Automatic determination method of optimal threshold based on the bootstrapping technology

In order to predict the extreme load of the mechanical components during the entire life,an automatic method based on the bootstrapping technology(BT)is proposed to determine the most suitable threshold.Based on all the turning points of the load history and a series of thresholds estimated in advance,the generalized Pareto distribution is established to fit the exceedances.The corresponding distribution parameters are estimated with the maximum likelihood method.Then,BT is employed to calculate the mean squared error(MSE)of each estimated threshold based on the exceedances and the specific distribution parameters.Finally,the threshold with the smallest MSE will be the optimal one.Compared to the kurtosis method and the mean excess function method,the average deviation of the probability density function of exceedances determined by BT reduces by 38.52%and 29.25%,respectively.Moreover,the quantile-quantile plot of the exceedances determined by BT is closer to a straight line.The results suggest the improvement of the modeling flexibility and the determined threshold precision.If the exceedances are insufficient,BT will enlarge their amount by resampling to solve the instability problem of the original distribution parameters.

Non-conventional modeling of extreme significant wave height through random sets

The analysis and design of offshore structures necessitates the consideration of wave loads. Realistic modeling of wave loads is particularly important to ensure reliable performance of these structures. Among the available methods for the modeling of the extreme significant wave height on a statistical basis, the peak over threshold method has attracted most attention. This method employs Poisson process to character- ize time-varying properties in the parameters of an extreme value distribution. In this paper, the peak over threshold method is reviewed and extended to account for subjectivity in the modeling. The freedom in selecting the threshold and the time span to separate extremes from the original time series data is incorpo- rated as imprecision in the model. This leads to an extension from random variables to random sets in the probabilistic model for the extreme significant wave height. The extended model is also applied to different periods of the sampled data to evaluate the significance of the climatic conditions on the uncertainties of the parameters.

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

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.

Characterizing the Seasonal and Directional Varying Properties in A Marine Environment

With noticing an increasing number of failure events for offshore structures in the present days, it is now realized that modeling the marine environment especially for exceptional environmental conditions is quite important. It is recognized that a possible improvement in the traditional modeling of environmental characteristics, which are the basis for the load models for structural analysis and design, may be needed. In this paper, the seasonal and directional varying properties in modeling the ocean parameter, the wave height, are studied. The peak over threshold（POT） method is selected to model the extreme wave height by utilizing a non-stationary discrete statistical extreme model. The varying parameters are taken into account with a changing pattern to reflect the seasonal and directional dependent behavior. Both the magnitude and the occurrence rate of the extreme values are investigated. Detailed discussion on the continuity of the established model is also given. The importance of the proposed model is demonstrated in reliability analysis for a jacket structure. The sensitivity to the changing marine environment in reliability analyses is investigated.

A fuzzy quantification approach of uncertainties in an extreme wave height modeling

A non-traditional fuzzy quantification method is presented in the modeling of an extreme significant wave height. First, a set of parametric models are selected to fit time series data for the significant wave height and the extrapolation for extremes are obtained based on high quantile estimations. The quality of these results is compared and discussed. Then, the proposed fuzzy model, which combines Poisson process and gener-alized Pareto distribution （GPD） model, is applied to characterizing the wave extremes in the time series data. The estimations for a long-term return value are considered as time-varying as a threshold is regarded as non-stationary. The estimated intervals coupled with the fuzzy theory are then introduced to construct the probability bounds for the return values. This nontraditional model is analyzed in comparison with the traditional model in the degree of conservatism for the long-term estimate. The impact on the fuzzy bounds of extreme estimations from the non stationary effect in the proposed model is also investigated.

Characteristics of wind pressure pulse on large-span flat roofs

The wind pressure pulse events, among the most important characteristics of wind pressure fluctuations on large-span flat roofs, were investigated by wind tunnel tests in this paper. Incorporating the formation mechanism of wind pressure pulse events, the peak over threshold method was employed to study properties of this kind of events. The event duration time, the energy contribution, the number of the pulse events, and the distribution of average peak pressure were calculated. Probability density functions of some typical samples in separation region were also given. Results show that the non-Gaussian roof pressure is strong in the flow separation region owing to the wind pressure pulse events. Evaluations of the extreme peak pressures, which can be determined by the peak over threshold method effectively, are important to the design of building cladding.