Environmental Contour Research Articles

Joint probability analysis and mapping of typhoon-induced wind, wave, and surge hazards along southeast China

The southeastern coastal region of China frequently faces typhoon attacks, posing significant threats to its ever-growing infrastructure. Quantifying multiple typhoon-induced hazards in terms of wind, wave, and surge would provide valuable data to support structural design, risk assessments, and disaster mitigation. This study simulated the evolution of wave and surge driven by typhoon wind fields using the SWAN + ADCIRC coupling model, generating extreme samples of wind speed, significant wave height, and surge height. Trivariate joint probability distributions were established at six typical coastal stations (Hong Kong, Xiamen, Fuzhou, Wenzhou, Zhoushan, and Shanghai) based on optimal copula functions. Using the environmental contour and conditional return period methods, appropriate combinations of design environmental loads were analyzed for a specific return period. The results revealed two reasonable combination types for the 100-year design period. One involves the combination of the 100-year dominant variable value computed using a univariate probability distribution, with two 20-year secondary variable values calculated using the second conditional return period. The second combination selects a variable group corresponding to the maximum value of the dominant variable on the environmental surface. These methods and findings were further extended to the entire computational area to develop hazard maps covering the Southeast Sea area of China. The hazard maps show that the design values of significant wave height increase with distance from the coast. In contrast, the spatial distribution of surge presents the opposite pattern. This study provides a novel perspective on structural design values subjected to multiple disasters and offers a reference for offshore engineering construction in the sea area of southeast China.

Estimating metocean environments associated with extreme structural response to demonstrate the dangers of environmental contour methods

Extreme value analysis (EVA) uses data to estimate long-term extreme environmental conditions for variables such as significant wave height and period, for the design of marine structures. Together with models for the short-term evolution of the ocean environment and for wave–structure interaction, EVA provides a basis for full probabilistic design analysis. Alternatively, environmental contours provide an approximate approach to estimating structural integrity, without requiring structural knowledge. These contour methods also exploit statistical models, including EVA, but avoid the need for structural modelling by making what are believed to be conservative assumptions about the shape of the structural failure boundary in the environment space. These assumptions, however, may not always be appropriate, or may lead to unnecessary wasted resources from over design. We demonstrate a methodology for efficient fully probabilistic analysis of structural failure. From this, we estimate the joint conditional probability density of the environment (CDE), given the occurrence of an extreme structural response. We use CDE as a diagnostic to highlight the deficiencies of environmental contour methods for design; none of the IFORM environmental contours considered characterise CDE well for three example structures.

Analysing the Directional Dependence of Wind and Wave Interactions for Offshore Wind Turbines Using Environmental Contours

The structural design of offshore wind turbines is dominated by environmental conditions such as wind and waves, in addition to deadweight loads and loads from operation. Probabilistic combination approaches exist for the ultimate limit state (ULS) to estimate the simultaneous occurrence of extreme meteorological and oceanographic (metocean) environmental conditions at the site of an offshore wind turbine. The site-specific direction of action of the load parameters is mostly neglected in these approaches; the design of offshore wind turbines in the ULS is usually carried out for the most structurally unfavourable directional superposition of load parameters—which is not based on physical principles and wastes potential material savings. The reasons for different load parameters in different directions of action are the influences of nearby land masses and the topographic shape of the sea floor, atmospheric air circulation, and marine current systems. In this paper, wind and sea state data from the coastDat-2 WAM database are statistically analysed for two sites in the North Sea, common environmental contours are estimated using the example of significant wave height and wind speed, and the site-specific influence of the direction of the load parameters on the environmental contours are investigated. It is shown that, depending on the site under consideration, the direction of action can significantly influence the metocean environmental conditions and that direction-resolved probabilistic combination approaches can contribute to a safe and economic structural design of offshore wind turbines.

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.

CovXtreme : MATLAB software for non-stationary penalised piecewise constant marginal and conditional extreme value models

The covXtreme software provides functionality for estimation of marginal and conditional extreme value models, non-stationary with respect to covariates, and environmental design contours. Generalised Pareto (GP) marginal models of peaks over threshold are estimated, using a piecewise-constant representation for the variation of GP threshold and scale parameters on the (potentially multidimensional) covariate domain of interest. The conditional variation of one or more associated variates, given a large value of a single conditioning variate, is described using the conditional extremes model of Heffernan and Tawn (2004), the slope term of which is also assumed to vary in a piecewise constant manner with covariates. Optimal smoothness of marginal and conditional extreme value model parameters with respect to covariates is estimated using cross-validated roughness-penalised maximum likelihood estimation. Uncertainties in model parameter estimates due to marginal and conditional extreme value threshold choice, and sample size, are quantified using a bootstrap resampling scheme. Estimates of environmental contours using various schemes, including the direct sampling approach of Huseby et al. 2013, are calculated by simulation or numerical integration under fitted models. The software was developed in MATLAB for metocean applications, but is applicable generally to multivariate samples of peaks over threshold data. The software and case study data can be downloaded from GitHub, with an accompanying user guide.

