估计结果如表7所示。
（3）冰载荷概率密度函数
考虑舯部与海冰作用，结合表6和表7的结果，可绘制不同工况对应的冰作用力概率密度函数，如图5所示。
（4）结果分析
由图5可以看出，自工况M01至M05，冰作用力的概率密度函数由“高瘦”型变化为“扁平”型，函数曲线由陡峭趋于平缓。
结合冰作用力均值、冰厚均值及接触区域宽度均值，计算得到不同工况下平均冰压力均值。冰作用力、平均冰压力随接触区域宽度的变化曲线如图6所示。
由表6~7及图5~6，对比5种工况的计算结果可以看出，随着接触区域宽度的增加，冰作用力的均值不断增大，对应的标准差也不断增大。接触区域宽度由M01变化至M05增加了9.3倍，对应的冰作用力均值增加了2.1倍左右。
由图6可以看出，随接触区域宽度的增加，平均冰压力的均值不断减小，M01工况最大值为5.03 MPa，M02工况相较于M01工况有大幅降低，降幅为63.5%，而M02工况至M05工况，平均冰压力变化不大。究其原因，主要是M01工况下接触区域宽高比w/h大于1且小于5，冰作用力计算时计及了公式中vAR项；而其他工况下宽高比大于5时，计算时可忽略vAR项。
3.2　船艏与海冰作用
（1）冰载荷的分布类型
结合表4给出的变量分布类型和统计参数，以及式（5）~（6）的冰作用力计算公式，按照本文所述的基于蒙特卡罗的冰载荷计算方法，可获得表5中不同工况的水平冰作用力和垂直冰作用力。基于计算结果所包含的一定数量的样本值，通过概率图纸判断样本值所符合的分布类型。
具体实施过程可参照3.1节的示例。
不同工况冰载荷分布类型的分析结果如表8所示。
（2）未知参数的确定
在确定冰载荷分布类型的基础上，采用极大似然估计方法确定概率密度函数中未知参数的值。
对于威布尔分布来说，需确定的未知参数为形状参数αu和尺度参数βu。未知参数的估计结果如表9所示。
（3）冰载荷概率密度函数
结合表8和表9的结果，可绘制不同工况对应的冰作用力的概率密度函数，如图7和图8所示。
（4）结果分析
由表9和图7可以看出，随着夹角φ的增大（<75°），水平冰作用力概率密度函数的尺度参数不断增大，形状参数变化不大，函数曲线的形状由陡峭变得平缓。
由表9和图8可以看出，垂直冰作用力的变化不受夹角φ的影响，概率密度函数曲线的形状较陡峭。
结合表8和表9，可计算得到不同工况下水平冰作用力和垂直冰作用力对应的均值、标准差和变异系数，如表10所示。
由表10可以看出，自工况S01至工况S03，随着夹角φ的增大，水平冰作用力的均值不断增大，夹角增大了78.8%，对应的水平冰作用力增加了271.5%。
由表10可以看出，自工况S01至工况S03，垂直冰作用力均值基本不变，同时变异系数变化也不大。
4　结论
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本文结合冰载荷估算公式和统计特性分析方法，考虑目标船“区域型”和“航线型”两种典型场景，研究了冰载荷的概率统计特性。主要结论如下：
（1）针对“区域型”冰况场景，主要考虑船舯与海冰作用，冰作用力计算结果均可使用正态分布来描述其概率特性；随着接触区域的增大，冰作用力的数据分布由相对集中趋于分散。
（2）针对“航线型”冰况场景，主要考虑船艏与海冰作用，水平冰作用力和垂直冰作用力的计算结果均可使用威布尔分布来描述其概率特性；随着冰层和倾斜面夹角的增大，水平冰作用力的数据分布分散度增加；垂直冰作用力不受夹角变化的影响，数据分布相对集中。
（3）结合“区域型”和“航线型”两种冰况场景的冰作用力计算结果，海冰压溃破坏时船舶受到的水平冰作用力比弯曲破坏时对应的冰作用力大得多，相同海冰厚度、接触区域宽度条件下，前者约是后者的100倍。
（4）基于冰载荷的概率特性，可进一步研究获得载荷的极值特征，为开展极地船舶的结构安全性评估及极端冰情下的结构损伤研究提供有力的支撑。
文献
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参考文献 引证文献
排序方式：
[1]
Jordaan I J, Maes M A, Brown P W, et al. Probabilistic analysis of local ice pressures[J]. Journal of Offshore Mechanics and Arctic Engineering, 1993, 115(1): 83-89.
