Extreme conditions modeling

2022

1. On limiting the influence of serial correlation in metocean data for prediction of extreme return levels and environmental contours

   Ryan G. Coe, Lance Manuel, and Andreas F. Haselsteiner

   Ocean Engineering, Dec 2022

   Abs DOI Bib HTML

   Metocean conditions change slowly, over the course of hours, sometimes even days, as storms develop and swells travel across the globe. Thus, measurements of these conditions are often serially correlated. However, many commonly employed methods for predicting metocean conditions for engineering design analyses are built upon an assumption of statistical independence of the data (e.g., hourly significant wave heights). In this brief study, we present an assessment of the serial (temporal) dependence in a selected metocean dataset. A method for processing a dataset that identifies and groups data sequences as “storm” events, and thus reduces serial dependence, is proposed and tested for estimating extreme metocean return levels. The results of this study show that the proposed procedure does indeed limit dependence and that environmental contours produced using this storm grouping procedure are reasonable based on the original dataset and when compared with associated alternative contours that ignore temporal dependence.

   @article{Coe:2022ab,
     author = {Coe, Ryan G. and Manuel, Lance and Haselsteiner, Andreas F.},
     bibtex_show = true,
     date-added = {2021-03-16 09:08:24 -0600},
     date-modified = {2025-06-25 12:01:07 -0600},
     doi = {10.1016/j.oceaneng.2022.113032},
     issn = {0029-8018},
     journal = {Ocean Engineering},
     keywords = {Environmental contour, Metocean extremes, Joint distribution, Serial correlation, Storms},
     month = dec,
     pages = {113032},
     title = {On limiting the influence of serial correlation in metocean data for prediction of extreme return levels and environmental contours},
     url = {https://www.sciencedirect.com/science/article/pii/S0029801822023150},
     volume = {266},
     year = {2022},
     bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0029801822023150},
     bdsk-url-2 = {https://doi.org/10.1016/j.oceaneng.2022.113032}
   }

2021

1. A benchmarking exercise for environmental contours

   Andreas F. Haselsteiner, Ryan G. Coe, Lance Manuel, Wei Chai, Bernt Leira, Guilherme Clarindo, C. Guedes Soares,  Hannesdóttir, Nikolay Dimitrov, Aljoscha Sander, Jan-Hendrik Ohlendorf, Klaus-Dieter Thoben, Guillaume Hauteclocque, Ed Mackay, Philip Jonathan, Chi Qiao, Andrew Myers, Anna Rode, Arndt Hildebrandt, Boso Schmidt, Erik Vanem, and Arne Bang Huseby

   Ocean Engineering, Dec 2021

   Abs DOI Bib HTML

   Environmental contours are used to simplify the process of design response analysis. A wide variety of contour methods exist; however, there have been a very limited number of comparisons of these methods to date. This paper is the output of an open benchmarking exercise, in which contributors developed contours based on their preferred methods and submitted them for a blind comparison study. The exercise had two components—one, focusing on the robustness of contour methods across different offshore sites and, the other, focusing on characterizing sampling uncertainty. Nine teams of researchers contributed to the benchmark. The analysis of the submitted contours highlighted significant differences between contours derived via different methods. For example, the highest wave height value along a contour varied by as much as a factor of two between some submissions while the number of metocean data points or observations that fell outside a contour deviated by an order of magnitude between the contributions (even for contours with a return period shorter than the duration of the record). These differences arose from both different joint distribution models and different contour construction methods, however, variability from joint distribution models appeared to be higher than variability from contour construction methods.

