The influence of wave-current sea states on the reliability estimates of offshore towers

Since offshore towers are high-cost, high-risk structures, reliability analysis is of great importance in their design. This paper presents a possible practical approach to certify a design through selective critical member reliability estimates. After a brief review of current research in this field, the authors outline a procedure for reliability estimation of structural members in extreme stress and fatigue limit states. A spectral approach for the extreme response statistics with stochastic loading is described. The reliabilities are computed by the Level II first-order second moment (advanced) method. The fatigue reliability is estimated with a narrow-banded stress assumption with discrete, but significant sea states within the life of the structure. Two numerical examples, a three shallow water model and a two-dimensional deep water model are presented along with the influences of stochastic variables (sea state, current, tubular member diameter) on reliabilities (extreme stress and fatigue damage).     

Expected fatigue damage and expected extreme response for Morison-type wave loading

Non-linear probability distributions for Morison-type wave loading are used to indicate the effect of drag forces on the expected fatigue damage and the expected extreme response of quasi-statically responding (members of) offshore structures. Results are compared with those from commonly used equivalent linear methods of analysis. It is found that the expected fatigue damage and the expected extreme response based on non-linear methods are approximately equal to results from linear methods when inertia is the dominant force. However, in the event of the drag forces forming a considerable part of the total wave loading, both fatigue damage and extreme response can significantly exceed those predicted by linear methods. The difference between the two methods is quantified in terms of a drag-inertia parameter, which is directly related to the sea state under consideration.     

极端海洋环境对海洋平台疲劳寿命的影响

基于渤海和南海的海洋平台设计环境条件,分析了近年来我国近海极端海洋环境条件的发生规律及其对海洋平台疲劳设计条件的冲击。采用Miner’s线性累积疲劳损伤准则和疲劳可靠性理论,研究了极端海况引起的疲劳损伤对海洋平台疲劳寿命的影响,提出了考虑极端海洋环境条件的海洋平台疲劳设计方法。研究表明,由于近年来全球气候变换带来的极端气象条件频发,导致海洋工程结构经历传统意义上的多年一遇海洋环境条件的概率大大增加,使得现行的海洋平台疲劳设计条件偏离了实际的海洋环境条件。数值算例表明,极端海况引起的疲劳损伤在总的疲劳损伤的比例大大增加,甚至成为疲劳损伤的主要部分。因此,这些极端海况引起的疲劳损伤对结构疲劳寿命的影响不容忽略,考虑极端海洋环境条件的海洋平台疲劳设计符合近年来的灾害性海况频发的现状。     

Numerical investigation into the application of response conditioned waves for long-term nonlinear fatigue analyses of rigid hulls

Previous studies of response conditioned wave methods have been focused on their applicability to the prediction of extreme nonlinear wave-induced load effects. The results showed that theses methods can be used to accurately and efficiently predict the nonlinear short-term probability distributions for rigid hull responses. This has led us to investigate how response conditioned wave methods can be used for long-term nonlinear fatigue analyses, and with which accuracy this can be done. In this paper we present the results from our investigation. The studies were performed using a container vessel with a length between perpendiculars of 281 m. Calculations were done with a nonlinear strip theory method in which the hull of the vessel was assumed to be rigid. The most likely response wave (MLRW) method was used to condition the waves. Only head seas were considered. We found that the MLRW method under-predicted the long-term fatigue damage by 3%. The method, however, required a simulation time that was approximately three orders of magnitude less than that required for a conventional long-term nonlinear analysis based on random irregular waves. A preliminary investigation showed that due to lacking springing and whipping contributions the MLRW method under-predicted the fatigue damage for a flexible hull by approximately 50%. Several comments about a more accurate extension of the proposed method to flexible hulls are included.     

Extreme dynamic, non-linear response of fixed platforms using a complete long-term approach

The general theoretical basis for application of the direct long-term approach to offshore structures with non-Gaussian response is outlined. The key to the method is the determination of the short-term response distribution. Special considerations should be taken, depending on the application, and the Weibull distribution with a special fitting procedure is suggested as a short-term probability model for fixed offshore platforms. The efficiency of the method is improved by introducing smoothing functions for the variation of the Weibull parameters with the seastate.

