Comparing different contour methods with response-based methods for extreme ship response analysis

Environmental contours are often applied in probabilistic structural reliability analysis to identify extreme environmental conditions that may give rise to extreme loads and responses. They facilitate approximate long term analysis of critical structural responses in situations where computationally heavy and time-consuming response calculations makes full long-term analysis infeasible. The environmental contour method identifies extreme environmental conditions that are expected to give rise to extreme structural response of marine structures. The extreme responses can then be estimated by performing response calculations for environmental conditions along the contours. Response-based analysis is an alternative, where extreme value analysis is performed on the actual response rather than on the environmental conditions. For complex structures, this is often not practical due to computationally heavy response calculations. However, by establishing statistical emulators of the response, using machine learning techniques, one may obtain long time-series of the structural response and use this to estimate extreme responses. In this paper, various contour methods will be compared to response-based estimation of extreme vertical bending moment for a tanker. A response emulator based on Gaussian processes regression with adaptive sampling has been established based on response calculations from a hydrodynamic model. Long time-series of sea-state parameters such as significant wave height and wave period are used to construct N-year environmental contours and the extreme N-year response is estimated from numerical calculations for identified sea states. At the same time, the response emulator is applied on the time series to provide long time-series of structural response, in this case vertical bending moment of a tanker. Extreme value analysis is then performed directly on the responses to estimate the N-year extreme response. The results from either method will then be compared, and it is possible to evaluate the accuracy of the environmental contour method in estimating the response. Moreover, different contour methods will be compared

On environmental contours for marine and coastal design

Environmental contours are used in structural reliability analysis of marine and coastal structures as an approximate means to locate the boundary of the distribution of environmental variables, and to identify environmental conditions giving rise to extreme structural loads and responses. There are different approaches to estimating environmental contours, some directly linked to methods of structural reliability. Each contouring approach has its pros and cons. Although procedures for applying contours in design have been reported in articles and standards, there is still ambiguity about detail, and the practitioner has considerable flexibility in applying contours. It is not always clear how to estimate environmental contours well. Over four years, DNV-GL, Shell, the University of Oslo and HR Walling-ford worked together to review current practice regarding the use of design contours. In this paper, we present a summary of our findings. We overview the motivations for different approaches to contours, and their resulting characteristics. Using different marine applications, we also explore the various sources of uncertainty present, their impact on contour estimates and the estimation of extreme environmental loads and responses

The Rare Decay D^0 -> gamma gamma

We present a calculation of the rare decay mode D^0 -> gamma gamma, in which the long distance contributions are expected to be dominant. Using the Heavy Quark Chiral Perturbation Theory Lagrangian with a strong g coupling as recently determined by CLEO from the D^* -> D pi width, we consider both the anomaly contribution which relates to the annihilation part of the weak Lagrangian and the one-loop pi, K diagrams. The loop contributions which are proportional to g and contain the a_1 Wilson coefficient are found to dominate the decay amplitude, which turns out to be mainly parity violating. The branching ratio is then calculated to be (1.0+-0.5)x10^(-8). Observation of an order of magnitude larger branching ratio could be indicative of new physics.Comment: 16 pages, 5 figures, additional reference and several remarks added, results unchange

Air and water pollution over time and industries with stochastic dominance

We employ a stochastic dominance (SD) approach to analyze the components that contribute to environmental degradation over time. The variables include countries\u2019 greenhouse gas (GHG) emissions and water pollution. Our approach is based on pair-wise SD tests. First, we study the dynamic progress of each separate variable over time, from 1990 to 2005, within 5-year horizons. Then, pair-wise SD tests are used to study the major industry contributors to the overall GHG emissions and water pollution at any given time, to uncover the industry which contributes the most to total emissions and water pollution. While CO2 emissions increased in the first order SD sense over 15 years, water pollution increased in a second-order SD sense. Electricity and heat production were the major contributors to the CO2 emissions, while the food industry gradually became the major water polluting industry over time. SD sense over 15 years, water pollution increased in a second-order SD sense. Electricity and heat production were the major contributors to the CO2 emissions, while the food industry gradually

Quantitative comparison of environmental contour approaches

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record All primary data used on this study (wave datasets, contours and response transfer functions) can be found on the benchmark github repository, available at : https://github.com/ec-benchmark-organizers/ ec-benchmarkEnvironmental contours are a pragmatic and widespread method to estimate the long-term extreme response of marine structures. Over the years, a range of approaches have been proposed. A benchmarking study was recently conducted to compare the various methods using a common set of data. The current work extends this benchmark study by providing a quantitative assessment of the contours submitted to the exercise. The estimates of long-term responses from the contours were compared against a response-based analysis (RBA) for a wide range of responses. While some contour methods agreed well with estimates from the RBA (relative errors less than 10%), most methods were found to give large errors relative to the RBA. For the 1-year responses most methods showed a large positive bias, whilst both positive and negative biases were found for the 20-year responses. The reasons for the differences between the contours and RBA were explored. It was shown that the fitted statistical models accounted for a large portion of the error in some approaches, with both positive and negative biases of the order of 50% for some contributions, depending on the response type. Whilst for other methods, the statistical model gave accurate predictions for most responses, no models were able to capture all response behaviours for all locations. Secondly, most contour methods do not account for serial correlation in the data. It is shown that this introduces a significant positive bias into long-term response estimates, especially for lower return periods. The level of error introduced by the type of contour method is dependent on the assumption made about the shape of the failure region in the contour definition. For the predominantly unimodal response types considered, contours which approximate the failure region as having a linear boundary (IFORM and direct sampling contours), introduce relatively little error for most responses. However, for some responses, the direct sampling contours were found to introduce errors in the range 20-40%, depending on the variable space in which they are constructed. The ISORM and highest density contours were found to have a significant over-conservatism bias, which would be expected for the response types considered.Engineering and Physical Sciences Research Council (EPSRC

The effect of serial correlation in environmental conditions on estimates of extreme events

In offshore engineering, it is common practice to estimate long-term extremes under the assumption that environmental conditions are independent. However, many environmental variables, such as winds and waves, exhibit correlation over several days. In this work, we consider the impact that this has on estimates of return values of metocean variables, environmental contours and long-term extreme responses. It is shown that methods which neglect serial correlation over-estimate the size of extreme events at a given return period. We introduce a new definition of a sub-asymptotic extremal index, and show how this can be used to quantify the effect of neglecting serial correlation. Simple examples are presented to illustrate why neglecting serial correlation leads to positive bias. We show how the size of the bias is related to the average shape of storm events and the shape of the tail of the distribution of storm peak values, with the latter having the dominant effect. Storm peak distributions with longer tails lead to larger biases when serial correlation is neglected. In the examples presented, neglecting serial correlation resulted in relative errors of over 50% in the 25-year extreme response estimates in some cases. The examples presented show that accounting for serial correlation in estimates of environmental contours and long-term extreme responses can reduce over-conservatism and result in more efficient designs