Marginal and total exceedance probabilities of environmental contours

This is the final version. Available on open access from Elsevier via the DOI in this recordData availability: The analysis of the examples presented in Section 5 can be reproduced by running the MATLAB files Example1and2.m and Example3.m that are available at the GitHub repository https://github.com/ahaselsteiner/2020-note-on-contours. Matlab implementations of the IFORM, ISORM, DS and HD methods are available in the software package compute-hdc that is available at https://github.com/ahaselsteiner/compute-hdc.Various methods have been proposed for defining an environmental contour, based on different concepts of exceedance probability. In the inverse first-order reliability method (IFORM) and the direct sampling (DS) method, contours are defined in terms of exceedances within a region bounded by a hyperplane in either standard normal space or the original parameter space, corresponding to marginal exceedance probabilities under rotations of the coordinate system. In contrast, the more recent inverse second-order reliability method (ISORM) and highest density (HD) contours are defined in terms of an isodensity contour of the joint density function in either standard normal space or the original parameter space, where an exceedance is defined to be anywhere outside the contour. Contours defined in terms of the total probability outside the contour are significantly more conservative than contours defined in terms of marginal exceedance probabilities. In this work we study the relationship between the marginal exceedance probability of the maximum value of each variable along an environmental contour and the total probability outside the contour. The marginal exceedance probability of the contour maximum can be orders of magnitude lower than the total exceedance probability of the contour, with the differences increasing with the number of variables. For example, a 50-year ISORM contour for two variables at 3-hour time steps, passes through points with marginal return periods of 635 years, and the marginal return periods increase to 10,950 years for contours of four variables. It is shown that the ratios of marginal to total exceedance probabilities for DS contours are similar to those for IFORM contours. However, the marginal exceedance probabilities of the maximum values of each variable along an HD contour are not in fixed relation to the contour exceedance probability, but depend on the shape of the joint density function. Examples are presented to illustrate the impact of the choice of contour on simple structural reliability problems for cases where the use of contours defined in terms of either marginal or total exceedance probabilities may be appropriate. The examples highlight that to choose an appropriate contour method, some understanding about the shape of a structure’s failure surface is required.Engineering and Physical Sciences Research Council (EPSRC)European UnionEuropean Regional Development Fund (ERDF

A second benchmarking exercise on estimating extreme environmental conditions: methodology and baseline results

This is the author accepted manuscript. The final version is available from ASME via the DOI in this recordEstimating extreme environmental conditions remains a key challenge in the design of offshore structures. This paper describes an exercise for benchmarking methods for extreme environmental conditions, which follows on from an initial benchmarking exercise introduced at OMAE 2019. In this second exercise, we address the problem of estimating extreme metocean conditions in a variable and changing climate. The study makes use of several very long datasets from a global climate model, including a 165-year historical run, a 700-year pre-industrial control run, which represents a quasi-steady state climate, and several runs under various future emissions scenarios. The availability of the long datasets allows for an in-depth analysis of the uncertainties in the estimated extreme conditions and an attribution of the relative importance of uncertainties resulting from modelling choices, natural climate variability, and potential future changes to the climate. This paper outlines the methodology for the second collaborative benchmarking exercise as well as presenting baseline results for the selected datasets.Engineering and Physical Sciences Research Council (EPSRC)UT AustinUS Department of Energ

Reducing conservatism in highest density environmental contours

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.The analysis of the example presented in section 3 can be reproduced by running the MATLAB file Example1.m that is available at the GitHub repository https://github.com/ahaselsteiner/2020-paper-contour-conservatism.Environmental contours are often used to define design loads acting on a marine structure. An environmental contour describes joint extremes of variables such as wave height, wave period and wind speed that are exceeded with a target return period. These extreme environmental conditions should lead to a structural response with a similar return period. Environmental contours can be defined based on different probabilistic definitions, one of them being that a contour surrounds a so-called highest density region. Highest density contours are a conservative concept that implies that any structure that is designed based on it will have an extreme response that has a return period that is higher than the contour’s return period (when short-term variability is accounted for). For some structures, however, the design loads are overly conservative because in the contour construction phase also environmental conditions, which will clearly not lead to an extreme response, are counted as exceedance. Here, we show how this over-conservatism can be avoided by predefining a region in the variable space that will not lead to extreme loads. We give an example where we define such “mild regions” for sea state contours. By assuming a structural response, we explore the effect of mild regions on the estimated extreme response. In the presented example, a normal highest density contour leads to a design response that is 13% too conservative, while a contour that is adjusted using a reasonable mild region can reduce conservatism to 7%.Engineering and Physical Sciences Research Council (EPSRC

Long-term extreme response of an offshore turbine: How accurate are contour-based estimates?

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordData availability: The artificial time series and the results of the multiphysics simulation are available as a Zenodo repository at https://doi.org/10.5281/zenodo.5013306. The scripts that were used in the analysis of this study are available as a GitHub repository at https://github.com/ahaselsteiner/2021-extreme-response.According to design standards, offshore wind turbines need to withstand environmental loads with a return period of 50 years. This work compares the extreme response along the 50-year environmental contour with the true 50-year wind turbine response. It was found that the environmental contour method that is currently described in the IEC design standard for offshore wind turbines can strongly under-predict the 50-year return value of response variables whose annual maxima typically occur during power production. The bias in the contour-based estimate of the 50-year response can be attributed to three sources: (1) the method used to construct the contour; (2) neglecting serial correlation in environmental conditions; and (3) neglecting the short-term variability in the response. In our analysis the 50-year maximum mudline overturning moment was underestimated by 4–8% by the contour-based approach that is currently recommended, whereas the bending moment at 10 m water depth was underestimated by 25–28%. This underestimation was mainly due to ignoring the short-term variability in the response. The bias associated with contour construction, an effect much discussed in recent publications, was of much smaller magnitude.Engineering and Physical Sciences Research Council (EPSRC

Sensing in the Urban Technological Deserts-A Position Paper for Smart Cities in Least Developed Countries

Technological progress in recent years have allowed to produce sensors, on macroscopic and microscopic scales, that are now essential to ubiquitous computing. This paradigm has made the concept of smart cities a reality that is now in synchrony with the needs and requirements for living in this era. Whether it concerns commuters in public transportations or users of existential services such as hospitals, the implementation of smart cities is equally important in developed countries than in the least developed countries. Unfortunately, in the latter, sensors and the associated technologies are not readily available to implement smart cities. It is therefore necessary to identify surrogate ways of sensing the ambiant environment. In this position paper, we discuss the situations in least developed countries and the obstacles to common implementations of smart cities. We also provide a preliminary enumeration of how mobile-phones with SMS-based services and the cultural model can be leveraged to build smart cities in such urban technological deserts