Estimation Of Extreme Responses Research Articles

A novel design approach for estimation of extreme responses of a subsea shuttle tanker hovering in ocean current considering aft thruster failure

The subsea shuttle tanker (SST) is an innovative 33 600-ton underwater cargo tanker designed to transport CO2 to marginal fields. During offloading, the SST will approach and hover in the vicinity of the subsea well. A remotely operated vehicle (ROV) will carry and connect a flexible flowline from the subsea well to the SST. CO2 is then offloaded via this flexible flowline. The offloading process takes four hours. During this time, the SST is subjected to time-varying current load effects, and it will dynamically keep its position using its ballast tanks, propeller, and thrusters. Knowing the extreme positional responses is essential. The extreme heave motion determines the maximum depth and corresponding the maximum hydrostatic loading; hydrostatic loading is a dominating load and drives the collapse design of the SST hull. Further, the extreme surge motion determines the flowline length required to avoid snap loads. In this paper, the extreme positional responses of the SST when the aft thruster fails during offloading is investigated for mean current velocities of 0.5 and 1.0 m/s using the averaged conditional exceedance rate (ACER) method. The empirical data is generated using time-domain simulations with a 2D planar Simulink model. The proposed methodology provides an accurate bivariate extreme value prediction, utilizing all available data efficiently. In this study, the estimated vessel response 5 years return level values and contours, obtained by ACER 1D and 2D methods. It is shown that the extreme responses with return periods of 5 years are, in general, higher than the maxima of the 4 h response by a factor of two. Further, it is seen that the response at the aft where the thruster fails is 1.3–2.6 times larger than the response at the fore of the SST. Based on the overall performance of the proposed method, it was concluded that the ACER 1D and 2D methods could provide robust and accurate both univariate and bivariate predictions based on accurate dynamic vessel motion numerical simulations.

The effect of serial correlation in environmental conditions on estimates of extreme events

In offshore engineering, it is common practice to estimate long-term extremes under the assumption that environmental conditions are independent. However, many environmental variables, such as winds and waves, exhibit correlation over several days. In this work, we consider the impact that this has on estimates of return values of metocean variables, environmental contours and long-term extreme responses. It is shown that methods which neglect serial correlation over-estimate the size of extreme events at a given return period. We introduce a new definition of a sub-asymptotic extremal index, and show how this can be used to quantify the effect of neglecting serial correlation. Simple examples are presented to illustrate why neglecting serial correlation leads to positive bias. We show how the size of the bias is related to the average shape of storm events and the shape of the tail of the distribution of storm peak values, with the latter having the dominant effect. Storm peak distributions with longer tails lead to larger biases when serial correlation is neglected. In the examples presented, neglecting serial correlation resulted in relative errors of over 50% in the 25-year extreme response estimates in some cases. The examples presented show that accounting for serial correlation in estimates of environmental contours and long-term extreme responses can reduce over-conservatism and result in more efficient designs.

Evaluating the impact of climate change on offshore structures design: A practical case study

Climate change is a topic discussed worldwide. There is concern about how climate change will influence human activities, including offshore engineering. Climate change will alter the metocean data used for design purposes. These changes will possibly cause some impact on the structural responses of ships and offshore structures, more specifically fatigue damage accumulation and extreme responses. These possible impacts will depend on the structure life span, structure geographic location and climate change scenario assessed, among other aspects. This paper discusses the results of dynamic stochastic analyses and long-term extreme response estimates of a Steel Catenary Riser (SCR) connected to a semi-submersible platform considering future climate change scenarios for two locations: South East Brazilian Coast and North Atlantic Ocean. The long-term response is estimated by the Environmental Contour Method (ECM). Climate change is assessed by using different climate change scenarios available. The climate change scenarios considered in this work are the Representative Concentration Pathways (RCPs) RCP 4.5 and RCP 8.5 proposed and described by the Intergovernmental Panel on Climate Change (IPCC). Specifically, this work focuses at the influence of climate change on the wave parameters, significant wave height (Hs) and zero up-crossing period (Tz), and their impact on the structural responses of a SCR, for both locations aforementioned.The results obtained suggest that climate change can affect the structure response in different ways, depending on the geographic location. They show an increasing trend for the long-term structural response in the Brazilian location and a slight decreasing trend for the North Atlantic Ocean location. However, these results show high variability due to considerable uncertainties in the ocean climate forecasts, related mainly to shortcomings in global climate models.

