Abstract Ships and offshore structures are exposed to various cyclic loads such as winds, waves and currents in their lifetime. These loads can result in fatigue failures at hot spots, and so to prevent such failures, accurate estimates of the fatigue life of hot spots should be performed in the design stage. The cycle distribution indicative of the probability distribution of cycles is an important factor in estimation of fatigue damage to mechanical systems in frequency-domain methods. It depends on not only the counting method but also the statistical properties of random processes. Many studies deriving both theoretical and approximate models of rainflow-counted cycle distributions in wide-banded non-Gaussian processes have been conducted. However, some of the existing models require multi-dimensional integrations that require much computational time or yield inaccurate representations of rainflow-cycle distributions. Therefore, a new model providing accurate cycle distributions is needed for fatigue analysis of offshore structures under wide-banded non-Gaussian random loadings. This paper consists of two parts: Part I is devoted to the development of a new approximate model of the joint probability distribution (JPD) of mean and amplitude of rainflow-counted cycles in wide-banded Gaussian random processes. Nonlinear regression analysis is performed to approximate the conditional probability density function (PDF) of the cycle mean value. The accuracy of the proposed model was verified through two numerical examples. This probabilistic model derived in Gaussian random processes could be transformed to the corresponding non-Gaussian processes through a non-linear transformation technique. In the forthcoming Part II, the accuracy of the proposed model for fatigue-damage assessment of offshore structures under non-Gaussian random loading will be discussed.

中文翻译：

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宽带非高斯随机载荷下船舶和海上结构的疲劳损伤预测 第一部分：宽带高斯随机过程中循环分布的近似

摘要 船舶和海上结构在其生命周期中会承受各种循环载荷，如风、波浪和水流。这些载荷会导致热点疲劳失效，因此为防止此类失效，应在设计阶段对热点疲劳寿命进行准确估计。表示循环概率分布的循环分布是频域方法中估计机械系统疲劳损伤的重要因素。它不仅取决于计数方法，还取决于随机过程的统计特性。已经进行了许多研究，推导了宽带非高斯过程中雨流计数循环分布的理论和近似模型。然而，一些现有模型需要多维积分，这需要大量计算时间或产生不准确的雨流循环分布表示。因此，在宽带非高斯随机载荷下，海上结构的疲劳分析需要一个提供准确循环分布的新模型。本文由两部分组成： 第一部分致力于开发宽带高斯随机过程中雨流计数周期均值和幅度的联合概率分布 (JPD) 的新近似模型。执行非线性回归分析以近似周期平均值的条件概率密度函数 (PDF)。通过两个数值算例验证了所提出模型的准确性。这种在高斯随机过程中导出的概率模型可以通过非线性变换技术转换为相应的非高斯过程。在即将发布的第二部分中，将讨论在非高斯随机载荷下对海上结构进行疲劳损伤评估的拟议模型的准确性。