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Article(id=1281324279694332655, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1281323885077447100, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2026.02.008, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1754755200000, receivedDateStr=2025-08-10, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1783421114133, onlineDateStr=2026-07-07, pubDate=1771084800000, pubDateStr=2026-02-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1783421114133, onlineIssueDateStr=2026-07-07, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1783421114133, creator=13701087609, updateTime=1783421114133, updator=13701087609, issue=Issue{id=1281323885077447100, tenantId=1146029695717560320, journalId=1240685776644648972, year='2026', volume='30', issue='2', pageStart='177', pageEnd='340', issueExtLink='null', onlineDate='null', pubDate='1771084800000', pubDateStr='2026-02-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1783421020049, creator='13701087609', updateTime=1783422086911, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1281328359892303896, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1281323885077447100, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1281328359892303897, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1281323885077447100, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=271, endPage=281, ext={EN=ArticleExt(id=1281324280151511792, articleId=1281324279694332655, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Derivation and application of directional metocean design conditions, columnId=1242129251223274417, journalTitle=Journal of Ship Mechanics, columnName=Structural Mechanics, runingTitle=null, highlight=null, articleAbstract=

Considering the directional differences in the distribution of environmental conditions, the directional design criteria can be adopted as long as no jeopardizing to the structure reliability is introduced. Compared with the omnidirectional design condition, the directional criteria can optimize the structural design by redistributing the exceedance probability on all directional sectors. The directional design conditions that meet the requirements of the target reliabilities can be determined by the iterative method proposed in this paper, and the optimal structural design and the corresponding directional design condition can be determined by design analysis and comparison for specific structures. The statistical uncertainty impact caused by distribution fitting and large extrapolation needs to be carefully considered, and using the proposed "combination method" to derive the environmental condition distribution is an effective solution to reduce this impact.

, authors=Ye LI, Lin-bin LI, Wei WEI, Si-jun WEI, authorsList=Ye LI, Lin-bin LI, Wei WEI, Si-jun WEI, authorCompany=null, correspAuthors=Lin-bin LI, authorNote=null, correspAuthorsNote=null, copyrightStatement=Copyright ©2026 Journal of Ship Mechanics. All rights reserved., copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1281324326062362669, articleId=1281324279694332655, tenantId=1146029695717560320, journalId=1240685776644648972, language=CN, title=方向性海洋环境设计条件的确定和应用, columnId=1241023038926410098, journalTitle=船舶力学, columnName=结构力学, runingTitle=null, highlight=null, articleAbstract=

考虑到海洋环境条件分布的方向性差异，在不降低海工结构可靠度的前提下，结构设计可采用方向性设计条件。与全方向设计条件相比，方向性设计条件通过重新分配各方向上的超越概率，来达到优化结构设计的目的。满足规范可靠度目标要求的方向性设计条件可采用本文提出的迭代方法确定，并针对具体结构进行设计分析和比较，以确定最优结构设计方案及其对应的最优方向性设计条件。分布拟合和大幅外推所带来的统计不确定性影响需要充分考虑，而采用本文提出的“组合法”来获得方向性环境要素分布是降低统计不确定性影响的有效途径。

, authors=李晔, 李林斌, 位巍, 韦斯俊, authorsList=李晔, 李林斌, 位巍, 韦斯俊, authorCompany=null, correspAuthors=李林斌, authorNote=