Estimation of multiple limit state responses with various mean recurrence intervals considering directionality effects

Assessment of system reliability of structures against wind loading requires evaluation of the joint probability distribution of multiple limit state responses with consideration of wind and aerodynamic directionality effects. While the directionality effect has been extensively addressed in literature on the estimation of probabilistic single limit state response, it is not the case for multiple limit state responses. This study revisits estimation of extreme responses with various mean recurrence intervals, with a focus on adequate definition of directionality factor. A new framework is then presented for estimation of joint probability distribution of multiple extreme responses with consideration of directionality effect. This new framework can be considered as an extension of existing efforts on directionality effect for single limit state response to multiple ones, thus help in better assessing system reliability of structures against wind loading. The proposed framework is applied to responses of claddings on a large-span saddle type roof.

Comparison of stationary and non-stationary wind-induced responses of a super-large cooling tower based on field measurements

Recent measurements made by our research group of a super-large cooling tower indicate that its fluctuations in wind-induced responses exhibit a degree of nonstationarity, echoing similar observations reported for other structures. This might cause errors in estimates of extreme responses and misunderstanding of wind-induced effects if nonstationarity is neglected. In this study, the wind-induced response signals of a super-large cooling tower (height 190 m) in a coastal region were measured for the first time under real Reynolds number and turbulent flow conditions. After noise reduction had been performed, nonstationarity of the signals was identified within various time intervals. The mean wind effect, pulsating wind effect, probability density distribution, dynamic amplification factor, and extreme responses of the super-large cooling tower were studied based on stationary and non-stationary models. Finally, the power spectral density (PSD) and evolutionary power spectral density (EPSD) of the wind-induced response signal were analyzed. The resonance spectral expression of wind-induced responses at resonance excitation points, which is applicable to super-large cooling towers, is summarized. The wind-induced responses presented strong nonstationarity. Non-stationary models that consider response nonstationarity are important in the authentic assessment of the extreme responses of super-large cooling towers. The extreme constant calculated by the stationary model cannot provide an adequate assurance rate and reduces the economic efficiency of extreme response estimates. The vibration energy distributions of resonance excitation points in different regions of the cooling tower were similar, but the PSD functions at quasi-static points were dramatically different from each other. The energy distribution of the resonant excitation points showed a phased trend, and the proposed resonance spectral expression considers three stages of variation in the PSD function of the responses to achieve high predictive accuracy.

Extreme Response Prediction of Steel Risers Using a Four Parameter Distribution

Short-term extreme response estimates are required in many areas of ocean and offshore engineering, such as steel risers design. As in many cases, the response in non-Gaussian, a theoretical solution, is usually not readily available for this purpose. Hermite transformation and Weibull-based models, among others, are some alternatives that have been used in connection with sampled response time series. In this work, a new approach is investigated. Recently, a four-parameter distribution known as the shifted generalized lognormal distribution (SGLD) has been presented in the literature. One of its main advantages is that it covers regions of skewness–kurtosis not covered by other distributions of common use in engineering. In this paper, the performance of this distribution is evaluated in the extreme values' estimation of the utilization ratios of steel riser sections. Three alternatives for using SGLD are investigated in two case studies of different dynamic behavior. The first one is a steel-lazy wave riser (SLWR) connected to a turret-moored FPSO (floating, production, storage and offloading unit) in 914 m water depth, and the second is a SLWR connected to a spread-mooring FPSO in a water depth of 1400 m. The results obtained by the SGLD-based analysis, which considered several simulation lengths, are compared to those obtained by means of an extreme value distribution fitted to episodical extremes obtained from many distinct realizations. The results of a traditional Weibull-fitting approach to the response peaks and those obtained with a Hermite transformation-based model are also presented for comparison.

Extreme response estimation of offshore wind turbines with an extended contour-line method

The contour-line method is a simplified approach for finding the long-term extreme values by a small number of short-term analyses. It is assumed the response with a return period of T years occurs during a sea-state with a shorter or equal return period. This provides good extreme response estimates for structures with a response behaviour monotonically increasing with the severity of the sea-state. For an offshore wind turbine, the power production stops at a certain wind speed to reduce wear, changing the dynamics of the system dramatically, from wind to wave load dominated. Also, there is a non-negligible probability for the turbine being unable to operate although the wind speeds would suggest so, due to e.g. grid- or mechanical failure. Therefore, the original contour-line method for extreme response estimation is not applicable without some modifications to account for changing dynamics. In the present work, it is suggested to treat the operational and non-operational conditions as two sub-populations and estimate the T-year response in each population by a standard contour-line method. Next, the results from each sub-population are combined in order to estimate the total T-year response in consistent manner.

