Uncertainty analysis of extreme mooring loads associated with environmental contours and peak tension distributions

This paper aims to assess the uncertainty on the extreme mooring loads of floating system considering short-term variability. Two environmental contour approaches based on the inverse First and Second Order Reliability Methods are employed to identify critical sea states that may give rise to extreme loads. The uncertainty related to the construction of environmental contours is addressed including significant differences due to marginal distribution fitting, parameter estimation methods and joint models. Three measured datasets are analysed using a known conditional joint distribution and proposed mixed copula model. 3-h time domain numerical simulation for each sea state is conducted and the characteristic extreme responses of mooring lines subjected to design loads are assessed. The uncertainties due to various statistical models including the average conditional exceedance rate method as well as global maxima, peak-over-threshold method combined with Gumbel distribution, Generalized Extreme Value distribution, Generalized Pareto distribution and 3-parameter Weibull distribution are investigated and quantified. It is observed that marginal distributions, joint models and parameters estimation methods have apparent effect on design loads estimation, and the extreme tensions of the semi-submersible platform shows significant difference using various probabilistic models. The results indicate that those epistemic uncertainties should be account for in the reliability analysis or safety factor calibration for mooring systems.     

Numerical prediction of wave-induced long-term extreme load effects in a flexible high-speed pentamaran

The theory and procedure established by Wu and Moan in 1996 and 2005 and Wu and Hermundstad in 2002 were applied to a high-speed transatlantic pentamaran containership. Nonlinear time-domain simulations of ship motions and load effects were carried out in different sea states. The simulated responses were validated against model tests with satisfactory results. The short-term probabilities of exceedance were estimated by using different stochastic analysis procedures. The long-term probabilities of exceedance were obtained based on the short-term results. These served as information about loading in a reliability-based design approach. The load effects in a semiprobabilistic design were also calculated at an appropriate probability of exceedance level.     

半潜式起重船波浪载荷预报

采用数值分析软件Sesam/HydroD对某半潜式起重船在航行状态和起重作业状态下的波浪载荷进行长期预报和短期预报.在航行状态下,预报得到的最大波浪弯矩和剪力分别为规范值的1.4倍和2.0倍,用于进行结构疲劳评估(超越概率为10-2)的波浪弯矩最大预报值约为用于进行结构强度评估(超越概率为10-8)的波浪弯矩最大预报值...     

水深对半潜式平台水动力性能及波浪载荷的影响*

本文根据有条件的建模方法（CMA）和一次逆可靠度方法(IFORM),运用Matlab编程计算确定百年一遇波高-周期的等概率曲线,设计了一组百年一遇波浪海况。根据Morison方程与绕射理论计算海洋平台波浪载荷的各自特点,本文采用Morison方程和绕射理论相结合的方法,运用挪威船级社研发的SESAM程序,就水深对半潜式海洋平台水动力性能和波浪载荷的影响进行了分析。某半潜式海洋平台计算分析水深对平台的运动响应、气隙、波浪二阶平均漂移力和纵向剪切力等六个波浪载荷的影响。     

Modified environmental contour method for predicting long-term extreme responses of bottom-fixed offshore wind turbines

Predicting extreme responses is very important in designing a bottom-fixed offshore wind turbines. The commonly used method that account for the variability of the response and the environmental conditions is the full long-term analysis (FLTA), which is accurate but time consuming. It is a direct integration of all the probability distribution of short-term extremes and the environmental conditions. Since the long-term extreme responses are usually governed by very few important environmental conditions, the long-term analysis can be greatly simplified if such conditions are identified. For offshore structures, one simplified method is the environmental contour method (ECM), which uses the short-term extreme probability distribution of important environmental conditions selected on the contour surface with the relevant return periods. However, because of the inherent difference of offshore wind turbines and ordinary offshore structures, especially their non-monotonic behavior of the responses under wind loads, ECM cannot be directly applied because the environmental condition it selects is not close to the actual most important one.The paper presents a modified environmental contour method (MECM) for bottom-fixed offshore wind turbine applications. It can identify the most important environmental condition that governs the long-term extreme. The method is tested on the NREL 5 MW wind turbine supported by a simplified jacket-type support structure. Compared to the results of FLTA, MECM yields accurate results and is shown to be an efficient and reliable method for the prediction of the extreme responses of bottom-fixed offshore wind turbines.     

