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Prediction of Short-Term distributions of Load Extremes of Offshore Wind Turbines

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China Ocean Engineering 2016年第6期30卷 851-866页

作者：王迎光 State Key Laboratory of Ocean Engineering Shanghai Jiao Tong UniversityShanghai 200240China Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration(CISSE) Shanghai 200240China School of Naval Architecture Ocean and Civil EngineeringShanghai Jiao Tong UniversityShanghai 200240China

This paper proposes a new methodology to select an optimal threshold level to be used in the peak over threshold （POT） method for the prediction of short-term distributions of load extremes of offshore wind turbines. Such an optimal threshold level is found based on the estimation of the variance-to-mean ratio for the occurrence of peak values, which characterizes the Poisson assumption. A generalized pareto distribution is then fitted to the extracted peaks over the optimal threshold level and the distribution parameters are estimated by the method of the maximum spacing estimation. This methodology is applied to estimate the short-term distributions of load extremes of the blade bending moment and the tower base bending moment at the mudline of a monopile-supported 5MW offshore wind turbine as an example. The accuracy of the POT method using the optimal threshold level is shown to be better, in terms of the distribution fitting, than that of the POT methods using empirical threshold levels. The comparisons among the short-term extreme response values predicted by using the POT method with the optimal threshold levels and with the empirical threshold levels and by using direct simulation results further substantiate the validity of the proposed new methodology.

关键词： extreme responses monopile-supported offshore wind turbine peak over threshold method optimalthreshold level variance-to-mean ratio generalized pareto distribution maximum spacing estimation

A Newly-Discovered GPD-GEV Relationship Together with Comparing Their Models of Extreme Precipitation in Summer

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Advances in Atmospheric Sciences 2008年第3期25卷 507-516页

作者：丁裕国程炳岩江志红 National Key Laboratory of Meteorological Diseases of Jiangsu Nanjing University of Information Science and TechnologyNanjing 210044 Climate Center of Chongqing City Meteorological Bureau Chongqing 401147

It has been theoretically proven that at a high threshold an approximate expression for a quantile of GEV （generalized Extreme Values） distribution can be derived from GPD （generalized pareto distribution）. Afterwards, a quantile of extreme rainfall events in a certain return period is found using L-moment estimation and extreme rainfall events simulated by GPD and GEV, with all aspects of their results compared. Numerical simulations show that POT （Peaks Over Threshold）-based GPD is advantageous in its simple operation and subjected to practically no effect of the sample size of the primitive series, producing steady high-precision fittings in the whole field of values （including the high-end heavy tailed）. In comparison, BM （Block Maximum）-based GEV is limited, to some extent, to the probability and quantile simulation, thereby showing that GPD is an extension of GEV, the former being of greater utility and higher significance to climate research compared to the latter.

关键词： generalized pareto distribution generalized Extreme Value daily rainfall extreme precipitation rainstorm

Extreme air pollution events:Modeling and prediction

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Journal of Central South University 2012年第6期19卷 1668-1672页

作者：周松梅邓启红刘蔚巍 School of Energy Science and Engineering Central South University

In order to get prepared for the coming extreme pollution events and minimize their harmful impacts, the first and most important step is to predict their possible intensity in the future. Firstly, the generalized pareto distribution （GPD） in extreme value theory was used to fit the extreme pollution concentrations of three main pollutants： PM10, NO2 and SO：, from 2005 to 2010 in Changsha, China. Secondly, the prediction results were compared with actual data by a scatter plot. Four statistical indicators： EMA （mean absolute error）, ERMS （root mean square error）, IA （index of agreement） and R2 （coefficient of determination） were used to evaluate the goodness-of-fit as well. Thirdly, the return levels corresponding to different return periods were calculated by the fitted distributions. The fitting results show that the distribution of PM10 and SO2 belongs to exponential distribution with a short tail while that of the NOe belongs to beta distribution with a bounded tail. The scatter plot and four statistical indicators suggest that GPD agrees well with the actual data. Therefore, the fitted distribution is reliable to predict the return levels corresponding to different return periods. The predicted return levels suggest that the intensity of coming pollution events for PM10 and SO2 will be even worse in the future, which means people have to get enough preparation for them.

关键词： extreme pollution event generalized pareto distribution return level return period

Experimental Simulations of Extreme Precipitation Based on the Multi-Status Markov Chain Model

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Acta meteorologica Sinica 2010年第4期24卷 484-491页

作者：丁裕国张金玲江志红 Key Laboratory of Meteorological Disaster/Ministry of Education Nanjing University of Information Science & Technology

A multi-status Markov chain model is proposed to produce daily rainfall, and based on which extreme rainfall is simulated with the generalized pareto distribution （GPD）. The simulated daily rainfall shows high precision at most stations, especially in pluvial regions of East China. The analysis reveals that the multi- status Markov chain model excels the bi-status Markov chain model in simulating climatic features of extreme rainfall. Results from the selected six stations demonstrate excellent simulations in the following aspects： standard deviation of monthly precipitation, daily maximum precipitation, the monthly mean rainfall days, standard deviation of daily precipitation and mean daily precipitation, which are proved to be consistent with the observations. A comparative study involving 78 stations in East China also reveals good consistency in monthly mean rainfall days and mean daily maximum rainfall, except mean daily rainfall. Simulation results at the above 6 stations have shown satisfactory fitting capability of the extreme precipitation GPD method. Good analogy is also found between simulation and observation in threshold and return values. As the errors of the threshold decrease, so do the differences between the return and real values. All the above demonstrates the applicability of the Markov chain model to extreme rainfall simulations.