李　晔（1975–），男，硕士，高级工程师，Email：

位　巍（1990–），女，博士，高级工程师

韦斯俊（1988–），男，硕士，工程师

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李林斌（1973–），男，正高级工程师，通讯作者，Email：
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San Francisco, California, USA, 2014., articleTitle=null, refAbstract=null), Reference(id=1281324337126936704, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=12, rfOrder=12, authorNames=null, journalName=null, refType=null, unstructuredReference=中国船级社. 海上浮动设施入级规范[S]. 北京: 中国船级社, 2023., articleTitle=null, refAbstract=null), Reference(id=1281324337194045570, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=12, rfOrder=13, authorNames=null, journalName=null, refType=null, unstructuredReference=China Classification Society. Rules for classification of offshore floating installation[S]. Beijing: China Classification Society, 2023. (in Chinese), articleTitle=null, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1281324326347575342, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, xref=null, ext=[AuthorCompanyExt(id=1281324326355963951, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, companyId=1281324326347575342, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=China Classification Society, Beijing 100007, China), AuthorCompanyExt(id=1281324326364352560, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, companyId=1281324326347575342, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=中国船级社，北京 100007)])], figs=[ArticleFig(id=1281324330407661645, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=EN, label=Fig.1, caption=Locations of the data points P1~P5, figureFileSmall=7da7zYU/Ro892Wc8QFzvGw==, figureFileBig=LuKd+unOyRgDRrOrREUadg==, tableContent=null), ArticleFig(id=1281324330466381902, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=CN, label=图1, caption=点位P1 ~ P5的位置, figureFileSmall=7da7zYU/Ro892Wc8QFzvGw==, figureFileBig=LuKd+unOyRgDRrOrREUadg==, tableContent=null), ArticleFig(id=1281324330650931279, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=EN, label=Fig.2, caption=Scattering of typhoon peak $ {H}_{\mathrm{s}} $ on different directional sectors, figureFileSmall=4TyMF+1hqPnpiwnNGbdpSA==, figureFileBig=0wJFRM8vYVyRp1I+on+rrg==, tableContent=null), ArticleFig(id=1281324330856452176, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=CN, label=图2, caption=台风峰值$ {H}_{\mathrm{s}} $在方向扇区上的散布, figureFileSmall=4TyMF+1hqPnpiwnNGbdpSA==, figureFileBig=0wJFRM8vYVyRp1I+on+rrg==, tableContent=null), ArticleFig(id=1281324332454482001, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=EN, label=Fig.3, caption=Directional scattering of $ {H}_{\mathrm{s}} $ at P3 during typhoon Winnie （1964）, figureFileSmall=JNwO6dvmNVqv5sQnbWPynw==, figureFileBig=0ov+I72zc/qLdgWKswYoRA==, tableContent=null), ArticleFig(id=1281324332534173778, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=CN, label=图3, caption=1964年Winnie台风过程中$ {H}_{\mathrm{s}} $在P3点位的扇区分布, figureFileSmall=JNwO6dvmNVqv5sQnbWPynw==, figureFileBig=0ov+I72zc/qLdgWKswYoRA==, tableContent=null), ArticleFig(id=1281324332592894035, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=EN, label=Fig.4, caption= $ {H}_{\mathrm{s}} $ distribution curves, figureFileSmall=vrjfFB/Sb3/2fVaw1sHdvw==, figureFileBig=vxCfJiSMvMzZJ/zbFoJxgA==, tableContent=null), ArticleFig(id=1281324332647419988, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=CN, label=图4, caption= $ {H}_{\mathrm{s}} $分布曲线, figureFileSmall=vrjfFB/Sb3/2fVaw1sHdvw==, figureFileBig=vxCfJiSMvMzZJ/zbFoJxgA==, tableContent=null), ArticleFig(id=1281324332706140245, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=EN, label=Fig.5, caption= $ {H}_{\mathrm{s}} $ directional distributions, figureFileSmall=g6FJ31d2f4JZMsWHkM3eMA==, figureFileBig=biR7ann2m/Jj/FKG8klYhQ==, tableContent=null), ArticleFig(id=1281324332764860502, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=CN, label=图5, caption= $ {H}_{\mathrm{s}} $的方向性分布, figureFileSmall=g6FJ31d2f4JZMsWHkM3eMA==, figureFileBig=biR7ann2m/Jj/FKG8klYhQ==, tableContent=null), ArticleFig(id=1281324332819386455, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=EN, label=Fig.6, caption=Return periods of $ {H}_{\mathrm{s}}=13.96\;\mathrm{m} $ at all directional sectors, figureFileSmall=yAtDecporCR+K3H0kaIb8g==, figureFileBig=NjP8icvyfcPo5W5WlkWT4Q==, tableContent=null), ArticleFig(id=1281324332890689624, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=CN, label=图6, caption= $ {H}_{\mathrm{s}}=13.96\;\mathrm{m} $在各方向扇区上的重现期, figureFileSmall=yAtDecporCR+K3H0kaIb8g==, figureFileBig=NjP8icvyfcPo5W5WlkWT4Q==, tableContent=null), ArticleFig(id=1281324332957798489, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=EN, label=Fig.7, caption=Directional design conditions with $ \Delta {H}_{\mathrm{s}}=0.3\;\mathrm{m} $, figureFileSmall=P1/LzwV5qYxCvuvkIT1GzQ==, figureFileBig=HQglSVTx6L4SYbLEqCmNcA==, tableContent=null), ArticleFig(id=1281324333012324442, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=CN, label=图7, caption=方向性设计条件（$ \Delta {H}_{\mathrm{s}}=0.3\;\mathrm{m} $）, figureFileSmall=P1/LzwV5qYxCvuvkIT1GzQ==, figureFileBig=HQglSVTx6L4SYbLEqCmNcA==, tableContent=null), ArticleFig(id=1281324333062656091, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=EN, label=Fig.8, caption= $ {H}_{\mathrm{s}} $ distributions at data point P3, figureFileSmall=CqJuYdNXk/0dXcREwqPOPA==, figureFileBig=g1LF1fbYUfaiE3q/l+PT1Q==, tableContent=null), ArticleFig(id=1281324333125570652, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=CN, label=图8, caption=P3点位的$ {H}_{\mathrm{s}} $分布, figureFileSmall=CqJuYdNXk/0dXcREwqPOPA==, figureFileBig=g1LF1fbYUfaiE3q/l+PT1Q==, tableContent=null), ArticleFig(id=1281324333188485213, 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caption=系泊分析耦合模型, figureFileSmall=rz/1fu+RxFWWXye2n9Herg==, figureFileBig=l0SIMA3qXkJ8D/s6hpZMYw==, tableContent=null), ArticleFig(id=1281324333461114977, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=EN, label=Fig.11, caption=Mooring system layout and incident wave directions, figureFileSmall=IAWp7hoqwuhTtE8vh6/lkw==, figureFileBig=UKy02p4NTcgWz2cCK8aVKw==, tableContent=null), ArticleFig(id=1281324333536612450, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=CN, label=图11, caption=锚泊系统布置及波浪入射方向, figureFileSmall=IAWp7hoqwuhTtE8vh6/lkw==, figureFileBig=UKy02p4NTcgWz2cCK8aVKw==, tableContent=null), ArticleFig(id=1281324333599527011, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=EN, label=Fig.12, caption=Maximum tensions of mooring line under omnidirectional and directional design criteria, figureFileSmall=gIff45Oeh63HhHvPju5Ktg==, figureFileBig=vcprc/FKl1aoynQbvJHsaQ==, tableContent=null), ArticleFig(id=1281324333662441572, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=CN, label=图12, caption=全方向及方向性设计条件下的系泊缆最大张力, figureFileSmall=gIff45Oeh63HhHvPju5Ktg==, figureFileBig=vcprc/FKl1aoynQbvJHsaQ==, tableContent=null), ArticleFig(id=1281324333729550437, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=EN, label=Tab.1, caption=

Distribution function parameters of $ {H}_{\mathrm{s}} $

, figureFileSmall=null, figureFileBig=null, tableContent=
扇区样本量年发生率（$ \nu $）位置参数（$ \mu $）尺度参数（$ \sigma $）
Omni（全方向）2280.7731.30128.3080
S1450.1530.86487.4072
S2690.2340.85375.2392
S3500.1690.65885.0263
S4700.2370.65465.0701
S5490.1660.99386.3152
S6870.2951.0298.0106
S7950.3221.25789.2261
S8850.2881.20068.1091
), ArticleFig(id=1281324333817630822, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=CN, label=表1, caption=

$ {H}_{\mathrm{s}} $分布函数的参数

, figureFileSmall=null, figureFileBig=null, tableContent=
扇区样本量年发生率（$ \nu $）位置参数（$ \mu $）尺度参数（$ \sigma $）
Omni（全方向）2280.7731.30128.3080
S1450.1530.86487.4072
S2690.2340.85375.2392
S3500.1690.65885.0263
S4700.2370.65465.0701
S5490.1660.99386.3152
S6870.2951.0298.0106
S7950.3221.25789.2261
S8850.2881.20068.1091
), ArticleFig(id=1281324333888933991, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=EN, label=Tab.2, caption=

Values of $ {H}_{\mathrm{s}} $ and return period derived by two methods: qual ratio escalation and equal return period escalation

