Environmental Contour Method Research Articles

Comparison of probabilistic structural reliability methods for ultimate limit state assessment of wind turbines

The probabilistic design of offshore wind turbines aims to ensure structural safety in a cost-effective way. This involves conducting structural reliability assessments for different design options and considering different structural responses. There are several structural reliability methods, and this paper will apply and compare different approaches in some simplified case studies. In particular, the well known environmental contour method will be compared to a more novel approach based on sequential sampling and Gaussian processes regression for an ultimate limit state case study on the maximum flapwise blade root bending moment. For one of the case studies, results will also be compared to results from a brute force simulation approach. Interestingly, the comparison is very different from the two case studies. In one of the cases the environmental contours method agrees well with the sequential sampling method but in the other, results vary considerably. Probably, this can be explained by the violation of some of the assumptions associated with the environmental contour approach, i.e. that the short-term variability of the response is large compared to the long-term variability of the environmental conditions. Results from this simple comparison study suggests that the sequential sampling method can be a robust and computationally effective approach for structural reliability assessment.

Response Extremes of Floating Offshore Wind Turbine Based on Inverse Reliability and Environmental Contour Method

Floating structures are subject to complex marine conditions. To ensure their safety, reliability analysis needs to be conducted during the design phase. However, because of the complexity of traditional full long-term analysis, the environmental contour method (ECM) based on the inverse reliability method, which can combine accuracy and efficiency, is extensively used. Due to the unique environment in the South China Sea, the probabilistic characteristics of three-dimensional (3D) environmental parameters of wind, wave and current are investigated. The ECs of the target sea are established via the ECM based on both the inverse first-order reliability method (IFORM) and inverse second-order reliability method (ISORM). It is found that the sea state forecasted by ISORM is more extreme and may lead to a more conservative design than IFORM. Furthermore, the wind–wave–current combination coefficient matrixes developed using the 3D ECs are proposed for the design of FOWTs in the South China Sea. The validity and practicality of the contours and matrixes are tested by using a floating offshore wind turbine (FOWT) as a numerical example. Then, the short-term response of the structure under the combined wind, wave and current conditions is calculated, providing a theoretical reference for the design of FOWTs.

Simplified Strength Assessment for Preliminary Structural Design of Floating Offshore Wind Turbine Semi-Submersible Platform

The study aims to develop a simplified strength assessment method for the preliminary structural design of a semi-submersible floating offshore wind turbine platform. The method includes load cases with extreme wave load effects and a load case dominated by wind load. The extreme load effects due to waves are achieved using the design waves. Seven characteristic responses of the semi-submersible platform due to waves are chosen. The design waves for the extreme characteristic responses are all from extreme wave conditions where the significant wave heights are close to the one for a return period of 100 years. The extreme load effects dominated by wind loads are approximated using the modified environmental contour method. The load effects are the tower base shear force and bending moment. The two load effects are correlated, and a linear equation can approximate the relationship between their extreme values. The finite element analysis results show that the frame design of the bottom of the outer column is essential for structural strength. The wave load can also result in significant stress in the area close to the tower base.

Assessing some statistical and physical modelling uncertainties of extreme responses for monopile-based offshore wind turbines, using metocean contours

This study examines the influence of probabilistic models for wave parameters in the joint environmental model and hydrodynamic/soil models on extreme mudline bending moments for monopile-based wind turbines at representative wind speeds, using the environmental contour method. For significant wave height, the 3-parameter Weibull model using the method of moments (MoM) provides the best fit to hindcast data across different wind classes, for the statistical models and data considered in the study. The hybrid Log-normal-Weibull (LonoWe) model also provides a reasonable fit but is sensitive to the transition point between distributions. Both models yield the largest extreme responses, with differences of approximately 0.5–3.5%. The 3-parameter Weibull model with maximum likelihood estimation (MLE) and the 2-parameter Weibull model result in less conservative contours, leading to up to 13% lower extreme responses, compared to LonoWe and Weibull (MoM). Regarding peak period, both the Log-normal and 3-parameter Weibull models provide reasonable fits, with the latter being more accurate near the steepness (breaking) limit. The stochastic variation among maxima due to seed variability and the uncertainty in quantile estimates as a function of number of samples was found to be crucial, particularly for severe sea states at the cut-out speed. Soil modelling is particularly important when the turbine is parked and encounters peak wave periods close to the turbine’s natural periods, while the effect of soil modelling on the extremes during turbine operation is negligible. Additionally, the impact of diffraction becomes relatively important for short wave periods. However, it is worth noting that the choice of load models has less impact on extreme responses compared to variations in the contours caused by different statistical models or seed variability.