关键词： extreme precipitation simulation experiment Markov chain generalized pareto distribution

AN ANALYSIS OF THE WINTER EXTREME PRECIPITATION EVENTS ON THE BACKGROUND OF CLIMATE WARMING IN SOUTHERN CHINA

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Journal of Tropical Meteorology 2010年第4期16卷 325-332页

作者：智协飞张玲潘嘉璐 KLME Nanjing University of Information Science & Technology

Based on daily precipitation and monthly temperature data in southern China, the winter extreme precipitation changes in southern China have been investigated by using the Mann-Kendall test and the return values of generalized pareto distribution. The results show that a winter climate catastrophe in southern China occurred around i99I, and the intensity of winter extreme precipitation was strengthened after climate wanning. The anomalous circulation characteristics before and after the climate wanning was further analyzed by using the U.S. National Centers for Environmental Prediction/National Center for Atmospheric Research reanalysis data. It is found that the tropical winter monsoon over East Asia is negatively correlated with the precipitation in southeastern China. After climate warming the meridionality of the circulations in middle and high latitudes increases, which is favorable for the southward movement of the cold air from the north. In addition, the increase of the temperature over southern China may lead to the decrease of the differential heating between the continent and the ocean. Consequently, the tropical winter monsoon over East Asia is weakened, which is favorable for the transport of the warm and humid air to southeastem China and the formation of the anomalous convergence of the moisture flux, resulting in large precipitation over southeastern China. As a result, the interaction between the anomalous circulations in the middle and high latitudes and lower latitudes after the climate warming plays a major role in the increase of the winter precipitation intensity over southeastem China.

关键词： extreme precipitation climate warming generalized pareto distribution tropical winter monsoon over East Asia

Network Traffic Based on GARCH-M Model and Extreme Value Theory

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Transactions of Tianjin University 2005年第5期11卷 386-390页

作者：沈菲王洪礼史道济李栋 School of Sciences Tianjin University School of Mechanical Engineering Tianjin University School of Management Tianjin University

GARCH-M ( generalized autoregressive conditional heteroskedasticity in the mean) model is used to analyse the volatility clustering phenomenon in mobile communication network traffic. Normal distribution, t distribution and generalized pareto distribution assumptions are adopted re- spectively to simulate the random component in the model. The demonstration of the quantile of network traffic series indicates that common GARCH-M model can partially deal with the "fat tail" problem. However, the "fat tail" characteristic of the random component directly affects the accura- cy of the calculation. Even t distribution is based on the assumption for all the data. On the other hand, extreme value theory, which only concentrates on the tail distribution, can provide more ac- curate result for high quantiles. The best result is obtained based on the generalized pareto distribu- tion assumption for the random component in the GARCH-M model.

关键词： network traffic GARCH-M extreme value theory generalized pareto distribution

Tail risks and infectious disease: Influenza mortality in the U.S., 1900-2018

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Infectious Disease Modelling 2021年第1期6卷 1135-1143页

作者： Michele Campolieti Department of Management University of Toronto Scarborough1095 Military TrailTorontoOntarioM1C 1A4Canada

I use extreme values theory and data on influenza mortality from the *** 1900 to 2018 to estimate the tail risks of mortality.I find that the distribution for influenza mortality rates is heavy-tailed,which suggests that the tails of the mortality distribution are more informative than the events of high frequency(i.e.,years of low mortality).I also discuss the implications of my estimates for risk management and pandemic planning.

关键词： Influenza mortality rates Extremes value theory generalized pareto distribution Heavy-tails Tail risks

Peaks over Manifold (POM): A Novel Technique to Analyze Extreme Events over Surfaces

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Advances in Pure Mathematics 2022年第1期12卷 48-62页

作者： Gonzalo Perera Angel M. Segura CURE Rocha Uruguay

We present a novel method to analyze extreme events of flows over manifolds called Peaks Over Manifold (POM). Here we show that under general and realistic hypotheses, the distribution of affectation measures converges to a generalized pareto distribution (GPD). The method is applicable to floods, ice cover extent, extreme rainfall or marine heatwaves. We present an application to a synthetic data set on tide height and to real ice cover data in Antartica.

关键词： Peaks Over Thresholds (POT) generalized pareto distribution Extreme Events

Calendar Effects in AAPL Value-at-Risk

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Journal of Mathematics and System Science 2016年第6期6卷 215-233页

作者： Hong-Kun Zhang Zijing Zhang Department of Mathematics and Statistics University of Massachusetts Amherst Amherst MA 01003 USA.

This study investigates calendar anomalies： day-of-the-week effect and seasonal effect in the Value-at-Risk （VaR） analysis of stock returns for AAPL during the period of 1995 through 2015. The statistical properties are examined and a comprehensive set of diagnostic checks are made on the two decades of AAPL daily stock returns. Combing the Extreme Value Approach together with a statistical analysis, it is learnt that the lowest VaR occurs on Fridays and Mondays typically. Moreover, high Q4 and Q3 VaR are observed during the test period. These results are valuable for anyone who needs evaluation and forecasts of the risk situation in AAPL. Moreover, this methodology, which is applicable to any other stocks or portfolios, is more realistic and comprehensive than the standard normal distribution based VaR model that is commonly used.

关键词： Risk Measures Value-at-Risk Extreme value theory generalized pareto distribution Day-of-the-week effect Seasonaleffect