城际动车组车轴应力谱的极值推断

为评估车轴的可靠性或扩展车轴的应力谱，需要预判车轴全寿命期内的最大应力. 首先，综合考虑推断精度和统计效率等因素，基于Sturges公式选取0.5 MPa为组距对实测车轴应力-时间历程进行雨流计数，得到车轴应力的经验累积分布函数. 其次，针对不同的门槛限值计算应力的经验均值超限函数，通过确定经验均值超限函数的拐点确定合理门槛限值. 然后，基于Pickands-Balkema-de Haan定理，利用广义帕累托分布拟合车轴应力的超限分布函数，并通过拟合分布外推车轴全寿命期内的最大应力. 最后，利用实测车轴应力数据进行了验证. 研究结果表明:为评估车轴寿命期内的最大应力，大约需要不少于 3000 km 的线路测试；基于13.5 t轴重实测数据推断的应力极值比基于14.1 t轴重计算的校核应力高出13%，因此完全按照设计轴重满载运营，需格外谨慎. 

Extreme Value Inference of Axle Stress Spectrum for Intercity EMU

In order to evaluate the reliability and extend stress spectra of axles, the maximum stress during its full life need to be predicted. First, to obtain the empirical cumulative distribution function of axle stress, the bin width of 0.5 MPa is chosen, which is based on the Sturges formula as a tradeoff between the inferred accuracy and statistical efficiency, and the rain flow counting is performed against the measured axial stress-time history. Secondly, the empirical mean excess function is calculated according to different threshold values and the reasonable threshold is determined by identifying the turning point of the mean excess function. Then, based on Pickands-Balkema-de Haan theorem, the excess distribution function of the axle stress is fitted with the generalized Pareto distribution, and the maximum stress during the full life is inferred with the fitted distribution. Finally, this method is verified with the measured data. The results show that in order to assess the maximum axle stress during its full life, the tests of 3000 km are required at least. The inferred maximum stress with the measured data of 13.5 t wheel load is about 13% higher than that with the one of 14.1 t wheel load. Therefore it should be particularly cautious to operate at axle design weight.