, figureFileSmall=null, figureFileBig=null, tableContent=
扇区100年$ {H}_{\mathrm{s}} $/m等比放大等重现期放大
$ {H}_{\mathrm{s}} $/m重现期/Y $ {H}_{\mathrm{s}} $/m重现期/Y
S19.7310.0013410.00134
S27.918.141288.17134
S36.877.061317.07134
S47.137.331347.32134
S59.089.331269.38134
S611.4811.8013511.78134
S713.5713.9613413.96134
S812.1212.4713112.48134
), ArticleFig(id=1281324333972820072, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=CN, label=表2, caption=

“等比放大”与“等重现期放大”方法得到的方向性$ {H}_{\mathrm{s}} $及其重现期

, figureFileSmall=null, figureFileBig=null, tableContent=
扇区100年$ {H}_{\mathrm{s}} $/m等比放大等重现期放大
$ {H}_{\mathrm{s}} $/m重现期/Y $ {H}_{\mathrm{s}} $/m重现期/Y
S19.7310.0013410.00134
S27.918.141288.17134
S36.877.061317.07134
S47.137.331347.32134
S59.089.331269.38134
S611.4811.8013511.78134
S713.5713.9613413.96134
S812.1212.4713112.48134
), ArticleFig(id=1281324334039928937, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=EN, label=Tab.3, caption=

Combinations of directional design conditions

, figureFileSmall=null, figureFileBig=null, tableContent=
扇区 $ \Delta {H}_{\mathrm{s}}=0.3 $ m $ \Delta {H}_{\mathrm{s}}=0.6 $ m $ \Delta {H}_{\mathrm{s}}=0.9 $ m $ \Delta {H}_{\mathrm{s}}=1.2 $ m $ \Delta {H}_{\mathrm{s}}=1.5 $ m
$ {H}_{\mathrm{s}} $重现期 $ {H}_{\mathrm{s}} $重现期 $ {H}_{\mathrm{s}} $重现期 $ {H}_{\mathrm{s}} $重现期 $ {H}_{\mathrm{s}} $重现期
S112.68291712.1149211.86113211.7498311.67906
S210.81291710.24149210.0011329.889839.81906
S39.1129178.6714928.4911328.399838.34906
S49.3529178.9114928.7311328.649838.58906
S512.46291711.79149211.52113211.3898311.29906
S614.26146814.27149213.99113213.8498313.76906
S714.2617014.5621614.8627415.1634715.46440
S814.2658114.5674614.8695814.8998314.79906
), ArticleFig(id=1281324334119620714, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=CN, label=表3, caption=

方向性设计条件组合

, figureFileSmall=null, figureFileBig=null, tableContent=
扇区 $ \Delta {H}_{\mathrm{s}}=0.3 $ m $ \Delta {H}_{\mathrm{s}}=0.6 $ m $ \Delta {H}_{\mathrm{s}}=0.9 $ m $ \Delta {H}_{\mathrm{s}}=1.2 $ m $ \Delta {H}_{\mathrm{s}}=1.5 $ m
$ {H}_{\mathrm{s}} $重现期 $ {H}_{\mathrm{s}} $重现期 $ {H}_{\mathrm{s}} $重现期 $ {H}_{\mathrm{s}} $重现期 $ {H}_{\mathrm{s}} $重现期
S112.68291712.1149211.86113211.7498311.67906
S210.81291710.24149210.0011329.889839.81906
S39.1129178.6714928.4911328.399838.34906
S49.3529178.9114928.7311328.649838.58906
S512.46291711.79149211.52113211.3898311.29906
S614.26146814.27149213.99113213.8498313.76906
S714.2617014.5621614.8627415.1634715.46440
S814.2658114.5674614.8695814.8998314.79906
), ArticleFig(id=1281324334207701099, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=EN, label=Tab.4, caption=

Global mass data of FPSO

, figureFileSmall=null, figureFileBig=null, tableContent=
吃水（距基线）/m22.80排水量/t100 932
重心位置/mXG0.00回转半径/mRXX24.00
YG0.00RYY23.50
ZG（距基线）20.22RZZ26.30
), ArticleFig(id=1281324334270615660, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=CN, label=表4, caption=

FPSO整体质量参数

, figureFileSmall=null, figureFileBig=null, tableContent=
吃水（距基线）/m22.80排水量/t100 932
重心位置/mXG0.00回转半径/mRXX24.00
YG0.00RYY23.50
ZG（距基线）20.22RZZ26.30
), ArticleFig(id=1281324334337724525, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=EN, label=Tab.5, caption=

Design environmental conditions

, figureFileSmall=null, figureFileBig=null, tableContent=
方向扇区波浪*风流
$ {H}_{\mathrm{s}} $/m $ {T}_{\mathrm{p}} $/s1小时平均风速/（m·s−1）表面流速（m·s−1）中层流速（m·s−1）底层流速（m·s−1）
*波浪采用JONSWAP谱，谱峰升高因子Gamma=1.5，方向散布系数n=2.0。
全方向13.9614.538.31.991.040.59
S112.6814.034.71.991.040.59
S210.8113.329.41.991.040.59
S39.1112.724.71.991.040.59
S49.3512.725.31.991.040.59
S512.4614.034.11.991.040.59
S614.2614.739.11.991.040.59
S714.2614.739.11.991.040.59
S814.2614.739.11.991.040.59
), ArticleFig(id=1281324334400639086, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=CN, label=表5, caption=

设计环境条件（$ \Delta {H}_{\mathrm{s}}=0.3 $ m）

, figureFileSmall=null, figureFileBig=null, tableContent=
方向扇区波浪*风流
$ {H}_{\mathrm{s}} $/m $ {T}_{\mathrm{p}} $/s1小时平均风速/（m·s−1）表面流速（m·s−1）中层流速（m·s−1）底层流速（m·s−1）
*波浪采用JONSWAP谱，谱峰升高因子Gamma=1.5，方向散布系数n=2.0。
全方向13.9614.538.31.991.040.59
S112.6814.034.71.991.040.59
S210.8113.329.41.991.040.59
S39.1112.724.71.991.040.59
S49.3512.725.31.991.040.59
S512.4614.034.11.991.040.59
S614.2614.739.11.991.040.59
S714.2614.739.11.991.040.59
S814.2614.739.11.991.040.59
), ArticleFig(id=1281324334471942255, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=EN, label=Tab.6, caption=

Incident wave directions and the associated sectors for design environmental conditions