轴向载荷下多平面DT型管节点应力集中系数概率模型研究

应力集中系数作为一个随机变量,对管节点及导管架平台的疲劳可靠性评估结果有着重要影响。文章以多平面DT型管节点为研究对象,建立了352个几何参数不同的三维管节点有限元模型,并分析了沿弦管-撑管焊缝处的应力集中系数分布。采用密度直方图描述最大应力集中系数统计样本的特征,利用疲劳可靠性分析中常用的几种概率分布进行拟合。各个概率模型中的参数通过极大似然估计方法得到。根据卡方检验的结果对比发现,Birnbaum-Saunders分布是最适合的概率模型。因此,文中提出一组适用于描述在轴向载荷即单向轴向和平衡轴向载荷作用下多平面DT型管节点弦管侧和撑管侧最大应力集中系数分布的概率模型,对今后导管架式海洋平台结构的疲劳可靠性分析具有重要意义。     

Shallow water effects on high order statistics and probability distributions of wave run-ups along FPSO broadside

Ship hydrodynamics in shallow water becomes especially complicated since the nonlinearities in both the incident waves and the wave–hull interactions will be affected by the water depth. For a ship-shaped Floating Production, Storage and Offloading unit (FPSO) operating in shallow water, the broadside often suffers from the wave run-up and green water incidents in non-collinear harsh ocean environments. By applying the methods of ordinary moments and L-moments and the empirical Weibull distribution on the data measured in a series of model experiments, the high order statistics and the exceedance probability distribution of the run-ups along the FPSO broadside are evaluated and the effects of the shallow water depth and the incident environments are analyzed in this paper. It is seen that both the incident waves and the wave run-ups are non-Gaussian in shallow water and that the wave run-up characteristics are significantly influenced by the water depth and the incident environments, while the contribution due to the vessel vertical motions is negligible for the FPSO used in this study. The exceedance probabilities of the wave run-ups show that the broadside will be more likely to suffer from serious wave run-up and green water incidents in shallower water, in a higher incident wave and a non-collinear environment, especially so at locations around the FPSO midship within a range of 3/8L_pp ∼ 5/8L_pp. The dependency of the shape and scale parameters of the wave run-up probability distributions on the locations and the environment is quantified by model tests. The present study leads to the conclusion that the wave run-up characteristics and the shallow water effects should be considered carefully in determining the wave loads and the freeboard of a large FPSO in non-collinear environment conditions.     

Comparing different contour methods with response-based methods for extreme ship response analysis

Environmental contours are often applied in probabilistic structural reliability analysis to identify extreme environmental conditions that may give rise to extreme loads and responses. They facilitate approximate long term analysis of critical structural responses in situations where computationally heavy and time-consuming response calculations makes full long-term analysis infeasible. The environmental contour method identifies extreme environmental conditions that are expected to give rise to extreme structural response of marine structures. The extreme responses can then be estimated by performing response calculations for environmental conditions along the contours.Response-based analysis is an alternative, where extreme value analysis is performed on the actual response rather than on the environmental conditions. For complex structures, this is often not practical due to computationally heavy response calculations. However, by establishing statistical emulators of the response, using machine learning techniques, one may obtain long time-series of the structural response and use this to estimate extreme responses.In this paper, various contour methods will be compared to response-based estimation of extreme vertical bending moment for a tanker. A response emulator based on Gaussian processes regression with adaptive sampling has been established based on response calculations from a hydrodynamic model. Long time-series of sea-state parameters such as significant wave height and wave period are used to construct N-year environmental contours and the extreme N-year response is estimated from numerical calculations for identified sea states. At the same time, the response emulator is applied on the time series to provide long time-series of structural response, in this case vertical bending moment of a tanker. Extreme value analysis is then performed directly on the responses to estimate the N-year extreme response. The results from either method will then be compared, and it is possible to evaluate the accuracy of the environmental contour method in estimating the response. Moreover, different contour methods will be compared.     