New prediction method for reliability analysis of ocean sustainable energy systems

With the aim of overcoming the shortcomings of traditional approaches, in this paper, an exponential Weibull distribution for fitting the significant wave height data is proposed in order to calculate more accurately the sea-state parameter distribution tails and to extrapolate well. This proposal is applied in predicting the probability distribution tails of a measured ocean wave dataset, and its accuracy is clearly demonstrated. The proposal is subsequently utilised in combination with Monte Carlo sampling to form a new environmental contour method for deriving a 50 year contour line based on the aforementioned measured ocean wave dataset. The derived environmental contour line is compared with that predicted by using a traditional contour line approach. Additionally, the engineering significance of using a more reliable environmental contour line, such as the one derived using the proposed new method for predicting the long-term design force values for an ocean sustainable energy system is highlighted. In conclusion, the newly proposed environmental contour method is recommended to be used when predicting the extreme dynamic response values for the safe and successful design of ocean sustainable energy systems.

Effects of inhomogeneous wave modeling on extreme responses of a very long floating bridge

Floating bridges are usually deployed in fjords where the wave fields are inhomogeneous. The wave inhomogeneity has been found to induce significant effects on dynamic responses, however, it was rarely considered during the extreme response analyses of floating bridges. The present study deals with the effects of inhomogeneous wave modeling on extreme responses of a very long end-anchored floating bridge. The inhomogeneous wave field modeling accounts for the spatial variation of wave spectral parameters as well as the coherence of wave elevations between different positions. Structural responses under various wave conditions are simulated through fully-coupled hydro-elastic simulations. The long-term extreme responses are investigated by a simplified environmental contour method, where the long-term extremes are approximated by extremes at a high quantile in carefully selected short-term sea states. The characteristics of simulated waves and responses are first analyzed to serve as a basis for extreme prediction. Uncertainties associated with extreme analyses are also studied. It is found that the coherence of wave elevations has significant influences on the standard deviation and the spatial correlation of the responses. The extreme values of the axial force vary between different modeling of inhomogeneous wave loads and become significantly larger considering partially correlated wave fields.

Extreme response analysis of a floating vertical axis wind turbine based on modified environmental contour method

Floating vertical axis wind turbine (FVAWT) is a potential concept that could compete with the floating horizontal axis wind turbine (FHAWT) in the offshore wind industry. For a reliable FVAWT design, accurate prediction of extreme structural responses is crucial for ultimate limit state (ULS) design evaluation. Extreme structural responses of offshore wind turbines depend on operational modes and could present non-monotonic behavior with respect to environmental parameters. In this study, the extreme responses of a 3-bladed H-rotor semi-submersible FVAWT are evaluated using a simplified engineering approach, i.e., the modified environmental contour method (MECM). Judging from the response characteristics of the FVAWT with respect to increasing wind speed, the environmental contour with a return period of the cut-out wind speed is used. Along the selected environmental contour, the cut-out wind speed and the corresponding most probable sea state is chosen as the environmental design point. To generate statistical samples of structural responses, the Monte Carlo (MC) method is applied by carrying out fully-coupled time domain simulations under the selected environmental loadings. The Gumbel method, the Weibull tail method and the mean upcrossing rate (MUR) method are used to extrapolate the 50-yr long-term extreme responses. With a sufficiently large sample size, e.g. 100 MC simulations, the estimated extremes using different extrapolation methods are in close agreement with each other. However, the Weibull tail and MUR methods reduce the statistical uncertainty of the estimates due to higher data utilization. For practical engineering applications, massive amount of MC simulations is often not desirable. Therefore, the accuracy and statistical uncertainty of the estimated extreme responses associated with a reduced sample size is also investigated. For a sample of 10 simulations, the Weibull tail and MUR methods are able to predict extreme responses that are closer to the estimates using 100 simulations. The MUR method results in the lowest statistical uncertainty of the estimates.