The method is applied to a jacket and jackup platform. The results show that smoothing functions increase the efficiency considerably. The design storm method compares well with the long-term results for the selected structures, but only the long-term approach yields realistic estimates of the design extreme response when both extreme and resonant seastates contribution to the 100-year response.     

A statistical analysis of low frequency second-order forces and motions

Probability density functions are derived for low frequency second-order forces and motions using a method which represents the random seastate as a sum of regular waves. The method is shown to agree with another recently developed technique and to give a physical insight into the level of approximation which is employed. A convergence check indicates the importance of including a sufficient number of wave components and it is demonstrated that too few components have been considered previously. A method of predicting the extreme value of the response is also presented, and the relationship between the damping coefficient and the response statistics is investigated by considering the response of an example structure.     

Reliability-Based Optimum Design of a Simple Offshore Platform Based on Genetic Algorithms

In this paper,the problem of reliability-based optimal design of simple offshore platform isstudied,and a nonlinear fatigue damage model based on damage mechanics and genetic algorithms areused in the fatigue reliability optimum design of the structure under stochastic wave load.The fatigue dam-age model and the yield failure reliability analyzing model are used in the paper.The reliability of the mod-els and the effectiveness of genetic algorithm are shown by the results of optimum design.     

非线性管土耦合作用下钢悬链式立管触地区敏感性分析

浮体运动和海床土刚度是引起钢悬链式立管(steel catenary riser,简称SCR)管土相互作用的关键因素,将导致SCR触地区的疲劳损伤。以工作水深为1500 m的浮式平台上生产立管SCR为研究对象,基于法向抗力模型和侧向阻力模型建立管土作用模型,在环境载荷和浮体运动作用下,开展SCR与浮式平台的整体分析,研究海床土参数对SCR触地区动态响应和疲劳寿命的敏感性。通过改变海床土的不排水抗剪强度Su0、强度梯度ρ、吸力因子f_suc、吸力衰减参数λ_suc以及再贯入系数λ_rep等,得到不同参数对触地区动力响应、疲劳寿命的影响规律。研究结果表明:①基于软黏土海床,随着不排水抗剪强度Su0的增加,触地区立管疲劳寿命减幅达到33.23%,敏感性最高;②吸力因子f_suc越大,立管疲劳寿命越小且减幅达23.77%,其敏感性较高;③随着再贯入系数λ_rep增大,触地区立管疲劳寿命增幅达到15.48%;④海床抗剪强度梯度ρ和吸力衰减参数λ_suc对立管疲劳寿命影响较小。研究结论能为SCR设计分析及安全服役提供重要参考。     

Effect of wave nonlinearity on fatigue damage and extreme responses of a semi-submersible floating wind turbine

Floating wind turbine has been the highlight in offshore wind industry lately. There has been great effort on developing highly sophisticated numerical model to better understand its hydrodynamic behaviour. A engineering-practical method to study the nonlinear wave effects on floating wind turbine has been recently developed. Based on the method established, the focus of this paper is to quantify the wave nonlinearity effect due to nonlinear wave kinematics by comparing the structural responses of floating wind turbine when exposed to irregular linear Airy wave and fully nonlinear wave. Critical responses and fatigue damage are studied in operational conditions and short-term extreme values are predicted in extreme conditions respectively. In the operational condition, wind effects are dominating the mean value and standard deviation of most responses except floater heave motion. The fatigue damage at the tower base is dominated by wind effects. The fatigue damage for the mooring line is more influenced by wind effects for conditions with small wave and wave effects for conditions with large wave. The wave nonlinearity effect becomes significant for surge and mooring line tension for large waves while floater heave, pitch motion, tower base bending moment and pontoon axial force are less sensitive to the nonlinear wave effect. In the extreme condition, linear wave theory underestimates wave elevation, floater surge motion and mooring line tension compared with fully nonlinear wave theory while quite close results are predicted for other responses.     