Inference for New Environmental Contours Using Extreme Value Analysis

AbstractEnvironmental contours are often used in engineering applications to describe risky combinations of variables according to some definition of an exceedance probability. These contours can be used to both understand multivariate extreme events in environmental processes and mitigate against their effects, e.g. in the design of structures. Such ideas are also useful in other disciplines, with the types of extreme events of interest depending on the context. Despite clear connections with extreme value modelling, much of this methodology has so far not been exploited in the estimation of environmental contours; in this work, we provide a way to unify these areas. We focus on the bivariate case, introducing two new definitions of environmental contours. We develop techniques for their inference which exploit a non-standard radial and angular decomposition of the variables, building on previous work for estimating limit sets. Specifically, we model the upper tails of the radial distribution using a generalised Pareto distribution, with adaptable smoothing of the parameters of this distribution. Our methods work equally well for asymptotically independent and asymptotically dependent variables, so do not require us to distinguish between different joint tail forms. Simulations demonstrate reasonable success of the estimation procedure, and we apply our approach to an air pollution data set, which is of interest in the context of environmental impacts on health.Supplementary materials accompanying this paper appear online.

A new method for analysis of marine sustainable energy systems

This paper proposes to utilise a new adaptive kernel density estimation (KDE) methodology based on linear diffusion processes for predicting the probability distribution tails of sea-state parameters. A key conclusion was reached that the proposed new methodology can lead to more accurate prediction results than traditional methods based on fittings to a measured significant wave height data set at National Data Buoy Center station 46014. This proposed methodology was subsequently utilised for deriving an accurate 50-year environmental contour line that was used in the dynamic analysis of a two-body point absorber wave energy converter. After systematically analysing the calculation results, another key conclusion was drawn that it is advantageous to use a more reliable contour line derived using the proposed new methodology for long-term dynamic analysis of wave energy converters. In summary, the proposed new adaptive KDE methodology is recommended to be utilised and to be refined continuously in future research work in the field of long-term reliability analysis of marine sustainable energy systems.

A Joint Probability Distribution for Multivariate Wind-Wave Conditions and Discussions on Uncertainties

Abstract This article presents a joint statistical model, which is needed in probabilistic design and structural risk assessment, that has been fitted to data of wind and wave conditions for an offshore location off South Brittany. The data are from a numerical model and contain hourly values for several wind and wave variables over a period of 32 years. The joint distribution presented in this article considers the variables wind direction, mean wind speed, significant wave height, wave direction, and peak period. A conditional model for turbulence given wind speed is introduced to yield an additional variable for the joint model. The joint model is constructed as a product of marginal and conditional models for the various variables. Additionally, the fitted models will be used to construct environmental contours for some of the variables. For significant wave height, various models are used to obtain different extreme value estimates, illustrating the uncertainties involved in extrapolating statistical models beyond the support of the data, and a discussion on the use of nonparametric copulas for the joint distribution is presented. Moreover, bootstrap has been performed to estimate the uncertainty in estimated model parameters from sampling variability. The effect of changing which variable to model as the marginal in a conditional model is illustrated by switching from wind speed to significant wave height. Such joint distribution models are important inputs for design of offshore structures, and in particular for offshore wind turbines, and the influence of the joint model in design is illustrated by a simple case study. This article is an extension of the conference paper by Vanem et al. (2023, “A Joint Probability Distribution Model for Multivariate Wind and Wave Conditions,” 42nd International Conference on Ocean, Offshore and Arctic Engineering).

A new method for long-term safety analysis of marine structures

This paper proposes to utilise a new adaptive kernel density estimation (KDE) method based on a linear diffusion process for fitting the significant wave height data in order to calculate the sea state parameter distribution tails more accurately, particularly the higher, more extreme values. The accuracy of the proposed method has been demonstrated based on fittings to two measured ocean wave datasets. This proposed method has subsequently been utilised for deriving accurate 50-year and 500-year environmental contour lines. The advantages of using a more reliable contour line derived from using the proposed new method for long-term safety analysis of marine structures have been substantiated.

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.

A time-varying copula approach for describing seasonality in multivariate ocean data

Characterizing multivariate ocean variables is quite critical for reliability design and risk assessment of marine structures. A robust, precise, and practical multivariate statistic model is necessary for comprehending ocean characteristics. As the time-varying characteristics exist in the ocean data, it is unreasonable to employ a simple constant statistical model to characterize all the multivariate data at one time. Therefore, in this paper, a time-varying copula approach is developed for modeling time-varying multivariate ocean data. Considering climate variations, a time-varying formula for return period and environment contour is also derived. The developed approach is demonstrated based on a site-specific ocean dataset collected from a buoy on the US coast. The climate effects associated with the multivariate ocean variables are characterized. The developed time-varying copula approach is also compared to the conventional copula and the conditional model in estimating the return period. The results showed that the time-varying model is helpful to explore the most critical environmental conditions for marine structures.