Coastal distributions of design environmental loads in typhoon-affected sea area based on the trivariate joint distribution and environmental contour method

Southeast China's coastal areas usually suffer from typhoons, accompanied by extreme wind, waves, and currents, which threaten offshore structural safety. To mitigate the risk of failure, herein, an integrated assessment framework is developed to estimate typhoon-induced environmental loads along the coast. An environmental database of 30-year is obtained from verified numerical simulations. A methodology for extracting typhoon-induced extreme values is proposed to determine the extreme environmental variables and trivariate joint distributions are constructed. The structure of vine copula ensures that the marginal, bivariate, and trivariate distributions can match their respective optimal model, and provide appropriate correlations for three-dimensional environmental contours (ECs). Thus, physical information from the metoceanic environment is transferred to the probabilistic space and structural response. The results reveal that the EC profiles exhibit a pronounced layered distribution along the wind axis, which indicates the dominant role of wind loads in structural safety. The spatial distributions of 137 sites along the coastal areas are analyzed to reveal the inherent relationships between typhoon propagation, environmental loads, topographical change, and structural response. The central part of the coast is prone to failure owing to undiminished typhoon intensity.

Update 2.0 to “ViroCon: A software to compute multivariate extremes using the environmental contour method”

Update 2.0 to “ViroCon: A software to compute multivariate extremes using the environmental contour method”

A new method for structural safety and reliability analysis of offshore wind turbines

With the motivation to overcome the shortcomings of the Rosenblatt inverse-first-order reliability environmental contour method (IFORM), in this study, the use of bivariate kernel density estimation with smoothed cross-validation bandwidth selection method is proposed for generating more accurate environmental contour lines. The environmental contour lines at a chosen offshore site obtained by using the proposed new method were compared with those obtained by using the Rosenblatt IFORM, and the accuracy and effectiveness of the proposed new method have been fully and clearly substantiated. Next, the 50 year extreme structural dynamic responses of a monopile-supported 5 MW offshore wind turbine installed at this chosen offshore site based on the proposed new method and the Rosenblatt IFORM were calculated. Analysing the calculated results, it can be found that the 50 year extreme fore−aft shear force value based on the 50 year extreme sea state obtained using the proposed new method is 78.9% larger than the corresponding value obtained based on the Rosenblatt IFORM. The calculation results in this paper were further systematically analysed and compared, and the necessity and importance of using more realistic environmental contour lines (such as those generated using the proposed new method) have been finally highlighted.

Environmental contours for wind-resistant bridge design in complex terrain

Accurate estimation of the extreme wind fields is crucial for long-span bridge design. The current practice is focused on estimating the extreme mean wind speed, neglecting the inherent uncertainty in the turbulence model parameters. However, full-scale measurements on bridges show that such uncertainties are significant and should be considered in design. Here, the environmental contour method (ECM) is used to obtain long-term extreme wind fields considering uncertainties from the mean wind speed, turbulence intensities and spectral parameters measured at the Sulafjord Bridge site. Design contours of combinations of wind field parameters are obtained for target return periods of 4, 50 and 100 years. The contours are based on a proposed probabilistic modeling strategy that combines hindcast mesoscale simulations and field measurements. The contour estimates are also compared with state-of-the-art design values from the design recommendations. It is concluded that the environmental contours provide a more complete and yet intuitive description of the wind field at the bridge site compared to the current design methodology. The ECM is found suitable for obtaining design wind fields at new long-span bridge sites as it makes use of the limited site data more efficiently and it is still easy-to-use for the practicing engineer.