, figureFileSmall=null, figureFileBig=null, tableContent=
设计条件波浪入射方向编号波浪入射角度/（°）入射角度说明设计环境条件对应的扇区
全方向设计条件O122.5沿第2组锚缆入射全方向
O2142.5沿第3组锚缆入射全方向
O3202.5沿第1组和第3组锚缆中线入射全方向
O4262.5沿第1组锚缆入射全方向
方向性设计条件D10.0沿方向扇形S2和S3边界入射S2
D222.5沿第2组锚缆入射S3
D345.0沿方向扇形S3和S4边界入射S4
D482.5沿第2组和第3组锚缆中线入射S4
D590.0沿方向扇形S4和S5边界入射S5
D6135.0沿方向扇形S5和S6边界入射S6
D7142.5沿第3组锚缆入射S6
D8202.5沿第1组和第3组锚缆中线入射S7
D9262.5沿第1组锚缆入射S8
D10270.0沿方向扇形S8和S1边界入射S8
D11315.0沿方向扇形S1和S2边界入射S1
D12322.5沿第1组和第2组锚缆中线入射S2
), ArticleFig(id=1281324334539051120, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=CN, label=表6, caption=

波浪入射角度及设计环境条件对应的扇区

, figureFileSmall=null, figureFileBig=null, tableContent=
设计条件波浪入射方向编号波浪入射角度/（°）入射角度说明设计环境条件对应的扇区
全方向设计条件O122.5沿第2组锚缆入射全方向
O2142.5沿第3组锚缆入射全方向
O3202.5沿第1组和第3组锚缆中线入射全方向
O4262.5沿第1组锚缆入射全方向
方向性设计条件D10.0沿方向扇形S2和S3边界入射S2
D222.5沿第2组锚缆入射S3
D345.0沿方向扇形S3和S4边界入射S4
D482.5沿第2组和第3组锚缆中线入射S4
D590.0沿方向扇形S4和S5边界入射S5
D6135.0沿方向扇形S5和S6边界入射S6
D7142.5沿第3组锚缆入射S6
D8202.5沿第1组和第3组锚缆中线入射S7
D9262.5沿第1组锚缆入射S8
D10270.0沿方向扇形S8和S1边界入射S8
D11315.0沿方向扇形S1和S2边界入射S1
D12322.5沿第1组和第2组锚缆中线入射S2
), ArticleFig(id=1281324334627131505, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=EN, label=Tab.7, caption=

Minimum designed mooring line tensions under omnidirectional and directional design conditions

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系泊缆全方向条件下
系泊缆最小设计
张力/kN		方向性条件下系泊缆
最小设计张力增加量
初始设计优化设计
第1组2.07E+04+5.6%+6.3%
第2组2.06E+04–21.2%–3.9%
第3组2.07E+04+4.4%+3.5%
), ArticleFig(id=1281324334702628978, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1281324279694332655, language=CN, label=表7, caption=

全方向及方向性设计条件下系泊缆最小设计张力

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系泊缆全方向条件下
系泊缆最小设计
张力/kN		方向性条件下系泊缆
最小设计张力增加量
初始设计优化设计
第1组2.07E+04+5.6%+6.3%
第2组2.06E+04–21.2%–3.9%
第3组2.07E+04+4.4%+3.5%
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方向性海洋环境设计条件的确定和应用
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李晔 , 李林斌 , 位巍 , 韦斯俊
船舶力学 | 结构力学 2026,30(2): 271-281
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船舶力学 |结构力学 2026 , 30 (2) : 271 -281
方向性海洋环境设计条件的确定和应用
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李晔 , 李林斌 , 位巍, 韦斯俊
作者信息
  • 中国船级社，北京 100007
通讯作者:
李林斌（1973–），男，正高级工程师，通讯作者，Email：
作者简介:

李　晔（1975–），男，硕士，高级工程师，Email：

位　巍（1990–），女，博士，高级工程师

韦斯俊（1988–），男，硕士，工程师

Derivation and application of directional metocean design conditions
Ye LI , Lin-bin LI , Wei WEI, Si-jun WEI
Affiliations
  • China Classification Society, Beijing 100007, China
出版时间: 2026-02-15 doi: 10.3969/j.issn.1007-7294.2026.02.008
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摘要
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考虑到海洋环境条件分布的方向性差异，在不降低海工结构可靠度的前提下，结构设计可采用方向性设计条件。与全方向设计条件相比，方向性设计条件通过重新分配各方向上的超越概率，来达到优化结构设计的目的。满足规范可靠度目标要求的方向性设计条件可采用本文提出的迭代方法确定，并针对具体结构进行设计分析和比较，以确定最优结构设计方案及其对应的最优方向性设计条件。分布拟合和大幅外推所带来的统计不确定性影响需要充分考虑，而采用本文提出的“组合法”来获得方向性环境要素分布是降低统计不确定性影响的有效途径。

方向性设计条件  /  全方向设计条件  /  结构可靠度  /  年超越概率

Considering the directional differences in the distribution of environmental conditions, the directional design criteria can be adopted as long as no jeopardizing to the structure reliability is introduced. Compared with the omnidirectional design condition, the directional criteria can optimize the structural design by redistributing the exceedance probability on all directional sectors. The directional design conditions that meet the requirements of the target reliabilities can be determined by the iterative method proposed in this paper, and the optimal structural design and the corresponding directional design condition can be determined by design analysis and comparison for specific structures. The statistical uncertainty impact caused by distribution fitting and large extrapolation needs to be carefully considered, and using the proposed "combination method" to derive the environmental condition distribution is an effective solution to reduce this impact.