Research on Analytical Method of Fatigue Characteristics of Soft Yoke Mooring System Based on Full-Scale Measurement

By focusing on the vulnerability of the structure of marine equipments, together with considering the randomness of meta-ocean load in statistics, a kind of analytical method of fatigue characteristics of marine structure based on full-scale and actual measurement of prototype is proposed. On the basis of short-term field measurement results of structural response, research is carried out on the fatigue analysis of hinge joints at the upper part of the Soft Yoke single point Mooring System (SYMS) by simultaneously monitoring the environmental load and considering the design criteria of offshore structure. Through analysis of finite element modeling, the time-histories of typical stress response are obtained, and then the assessment of fatigue damage at key hinge joints is conducted. The simulation results indicate that the proposed method can accurately analyze the fatigue damage of offshore engineering structure caused by the effect of wave load. The present analytical method of fatigue characteristics can be extended on other offshore engineering structures subjected to meta-ocean load.     

Application of system identification techniques in efficient modelling of offshore structural response. Part I: Model development

Offshore structures are exposed to random wave loading in the ocean environment and hence the probability distribution of the extreme values of their response to wave loading is of great value in the design of these structures. Wave loading on slender members of bottom-supported jacket or jack-up structures is frequently calculated by Morison’s equation. Due to nonlinearity of the drag component of Morison wave loading and also due to intermittency of wave loading on members in the splash zone, the response is often non-Gaussian; therefore, simple techniques for derivation of their extreme response probability distribution are not available. Finite-memory nonlinear systems (FMNS) are extensively used in establishing a simple relationship between the output and input of complicated nonlinear systems. In this paper, it will be shown how the response of an offshore structure exposed to Morison wave loading can be approximated by the response of an equivalent finite-memory nonlinear system. The approximate models can then be used to determine the probability distribution of response extreme values with great efficiency. Part I of this paper is devoted to the development of an efficient FMNS model for offshore structural response while part II is devoted to the validation of the developed models.     

Design wave method for the extreme horizontal slow-drift motion of moored floating platforms

The present study introduces a design wave method for estimating the extreme horizontal slow-drift motion of moored floating offshore platforms under extreme conditions. Here, the design wave refers to an irregular incident wave of short duration that induces the extreme response of the desired return period. The present method is composed of the following four steps: linearization of the dynamic system, probabilistic analysis of the second-order Volterra series, generation of the irregular design waves, and the fully-coupled nonlinear simulations. For generating the design waves, two different conditioning methods are presented and compared: the conditioning of the extreme response amplitude and the conditioning of the most likely extreme response profile. The procedure was applied to a deep-water semi-submersible, and the results appeared to be promising compared to the full-length nonlinear simulations.     

基于遗传算法的简易海洋平台的疲劳可靠性优化设计

本文提出了利用损伤力学的非线性疲劳损伤模型，在随机海浪交变荷载作用下，简易海洋平台疲劳可靠性优化设计的遗传算法。计算结果表明了计算模型的可靠性与遗传算法解决结构物疲劳可靠性优化设计的有效性     

考虑涡激运动下海洋柔性立管的疲劳损伤分析

基于ABAQUS/AQUA模块,当Spar平台发生涡激运动时,对与平台相连接的柔性立管进行时域动态响应分析,得到了不同折合速度下柔性立管的应力响应曲线.对立管触地区域和悬垂段进行了细化的分析,并利用S-N曲线和Miner线性累积损伤理论对平台涡激运动引起的柔性立管疲劳损伤进行了计算.研究结果表明:平台涡激运动对立管触地区域和悬垂段的影响较大,这两部分最容易在长时间的工作中产生疲劳损伤.特别是平台运动到近点时,立管触地区域受到的应力急剧增加,这个区域是立管工作的危险区域,应该特别注意.该研究结论可以作为立管结构设计和海底铺设时的参考,通过增加立管触地区域的结构强度和优化铺设方式,从而来提高立管的疲劳寿命和系统的安全性.     

