Short-term Extreme Response Research Articles

Effects of wave directionality on extreme response for a long end-anchored floating bridge

Reliable design codes are of great importance when constructing new civil engineering concepts such as floating bridges. Previously only a scarce number of floating bridges have been built in rough wave conditions and only limited knowledge of the extreme environmental conditions and the associated extreme response exists. To form a better design basis an increased understanding of the sensitivity in the structural response towards changes in short-crested sea parameters is needed. Furthermore, acquiring the necessary accuracy in simulated extreme response is often a computationally expensive endeavour and the number of simulations needed is often based on experience. The present study investigates the wave-induced short-term extreme response of a simplified end-anchored floating bridge concept for several wave environments with a return period of 100 years. The study includes convergence of the coefficient of variation for the extreme response for different realization lengths as well as number of realizations. The sensitivity in the structural response towards different main wave directions and spreading exponents is investigated and includes both transverse and vertical displacement response spectra and extreme Von Mises stress in the bridge girder cross-section. The extreme response is based on an accuracy of 2% in the coefficient of variation equivalent to 40 3-h realizations and a low sensitivity in the response is found for natural occurring spreading exponents and for main wave directions within 15° from beam sea.

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.

A semi-analytical frequency domain model for efficient design evaluation of spar floating wind turbines

A linear model for efficient design evaluation of spar floating wind turbines is presented, and verified against a nonlinear time domain model with regards to long-term fatigue and short-term extreme response for two different spar designs. The model uses generalized displacements and a semi-analytical approach to establish the equations of motion for the system, which are solved in the frequency domain. The results show agreement within ± 30% for the long-term fatigue considering operational conditions, however, the linear fatigue damage estimates are sensitive to the accuracy of the estimated natural frequency of the first bending mode. The results also suggest that a small number of environmental conditions can be simulated with a nonlinear time domain model to verify and possibly tune the linear model, which then can be used to run the full long-term analysis. Short-term extreme tower base bending moments and surge and pitch motions are observed to be nearly Gaussian above cut-out wind speed, as the response is dominated by wave forces. Consequently, the linear model is able to accurately capture the upcrossing rates, which are used to calculate the characteristic largest extreme response. For an operational case near rated wind speed, the response is somewhat non-Gaussian, which gives larger discrepancies between the linear and nonlinear models. However, due to large mean values in this condition, the total error in the extreme response is reduced, and reasonable agreement is achieved.

Capacity assessment of existing corroded overhead power line structures subjected to synoptic winds

The physical infrastructure of the power systems, including the high-voltage transmission towers and lines as well as the poles and wires for power distribution at a lower voltage level, is critical for the resilience of the community since the failures or nonfunctioning of these structures could introduce large area power outages under the extreme weather events. In the current engineering practices, single circuit lattice steel towers linked by transmission lines are widely used to form power transmission systems. After years of service and continues interactions with natural and built environment, progressive damages accumulate at various structural details and could gradually change the structural performance. This study is to evaluate the typical existing transmission tower-line system subjected to synoptic winds (atmospheric boundary layer winds). Effects from the possible corrosion penetration on the structural members of the transmission towers and the aerodynamic damping force on the conductors are evaluated. However, corrosion in connections is not included. Meanwhile, corrosion on the structural members is assumed to be evenly distributed. Wind loads are calculated based on the codes used for synoptic winds and the wind tunnel experiments were carried out to obtain the drag coefficients for different panels of the transmission towers as well as for the transmission lines. Sensitivity analysis is carried out based upon the incremental dynamic analysis (IDA) to evaluate the structural capacity of the transmission tower-line system for different corrosion and loading conditions. Meanwhile, extreme value analysis is also performed to further estimate the short-term extreme response of the transmission tower-line system.

Stochastic Response Analysis for a Floating Offshore Wind Turbine Integrated with a Steel Fish Farming Cage

A state-of-the-art concept integrating a deepwater floating offshore wind turbine with a steel fish-farming cage (FOWT-SFFC) is presented in this paper. The configurations of this floating structure are given in detail, showing that the multi-megawatt wind turbine sitting on the cage foundation possesses excellent hydrostatic stability. The motion response amplitude operators (RAOs) calculated by the potential-flow program WAMIT demonstrate that the hydrodynamic performance of FOWT-SFFC is much better than OC3Hywind spar and OC4DeepCwind semisubmersible wind turbines. The aero-hydro-servo-elastic modeling and time-domain simulations are carried out by FAST to investigate the dynamic response of FOWT-SFFC for several environmental conditions. The short-term extreme stochastic response reveals that the dynamic behavior of FOWT-SFFC outperforms its counterparts. From the seakeeping and structural dynamic views, it is a very competitive and promising candidate in offshore industry for both power exploitation and aquaculture in deep waters.