directional design condition  /  omnidirectional design condition  /  structural reliability  /  annual exceedance probability
李晔, 李林斌, 位巍, 韦斯俊. 方向性海洋环境设计条件的确定和应用. 船舶力学, 2026 , 30 (2) : 271 -281 . DOI: 10.3969/j.issn.1007-7294.2026.02.008
Ye LI, Lin-bin LI, Wei WEI, Si-jun WEI. Derivation and application of directional metocean design conditions[J]. Journal of Ship Mechanics, 2026 , 30 (2) : 271 -281 . DOI: 10.3969/j.issn.1007-7294.2026.02.008
正文
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0　引　言
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海洋工程结构的可靠性由其设计环境载荷重现期和相应的安全系数决定。一般采用方向上相同的环境设计条件，即全方向设计条件，从各个方向上对结构抗力进行校核，来满足目标可靠度的要求。在南海等诸多海域，风、浪、流等环境要素具有明显的方向性特征，如大的波浪往往集中出现在某些方向上。在工程实践中，设计者有时会利用这一方向性特点，在不同方向上采用不同的设计条件，即方向性设计条件，设计出抗力具有方向性差异的结构，从而达到降低结构建造成本的目的。
海工结构设计规范主要来自船级社或ISO等国际标准。关于方向性设计条件的应用，相关规范要求不尽相同，甚至存在矛盾。其中ISO 19901-1[1]作为海工结构环境设计条件的通用标准，其核心要求是：与全方向设计条件相比，方向性设计条件的应用不应导致结构可靠度降低（5.6款）；而ISO 19902[2]作为导管架结构设计的专门标准，推荐采用所谓“等比放大”法（9.4.2款），该方法将导致结构可靠度大大降低，与ISO 19901-1的要求相矛盾。船级社规范方面，挪威船级社DNV[3]（3.6.5款）与中国船级社CCS[4]（2.3.7款）的要求相似，与ISO 19901-1的要求保持一致，并特别指出：与全方向条件相比，方向性设计条件在某些方向降低的同时，其他某些方向需要适当提高方可实现结构总体可靠度不变的目标。而法国船级社BV[5]推荐采用所谓“等重现期放大”法（APPENDIX 2，2.2.2款），该方法与“等比放大”法类似，都会导致结构可靠度大大降低。由于方向性设计条件本身所涉及的概率逻辑较为复杂，而不同规范要求之间存在差异甚至矛盾，使得设计者很容易在工程实践中产生理解和应用上的偏差，所采用的方向性设计条件可能会导致结构实际可靠度严重偏离规范所要求的目标。
Forristall[6]首次从概率关系角度对方向性设计条件的应用进行了系统阐述，但并未给出如何获得合理的方向性设计条件的建议。Feld等[7]基于挪威、巴西等海域的条件，对方向性设计条件进一步研究，提出了通过迭代获得方向性设计条件的方法，但该方法在受热带气旋控制的我国南海和东海海域尚无应用先例。
本文以南海北部某深水海域长期后报波浪数据为实例，以方向性设计条件在全方向上的总体年超越概率为主线，阐明热带气旋海域确定方向性设计条件的方法和步骤；分析相关规范标准所存在的问题；同时针对分布拟合和数据外推所带来的统计不确定性影响，提出具体解决方案；最后结合具体项目案例，进一步说明如何应用方向性设计条件对结构进行设计优化，以期达到澄清规范要求，指导工程实践之目的。
1　数　据
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本研究针对台风条件下的波浪（有义波高$ {H}_{\mathrm{s}} $）开展分析。点位（P1~P5）数据来自SEAFINE JIP数据库[8]，如图1 所示，时间跨度为1956年7月至2015年6月合计59年。考虑到方向性设计条件需要进行超长重现期的数据外推，将5个点位进行样本池化（Pooling），从而将样本时长扩大到295年（59×5=295），以降低数据外推所导致的不确定性。关于池化技术可参见Heideman等[9]及Li等[10]的研究，由于不是本文的重点，在此不作赘述。
根据相关规范[1,4]要求，方向扇区的划分不应小于45°，以避免过度优化。本文将方向扇区平均划分为8个，将台风过程中$ {H}_{\mathrm{s}} $（有义波高）在各个方向扇区中的峰值作为样本数据，进行分区池化和分布拟合。$ {H}_{\mathrm{s}} $在扇区方向上的峰值散布如图2所示，从中可以看出$ {H}_{\mathrm{s}} $具有明显的方向性特征，在S7扇区最大，S8和S6扇区其次，S4和S3扇区最小。
2　数据统计分析
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在确定方向性设计条件时，我们假设各个方向扇区在统计学上是独立的，但实际情况并非如此。台风作为独立事件，在其发展过程中，波浪方向持续变化，并可能落在不同的方向扇区内，产生$ {H}_{\mathrm{s}} $扇区峰值样本，而这些样本是相关的。图3显示了1964年Winnie台风过程中，$ {H}_{\mathrm{s}} $在P3点位的扇区分布，该台风在S7、S8、S1和S2扇区均产生了样本数据。如果不考虑样本的方向相关性，将可能高估台风发生率和样本值，获得的$ {H}_{\mathrm{s}} $方向性条件是偏于保守的。
另外一种基于独立性考虑的方法是仅将全方向$ {H}_{\mathrm{s}} $峰值作为样本，如图3 所示的情况，Winnie台风仅在S7扇区产生一个$ {H}_{\mathrm{s}} $样本，而这样可能会低估某些扇区的台风发生率和样本值。因此，真实的方向性分布应介于两种方法之间，具体见Feld等[7]的研究。本研究采用前者方法，忽略方向上的相关性。
本文采用Gumbel分布函数和最大似然估计法，对全方向和方向性样本进行统计分析，$ {H}_{\mathrm{s}} $的累积概率为
$ P\left({H}_{\mathrm{s}}\right)={\mathrm{exp}} \left[-\mathit{\exp } \left(-\frac{{H}_{\mathrm{s}}-\mu }{\sigma }\right)\right] $
式中：$ \mu $为位置参数，$ \sigma $为尺度参数。
年超越概率$ F\left({H}_{\mathrm{s}}\right) $为
$ F\left({H}_{\mathrm{s}}\right)=1-{\left[P\left({H}_{\mathrm{s}}\right)\right]}^{\nu } $
式中：$ \nu $为台风年发生率。
$ {H}_{\mathrm{s}} $在全方向或方向性扇区对应的重现期T$ \left({H}_{\mathrm{s}}\right) $为年超越概率F$ \left({H}_{\mathrm{s}}\right) $的倒数，即
