A study on an improved stochastic design wave approach based on the probability model optimized for maximum structural responses
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摘要: 浮式风机平台在深远海环境中的稳定性和安全性是浮式风机系统的核心问题，目前随机性设计波法是结构设计最常用的方法，但其假设结构响应最大值分布服从Rayleigh分布不一定符合实际情况。为此，本文提出了一种合理考虑结构响应极值随机特性的改进随机性设计波法，该方法通过结构响应平均跨零周期的最大值样本建立其局部时段最大值分布概率模型，在此基础建立结构响应总持续时间内的最大值概率模型，根据该最大值概率模型确定结构响应的最大值取值，从而确定设计波要素。以某实际5 MW Braceless浮式风机平台为研究对象，分别采用常规随机性设计波法和本文改进方法对该平台的波浪载荷和应力进行对比分析。分析结果表明：改进方法能更准确地反映极值响应随机特性，结构的应力计算结果更加符合实际情况，常规随机性设计波法低估结构的应力最大误差达4.63%，按此设计的结构会带来安全风险。研究结果对于类似浮式风机平台的结构设计和安全评估具有重要意义。Abstract: The stability and safety of floating offshore wind turbine (FOWT) platforms in deep-sea and far-sea environments are crucial for the entire system. Currently, the stochastic design wave method is the conventional approach for structural design; however, its assumption that the maximum structural response follows a Rayleigh distribution may not accurately reflect reality. To address this, this paper proposes an improved stochastic design wave method that reasonably considers the stochastic characteristics of extreme structural responses. Specifically, this method establishes a probability model for the local short-term maximum distribution using samples of the maximum structural response derived from the mean zero-crossing period. Subsequently, a global probability model for the maximum value over the total duration is derived to determine the design wave parameters. A 5 MW Braceless FOWT is selected as the case study for a comparative analysis of wave loads and stresses using both the conventional and improved methods. The results indicate that the improved method more accurately characterizes the stochastic characteristics of extreme responses, and thus the calculated structural stress aligns better with actual conditions. Notably, the conventional stochastic design wave method is found to underestimate the structural stress with a maximum error of 4.63%, which implies that structures designed with this approach may pose potential safety hazards. The findings of this study have significant implications for the structural design and safety assessment of similar FOWT platforms.
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图 1 浮式风机平台骨材布置示意图
Fig. 1 Schematic of the structural arrangement of the floating offshore wind turbine platform
图 2 浮式风机平台水动力模型
Fig. 2 Hydrodynamic model of the floating offshore wind turbine platform
图 5 改进随机性设计波法结构响应及局部时段极值分布拟合
Fig. 5 Structural response and local extreme value distribution fitting using the improved stochastic design wave method
图 7 改进设计波法应力最大工况下浮式风机平台应力分布云图
Fig. 7 Stress contour of the floating offshore wind turbine platform under the maximum stress case using the improved design wave method
图 8 不同设计波幅计算应力对比
Fig. 8 Comparison of calculated stresses under different design wave amplitudes
表 1 Braceless 浮式风机平台设计参数
Tab. 1 Braceless floating offshore wind turbine platform design parameters
设计参数名称 设计参数 立柱直径/m 6.5 主立柱高度/m 34 边柱高度/m 44 边柱压载水高度/m 7.7 浮筒宽度/m 9 浮筒高度/m 6 浮筒夹角/（°） 120 浮体板厚/m 0.03 浮体质量/kg 1804000 压载水质量/kg 7934000 总质量/kg 9738000 排水质量/kg 10555000 工作水深/m 200 
