Probability Distribution Functions of Maximum Wheel Unloading Rate Based on Extremal Index

Abstract

To study the probabilistic distribution of maximum wheel unloading rate of high-speed trains and its temporal correlation when a train passes over a bridge, a method for the estimation of the extremal index is proposed. Using the time series threshold theory, the maximum value cumulative distribution function (CDF) when the wheel unloading rate is regarded as a time series is derived and validated. This approach can also address dependent series, which the traditional probability distribution function formulas could not. Then, the difference between treating the wheel unloading rate as a time series and independent series is investigated using Monte Carlo simulations. Finally, the influence of the number of calculation steps on the threshold is studied, and the differences between thresholds calculated by different extremal indices when considering the number of trains running during the service period of the bridge are explored. The maximum value CDFs of the wheel unloading rate for different track irregularities, bridge lengths, and vehicle speeds are investigated for a three-span simply-supported bridge. The results show that the differences in the maximum value probability density functions (PDFs) obtained by considering the wheel unloading rate as time series and independent random series cannot be ignored. However, when studying a high-confidence level problem, such as the threshold of the wheel unloading rate, the difference between the two approaches is small enough. As the number of calculation steps increases, the extremal index will gradually decrease. When considering a long-distance high-speed rail line, its shorter segment can be used to study the threshold of the wheel unloading rate.