$ T\left({H}_{\mathrm{s}}\right)=\frac{1}{F\left({H}_{\mathrm{s}}\right)} $
分布函数的参数如表1所列，分布曲线如图4所示，从中可以看出，S7扇区是$ {H}_{\mathrm{s}} $最恶劣的方向，其前4个最大值样本与全方向样本是重合的。
图5显示了重现期分别为100年和800年时$ {H}_{\mathrm{s}} $的方向性分布，全方向100年有义波高$ H_{\mathrm{s},~100}^{\text{omni}}= 13.96\; \mathrm{m} $，大于100年重现期的任何一个方向性$ {H}_{\mathrm{s}} $。
3　方向性设计条件的内在概率逻辑
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3.1　方向性与全方向设计条件年超越概率之间的关系
一般的海工结构，其抗力存在方向上的差异，同时环境因素（如有义波高$ {H}_{\mathrm{s}} $）的长期分布也存在方向性差异。因此结构的失效以不同可能性（概率）发生于各个方向。为便于阐述核心问题，可认为任一方向上，$ {H}_{\mathrm{s}} $超过其设计值时结构即失效。结构的年失效概率为$ 1/T $，即方向性设计条件$ {H}_{\mathrm{s}} $在所有方向上的总体年超越概率，可通过如下公式获得
$ 1-\frac{1}{T}=\prod \limits_{i=1}^{N}\left(1-\frac{1}{{T}_{{i}}}\right) $
式中：$ N $为方向扇区个数，$ {T}_{{i}} $为方向性设计条件$ {H}_{\mathrm{s}} $在第i扇区所对应的重现期。
如当$ N=3 $时，
$ \frac{1}{T}=\frac{1}{{T}_{1}}+\frac{1}{{T}_{2}}+\frac{1}{{T}_{3}}-\left(\frac{1}{{T}_{1}{T}_{2}}+\frac{1}{{T}_{1}{T}_{3}}+\frac{1}{{T}_{2}{T}_{3}}\right)+\frac{1}{{T}_{1}{T}_{2}{T}_{3}} $
当$ {T}_{{i}} $较大时（如：$ {T}_{{i}}\geq 10 $），可忽略公式（5）中的二阶和三阶项，即
$ \frac{1}{T}=\frac{1}{{T}_{1}}+\frac{1}{{T}_{2}}+\frac{1}{{T}_{3}} $
一般的，当$ {T}_{{i}} $较大时
$ \frac{1}{T}=\sum \limits_{i=1}^{N}\frac{1}{{T}_{{i}}} $
图4中的“Si Combined”为按照公式（7）获得的$ {H}_{\mathrm{s}} $分布，其与全方向样本独立拟合所得到的全方向$ {H}_{\mathrm{s}} $分布非常接近。之所以存在微小差别，原因在于分布拟合过程中不可避免的不确定性因素。
由公式（4）和公式（7）可以得出一个明确结论：相同$ {H}_{\mathrm{s}} $的全方向重现期一定小于任何一个方向性重现期，或者说相同重现期的全方向$ {H}_{\mathrm{s}} $一定大于任何一个方向性$ {H}_{\mathrm{s}} $，就如图4所示。
3.2　全方向设计条件的方向性诠释
全方向设计条件可以认为是一个特殊的方向性设计条件，即各方向上的设计值是相同的。全方向100年有义波高（$ {H}_{\mathrm{s}}=H_{\mathrm{s},~100}^{\text{omni}}=13.96\;\mathrm{m} $）在各方向扇区上的重现期可由式（3）获得，如图6所示。
当按照规范要求，以100年重现期的全方向设计条件进行结构设计时，即以$ {H}_{\mathrm{s}} $=13.96 m对结构从各个方向进行抗力校核，所期望的结构可靠度目标为年失效概率的1/100。
从方向性的角度看，结构的失效以不同可能性（概率）发生在各个方向。结构的年失效概率，即$ {H}_{\mathrm{s}} $=13.96 m在所有方向上的总体年超越概率，可由公式（7）得到，即
$\begin{split}&\frac{1}{12\;802}+\frac{1}{116\;739}+\frac{1}{4\;573\;196}+\frac{1}{3\;332\;881}+\\&\qquad \frac{1}{13\;196}+\frac{1}{1100}+\frac{1}{134}+\frac{1}{454}\approx \frac{1}{94}\end{split} $
1/94的失效概率与1/100的目标值是一致的，反映了采用全方向设计条件时，结构可靠度目标得以实现的内在逻辑。
4　方向性设计条件应用的误区
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考虑到环境条件分布的方向性差异，不少设计方为降低温和扇区方向上的设计载荷，想当然地采用方向性100年设计条件，即本例中如图5所示的方向性100年$ {H}_{\mathrm{s}} $进行结构设计，此时的结构年失效概率为
$ \frac{1}{100}+\frac{1}{100}+\frac{1}{100}+\frac{1}{100}+\frac{1}{100}+\frac{1}{100}+\frac{1}{100}+\frac{1}{100}\approx \frac{1}{13} $
1/13的年失效概率远大于规范所要求的1/100年失效概率的目标值。此结果是可想而知的：这种方向性设计条件与全方向设计条件相比，在所有方向上$ {H}_{\mathrm{s}} $年超越概率均得到提高，特别是将超越概率极低的S2、S3、S4扇区统统变成了1/100的年超越概率，从而导致结构总体可靠度大大降低。
为避免以上简单采用方向性100年$ {H}_{\mathrm{s}} $设计条件所导致的结构可靠性降低问题，有的工程项目会采用ISO 19902[2]推荐的所谓“等比放大”法，或BV船级社规范[5]推荐的“等重现期放大”法。即：首先将最恶劣扇区（S7）的100年$ {H}_{\mathrm{s}} $放大到$ H_{\mathrm{s},~100}^{\text{omni}} $；“等比放大”的放大比例为$ 13.96/13.57=1.029 $，以此比例放大其他扇区的100年$ {H}_{\mathrm{s}} $，并由公式（3）得到相应的重现期；“等重现期放大”为所有扇区均采用$ H_{\mathrm{s},~100}^{\text{omni}} $在最恶劣扇区（S7）的重现期（134年），并由公式（3）反推获得对应的$ {H}_{\mathrm{s}} $。最终结果汇总如表2。
采用“等比放大”时，结构的年失效概率为
$ \frac{1}{134}+\frac{1}{128}+\frac{1}{131}+\frac{1}{134}+\frac{1}{126}+\frac{1}{135}+\frac{1}{134}+\frac{1}{131}\approx \frac{1}{17} $