A comparison study on the estimation of extreme structural response from different environmental contour methods

Environmental contours are often applied in probabilistic structural reliability analysis of marine structures in order to identify extreme environmental conditions that may give rise to extreme loads and responses. The perhaps most common way of establishing such environmental contours is based on the IFORM approximation (Inverse First Order Reliability Method), but recently an approach based on direct Monte Carlo simulations with importance sampling has been proposed as an alternative. Even though these contours should be used in the same way and address the same problem, there might be rather large differences between such contours in certain cases. In particular, the alternative contour method will always yield convex contours, whereas the traditional contours may be either convex or non-convex.In this paper, recent comparison studies are extended to include applications on simplified response examples. The contours are applied to simple response problems with known response surfaces in order to study how large the differences between the methods may be in terms of estimated maximum response and associated return periods. These case studies clearly illustrate the influence of the environmental contour method on the estimated extreme structural response. Whereas the different methods yield comparable results for some structural problems, they may give very different estimates of the extreme response for other. The estimated extreme responses and associated return periods from either method will also be compared to the correct extreme response, as estimated by simulation studies, for the desired return period. It is demonstrated that in certain cases, the estimates from some of the contour methods are highly conservative, whereas they in other cases might be very optimistic. The reason for these results are discussed and some requirements on the response functions for obtaining conservative estimates will be stated.

Stochastic procedures for extreme wave induced responses in flexible ships

Different procedures for estimation of the extreme global wave hydroelastic responses in ships are discussed. Firstly, stochastic procedures for application in detailed numerical studies (CFD) are outlined. The use of the First Order Reliability Method (FORM) to generate critical wave episodes of short duration, less than 1 minute, with prescribed probability content is discussed for use in extreme response predictions including hydroelastic behaviour and slamming load events. The possibility of combining FORM results with Monte Carlo simulations is discussed for faster but still very accurate estimation of extreme responses. Secondly, stochastic procedures using measured time series of responses as input are considered. The Peak-over-Threshold procedure and the Weibull fitting are applied and discussed for the extreme value predictions including possible corrections for clustering effects.

Estimation of long-term extreme response of operational and parked wind turbines: Validation and some new insights

In current wind turbine design standard, the long-term extreme responses of operational and parked wind turbines with various mean recurrence intervals (MRIs) are estimated from probability distribution of short-term 10-min extreme response under the assumption that the short-term extremes are statistically independent. This study examines the adequacy of this critical assumption through a Monte Carlo simulation procedure. The 10-min mean wind speed series are simulated based on translation process theory with prescribed Weibull distribution and power spectrum. The extreme response series are then generated using the distribution of extreme response under various mean wind speeds. The distribution of annual extreme response is determined from simulated samples and compared to that from distribution of short-term extreme. The results illustrate that the short-term extreme responses can be considered to be independent, while the mean wind speeds exhibit certain level of correlation. This study also presents improved methods for estimating long-term extreme response of parked turbines by using more accurate modeling of distribution tail of mean wind speed. A mixed distribution is suggested, which combines bulk distribution estimated from moderate wind speed data and tail distribution estimated by fitting the excesses above a given threshold with generalized Pareto and three parameters Weibull distributions. A new method of directly using annual maximum wind speed distribution is also proposed that takes into account the independent number of wind speed process in terms of extremal index. The results reveal the importance of better modeling of wind speed distribution tail in the estimation of extreme response of parked turbines.

Assessing small failure probability by importance splitting method and its application to wind turbine extreme response prediction

This study presents an effective simulation framework with importance splitting (ISp) method for estimating small failure probabilities of dynamic structures with multi-correlated stochastic excitations, and addresses its application to predictions of large wind turbine extreme responses. The ISp method, also referred to as subset simulation with splitting, splits important sample paths into multiple branches at various stages in the simulation. It permits the estimation of a small failure probability of a rare event through estimations of conditional probabilities of intermediate subset events. The framework presented in this study combines the ISp method with multivariate autoregressive (MAR) modeling of stochastic excitations. The MAR model of excitations is established based on their cross power spectral density matrix, which transfers the stochastic excitations as the output of a loading system with a vector-valued uncorrelated white noise process as input. This scheme is very efficient in generating offsprings of loading and response time histories conditional on the intermediate events with very low rejection rate, which facilities the application of ISp method to different kinds of stochastic single and multiple excitations. The effectiveness and accuracy of the proposed new scheme are verified by a reliability problem of earthquake-excited 5-story building, and by the estimation of extreme responses of a 5MW onshore wind turbine with very small exceeding probabilities. Finally, this framework is applied to validate the extrapolation procedure of estimating wind turbine long-term extreme responses with various mean recurrence intervals from short-term simulations of turbine response histories, which is mandated by current wind turbine design standards.