   @article{Haselsteiner:2021ab,
     author = {Haselsteiner, Andreas F. and Coe, Ryan G. and Manuel, Lance and Chai, Wei and Leira, Bernt and Clarindo, Guilherme and {Guedes Soares}, C. and {\'A}sta Hannesd{\'o}ttir and Dimitrov, Nikolay and Sander, Aljoscha and Ohlendorf, Jan-Hendrik and Thoben, Klaus-Dieter and de Hauteclocque, Guillaume and Mackay, Ed and Jonathan, Philip and Qiao, Chi and Myers, Andrew and Rode, Anna and Hildebrandt, Arndt and Schmidt, Boso and Vanem, Erik and Huseby, Arne Bang},
     bibtex_show = true,
     date-added = {2020-10-15 13:00:54 -0600},
     date-modified = {2025-06-25 12:01:07 -0600},
     doi = {10.1016/j.oceaneng.2021.109504},
     issn = {0029-8018},
     journal = {Ocean Engineering},
     keywords = {Environmental contour, Metocean extremes, Joint distribution, Extreme response, Structural reliability},
     pages = {109504},
     title = {A benchmarking exercise for environmental contours},
     url = {https://www.sciencedirect.com/science/article/pii/S0029801821009033},
     volume = {236},
     year = {2021},
     bdsk-url-1 = {https://github.com/ec-benchmark-organizers/ec-benchmark/blob/master/publications/2021-01-19_EC_Benchmark_Joint_Paper_WithFrontPages.pdf},
     bdsk-url-2 = {https://tinyurl.com/2ubs935k}
   }

2. Development of a comparison framework for evaluating environmental contours of extreme sea states

   Aubrey Eckert, Nevin Martin, Ryan G. Coe, Bibiana Seng, Zacharia Stuart, and Zachary Morrell

   Journal of Marine Science and Engineering, Dec 2021

   Abs DOI Bib HTML

   Environmental contours of extreme sea states are often utilized for the purposes of reliability-based offshore design. Many methods have been proposed to estimate environmental contours of extreme sea states, including, but not limited to, the traditional inverse first-order reliability method (I-FORM) and subsequent modifications, copula methods, and Monte Carlo methods. These methods differ in terms of both the methodology selected for defining the joint distribution of sea state parameters and in the method used to construct the environmental contour from the joint distribution. It is often difficult to compare the results of proposed methods to determine which method should be used for a particular application or geographical region. The comparison of the predictions from various contour methods at a single site and across many sites is important to making environmental contours of extreme sea states useful in practice. The goal of this paper is to develop a comparison framework for evaluating methods for developing environmental contours of extreme sea states. This paper develops generalized metrics for comparing the performance of contour methods to one another across a collection of study sites, and applies these metrics and methods to develop conclusions about trends in the wave resource across geographic locations, as demonstrated for a pilot dataset. These proposed metrics and methods are intended to judge the environmental contours themselves relative to other contour methods, and are thus agnostic to a specific device, structure, or field of application. The metrics developed and applied in this paper include measures of predictive accuracy, physical validity, and aggregated temporal performance that can be used to both assess contour methods and provide recommendations for the use of certain methods in various geographical regions. The application and aggregation of the metrics proposed in this paper outline a comparison framework for environmental contour methods that can be applied to support design analysis workflows for offshore structures. This comparison framework could be extended in future work to include additional metrics of interest, potentially including those to address issues pertinent to a specific application area or analysis discipline, such as metrics related to structural response across contour methods or additional physics-based metrics based on wave dynamics.

   @article{Eckert:2021aa,
     author = {Eckert, Aubrey and Martin, Nevin and Coe, Ryan G. and Seng, Bibiana and Stuart, Zacharia and Morrell, Zachary},
     bibtex_show = true,
     date-added = {2020-10-15 12:58:26 -0600},
     date-modified = {2025-06-25 12:01:07 -0600},
     doi = {10.3390/jmse9010016},
     journal = {Journal of Marine Science and Engineering},
     number = {1},
     pages = {16},
     title = {Development of a comparison framework for evaluating environmental contours of extreme sea states},
     url = {https://doi.org/10.3390/jmse9010016},
     volume = {9},
     year = {2021},
     bdsk-url-1 = {https://doi.org/10.3390/jmse9010016}
   }