采用“等重现期放大”时，结构的年失效概率为
$ \frac{1}{134}+\frac{1}{134}+\frac{1}{134}+\frac{1}{134}+\frac{1}{134}+\frac{1}{134}+\frac{1}{134}+\frac{1}{134}\approx \frac{1}{17} $
1/17的年失效概率仍然远高于1/100的目标值。因此，“等比放大”或“等重现期放大”方法本身是错误的，将导致结构实际可靠度严重偏离相关规范所要求的目标。
5　确定方向性设计条件的推荐做法
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回到问题源头，方向性设计条件的应用不应导致结构可靠度降低。由3.2节的分析不难发现，如果采用方向性设计条件，在某些方向上采用小于$ H_{\mathrm{s},~100}^{\text{omni}} $的设计波高，则其他方向上的设计波高就必须大于$ H_{\mathrm{s},~100}^{\text{omni}} $，方有可能实现年超越概率1/100不变的目标。而这种方向性设计条件组合理论上有无数个，其中Forristall[6]出于直观解释的目的，给出了一种特殊组合，即各扇区均取800年重现期方向性$ {H}_{\mathrm{s}} $作为设计条件，如图5所示。在S7和S8方向上，800年$ {H}_{\mathrm{s}} $均超过了$ H_{\mathrm{s},~100}^{\text{omni}} $，但在其他方向上，800年$ {H}_{\mathrm{s}} $都远低于$ H_{\mathrm{s},~100}^{\text{omni}} $。此设计条件下，结构的年失效概率为
$ \frac{1}{800}+\frac{1}{800}+\frac{1}{800}+\frac{1}{800}+\frac{1}{800}+\frac{1}{800}+\frac{1}{800}+\frac{1}{800}=\frac{1}{100} $
达到了规范所要求的1/100年失效概率的可靠度目标，但在最恶劣的S7方向上，$ {H}_{\mathrm{s}} $比$ H_{\mathrm{s},~100}^{\text{omni}} $增大了16%。如果按照这种方向性设计条件，结构的建造成本有可能比全方向还要高，也偏离了采用方向性条件的初衷。
针对具体结构，如何获得最优的方向性设计条件组合是问题关键，为此Feld等[7]提出了一个更具工程价值的方法，其核心思想是利用环境条件分布函数的非线性特征，适当增加一个或多个恶劣方向上的设计条件，从而大大减少其他温和方向上的设计条件，以达到$ {H}_{\mathrm{s}} $在全方向上总体年超越概率不变的目标。以方向扇区数为4的情况为例，说明该方法的步骤如下
（1） 设定$ {H}_{\mathrm{s}} $增加量$ \Delta {H}_{\mathrm{s}} $（如：$ \Delta {H}_{\mathrm{s}}=0.3 $）；
（2） 在最恶劣扇区，将100年$ {H}_{\mathrm{s}} $变为$ H_{\mathrm{s},~100}^{\text{omni}}+\Delta {H}_{\mathrm{s}} $，并计算其年超越概率X；
（3） 将剩余3个扇区的超越概率取为（0.01–X）/ 3，计算此超越概率在这3个扇区对应的$ {H}_{\mathrm{s}} $；
（4） 如果由步骤（3）获得的最大$ {H}_{\mathrm{s}} $小于$ H_{\mathrm{s},~100}^{\text{omni}}+\Delta {H}_{\mathrm{s}} $，则结束迭代；否则将此扇区$ {H}_{\mathrm{s}} $设为为$ H_{\mathrm{s},~100}^{\text{omni}}+ \Delta {H}_{\mathrm{s}} $，并计算其超越概率Y；
（5） 将剩余2个扇区的超越概率取为（0.01–X–Y）/ 2，计算此超越概率在这2个扇区对应的$ {H}_{\mathrm{s}} $；
（6） 如果由步骤（5）获得的最大$ {H}_{\mathrm{s}} $小于$ H_{\mathrm{s},~100}^{\text{omni}}+\Delta {H}_{\mathrm{s}} $，则结束迭代；否则将此扇区$ {H}_{\mathrm{s}} $改为$ H_{\mathrm{s},~100}^{\text{omni}}+\Delta {H}_{\mathrm{s}} $，并计算其对应的超越概率Z；
（7） 将剩余的1个扇区的超越概率取为（0.01–X–Y–Z），计算此超越概率在此扇区对应的$ {H}_{\mathrm{s}} $；
（8） 如果由步骤（7）获得的$ {H}_{\mathrm{s}} $小于$ H_{\mathrm{s},~100}^{\text{omni}}+\Delta {H}_{\mathrm{s}} $，则结束迭代；否则增加$ \Delta {H}_{\mathrm{s}} $值，重复（1）~（7）步骤。
表3给出了不同$ \Delta {H}_{\mathrm{s}} $下的设计条件组合，按照这些方向性条件进行结构设计，均可达到1/100年失效概率的可靠度目标。
图7显示了$ \Delta {H}_{\mathrm{s}}=0.3 $ m时的设计条件，其中在S6、S7、S8三个方向上，$ {H}_{\mathrm{s}} $较$ H_{\mathrm{s},~100}^{\text{omni}} $有稍许增加（0.3 m），但在其他方向上则大幅减小，这样既可能达到了结构设计优化的目的，又满足了规范对结构可靠度的要求，即结构年失效概率为
$\frac{1}{2917}+\frac{1}{2917}+\frac{1}{2917}+\frac{1}{2917}+\frac{1}{2917}+\frac{1}{1468}+\frac{1}{170}+\frac{1}{581}=\frac{1}{100} $
实际工程项目中，可根据具体情况，采用不同的方向性条件组合进行试算比较，以确定最优结构设计方案及其对应的最优方向性设计条件（即最优的$ \Delta {H}_{\mathrm{s}} $取值）。
6　统计不确定性影响及解决方案
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如第5章所述，方向性设计条件在某些方向上往往对应着几千年的超长重现期，而数据样本时长一般在几十年左右，同时台风样本量本来就很有限，分配到各方向扇区后就会进一步缩减，虽然采用池化等技术可以在一定程度上增加样本时长，但如此大幅的数据外推势必造成巨大的统计不确定性（Statistical Uncertainty）[11]。极值分析中的统计不确定性问题是客观存在的，而如何降低其影响是确定方向性设计条件的关键，以P3点位数据为例进一步说明。
图8显示了通过拟合获得的P3点位$ {H}_{\mathrm{s}} $在全方向和最恶劣方向S7上的分布。全方向样本中的前3个最大值均来自S7方向，两者具有相同的经验超越概率，而在其他相同超越概率水平上，S7方向均小于全方向，使得S7样本走向更陡，以至于拟合曲线外推至某个重现期（本例为89年）后，$ {H}_{\mathrm{s}} $在S7方向上的超越概率超过了全方向，违背了公式（4）和（7）所表达的方向性和全方向超越概率之间的关系，也使得方向性设计条件失去了意义。导致这一问题的根本原因在于分布拟合和数据外推所带来的统计不确定性。