Prediction of long-term extreme response of two-rotor floating wind turbine concept using the modified environmental contour method

The modified environmental contour method (MECM) is assessed for the prediction of 50-year extreme response of a two-rotor floating wind turbine concept (2WT) deployed in two offshore sites in the northern North Sea (Norway 5) and the North Atlantic Ocean (Buoy Cabo Silleiro). The sites considered are in areas known for their floating wind development potential. The environmental contour method (ECM) is used to reduce the computational effort of full long-term analysis (FLTA) by only considering environmental conditions associated with a given return period. MECM is a modification of the ECM where additional environmental contours are included to account for discontinuous operation modes of dynamic structures. The results obtained in MECM are benchmarked against FLTA results and compared to ECM results. ECM leads to large underpredictions of responses governed by wind loads if compared to FLTA, as it is not capable of taking into account important operational modes of the 2WT. It is found that MECM, which includes the wind turbines cut-off contour, is able to reduce most response underpredictions within 15% difference compared to FLTA results. MECM may thus be considered as a sufficiently accurate and computationally efficient method for the long-term extreme analysis of 2WT concepts.

Effects of Simulation Length and Flexible Foundation on Long-Term Response Extrapolation of a Bottom-Fixed Offshore Wind Turbine

Abstract This paper deals with statistical and modeling uncertainty on the estimation of long-term extrapolated extreme responses in a monopile offshore wind turbine. The statistical uncertainty is addressed by studying the effect of simulation length. Modeling uncertainty is explored by evaluating the effects of considering a rigid and flexible foundation. The soil's flexibility is taken into account by considering the improved apparent fixity method. To identify the most relevant environmental conditions, the modified environmental contour method is used. The analysis focuses on the fore-aft shear force (FASF) and the fore-aft bending moment (FABM) at the mudline. The results show that using a simulation length of 10 min does not provide sufficient accuracy. It was found that for the FASF, simulation lengths of at least 30 min are required to achieve an accuracy of about +/−5%. For the FABM, it was found that both the extrapolations made with 20 min and 30 min simulations achieved similar levels of accuracy of about 20%. Meanwhile, the results obtained from 10 min simulations reached deviations of about 40%. Finally, from the comparison made between a rigid and flexible foundation, it was found that the extrapolated responses exhibit maximum deviations up to around 5% and 10% for the FASF and the FABM, respectively. Also, for the FABM, it was observed that the consideration of a flexible foundation causes the critical wind speed to shift from 16.5 m/s (rigid) to 18 m/s (flexible).

A new method for predicting the extreme dynamic responses of wave energy converters

The copula-based environmental contour approach in the existing literature is only ‘partially’ non-parametric. Theoretically, the derived environmental contours from this ‘non-parametric’ copula-based approach will still be somewhat rigid. Optimally, the environmental contours for a specific ocean site should be developed based on a joint model of the environmental variables and the joint model should be directly estimated by a two-dimensional non-parametric approach. In this study, the use of a bivariate kernel density estimation approach for generating environmental contours is proposed. The advantages of the proposed new method were validated using two calculation examples based on measured wave data at two offshore locations. It was found, in a wave energy converter (WEC) application example, that the design value will increase by 23.4% if the proposed method is used in comparison to using the technique based on the non-parametric Gumbel copula environmental contour method. It was also concluded that the design value will increase by 15.98% if the proposed method is used in comparison to using the technique based on the non-parametric Clayton copula environmental contour method. The calculation results in this paper clearly demonstrate that the proposed new method can be used to effectively forecast the extreme dynamic responses of WECs.

Prediction of Long-Term Extreme Response of Fish Cage Using Environmental Contour Method

Prediction of Long-Term Extreme Response of Fish Cage Using Environmental Contour Method

On Characteristics of Ice Ridges and Icebergs for Design of Ship Hulls in Polar Regions Based on Environmental Design Contours