2019

1. A Wave Energy Converter Design Load Case Study

   Jennifer Van Rij, Yi-Hsiang Yu, Yi Guo, and Ryan G. Coe

   Journal of Marine Science and Engineering, Jul 2019

   Abs DOI Bib HTML

   This article presents an example by which design loads for a wave energy converter (WEC) might be estimated through the various stages of the WEC design process. Unlike previous studies, this study considers structural loads, for which, an accurate assessment is crucial to the optimization and survival of a WEC. Three levels of computational fidelity are considered. The first set of design load approximations are made using a potential flow frequency-domain boundary-element method with generalized body modes. The second set of design load approximations are made using a modified version of the linear-based time-domain code WEC-Sim. The final set of design load simulations are realized using computational fluid dynamics coupled with finite element analysis to evaluate the WEC’s loads in response to both regular and focused waves. This study demonstrates an efficient framework for evaluating loads through each of the design stages. In comparison with experimental and high-fidelity simulation results, the linear-based methods can roughly approximate the design loads and the sea states at which they occur. The high-fidelity simulations for regular wave responses correspond well with experimental data and appear to provide reliable design load data. The high-fidelity simulations of focused waves, however, result in highly nonlinear interactions that are not predicted by the linear-based most-likely extreme response design load method.

   @article{Rij:2019aa,
     author = {Rij, Jennifer Van and Yu, Yi-Hsiang and Guo, Yi and Coe, Ryan G.},
     bibtex_show = true,
     date-added = {2020-10-07 12:58:13 -0600},
     date-modified = {2025-06-25 12:01:07 -0600},
     doi = {10.3390/jmse7080250},
     issn = {2077-1312},
     journal = {Journal of Marine Science and Engineering},
     month = jul,
     number = {8},
     pages = {250},
     publisher = {MDPI AG},
     title = {A Wave Energy Converter Design Load Case Study},
     url = {http://dx.doi.org/10.3390/jmse7080250},
     volume = {7},
     year = {2019},
     bdsk-url-1 = {http://dx.doi.org/10.3390/jmse7080250}
   }

2. CFD design-load analysis of a two-body wave energy converter

   Ryan G. Coe, Brian J. Rosenberg, Eliot W. Quon, Chris C. Chartrand, Yi-Hsiang Yu, Jennifer Van Rij, and Tim R. Mundon

   Journal of Ocean Engineering and Marine Energy, Jul 2019

   Abs DOI Bib HTML

   Wave energy converters (WECs) must survive in a wide variety of conditions while minimizing structural costs, so as to deliver power at cost-competitive rates. Although engineering design and analysis tools used for other ocean systems, such as offshore structures and ships, can be applied, the unique nature and limited historical experience of WEC design necessitates assessment of the effectiveness of these methods for this specific application. This paper details a study to predict extreme loading in a two-body WEC using a combination of mid-fidelity and high-fidelity numerical modeling tools. Here, the mid-fidelity approach is a time-domain model based on linearized potential flow hydrodynamics and the high-fidelity modeling tool is an unsteady Reynolds-averaged Navier–Stokes model. In both models, the dynamics of the WEC power take-off and mooring system have been included. For the high-fidelity model, two design wave approaches (an equivalent regular wave and a focused wave) are used to estimate the worst case wave forcing within a realistic irregular sea state.These simplified design wave approaches aim to capture the extreme response of the WEC within a feasible amount of computational effort. When compared to the mid-fidelity model results in a long-duration irregular sea, the short-duration design waves simulated in CFD produce upper percentile load responses, hinting at the suitability of these two approaches.