为解决此问题，提出如下“组合法”来获得方向性$ {H}_{\mathrm{s}} $分布：
（1） 分别拟合全方向及方向性分布。
（2） 取全方向样本前$ K $个最大值均值$ {M}_{\text{omni}} $，以及第$ i $方向扇区样本前$ K $个最大值均值$ {M}_{{i}} $，比例系数$ {R}_{{i}}={M}_{{i}}/{M}_{\text{omni}} $。
（3） 根据分布曲线，获得重现期T对应的全方向有义波高$ H_{\mathrm{s},{T}}^{\text{omni}} $及方向性有义波高$ H_{\mathrm{s},{T}}^{{i}} $，取$ H_{\mathrm{s},{T}}^{{i}}= {\mathrm{min}}\left\{H_{\mathrm{s},{T}}^i,{R}_{{i}}*H_{\mathrm{s},{T}}^{\text{omni}}\right\} $。
（4） $ K $的取值需要试算得到，从$ K=1 $开始逐步增加，确保$ {R}_{{i}}< 1.0 $且$ H_{\mathrm{s},{T}}^{{i}} $分布曲线与扇区样本获得满意的拟合。
采用“组合法”得到的方向性$ {H}_{\mathrm{s}} $分布如图8所示（$ K=5 $），既避免了全方向分布等比缩小（即：$ {R}_{{i}}\mathrm{*}H_{\mathrm{s},{T}}^{\text{omni}} $）所导致的低重现期样本数据拟合不佳的问题，又避免了方向性分布大幅外推导致的方向性$ {H}_{\mathrm{s}} $超越全方向$ {H}_{\mathrm{s}} $的问题。
7　应用案例分析
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以某圆筒形FPSO为例，进一步说明如何利用方向性条件对系泊系统进行设计优化。FPSO整体质量参数见表4。设计环境条件基于前述分析结果，如表5所示。其中，谱峰周期$ {T}_{\mathrm{p}} $和平均风速采用$ {H}_{\mathrm{s}} $的关联值；而考虑到流速与$ {H}_{\mathrm{s}} $的相关性较差，采用全方向设计流速；同时，根据规范[12]要求，对于固定方向系泊的浮动设施（如本例），假设风、浪、流作用在同一个方向，波浪入射方向定义如图9所示。
初始设计的系泊系统由3组系泊缆组成，每组4根；每组夹角为120°，同组内系泊缆夹角为2°；每根系泊缆由锚链、纤维缆和卸扣构成。采用AQWA软件进行数值模拟，建立浮体与系泊系统的耦合分析模型，如图10所示。由于S6-S7-S8方向$ {H}_{\mathrm{s}} $最大，将第1组和第3组系泊缆布置在这三个扇区，将第2组布置在$ {H}_{\mathrm{s}} $最小的S3扇区；同时，考虑到S1和S5扇区$ {H}_{\mathrm{s}} $非常接近，将第1组和第3组系泊缆相对于扇区边界对称布置，系泊布置如图11所示。
本文针对系泊系统在完整和破断状态下的满载自存工况进行系泊张力分析，所计算的波浪入射角度及设计环境条件对应的扇区如表6和图11所示。由于方向性设计条件的非对称性，需要计算更多的载荷入射角度，以便捕获到最恶劣的载荷工况。每个浪向角下计算时长为3小时，取10组种子，系泊缆最大张力为10组种子下最大值的平均值。
初始设计的系泊系统在全方向和方向性设计条件下，系泊缆最大张力结果见图12。根据规范[12]，系泊缆在完整和破断工况下的安全系数分别为1.67和1.25，由此得到系泊缆最小设计张力，如表7所示。可以看出，如采用方向性设计条件，第1组和第3组系泊缆最小设计张力有些许增加（5%左右），但第2组则大幅降低（20%左右），因此第2组存在优化空间，设计时可选择较小强度规格的系泊缆；或保持强度规格不变，减少系泊缆根数或缩短长度。
进一步研究将第2组系泊缆减少1根的优化方案，计算其在方向性设计条件下的最大张力，结果如图12所示，而最小设计张力如表7所示。可以看出，相较于全方向条件，优化后第1组和第3组系泊缆最小设计张力有些许增加（5%左右），而第2组则仍有所降低（3.9%）。
当然，最终的设计优化方案应根据项目具体情况而定，如优化前系泊系统的安全裕量、可用的系泊缆强度规格等，必要时采用不同的$ \Delta {H}_{\mathrm{s}} $取值进行试算比较，以确定最优的结构设计方案及其对应的最优方向性设计条件（即最优的$ \Delta {H}_{\mathrm{s}} $取值）。
8　结　语
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方向性设计条件的确定和应用并非如想象中简单和直接，需要设计者充分认识其对结构可靠性的影响，并通过简化的可靠性分析验证目标可靠度的符合性。某些规范标准所推荐的“等比放大”或“等重现期放大”方法是错误的，将导致结构实际可靠度严重偏离规范所要求的目标。
与全方向设计条件相比，方向性设计条件通过重新分配在各方向上的超越概率，以达到总体超越概率不变和优化结构设计的目标。即：利用环境条件分布函数的非线性特征，稍许增加一个或多个恶劣方向的设计条件，而大大减小其他温和方向的设计条件，这也是方向性设计条件的精髓所在。
分布拟合和大幅外推不可避免地带来设计条件的巨大不确定性，甚至导致相同重现期下方向性条件超越全方向条件的情况。建议采用点位池化技术来增加样本时长，必要时采用“组合法”来获得方向性环境要素分布，以降低统计不确定性的影响。
案例分析表明，方向性条件可以为设计者提供更多的结构方案选择。实际工程项目中，可根据具体情况，采用不同的方向性设计条件进行试算比较，以确定最优结构设计方案；同时选择方向性设计条件也意味着需要分析更多工况，计算工作量大大增加。
虽然本文仅以波浪（有义波高）为例，对方向性设计条件的确定和应用进行了阐述，但其理念和方法同样适用于风速和流速等具有方向性分布特点的其他环境要素。

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2026年第30卷第2期
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doi: 10.3969/j.issn.1007-7294.2026.02.008
  • 接收时间：2025-08-10
  • 首发时间：2026-07-07
  • 出版时间：2026-02-15
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李林斌（1973–），男，正高级工程师，通讯作者，Email：
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多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
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