简易海洋平台疲劳可靠性优化设计的进化算法

分别用进化计算中的遗传算法和进化规划进行了简易海洋平台基于非线性疲劳损伤模型的疲劳可靠性优化设计.计算结果表明了计算模型的可靠性以及遗传算法和进化规划解决结构疲劳可靠性优化设计的有效性,并对两种优化算法进行了比较和讨论。     

The statistics of second order wave forces

A starting point in the statistical analysis of the slow drift motions of moored offshore structures is the determination of the statistical distribution of the second order exciting forces. In the past^2,6 an exponential probability density function has been used, this being the limiting case as the incident seastate becomes infinitely narrow banded. In the present note the second order force distribution is found for a general seastate and a significant deviation from an exponential distribution is found for those seastates which are likely to occur in practice. The statistical theory is based on a heuristic approximation to the second order force, which is shown to be consistent with a frequently used frequency domain approximation which has been suggested by Newman.⁸ Although Roberts² has shown that for very lightly damped systems the response statistics are independent of those of the exciting force, the present results may have a significant effect on the response statistics for higher levels of damping.     

Reliability-Based Optimal Design for Very Large Floating Structure

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Long-term response analysis of FPSO mooring systems

The design of mooring systems for floating production units usually considers extreme environmental conditions as a primary design parameter. However, in the case of FPSO (Floating, Production, Storage and Offloading) units, the worst response for the mooring system may be associated with other sea state conditions due to the fact that its extreme response may be associated with a resonant period instead of an extreme wave height. The best way to deal with this problem is by performing long-term analysis in order to obtain extreme response estimates. This procedure is computationally very demanding, since many short-term environmental conditions, and their associated stochastic nonlinear time domain numerical simulations of the mooring lines, are required to obtain such estimates. A simplified approach for the long-term analysis is the environmental contour-line design approach. In this paper a Monte Carlo-based integration procedure combined with an interpolation scheme to obtain the parameters of the short-term response distribution is employed to hasten the long-term analysis. Numerical simulations are carried out for an FPSO at three different locations considering a North Sea joint probability distribution for the environmental parameters. The long-term analysis results are compared against those obtained using extreme environmental conditions and environmental contour-line methodology. These results represent the characteristic load effect for the design of mooring systems of floating units using the reliability analysis for mooring line. The results show that the long-term results are usually more critical than those obtained with the other approaches and even different mooring lines can be identified as the critical ones.     

Non-parametric prediction of the long-term fatigue damage for an instrumented top-tensioned riser

Marine risers are susceptible to sustained vortex-induced vibration (VIV) because of their slenderness and light damping. Commonly used tools for analyzing VIV and the associated fatigue damage are based on the finite element method and rely on simplifying assumptions on the riser's physical model, the flow conditions, and characteristics of the response. In order to assess the influence of VIV and to ensure the integrity of the riser, field monitoring campaigns are often undertaken wherein data loggers such as strain sensors and/or accelerometers are installed on such risers. Given the recorded riser's dynamic response, empirical techniques can be used in VIV-related fatigue estimation. These empirical techniques make direct use of the measurements and are intrinsically dependent on the actual current profiles. Damage estimation can be undertaken for the different current profiles encountered and can account explicitly even for complex riser response characteristics. With a significant amount of data, “short-term” fatigue damage probability distributions, conditional on current, can be established. If the relative frequency of different current types is known from a separate metocean study, the short-term fatigue damage distributions can be combined with the current distributions to yield an integrated “long-term” fatigue damage model, which then can be used to predict the long-term cumulative fatigue damage for the instrumented riser. Non-parametric statistical techniques (that do not assume a specific function for the underlying distribution as parametric techniques do) are employed to describe the short-term fatigue damage data. In this study, data from the Norwegian Deepwater Programme (NDP) model riser experiments are used to demonstrate the effectiveness of empirical procedures and non-parametric statistics applied to field measurements to predict long-term fatigue damage, life, and probability of fatigue failure.