Short-term extreme response and fatigue damage of an integrated offshore renewable energy system

Abstract This study addresses short-term extreme response and fatigue damage of an integrated wind, wave and tidal energy system. The integrated concept is based on the combination of a spar type floating wind turbine, a wave energy converter and two tidal turbines. Aero-hydro-mooring coupled analysis is performed in time-domain to capture the dynamic response of the combined concept in a set of environmental conditions. The mean up-crossing rate method is used to evaluate the extreme response, which takes advantage of an extrapolation method to reduce the simulation sample size. The cumulative fatigue damage is computed based on the S-N method. Simulation results show that the tower base fore-aft bending moment is improved, in terms of extreme value and fatigue damage. Nevertheless, the tension force of a mooring line is worsened. The mooring line bears increased maximum tension due to the tidal turbine thrust force and it is subjected to higher fatigue damage load as well.

Reliability analysis of wind turbines under non‐Gaussian wind load

SummaryBased on translation models, both Gaussian and non‐Gaussian wind fields are generated using the harmony superposition method for examining the reliability of a typical wind turbine at operational and parked conditions. Using the blade aerodynamic model and multibody dynamics, wind turbine responses are calculated and then probability characteristics are analyzed in details. The short‐term extreme response distribution is estimated by the average conditional exceedance rate method at each mean wind speed bin, and the long‐term extreme response distribution is then determined by further integrating the short‐term extreme response distribution conditional on wind speed with the distribution of mean wind speed. Additionally, crack initiation life and crack propagation life are evaluated using the linear cumulative damage theory and linear crack propagation theory, respectively. The results indicate that non‐Gaussian characteristics of wind inflows have a noticeably greater influence on both extreme response and fatigue damage, and the Gaussian assumption cannot suit wind turbine in complex terrain.

Optimal threshold selection in the POT method for extreme value prediction of the dynamic responses of a Spar-type floating wind turbine

This paper concerns the calculation of the short term extreme structural responses of a Spar-type floating wind turbine by applying the peak-over-threshold (POT) method. A new approach is proposed for finding an optimum threshold value by incorporating a declustering algorithm into the POT method. To select the clusters and check the Poisson character of the number of clusters we use the concept of a dispersion index. Then, the method of maximum product of spacing is utilized to estimate the parameters in the Generalized Pareto distribution of the largest values in all the selected clusters over the optimum threshold value. As examples of calculations, optimum threshold values of the out-of-plane and in-plane blade root bending moments and the tower – Spar interface bending moments of the NREL 5-MW OC3-Hywind floating wind turbine have been obtained by utilizing the new approach. The extreme response probability plot based on an optimum threshold value has been compared with the probability plot based on an empirical threshold value, and the accuracy and efficiency of the new approach have been convincingly validated. Goodness-of-fits plots have also been included in this article for testing the accuracy of the proposed new approach. Finally, in order to make a fair comparison, we have also extrapolated the short-term extreme values using the different POT methods and compared them with the reference values obtained directly from a large number of time-domain simulations.

A comparison of extreme structural responses and fatigue damage of semi-submersible type floating horizontal and vertical axis wind turbines

Currently development of floating wind turbines for deep water is mainly based on horizontal axis wind turbines (HAWTs). However, floating vertical axis wind turbines (VAWTs) are possible alternative due to their potential in the cost of energy reduction. This study deals with a comparison of stochastic dynamic responses of floating HAWTs and VAWTs with emphasis on the extreme structural responses and fatigue damages. A 5 MW three-bladed HAWT and three 5 MW VAWTs with blade number ranging from two to four were mounted on a semi-submersible platform. Their stochastic dynamic responses, short-term extreme structural responses and fatigue damages were estimated in both operational and parked conditions. The results show that the three- and four-bladed floating VAWTs and the three-bladed floating HAWTs considered have similar performances in the variation of generator power production, in the maximum tower base bending moment and in the fatigue damages at tower base and mooring lines. However, the maximum tensions in mooring line for the three- and four-bladed floating VAWTs are approximately four times higher than that of floating HAWTs, which implies a significant challenge for their mooring systems. The maximum tower base bending moment and fatigue damage in the two-bladed floating VAWT are extremely significant.

