Automatic determination method of optimal thresholdbased 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.