A model of extreme environmental conditions for wind–wave–swell and related structural analysis
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摘要: 准确评估海洋工程结构的长期极限响应是确保其生存条件的基础，而外部环境条件种类不清晰是影响这一评估的关键因素。现有研究普遍倾向于将风与风浪等纳入优先考虑范围，但实际海况往往呈现出风浪与涌浪相互叠加的多模态特征。基于单峰波谱的波浪时程生成方法难以表征其多模态特性，也无法揭示风、风浪与涌浪三者之间的统计依赖性，导致环境变量联合分布复杂性被低估，从而影响后续结构可靠性和安全性。涌浪作为强度可与风浪相当的低频波，易激发海上风电这类柔性结构的低频共振，进而放大动力响应和累积疲劳损伤。国际电工委员会（IEC）今年发布的行业规范《IEC 61400-3-2：2025》以及全国风电标准化技术委员会牵头制定的《风能发电系统漂浮式海上风力发电机组一体化计算分析导则》均已明确将涌浪列为必须考虑的工况。因此，本文将涌浪作为与风、风浪并列的灾种，基于南海、东海、渤海和黄海典型站点的再分析气象数据，构建了三者的联合概率模型，并通过相关性分析、Granger因果检验和条件概率分析，揭示了不同海域的多灾害相关结构规律。最后，以南海为例，结合环境等值线法（ECM）构建了包含风、风浪与涌浪的极限环境模型。结果表明，纳入涌浪后，环境变量组合的复杂性显著增加；忽略涌浪将导致环境条件模型失真，并低估极端环境的强度。该研究通过在传统风、风浪基础上进一步引入涌浪，并分析了其作为灾种的必要性，一定程度上弥补了现有海洋环境条件种类不清晰的问题，为海洋结构的长期极限响应评估提供了完整且精准的环境输入模型。Abstract: Accurate assessment of a marine structure’s long-term extreme response is fundamental to its survivability, yet an unclear taxonomy of external environmental conditions hampers such assessments. While many studies prioritize wind and wind sea, real sea states are frequently multimodal, with wind sea and swell superposed. Unimodal-spectrum time-series methods cannot represent this multimodality or the statistical dependence among wind, wind sea, and swell, leading to underestimated joint extremes and biased reliability/safety evaluations. Swell—a low-frequency component whose intensity can rival wind sea—readily excites low-frequency resonance in flexible systems such as offshore wind turbines, amplifying dynamic responses and cumulative fatigue. Recent standards (IEC 61400-3-2: 2025 and China’s guideline for integrated analysis of floating offshore wind turbines) explicitly require swell to be treated as a mandatory load case. Accordingly, we treat swell as a co-equal hazard with wind and wind sea. Using reanalysis data from representative stations in the South China Sea, East China Sea, Bohai Sea, and Yellow Sea, we build a joint probabilistic model of the three drivers and, via correlation analysis, Granger causality tests, and conditional probability analysis, reveal region-specific dependence structures. For the South China Sea, the environmental contour method is then used to construct an extreme-environment model that explicitly includes swell. Results show that incorporating swell markedly increases the complexity of environmental-variable combinations; omitting it distorts the environmental model and underestimates extremes. By extending the conventional wind–wave framework to include swell and demonstrating its necessity as a hazard, the study clarifies condition categories and supplies a more complete and accurate environmental input for long-term extreme-response assessment.
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图 2 风、风浪、涌浪数据的条形图
a. 南海三亚“三峡引领号”海上风电场，b. 东海大桥海上风电场址，c. 黄海华能山东半岛北L场址海上风电场，d. 华能天津港东疆北防波堤风电场
Fig. 2 Bar charts of wind, wind-generated wave, and swell data
a. Sanya “Three Gorges Yinling” offshore wind farm, South China Sea; b. Donghai Bridge offshore wind farm site; c. Huaneng Shandong Peninsula North-L site offshore wind farm, Yellow Sea; d. Huaneng Tianjin Port Dongjiang north breakwater wind farm
图 5 Pearson相关性热图
a. 南海三亚“三峡引领号”海上风电场，b. 东海大桥海上风电场址，c. 黄海华能山东半岛北L场址海上风电场，d. 华能天津港东疆北防波堤风电场
Fig. 5 Hot-map of correlation Pearson coefficient
a. Sanya “Three Gorges Yinling” offshore wind farm, South China Sea; b. Donghai Bridge offshore wind farm site; c. Huaneng Shandong Peninsula North-L site offshore wind farm, Yellow Sea; d. Huaneng Tianjin Port Dongjiang north breakwater wind farm
图 6 南海三亚“三峡引领号”海上风电场Spearman相关性热图
Fig. 6 Hot-map of correlation Spearman coefficient of Sanya Three Gorges “Yinling” offshore wind farm, South China Sea
图 7 GCT结果热图
a. 南海三亚“三峡引领号”海上风电场，b. 东海大桥海上风电场址，c. 黄海华能山东半岛北L场址海上风电场，d. 华能天津港东疆北防波堤风电场；NaN表无效的数值
Fig. 7 The heatmap of results of GCT
a. Sanya “Three Gorges Yinling” offshore wind farm, South China Sea; b. Donghai Bridge offshore wind farm site; c. Huaneng Shandong Peninsula North-L site offshore wind farm, Yellow Sea; d. Huaneng Tianjin Port Dongjiang north breakwater wind farm；NaN means not a number
图 8 南海三亚“三峡引领号”海上风电场不同涌浪强度下的条件概率密度函数
a. 平均风速和风浪有效波高，b. 风浪有效波高和平均周期
Fig. 8 Conditional joint PDF under the different swell intensity of Sanya “Three Gorges Yinling” offshore wind farm, South China Sea
a. Average wind speed with significant wave height of wind-generated wave; b. significant wave height and average period of wind-generated wave
图 9 东海大桥海上风电场址不同涌浪周期下的条件概率密度函数
a. 平均风速和风浪有效波高，b. 风浪有效波高和平均周期
Fig. 9 Conditional joint PDF under the different swell intensity of Donghai Bridge offshore wind farm site
a. Average wind speed with significant wave height of wind-generated wave; b. significant wave height and average period of wind-generated wave
图 10 风−风浪−涌浪相互作用示意图
Fig. 10 Schematic diagram of wind, wind-generated wave and swell interaction
图 11 联合累计分布函数（JCDF）与重现期
Fig. 11 Joint cumulative distribution function (JCDF) and return period
表 1 平均风速高阶统计特征
Tab. 1 Higher-order statistical features of average wind speed
测点 峰度 偏度 南海 3.97 0.31 东海 3.43 0.49 黄海 2.97 0.55 渤海 3.78 0.76 
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表 2 Vine-Copula相关结构
Tab. 2 The Vine-Copula correlation structure
结构树 主节点 其他节点 s1 s2 s3 s4 s5 Tree 1 s1 — Joe (4.16) Gumbel (1.41) Gumbel (1.45) Gumbel (6.08) Tree 2 s2 — — Amhaq (0.41) SurGumbel (1.12) T (−0.21,11.49) Tree 3 s5 — — T (−0.34,8.51) Amhaq (−0.71) — Tree 4 s4 — — Gumbel (2.14) — —
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