Fleet deployment optimization models.Part 2

The fleet deployment problem for the one origin,one destination fixed-price contract requiring the transport of a given total amount of cargo within a given period is formulated and solved for the case that one or more cost components are given staircase functions of time. A computer program has been developed to implement the solution of this problem. The fleet deployment problem with one or more costs being random variables with known probability density functions is also formulated. Analytical expressions for hte basic probabilistic quantities, i.e the probability density function,the mean and the variance of the total operating cost, are presented. Finally, sample results are presented and discussed and some extensions for further research are suggested.     

破碎波对随机波统计特性影响的实验研究(英文)

The influence of wave breaking on wave statistics for finite-depth random wave trains is investigated experimentally. This paper is to investigate the influence of wave breaking and water depth on the wave statistics for random waves on water of finite depth. Greater attention is paid to changes in wave statistics due to wave breaking in random wave trains. The results show skewness of surface elevations is independent of wave breaking and kurtosis is suppressed by wave breaking. Finally, the exceedance probabilities for wave heights are also investigated.     

Determinants of the probability of default: the case of the internationally listed shipping corporations

In this study, we use a sample of 192 listed shipping companies and employ a logit model in order to investigate the determinants of the probability of default. We enhance our analysis by isolating not only the cases of company liquidations but also those cases where companies had to change their legal status due to warning liquidity signals. Our key findings are in line with prior research and moreover we depict a changing trend in the marginal effects of relevant variables, on the probability of default. We further show, through an empirical application, how the obtained results can be used in a managerial decision-making process and in a bank credit underwriting process in order to assess the creditworthiness of a shipping company.     

基于IDW插值的测量数据等值线生成方法

航道测量是航道维护管理的重要工作,而测量数据的内业成图是电子航道图、数字航道等运行的数据基础。针对传统等值线绘制与检查流程耗费大量人力与工时的问题,采用IDW(反距离加权)插值方法与ArcGIS工具,设计了等值线生产方法与优化方案,并以此开发等值线生成平台。实践表明:新的等值线生产方法具有较高的生产效率,等值线生成平台可以推广应用于航道内业制图。     

Structural design considerations for ships operating in arctic regions北大核心CSCD

冰脊和冰山与极地船体发生碰撞将影响船体结构安全,并决定船体结构设计载荷。船体结构设计应遵循基于风险的设计原则,通常涉及以下极限状态设计准则:1)服务极限状态(SLS);2)最终极限状态(ULS);3)疲劳极限状态(FLS);4)事故极限状态(ALS)。最终极限状态和事故极限状态对应于发生概率极低的船与冰脊作用以及冰山撞击事件,旨在确保船体结构不会完全损毁。然而,对于较低概率水平的冰载荷分析,需进行较大数据量的工况分析,计算耗时无法承受。为此,引入环境等值轮廓方法,来大幅减少冰载荷分析所需工况数量,并给出设计工况最有可能的冰体参数组合方式。结合最终极限状态和事故极限状态,举例说明这一方法的运用方式。环境等值轮廓方法可为现有极地船舶船体结构设计方法提供有效补充。     

HCSR疲劳载荷概率水平及形状参数的研究

针对协调共同规范（HCSR）中疲劳评估的概率水平和形状参数的选取问题,通过理论分析和数值计算分析对结构疲劳损伤贡献率最大的长期应力范围所对应的超越概率水平,分析不同超越概率水平下形状参数对结构疲劳寿命的敏感性,通过实船谱分析计算,得到热点应力范围长期分布。     

集装箱船等效设计波法中疲劳载荷概率系数的确定

为了在应用等效设计波方法时将船体梁载荷规范包络值、运动包络值、加速度包络值转换为疲劳评估载荷,需得到疲劳载荷概率系数这一重要参数。采用基于三维势流理论的水动力计算软件,分析多型集装箱船不同航速及超越概率的载荷长期预报值,得到用于疲劳评估的疲劳载荷概率系数的直接计算值。对直接计算值进行回归分析,拟合出各载荷的概率系数简化公式。结果表明,简化公式比较理想。     