Nonlinear short term extreme response of spar type floating offshore wind turbines

In this work, the dynamic characteristics of spar based floating 5MW offshore wind turbine (OWT) are studied under operational and survival conditions for offshore Indian conditions. The spar with OWT is installed in 320m water depth. The OWT is subjected to combined wind and wave loads according to irregular Pierson-Moskowitz spectrum. After obtaining nonlinear spar platform responses, 3-h short term extreme motions are calculated which are useful for the design of an OWT. Extreme values provide realistic estimates to the associated risk of an event since the tail region governs the largest/smallest events or even the events over a threshold in a sample. In this paper, the extreme values are obtained by fitting the peaks in the tail regime using a Weibull-distribution. While one obtains Gaussian responses under the survival loads, the operational conditions have non-Gaussian responses and also larger than survival ones. The results show one should exercise caution for generating the extreme values for non-Gaussian responses and do a proper sensitivity analysis with respect to samples used for generation of extremes.

Prediction of short-term distributions of load extremes of offshore wind turbines

This paper proposes a new methodology to select an optimal threshold level to be used in the peak over threshold (POT) method for the prediction of short-term distributions of load extremes of offshore wind turbines. Such an optimal threshold level is found based on the estimation of the variance-to-mean ratio for the occurrence of peak values, which characterizes the Poisson assumption. A generalized Pareto distribution is then fitted to the extracted peaks over the optimal threshold level and the distribution parameters are estimated by the method of the maximum spacing estimation. This methodology is applied to estimate the short-term distributions of load extremes of the blade bending moment and the tower base bending moment at the mudline of a monopile-supported 5MW offshore wind turbine as an example. The accuracy of the POT method using the optimal threshold level is shown to be better, in terms of the distribution fitting, than that of the POT methods using empirical threshold levels. The comparisons among the short-term extreme response values predicted by using the POT method with the optimal threshold levels and with the empirical threshold levels and by using direct simulation results further substantiate the validity of the proposed new methodology.

Conventional and Linear Statistical Moments Applied in Extreme Value Analysis of Non-Gaussian Response of Jack-Ups

This work investigates numerically two different methods of moments applied to Hermite derived probability distribution model and variations of Weibull distribution fitted to the short-term time series peaks sample of stochastic response parameters of a simplified jack-up platform model which represents a source of high non-Gaussian responses. The main focus of the work is to compare the results of short-term extreme response statistics obtained by the so-called linear method of moments (L-moments) and the conventional method of moments using either Hermite or Weibull models as the distribution model for the peaks. A simplified mass-spring system representing a three-legged jack-up platform is initially employed in order to observe directly impacts of the linear method of moments (L-moments) in extreme analysis results. Afterward, the stochastic response of the three-legged jack-up platform is analyzed by means of 3D finite element model. Bias and statistical uncertainty in the estimated extreme statistics parameters are computed considering as the “theoretical” estimates those evaluated by fitting a Gumbel to a sample of episodical extreme values obtained from distinct short-term realizations (or simulations). Results show that the variability of the extreme results, as a function of the simulation length, determined by the linear method of moments (L-moments) is smaller than their corresponding ones derived from the conventional method of moments and the biases are more or less the same.

Predicting Short Term Extreme Response of Spar Offshore Floating Wind Turbine

In this paper, the short term extreme response of spar offshore 5MW NREL benchmark wind turbine is predicted. The spar is installed in a water depth of 320 m. The coupled wind and wave analysis is performed by coupling aerodynamic software FAST (Jonkman and Bull Jr,2005) and hydrodynamic software ANSYS-AQWA(2010). The global time domain responses of the spar type OWT is calculated for 600 s. The wave spectrum has significant wave height 6m and peak spectral period 10s and follows Pierson- Moskowitz spectrum. For safe operation, the structures should survive against different environmental conditions. The OWT can fail either in the operational regime or in the harsh environmental conditions. Therefore the dynamic simulation is carried out for two wind speeds, i.e., one in operational (hub height wind speed as 11.5 m/s) regime and another in idling condition (30 m/s) using the above wave parameters. Monte Carlo method is used to simulate the OWT responses in irregular wave loading condition. After obtaining the time-domain nonlinear responses, the 3-hr short term extreme responses are obtained which are useful for design of OWT. The 3-hr extreme response is obtained using Global Maxima Method (GMM). In Global Maxima Method, one maximum is taken from each time series and the maxima are fitted to two Generalized Extreme Value distributions, viz., Gumbel and Weibull distribution. The results show that Weibull fit is on a conservative side than Gumbel fit. Since the calculation of extremes is dependent on time domain simulations, a comparative study is also done for 100 and 20 samples so as to understand the sensitivity of extreme values due to lower sample size.

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.