Ice ridges and icebergs generally pose a major threat to both ships and offshore facilities that operate in Polar regions. In many cases these features will govern the structural design loads associated with the Ultimate Limit State (ULS) and the Accidental Limit State (ALS). In general, a large number of load cases must be considered in order to ascertain an adequate structural resistance. Alternatively, conservatively high values of the relevant design parameters can be applied, which implies cost penalties. Accordingly, it is natural to consider methods that can serve to reduce the number of relevant load cases. Based on relevant information about the statistical properties of the parameters that characterize ice ridges and icebergs, the most likely combinations of these parameters for design purposes are highly relevant. On this background, the so-called environmental contour method is applied. Probabilistic models of the key parameters that govern the ship and ice interaction process are introduced. Subsequently, the procedure referred to as inverse reliability methods (IFORM) is applied for identification of the environmental contour. Different forms (i.e., dimensions) of environmental contours are generated to reflect the characteristics of the interaction process. Furthermore, the effect of an increasing correlation between the basic parameters is studied. In addition, the increase of the design parameter values for increasing encounter frequencies is illustrated.

Inverse Directional Simulation: an environmental contour method providing an exact return period

This study presents an improved approach for drawing environmental contours, derived from the inverse First Order Reliability Method (iFORM). It is shown that the approach used in the iFORM method is not accurate as it only takes into account a fraction of the probability space behind the contour line-which means that the iFORM method provides inherently non-conservative environmental contours. iDS, an alternative solution based on the chi-square distribution is suggested, and its adequacy is demonstrated with a Monte Carlo simulation. An expression is derived for computing sector-constrained environmental contours where the exceedance probability is contained within specific range of interest for one or more variables. The newly suggested environmental contour methods are applied on measured wind and turbulence time series and compared with the iFORM method.

A novel environmental contour method for predicting long-term extreme wave conditions

Abstract This paper proposes a novel environmental contour line method based on measured ocean wave data for predicting the long-term extreme wave conditions. For implementing the proposed environmental contour line method, a bivariate kernel density estimation approach is used along with over-smoothed bandwidth selection. The environmental contours obtained using the proposed method have been compared with those obtained using the Gaussian copula (Nataf transformation) method and another parameterized model, and the effectiveness and superiority of the proposed method have been clearly substantiated. The research results in this paper demonstrate that the proposed method can be utilized as an effective tool for predicting the long-term extreme wave conditions.

Extended Environmental Contour Methods for Long-Term Extreme Response Analysis of Offshore Wind Turbines1

AbstractEnvironmental contour method is an efficient method for predicting the long-term extreme response of offshore structures. The traditional environmental contour is obtained using the joint distribution of mean wind speed, significant wave height, and spectral peak period. To improve the accuracy of traditional environmental contour method, a modified method was proposed considering the non-monotonic aerodynamic behavior of offshore wind turbines. Still, the modified method assumes constant wind turbulence intensity. In this paper, we extend the existing environmental contour methods by considering the wind turbulence intensity as a stochastic variable. The 50-year extreme responses of a monopile-based offshore wind turbine are compared using the extended environmental contour methods and the full long-term method. It is found that both the environmental contour method and the modified environmental contour method, with the wind turbulence intensity included as an individual variable, give more accurate predictions compared with those without. Using the full long-term method as a benchmark, this extended approach could reduce the nonconservatism of the environmental contour method and conservatism of the modified environmental contour method. This approach is effective under wind-dominated or combined wind-wave loading conditions, but may not be as important for wave-dominated conditions.

Buffeting response of long-span bridges considering uncertain turbulence parameters using the environmental contour method

Full-scale monitoring of the Hardanger Bridge has revealed significant turbulence-induced variability in the measured acceleration response. In this paper, a probabilistic model is used to describe the uncertain turbulence parameters, and the environmental contour method is used to investigate the long-term root-mean-square (RMS) response of the Hardanger Bridge. The results show that turbulence-induced variability has a significant impact on the bridge girder section moments. It is also interesting that the critical combination of environmental parameters does not necessarily involve the maximum mean wind velocity. By using the environmental contour method to account for turbulence uncertainty, the scattered acceleration RMS response measurements from the Hardanger Bridge are successfully eclipsed by 100-year return period response estimates, showing vast improvements compared with the traditional design methodology. The investigations presented in this paper show that the environmental contour method can be used to improve the accuracy and reduce the uncertainty in buffeting response calculations for long-span bridge design.