考虑随机材料、尺寸及初始缺陷的加筋板结构极限强度研究

为获得加筋板结构极限强度的统计规律,考虑结构材料、尺寸及初始缺陷的随机性（其数值可以认为是满足某种分布规律的随机量）,采用Monte Carlo结合非线性有限元进行强度的研究。在验证非线性有限元准确性的基础上,取结构尺寸、初始缺陷幅值、材料参数为随机变量,采用数值实验、最大熵法及K-S检验拟合获得极限强度的概率密度函数。结果表明,在较少样本时最大熵法可准确获得统计规律,为结构可靠性分析中复杂结构抗力模型的研究提供参考。     

Reliability analysis of fatigue life of the connectors—the US Mobile Offshore Base

Reliability-based design analysis of the fatigue life of the connectors of the five sections of the 2-km long US Mobile Offshore Base (MOB) is demonstrated. A performance function is defined in terms of the nominal stress range, inherent defect or starter crack, and appropriate material properties, which are considered random variables. The reliability analysis is performed for a sea state 1–8 (SS1–8) random loading having a Gumbel distribution. Where possible, uncertainty data for random variables are obtained from published data relating to the fatigue of metal and metal alloys. Otherwise, judgmental coefficients of variation are prescribed for purposes of demonstration. The fatigue life is assumed to follow the Weibull distribution. The reliability function is defined in terms of the mean life and the total uncertainty in the fatigue life. Preliminary reliability calculations suggest that current design stress levels be reduced to meet the current fatigue life target reliability level for the MOB connectors. An illustrative design is demonstrated and the metal selected for a fatigue design of the connectors for 10 million cycles with a reliability of 0.99 at a nominal stress of 203 MPa is HY-130 steel.     

基于二维关键参数平面的永磁同步电机参数设计

提出一套基于二维关键参数平面的设计方法,以一系列等高图反映恒功率弱磁倍数、额定电流、过载电流等性能指标,可以方便地选取关键参数,进而得到各个电机参数。该方法参数设计过程简单,并且可以实现额定电流和过载电流的优化选取。     

Contribution of supposed wave condition on the long-term distribution of a wave-induced load

This report is concerned with the statistical analysis of the long-term distribution of a wave-induced load, and examines which factors influence the long-term distribution of the load level, e.g., the significant wave height, the mean wave period of the supposed wave condition, and the relative angle between the ship's course and the wave direction. The long-term distribution is broken down into these factors, and a contribution rate analysis method for each factor in each load level in the long-term distribution is introduced. Based on the method used, the contribution rate of a specific mean wave period and a wave angle encountered is clarified, when the long-term distribution is larger than other wave periods and wave angles. The specific mean wave period and wave angle encountered are defined as the wave condition which governs the long-term distribution. The maximum wave-induced load in the vicinity of a probability of exceedance of around 10⁻⁸ in the long-term distribution is decided by the most severe short-term wave condition which has the largest significant wave height with a specific mean wave period. Based on S–N curves and Miner's rule, the relation between the fatigue damage and the supposed wave condition is examined. The contribution rate analysis method for fatigue damage is introduced. The governing wave condition and the most severe short-term wave condition also have an important effect on the fatigue damage. A simple estimation method for the long-term distribution, described by the Weibull distribution from the statistical properties of the most severe short-term wave condition, is introduced. Several examples show the applicability of the estimation method. Received: November 22, 2001 / Accepted: January 9, 2002     

水下爆炸载荷的统计特性

为研究水下爆炸载荷的概率密度,选取炸药密度、水密度作为随机变量,基于乘同余组合发生器,利用Fortran语言编写随机数生成程序,产生100组随机变量的样本;采用有限元程序LS-DYNA对水下爆炸冲击波进行仿真计算,得到冲击波的峰值压力;并检验其是否服从正态分布,验证最大熵法程序的正确性,采用最大熵法拟合其概率密度函数,研究爆炸载荷的统计规律,得到不同爆距,不同时刻的冲击波峰值压力的概率密度.该方法可较好地解决爆炸载荷的随机数理统计模型,为进一步进行结构的可靠性分析提供理论依据.