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.

Efficient estimation of extreme response of drag-dominated offshore structures by Monte Carlo simulation

The paper describes a novel approach to the problem of estimating the extreme response statistics of a drag-dominated offshore structure exhibiting a pronounced dynamic behaviour when subjected to harsh weather conditions. It is shown that the key quantity for extreme response prediction is the mean upcrossing rate function, which can be simply extracted from simulated response time histories. A commonly adopted practice for obtaining adequate extremes for design purposes requires the execution of 20 or more 3-h time domain analyses for several extreme sea states. For early phase considerations, it would be convenient if extremes of a reasonable accuracy could be obtained based on shorter and fewer simulations. The aim of the work reported in the present paper has therefore been to develop specific methods which make it possible to extract the necessary information about the extreme response from relatively short time histories. The method proposed in this paper opens up the possibility to predict simply and efficiently both short-term and long-term extreme response statistics. The results presented are based on extensive simulation results for the Kvitebjørn jacket structure, in operation on the Norwegian Continental Shelf. Specifically, deck response time histories for different sea states simulated from an MDOF model were used as the basis for our analyses.

Probabilistic Modeling and Analysis of Riser Collision

Analysis and design of deep-water riser arrays requires that both collision frequency and resulting stresses in the pipes are addressed. Within a probabilistic context, the joint modeling of the current magnitude and surface floater motions must be taken into account. The present paper gives an outline of the general analysis setup, and response statistics obtained as a result of time domain simulations are described. Utilization of the analysis is also discussed in relation to estimation of extreme response and fatigue lifetime. As an example of application, a specific Spar buoy riser configuration at a water depth of 900m is considered.

The Influence of Alternative Wave Loading and Support Modeling Assumptions on Jack-Up Rig Response Extremes

Abstract A study is conducted of the response of a jack-up rig to random wave loading. Steady current and wind load effects are also included. The effects of varying the relative motion assumption (in the Morison equation) and of varying the bottom fixity assumptions are investigated. One “fixity” model employs nonlinear soil springs. Time domain simulations are performed using linearized as well as fully nonlinear models for the jack-up rig. Comparisons of response statistics are made for two seastates. Hydrodynamic damping causes the rms response to be lower in the relative Morison case. The absence of this source of damping in the absolute Morison force model gives rise to larger resonance/dynamic effects—this tends to “Gaussianize” the response. Hence, the relative Morison model leads to stronger non-Gaussian behavior than the absolute Morison model. This is reflected in moments as well as extremes. The different support conditions studied are seen to significantly influence extreme response estimates. In general, stiffer models predict smaller rms response estimates, but also exhibit stronger non-Gaussian behavior. The choice of the Morison force modeling assumption (i.e., the relative versus the absolute motion formulation) is seen to have at least a secondary role in influencing response moments and extremes.

Nonlinear dynamic behaviour of jack-up platforms

Jack-up platforms may, under extreme wave loading conditions, exhibit significant nonlinear behaviour. This must be accounted for in the design of such platforms, in order to ensure satisfactory structural safety. In this paper an overview of the different sources of nonlinear platform behaviour is presented. Furthermore, it is outlined how those nonlinear effects may be modelled and handled in numerical simulation studies of structural response, with a special focus on the estimation of extreme response and dynamic amplification factors. Finally, it is discussed how nonlinear dynamic response may be accounted for in the design of jack-up platforms. The discussions and outlines are illustrated by examples from numerical simulation studies of jack-up behaviour.

Estimation of fatigue damage and extreme response for a jack-up platform

Results from four different methods for stochastic dynamic response analysis of a proposed jack-up platform are compared. This structure exhibits both significant dynamic amplification and non-linear transfer of sea elevation into load effects. Both estimation of extreme response and fatigue damage are considered. The most complex procedure based on time-domain simulation and step-by-step integration is employed as a benchmark for assessment of three simplified methods. The simplifications consist of various types of linearization in conjunction with transfer function approximations. Applicability of the methods to structures with increasingly non-linear behaviour and dynamic amplification is briefly discussed.