   @article{Coe:2019aa,
     author = {Coe, Ryan G. and Rosenberg, Brian J. and Quon, Eliot W. and Chartrand, Chris C. and Yu, Yi-Hsiang and Van Rij, Jennifer and Mundon, Tim R.},
     bibtex_show = true,
     da = {2019/05/01},
     date-added = {2020-10-07 12:52:26 -0600},
     date-modified = {2025-06-25 12:01:07 -0600},
     doi = {10.1007/s40722-019-00129-8},
     id = {Coe2019},
     isbn = {2198-6452},
     journal = {Journal of Ocean Engineering and Marine Energy},
     number = {2},
     pages = {99--117},
     title = {{CFD} design-load analysis of a two-body wave energy converter},
     ty = {JOUR},
     url = {https://doi.org/10.1007/s40722-019-00129-8},
     volume = {5},
     year = {2019},
     bdsk-url-1 = {https://doi.org/10.1007/s40722-019-00129-8}
   }

3. On the Development of an Efficient Surrogate Model for Predicting Long-Term Extreme Loads on a Wave Energy Converter

   Phong T. T. Nguyen, Lance Manuel, and Ryan G. Coe

   Journal of Offshore Mechanics and Arctic Engineering, Mar 2019

   061103

   Abs DOI Bib HTML

   Accurate prediction of long-term extreme loads is essential for the design of wave energy converters (WECs), but it is also computationally demanding due to the low probabilities associated with their occurrence. Although a full long-term probabilistic analysis using integration over all sea states or Monte Carlo simulation (MCS) may be used, these methods can be prohibitively expensive when individual response simulations are complex and time-consuming. The application of polynomial chaos expansion (PCE) schemes to allow the propagation of uncertainty from the environment through the stochastic sea surface elevation process and ultimately to WEC extreme load response prediction is the focus in this study. A novel approach that recognizes the role of long-term ocean climate uncertainty (in sea state variables such as significant wave height and spectral peak period) as well as short-term response uncertainty arising from the unique random phasing in irregular wave trains is presented and applied to a single-body point-absorber WEC device model. Stochastic simulation results in time series realizations of various response processes for the case-study WEC. We employ environmental data from a possible deployment site in Northern California (NDBC 46022) to assess long-term loads. MCS computations are also performed and represent the “truth” system against which the efficiency and accuracy of the PCE surrogate model are assessed. Results suggest that the PCE approach requires significantly less effort to obtain comparable estimates to MCS.

   @article{Nguyen:2019aa,
     author = {Nguyen, Phong T. T. and Manuel, Lance and Coe, Ryan G.},
     bibtex_show = true,
     date-added = {2020-10-07 12:53:41 -0600},
     date-modified = {2025-06-25 12:01:07 -0600},
     doi = {10.1115/1.4042944},
     eprint = {https://asmedigitalcollection.asme.org/offshoremechanics/article-pdf/141/6/061103/6403607/omae\_141\_6\_061103.pdf},
     issn = {0892-7219},
     journal = {Journal of Offshore Mechanics and Arctic Engineering},
     month = mar,
     note = {061103},
     number = {6},
     title = {{On the Development of an Efficient Surrogate Model for Predicting Long-Term Extreme Loads on a Wave Energy Converter}},
     url = {https://doi.org/10.1115/1.4042944},
     volume = {141},
     year = {2019},
     bdsk-url-1 = {https://doi.org/10.1115/1.4042944}
   }

2018

1. Full long-term design response analysis of a wave energy converter

   Ryan G. Coe, Carlos Michelen, Aubrey Eckert-Gallup, and Cédric Sallaberry

   Renewable Energy, Mar 2018

   Abs DOI Bib HTML

   Efficient design of wave energy converters requires an accurate understanding of expected loads and responses during the deployment lifetime of a device. A study has been conducted to better understand best-practices for prediction of design responses in a wave energy converter. A case-study was performed in which a simplified wave energy converter was analyzed to predict several important device design responses. The application and performance of a full long-term analysis, in which numerical simulations were used to predict the device response for a large number of distinct sea states, was studied. Environmental characterization and selection of sea states for this analysis at the intended deployment site were performed using principle-components analysis. The full long-term analysis applied here was shown to be stable when implemented with a relatively low number of sea states and convergent with an increasing number of sea states. As the number of sea states utilized in the analysis was increased, predicted response levels did not change appreciably. However, uncertainty in the response levels was reduced as more sea states were utilized.