Convex environmental contours for non-stationary processes

Environmental contours are tools frequently used in the early design of marine structures. They provide a description of critical design conditions and serve as a means for simplifying expensive long-term response calculations. Here, we consider convex contours based on the assumption of convex failure sets. We provide a rigorous foundation for the existence of such contours when the underlying environmental factors are modelled by a general, possibly non-stationary, process. This constitutes a generalisation of existing theory and is done to properly account for empirically observed increases in extreme sea-states.Two definitions are proposed, based respectively on averages or quantiles of exceedence times, along with minimal conditions on the environmental processes to guarantee existence. In order to illustrate these methods we give two examples, including an empirical study containing a method for constructing contours based on the presented theory.

Environmental contours of sea states by the I-FORM approach derived with the Burr-Lognormal statistical model

Environmental contours are constructed using the Inverse-First Order Reliability Method based on return periods of one and twenty years. The paper proposes the use of the Burr distribution to model the marginal distribution of long-term significant wave heights and uses the conditional approach, by combining this marginal with conditional log-normal distributions of peak wave periods. The resulting environmental contours constructed based on the implementation of the Burr-Lognormal model are compared with the contours constructed with the commonly applied Weibull-Lognormal model considered as the baseline. Statistical tests of fit are used, and they do not reject any of the two models being compared, indicating that both approaches are acceptable. The environmental contours from the newly implemented scheme are different from the ones of the reference approach, as expected. Return values obtained with both marginal distributions of significant wave heights show differences comparable to the ones reported in other comparisons of methods reported in the literature.

Analysis of extreme internal load effects in columns in a semi-submersible support structure for large floating wind turbines

Most studies on floating wind turbine floaters focus on rigid-body motion analysis, while analysis of structural load effects of the floaters is lacked. However, load effect analysis of hull structures is essential for the safety design checks throughout the service lifetime. Therefore, this study carries out the analysis of the extreme internal stress of columns in a 10-MW semi-submersible hull. A novel multibody approach is used for the numerical modelling of the hull structure, which can capture the internal forces and moments of the columns in the time domain. The environmental contour approach is employed to conduct the short-term analysis of the column extreme stresses. Important load cases are determined based on the sensitivity study of combined critical wave periods, important mean wind speeds, and the largest significant wave height with respect to column load effects. Long-term extreme values of the column stresses are predicted by the extrapolated method based on the short-term extreme analysis. Relative importance of internal load components on extreme value estimation of columns is studied. Simplified approaches are proposed to more efficiently predict the long-term extreme values of the column load effects, and applied in a case study. The analysis provides a good insight into the important global forces and moments as well as the direct wave load effect on the column stress analysis, which contributes to improve the design efficiency in engineering practice.

Endometrial Carcinoma: A Comprehensive Analysis of Clinical Parameters, Treatment Modalities, and Prognostic Outcomes at a Tertiary Oncology Center in the UAE.

Background Endometrial carcinoma (EC) remains a pressing global health issue, with a discernible upsurge in incidence, especially in developed countries. Notably, the United Arab Emirates (UAE) has witnessed a surge in EC cases, demanding an in-depth, region-specific exploration into the disease's clinical, treatment, and prognostic facets against the backdrop of its unique socio-genetic and environmental contours. Aim This study aimed to profess a comprehensive understanding of EC by examining clinical parameters, treatment modalities, and prognostic outcomes in the UAE context, thereby seeking to delineate potential correlations between varied therapeutic combinations, patient demographics, and tumor characteristics in affecting prognostic outcomes. Materials and methods A retrospective cohort study involving 93 patients diagnosed with EC from January 2011 to March 2023 at a leading oncology center in the UAE was conducted. Data, including demographic information, clinical presentation, treatment modalities, and prognostic outcomes, were meticulously extracted and analyzed. The R software (version 4.2.2) facilitated exhaustive statistical analyses, involving descriptive statistics, correlation analyses with the polycor package, and survival analyses utilizing the Kaplan-Meier method and Cox regression analysis via the survival and survminer packages, respectively. Results Although the correlation matrix revealed a noticeable relationship between "Family history"and "Age," most parameters displayed independence, offering a robust platform for ensuing multivariate analyses. Kaplan-Meier survival curves, stratified by therapeutic modalities, exhibited no statistically significant survival differences across therapeutic cohorts (p-values: 0.44, 0.86, and 0.83). Conversely, the composite Cox regression model underscored "non-national" demographic, Diabetes Mellitus II, and stromal invasion as pivotal prognostic factors, indicating the multifactorial nature of survival in EC patients and emphasizing demographic and tumor characteristics over therapeutic modalities as influential prognostic determinants. Conclusion In conclusion, while therapy types were not directly correlated with survival, demographic and tumor traits prominently impacted prognostic outcomes, advocating for an intricate, multidimensional approach to managing EC in the UAE. This study hopes to sow seeds for subsequent research, shaping clinically and culturally apt practices and policies in the region's healthcare landscape.