Establishing robust short-term distributions of load extremes of offshore wind turbines

A novel method with a rigorous theoretical foundation is proposed for establishing robust short-term distributions of load extremes of offshore wind turbines. Based on the wind turbine load time series, the proposed method begins with incorporating a declustering algorithm into the peaks over threshold (POT) method and searching for an optimum threshold level with the aid of a Mean Residual Life (MRL) plot. Then, the method of L-moments is utilized to estimate the parameters in the generalized Pareto distribution (GPD) of the largest values in all the selected clusters over the optimal threshold level. As an example of calculation, an optimal threshold level of the tower base fore-aft extreme bending moments of the National Renewable Energy Laboratory (NREL) 5-MW OC3-Hywind floating wind turbine has been obtained by utilizing the novel method. The short-term extreme response probability plots based on this optimal threshold level are compared with the probability plots based on the empirical and semi-empirical threshold levels, and the accuracy and efficiency of the proposed novel method are substantiated. Diagnostic plots are also included in this paper for validating the accuracy of the proposed novel method. The method has been further validated in another calculation example regarding an NREL 5-MW fixed-bottom monopile wind turbine.

A straightforward approach for using single time domain simulations to assess characteristic extreme responses

Short-term wave design approach of marine structures, using nonlinear time domain simulations, is a design procedure that is recognized by various modern standard codes. One of the most challenging points of this approach is the evaluation of the characteristic extreme values for response parameters used in the design check equations. The most straightforward and recommended way to evaluate a response characteristic value is by fitting an extreme value probability distribution to the N-sample of extreme values extracted from N independent time domain simulations with duration equal to the short-term period indicated by the code, which is usually taken as 3 h. However, this procedure would not be practical for some types of marine structures, such as risers and mooring lines, under numerous design load cases and demanding huge finite element models. A more feasible approach would be to assess the response extreme value distribution using only a single short-term time domain simulation with duration shorter than 3 h. But reduced time simulations always introduce some additional statistical uncertainty into the extreme values estimates. This paper discusses a workable way of properly taking into account the statistical uncertainty associated with the simulation length in the assessment of a characteristic short-term extreme response value based on a single time series.

Sensitivity of extreme hydroelastic load effects to changes in ship hull stiffness and structural damping

A new hybrid method for the time-domain nonlinear simulation of the hydroelastic load effects and the peak over threshold (POT) method for the calculation of the short-term extreme responses are briefly described and applied to a flexible SL-7 class containership and a flexible liquefied natural gas (LNG) ship. Three stiffness levels, three stiffness distributions and three modal damping ratios are used to study the influence of the hull flexibility and structural damping on the short-term prediction of extreme vertical hydroelastic load effects. The results give justification for some simplified treatment of the first vertical flexible mode in early design stage when structural details are not available.

Statistical analysis of wave-induced extreme nonlinear load effects using time-domain simulations

A new hybrid method for the time-domain nonlinear simulation of the hydroelastic load effects and the peak-over-threshold (POT) method for the calculation of the short-term extreme responses are briefly described and applied to a flexible containership of the latest design. Statistical analysis has been carried out to study the sensitivity of the predicted extreme vertical bending moments and vertical shear forces to the changes in the threshold of the POT method, as well as the statistical uncertainty in the prediction due to the limited duration of the nonlinear simulation. It is recommended that 90%–95% quantile should be used as the threshold in the POT method and more than 100 h of time-domain simulation should be carried out in order to obtain satisfactory predictions of the short-term extreme nonlinear load effects.

Probabilistic Models Applicable to the Short-Term Extreme Response Analysis of Jack-Up Platforms

There is a steadily increasing demand for the use of jack-up units in deeper water and harsher conditions. Confidence in their use in these environments requires jack-up analysis techniques to reflect accurately the physical processes occurring. However, nearly all analyses are deterministic in nature and do not account for the inherent variability in governing parameters and models. In this paper, probabilistic models are used to develop an understanding of the response behavior of jack-ups, with particular emphasis placed on the extreme deck displacement due to a short-term event. Variables within the structural, foundation and wave loading models are assigned probability distributions and their influence on the response statistics is quantified using a response surface methodology.

Evaluation of long-term extreme response statistics of jack-up platforms

This paper is concerned with the models appropriate for the dynamic assessment of jack-ups, concentrating particularly on the long-term response due to random ocean waves and on work-hardening plasticity models used for spud-can response. A methodology for scaling of short-term statistics, calculated using a Constrained NewWave technique, is shown in a numerical experiment for an example jack-up and central North Sea location. The difference in long-term extreme response statistics due to various footing assumptions is emphasised. Results for two environmental load conditions are described (one excluding and one including wind and current effects) and the role of sea-state severity in the variation of short-term extreme response statistics is also highlighted.