   @article{Coe:2018aa,
     author = {Coe, Ryan G. and Michelen, Carlos and Eckert-Gallup, Aubrey and Sallaberry, C{\'e}dric},
     bibtex_show = true,
     date-added = {2020-10-07 12:49:13 -0600},
     date-modified = {2025-06-25 12:01:07 -0600},
     doi = {10.1016/j.renene.2017.09.056},
     issn = {0960-1481},
     journal = {Renewable Energy},
     keywords = {Wave energy, Extreme conditions, Design load, Long-term response},
     pages = {356 - 366},
     title = {Full long-term design response analysis of a wave energy converter},
     url = {http://www.sciencedirect.com/science/article/pii/S0960148117309187},
     volume = {116},
     year = {2018},
     bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0960148117309187},
     bdsk-url-2 = {https://doi.org/10.1016/j.renene.2017.09.056}
   }

2. Alternative approaches to develop environmental contours from metocean data

   Lance Manuel, Phong T. T. Nguyen, Jarred Canning, Ryan G. Coe, Aubrey C. Eckert-Gallup, and Nevin Martin

   Journal of Ocean Engineering and Marine Energy, Mar 2018

   Abs DOI Bib HTML

   It is necessary to evaluate site-specific extreme environmental conditions in the design of wave energy converters (WECs) as well as other offshore structures. As WECs are generally resonance-driven devices, critical metocean parameters associated with a target return period of interest (e.g., 50 years) must generally be established using combinations, say, of significant wave height and spectral peak period, as opposed to identifying single-valued wave height levels alone. We present several methods for developing so-called “environmental contours”for any target return period. The environmental contour (EC) method has been widely acknowledged as an efficient way to derive design loads for offshore oil and gas platforms and for land-based as well as offshore wind turbines. The use of this method for WECs is also being considered. A challenge associated with its use relates to the need to accurately characterize the uncertainties in metocean variables that define the “environment”. The joint occurrence frequency of values of two or more random variables needs to be defined formally. There are many ways this can be done—the most thorough and complete of these is to define a multivariate joint probability distribution of the random variables. However, challenges arise when data from the site where the WEC device is to be deployed are limited, making it difficult to estimate the joint probability distribution. A more easily estimated set of inputs consists of marginal distribution functions for each random variable and pairwise correlation coefficients. Pearson correlation coefficients convey information that rely on up to the second moment of each variable and on the expected value of the product of the paired variables. Kendall’s rank correlation coefficients, on the other hand, convey information on similarity in the “rank”of two variables and are useful especially in dealing with extreme values. The EC method is easily used with Rosenblatt transformations when joint distributions are available. In cases where Pearson’s correlation coefficients have been estimated along with marginal distributions, a Nataf transformation can be used, and if Kendall’s rank coefficients have been estimated and are available, a copula-based transformation can be used. We demonstrate the derivation of 50-year sea state parameters using the EC method with all three approaches where we consider data from the National Data Buoy Center Station 46022 (which can be considered the site for potential WEC deployment). A comparison of the derived environmental contours using the three approaches is presented. The focus of this study is on investigating differences between the derived environmental contours and, thus, on associated sea states arising from the different dependence structure assumptions for the metocean random variables. Both parametric and non-parametric approaches are used to define the probability distributions.

   @article{Manuel:2018aa,
     author = {Manuel, Lance and Nguyen, Phong T. T. and Canning, Jarred and Coe, Ryan G. and Eckert-Gallup, Aubrey C. and Martin, Nevin},
     bibtex_show = true,
     da = {2018/11/01},
     date-added = {2020-10-07 12:44:32 -0600},
     date-modified = {2020-10-07 12:44:32 -0600},
     doi = {10.1007/s40722-018-0123-0},
     id = {Manuel2018},
     isbn = {2198-6452},
     journal = {Journal of Ocean Engineering and Marine Energy},
     number = {4},
     pages = {293--310},
     title = {Alternative approaches to develop environmental contours from metocean data},
     ty = {JOUR},
     url = {https://doi.org/10.1007/s40722-018-0123-0},
     volume = {4},
     year = {2018},
     bdsk-url-1 = {https://doi.org/10.1007/s40722-018-0123-0}
   }