[2]
Jordaan I, Bruce J, Masterson D, et al. Local ice pressures for multi-year ice accounting for exposure[J]. Cold Regions Science and Technology, 2010, 61(2-3): 97-106.
[3]
Suominen M, Kujala P, Romanoff J, et al. Influence of load length on short-term ice load statistics in full-scale[J]. Marine Structures, 2017, 52:153-172.
[4]
Kujala P, Suominen M, Riska K. Statistics of ice loads measured on MT Uikku in the Baltic[C]//Proceedings of the 20th International Conference on Port and Ocean Engineering under Arctic Conditions, Luleå, Sweden, June 8-12, 2009.
[5]
Suyuthi A, Leira B J, Riska K. A generalized probabilistic model of ice load peaks on ship hulls in broken-ice fields[J]. Cold Regions Science and Technology, 2014, 97:7-20.
[6]
Li F, Lu L, Suominen M, et al. Short-term statistics of ice loads on ship bow frames in floe ice fields: Full-scale measurements in the Antarctic ocean[J]. Marine Structures, 2021, 80:103049.
[7]
何林，柴威，余象鹏，等. 极地船舶冰载荷随机特性研究综述[J]. 船舶力学，2023, 27(7):1109-1117.
He L, Chai W, Yu X P, et al. Review on random nature of ice loads for Arctic ships[J]. Journal of Ship Mechanics, 2023, 27(7): 1109-1117. (in Chinese)
[8]
Chai W, Leira B J, Naess A. Probabilistic methods for estimation of the extreme value statistics of ship ice loads[J]. Cold Regions Science and Technology, 2018, 146:87-97.
[9]
Kujala P. Semi-empirical evaluation of long term ice loads on a ship hull[J]. Marine Structures, 1996, 9(9): 849-871.
[10]
张大勇，李刚，岳前进，等. 冰区海洋平台结构整体抗力及极值响应的概率统计特性[J]. 船舶力学，2013, 17(1-2):112-117.
Zhang D Y, Li G, Yue Q J, et al. Statistical properties of structural global resistance and extreme response of offshore platform in ice zone[J]. Journal of Ship Mechanics, 2013, 17(1-2): 112-117. (in Chinese)
[11]
Sinsabvarodom C, Chai W, Leira B J, et al. Uncertainty assessments of structural loading due to first year ice based on the ISO standard by using Monte-Carlo simulation[J]. Ocean Engineering, 2020, 198:106935.
[12]
ISO 19906, Petroleum and natural gas industries-arctic offshore structures[S]. Switzerland: International Organization for Standardization, 2019.
[13]
QQ/HSn 3000-2002，中国海海冰条件及应用规定[S]. 北京：中国海洋石油总公司，2002.
QQ/HSn 3000-2002, Regulations for offshore ice condition & application in China Sea[S]. Beijing: China National Offshore Oil Corporation, 2002. (in Chinese)
[14]
屈衍，张大勇，许宁，等. 《中国海冰条件及应用》与ISO 19906冰载荷规定比较[J]. 哈尔滨工程大学学报，2018, 39(4):629-634.
Qu Y, Zhang D Y, Xu N, et al. Comparison of ice load regulations in ISO 19906 and “The sea ice conditions and its application in China”[J]. Journal of Harbin Engineering University, 2018, 39(4): 629-634. (in Chinese)
[15]
Zubov N N. Arctic ice[M]. Moscow: Izdatel’stvo Glavsevmorputi, 1943.
[16]
Li H T, Bjerkås M, V Høyland K, et al. Panel loads and weather conditions at Norströmsgrund lighthouse 2000-2003[C]//23rd IAHR International Symposium on Ice, Ann Arbor, Michigan USA, May 31 to June 3, 2016.
[17]
梅浩. 基于船基图像分析的北极夏季海冰分布的时空变化研究[D]. 大连：大连理工大学，2020.
Mei H. Study on distribution and variation of sea ice in Arctic summer based on shipboard image analysis[D]. Dalian: Dalian University of Technology, 2020. (in Chinese)
[18]
Timco G W, O Brien S. Flexural strength equation for sea ice[J]. Cold Regions Science and Technology, 1994, 22(3): 285-298.
2025年第29卷第8期
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doi: 10.3969/j.issn.1007-7294.2025.08.007
  • 接收时间：2025-02-22
  • 首发时间：2026-03-26
  • 出版时间：2025-08-20
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  • 收稿日期：2025-02-22
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    1.哈尔滨工程大学　船舶工程学院，哈尔滨　150001
    2.中国船舶科学研究中心，江苏　无锡　214082
    3.船舶结构安全全国重点实验室，江苏　无锡　214082

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