Abstract Ships operating in ice might be exposed to significant ice loading. Using a probabilistic semi-empirical method known as the event-maximum method, the long-term maximum level of ice loading on a ship can be estimated based on parent distributions of short-term full-scale ice load measurements. The event-maximum method is used to model the relationship between extreme local ice pressures and impact area by estimating parameters corresponding to the inverse slope (α) and intercept ( x 0 ) for the line of best fit for the tail of ranked peak pressure data versus the natural logarithm of the Weibull plotting position. These best-fit lines are assumed to follow an exponential distribution and associated α and x 0 values are produced for different local design areas. This allows for the determination of α-area curves, which reflects the relationship between ice pressure and the local design area. Previous studies have determined α-area curves for different geographical areas such as the Beaufort Sea and South Bering Sea, representing different ice types including both first-year and multi-year ice. In this study, two separate sets of full-scale ice load measurements having been considered, namely measurements from the Kara Sea and the Barents Sea, as well as measurements from the Antarctic Ocean. Using these two datasets, two new α-area curves have been generated that represent among other operating areas (the Kara Sea and the Barents Sea), operating modes (icebreaker assisted operation) and impact areas (aft shoulder) not covered by other curves. Earlier formulations of the event-maximum method are based on local design areas in which the width and height of areas are defined by the size of instrumented rectangular panel areas (or combinations of those areas) on the bow of the vessel from which the data were collected. In that approach, ice thickness is not directly considered since the height of individual panels is based on the dimensions of instrumented areas and moreover, detailed ice thickness records were not available for those data sets. In the present study, an alternative approach has been developed to extend the event maximum method for use with ship line-load data. In this approach ice pressures are calculated by dividing the ice force measured on frames by the corresponding line-load area ( A L L ), which is the product of the width (W) that is based on frame spacing and an assumed line-load height (H) corresponding to 30% of the maximum prevailing ice thickness, as per best design practice, along the lines of the Finnish-Swedish ice class rules. Data already presented as line-loads (in units of force per unit width), are converted to pressures by dividing line-loads by height H. The event definition used in the present approach is defined as the maximum pressure corresponding to 10- or 20-min intervals, as opposed to the impact event definition used in earlier works. In applying this extended method to develop new α-area curves, valuable insights into the relationship between local peak ice pressure and prevailing ice thickness have been gained for the above-mentioned full-scale measurements. The determined curves indicate a negative correlation between prevailing ice thickness and maximum local nominal ice pressure. Finally, it has been demonstrated that it is feasible to apply such curves in combination with the principle of the event-maximum method to estimate the maximum nominal ice pressure expected for a ship given a specified transit distance in sea ice with different prevailing thicknesses.

中文翻译：

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冰中船舶的局部压力：全尺寸线载荷数据的概率分析

摘要 在冰上作业的船舶可能会承受大量的冰载荷。使用称为事件最大值法的概率半经验方法，可以根据短期全尺寸冰载荷测量值的父分布估计船舶上的长期最大冰载荷水平。事件最大值方法用于通过估计对应于反斜率 (α) 和截距 ( x 0 ) 的参数来模拟极端局部冰压和撞击面积之间的关系，以获得最佳拟合线的最佳拟合峰值压力数据的尾部与威布尔绘图位置的自然对数。假定这些最佳拟合线遵循指数分布，并且为不同的局部设计区域生成相关的 α 和 x 0 值。这允许确定 α 面积曲线，反映了冰压与当地设计面积的关系。先前的研究已经确定了波弗特海和南白令海等不同地理区域的 α 面积曲线，代表不同的冰类型，包括第一年和多年冰。在这项研究中，考虑了两组独立的全尺寸冰负荷测量，即来自喀拉海和巴伦支海的测量，以及来自南极洋的测量。使用这两个数据集，生成了两条新的 α 面积曲线，代表其他曲线未涵盖的其他作业区域（喀拉海和巴伦支海）、作业模式（破冰船辅助作业）和影响区域（后肩部）。事件最大值法的早期公式基于局部设计区域，其中区域的宽度和高度由船首的仪表矩形面板区域（或这些区域的组合）的大小定义，数据来自该区域集。在这种方法中，不直接考虑冰厚度，因为单个面板的高度基于仪器区域的尺寸，而且，这些数据集没有详细的冰厚度记录。在本研究中，已开发出一种替代方法来扩展事件最大值方法以用于船舶线载荷数据。在这种方法中，冰压力的计算方法是将框架上测得的冰力除以相应的线载荷面积 (ALL)，它是宽度 (W) 的乘积，该宽度 (W) 基于框架间距和假定的线载荷高度 (H) 对应于最大主流冰厚度的 30%，根据最佳设计实践，沿芬兰 -瑞典冰级规则。已经表示为线载荷（单位宽度的力的单位）的数据通过将线载荷除以高度 H 转换为压力。本方法中使用的事件定义被定义为对应于 10 或 20 的最大压力-min 间隔，与早期作品中使用的撞击事件定义相反。在应用这种扩展方法来开发新的 α 面积曲线时，对于上述全尺寸测量，已经获得了对局部峰值冰压与主要冰层厚度之间关系的宝贵见解。确定的曲线表明主要冰厚与最大局部标称冰压之间呈负相关。最后，已经证明，在给定特定通过距离的不同主要厚度的海冰中，将此类曲线与事件最大值法的原理相结合来估计船舶预期的最大名义冰压是可行的。