3. The Effect of Environmental Contour Selection on Expected Wave Energy Converter Response

   Samuel J. Edwards, and Ryan G. Coe

   Journal of Offshore Mechanics and Arctic Engineering, Aug 2018

   011901

   Abs DOI Bib HTML

   A wave energy converter must be designed to both maximize power production and to ensure survivability, which requires the prediction of future sea states. It follows that precision in the prediction of those sea states should be important in determining a final WEC design. One common method used to estimate extreme conditions employs environmental contours of extreme conditions. This report compares five environmental contour methods and their repercussions on the response analysis of Reference Model 3 (RM3). The most extreme power take-off (PTO) force is predicted for the RM3 via each contour and compared to identify the potential difference in WEC response due to contour selection. The analysis provides insight into the relative performance of each of the contour methods and demonstrates the importance of an environmental contour in predicting extreme response. Ideally, over-predictions should be avoided, as they can add to device cost. At the same time, any “exceedances,” that is to say sea states that exceed predictions of the contour, should be avoided so that the device does not fail. For the extreme PTO force response studied here, relatively little sensitivity to the contour method is shown due to the collocation of the device’s resonance with a region of agreement between the contours. However, looking at the level of observed exceedances for each contour may still give a higher level of confidence to some methods.

   @article{Edwards:2018aa,
     author = {Edwards, Samuel J. and Coe, Ryan G.},
     bibtex_show = true,
     date-added = {2020-10-07 12:57:24 -0600},
     date-modified = {2025-06-25 12:01:07 -0600},
     doi = {10.1115/1.4040834},
     eprint = {https://asmedigitalcollection.asme.org/offshoremechanics/article-pdf/141/1/011901/6375365/omae\_141\_01\_011901.pdf},
     issn = {0892-7219},
     journal = {Journal of Offshore Mechanics and Arctic Engineering},
     month = aug,
     note = {011901},
     number = {1},
     title = {{The Effect of Environmental Contour Selection on Expected Wave Energy Converter Response}},
     url = {https://doi.org/10.1115/1.4040834},
     volume = {141},
     year = {2018},
     bdsk-url-1 = {https://doi.org/10.1115/1.4040834}
   }

2017

1. A Survey of WEC Reliability, Survival and Design Practices

   Ryan G. Coe, Yi-Hsiang Yu, and Jennifer Van Rij

   Energies, Dec 2017

   Abs DOI Bib HTML

   A wave energy converter must be designed to survive and function efficiently, often in highly energetic ocean environments. This represents a challenging engineering problem, comprising systematic failure mode analysis, environmental characterization, modeling, experimental testing, fatigue and extreme response analysis. While, when compared with other ocean systems such as ships and offshore platforms, there is relatively little experience in wave energy converter design, a great deal of recent work has been done within these various areas. This paper summarizes the general stages and workflow for wave energy converter design, relying on supporting articles to provide insight. By surveying published work on wave energy converter survival and design response analyses, this paper seeks to provide the reader with an understanding of the different components of this process and the range of methodologies that can be brought to bear. In this way, the reader is provided with a large set of tools to perform design response analyses on wave energy converters.

   @article{Coe:2017ac,
     author = {Coe, Ryan G. and Yu, Yi-Hsiang and Rij, Jennifer Van},
     bibtex_show = true,
     date-added = {2020-10-07 14:18:44 -0600},
     date-modified = {2025-06-25 12:01:07 -0600},
     doi = {10.3390/en11010004},
     issn = {1996-1073},
     journal = {Energies},
     month = dec,
     number = {1},
     pages = {4},
     publisher = {MDPI AG},
     title = {A Survey of {WEC} Reliability, Survival and Design Practices},
     url = {http://dx.doi.org/10.3390/en11010004},
     volume = {11},
     year = {2017},
     bdsk-url-1 = {http://dx.doi.org/10.3390/en11010004}
   }