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表 2 5 MW风机结构的主要参数
Tab. 2 Main parameters of 5 MW wind turbine structure
设计参数名称 设计参数 额定功率/MW 5 风机转子直径/m 126 轮毂直径/m 3 轮毂高度/m 90 切入、额定、切出风速/（m·s−1） 3、11.4、25 单个叶片质量/kg 17740 机舱质量/kg 240000 轮毂质量/kg 56780
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表 4 常规随机性设计波法参数
Tab. 4 Parameters of the conventional stochastic design wave method
载荷工况 不利周期/s 不利浪向/（°） 相位角/（°） 响应最大值 设计波幅/m LC1 19 0 83.751 1.134 3.98 LC2 19 90 89.205 0.974 3.44 LC3 5 30 79.038 2.18 × 106 3.48 LC4 7 90 81.752 2.68 × 106 4.76 LC5 5.5 120 −104.414 1.32 × 108 5.50 LC6 5 90 −100.512 2.31 × 107 1.79 LC7 7 90 85.752 2.37 × 106 4.64 LC8 5 90 80.153 2.30 × 106 3.51 LC9 5 105 28.757 4.62 × 107 3.60 注：响应最大值的LC1、LC2为加速度，单位为m/s2；LC3、LC4、LC7、LC8为力，单位为N；LC5、LC6、LC9为力矩，单位为N·m。
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表 5 结构响应极值序列的AD检验参数
Tab. 5 Anderson–Darling test parameters for the extreme value series of structural response
载荷工况 Rayleigh（AD/P） Weibull-3（AD/P） Gumbel（AD/P） Frechet（AD/P） LC1 33.25/1.485 × 10−6 1.182/ 0.2744 11.08/2.034 × 10−6 2.908/ 0.03048 LC2 23.25/1.519 × 10−6 1.102/ 0.3077 9.332/2.203 × 10−5 3.252/ 0.02045 LC3 31.87/1.333 × 10−6 0.8899 /0.4204 10.07/7.244 × 10−6 10.54/3.557 × 10−6 LC4 14.48/1.285 × 10−6 0.869/ 0.4338 8.231/8.672 × 10−5 8.155/9.462 × 10−5 LC5 10.7/2.892 × 10−6 0.6731 /0.5816 6.417/ 0.0006191 11.46/1.548 × 10−6 LC6 20.2/8.174 × 10−7 1.326/0.224 14.21/8.174 × 10−7 12.48/8.193 × 10−7 LC7 28.6/1.25 × 10−6 1.718/0.132 9.826/1.053 × 10−5 10.31/4.956 × 10−6 LC8 14.49/1.333 × 10−6 1.287/ 0.2368 8.054/ 0.000106 7.256/ 0.0002534 LC9 40.01/1.152 × 10−6 0.4542 /0.7938 8.545/5.992 × 10−5 8.545/5.992 × 10−5 注：表中的AD值和P值用“AD/P”表示，其中AD值衡量了经验分布与理论分布的差异（值越小，差异越小），而P值则代表了拟合的优度（值越大，拟合效果越优）。
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表 6 不同设计波方法计算的响应最大值
Tab. 6 Maximum structural responses from different design wave approaches
载荷工况 常规随机性设计波法 改进随机性设计波法 相对误差/% LC1 1.134 1.273 12.26 LC2 0.974 1.134 16.43 LC3 2.18 × 106 2.266 × 106 3.95 LC4 2.68 × 106 2.845 × 106 6.16 LC5 1.32 × 108 1.352 × 108 2.42 LC6 2.31 × 107 2.558 × 107 10.74 LC7 2.37 × 106 2.447 × 106 3.25 LC8 2.30 × 106 2.523 × 106 6.70 LC9 4.62 × 107 4.719 × 107 2.14 注：响应最大值的LC1、LC2为加速度，单位为m/s2；LC3、LC4、LC7、LC8为力，单位为N；LC5、LC6、LC9为力矩，单位为N·m。
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表 7 不同方法设计波的波幅
Tab. 7 Amplitudes of design waves determined by different methods
载荷工况 常规随机性设计
波法波幅/m改进随机性设计
波法波幅/m相对误差/% LC1 3.98 4.47 12.31 LC2 3.44 4.00 16.28 LC3 3.48 3.62 4.02 LC4 4.76 5.06 6.30 LC5 5.50 5.63 2.36 LC6 1.79 1.98 10.61 LC7 4.64 4.77 2.80 LC8 3.51 3.85 9.69 LC9 3.60 3.67 1.94
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表 8 不同设计波方法应力计算结果
Tab. 8 Stress calculation results of different design wave methods
载荷工况 常规随机性设计
波法应力/MPa改进随机性设计
波法应力/MPa相对误差/% LC1 234 243 3.85 LC2 216 226 4.63 LC3 203 204 0.49 LC4 232 236 1.72 LC5 268 270 0.75 LC6 183 185 1.09 LC7 230 232 0.87 LC8 204 208 1.96 LC9 219 221 0.91
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