Urban vs. rural: Contrasting environmental concerns and sustainable practices in the Romanian HoReCa sector

This research questions the alignment of economic objectives with environmental management in the Romanian hospitality, restaurant and café (HoReCa) sector, with a focus on sustainable development. It juxtaposes the sector's sustainability imperatives in urban and rural settings, and discusses adaptation and resilience mechanisms against an increased global focus on environmental conservation. The sector's transition to sustainable development as a strategic imperative is examined. The urban-rural dichotomy reveals contrasting challenges: urban units face consumer-driven competition, while rural units face resource constraints and infrastructure deficits. Empirical studies suggest that regional development has a complex impact on the economic and environmental contours of the sector. The study uses a structured Likert scale questionnaire to measure environmental attitudes and practices within the sector. Data from companies were analysed using SPSS, revealing urban-rural differences in environmental commitment. Hierarchical roles within firms further delineate divergent perceptions of environmental action. The findings suggest an educational gap on environmental issues within the sector, coupled with a recognition of the urgency of more profound environmental action. The data also reflect scepticism about the current effectiveness of recycling and waste management, with varying perceptions of environmental threats. The research argues for stratified, context-specific sustainability interventions that take into account the diverse environmental perceptions of the sector and the specific socio-economic realities of Romanian localities.

Robust adaptive analysis of dynamic responses of wave energy converters

PurposeThe purpose of this paper is to exploit a new and robust method to forecast the long-term extreme dynamic responses for wave energy converters (WECs).Design/methodology/approachA new adaptive binned kernel density estimation (KDE) methodology is first proposed in this paper.FindingsBy examining the calculation results the authors has found that in the tail region the proposed new adaptive binned KDE distribution curve becomes very smooth and fits quite well with the histogram of the measured ocean wave dataset at the National Data Buoy Center (NDBC) station 46,059. Carefully studying the calculation results also reveals that the 50-year extreme power-take-off heaving force value forecasted based on the environmental contour derived using the new method is 3572600N, which is much larger than the value 2709100N forecasted via the Rosenblatt-inverse second-order reliability method (ISORM) contour method.Research limitations/implicationsThe proposed method overcomes the disadvantages of all the existing nonparametric and parametric methods for predicting the tail region probability density values of the sea state parameters.Originality/valueIt is concluded that the proposed new adaptive binned KDE method is robust and can forecast well the 50-year extreme dynamic responses for WECs.

Methodology of load effect analysis and ultimate limit state design of semi-submersible hulls of floating wind turbines: With a focus on floater column design

A main challenge in the design of hull structures of floating wind turbines (FWTs) is to properly estimate the load effects and resistance to perform the safety design check. While great efforts have been devoted to the load effects in terms of global motions, there is a lack of effective methods to calculate internal loads and lateral pressures of hulls in a fully coupled aero-hydro-servo-elastic environment, which should serve as the basis for the assessment of load effects in hulls. Moreover, very limited knowledge and experience exist in the current guidelines and research publications to deal with the detailed design of hull structures of FWTs. This study outlines an effective methodology and procedure to determine load effects for structural design of semi-submersible hulls, and demonstrates their application in a case study of column design based on the ultimate limit state (ULS) criteria. First, a novel multi-body floater model is established in a fully coupled FWT numerical system, which is capable of calculating floater internal loads. Second, the environmental contour approach is employed to initially choose load cases for ULS design, based on important wind speed conditions and criterial wave periods. Next, a screening of the critical load cases is made based on Von Mises stress analysis of columns considering global loads. Then, lateral pressure on columns is calculated, and a detailed design check is made based on combined global loads and lateral pressure as well as relevant safety factors for loads and resistance. Furthermore, the relative influence of global loads and lateral pressure on ULS performance of columns is investigated, which serves as the basis to reset the critical load cases for ULS design check. Subsequently, sensitivity analysis of ULS performance with respect to column design parameters, extreme value estimation, and shell buckling design checks, are performed to determine the plate thickness and ring stiffener distances of central and outer columns. Finally, optimized ring stiffener dimensions are estimated for different design cases based on panel buckling design criteria, and detailed design parameters for the central and outer columns are obtained. The methodology and procedure established and applied in a case study in this work, contribute to improving engineering practice and establishing improved design standards.