The wheel-rail contact stress solution is the precondition for many wheel-rail contact problems, such as wheel-rail contact fatigue, plastic deformation and wear, etc. However, vehicle-track interaction generally shows a high degree of randomness due to the uncertainty of excitations, e.g. track irregularities, in the estimation of wheel-rail contact point positions and contact stresses. Moreover, it is known that track irregularities are massive data, possessing evolution characteristics at time and space domain, thus it will consume much time if directly loading all of them into the vehicle-track interaction process. Regarding this, this work tries to introduce the track irregularity probabilistic model to select representative track irregularity sets with much smaller samples. To guarantee the representativeness of track irregularity data, track irregularities of up to five thousand kilometres are measured to ensure the ergodicity of the power spectral density function (PSD) of the track irregularities. Moreover, a fast-accurate contact model is introduced to extract the stress distribution of the wheel-rail contact patch. By effectively combing the vehicle-track dynamics method and random simulation methods, the wheel and rail contact stresses in amplitude and distribution range can be efficiently quantified from a statistical view.

轮轨接触应力求解是许多轮轨接触问题的前提，如轮轨接触疲劳、塑性变形和磨损等。 然而，由于不确定性，车轨相互作用通常表现出高度的随机性在估计轮轨接触点位置和接触应力中的激励，例如轨道不规则性。此外，众所周知，轨道不平顺是海量数据，具有时空域的演化特征，如果直接将它们全部加载到车轨交互过程中会消耗大量时间。对此，这项工作试图引入轨道不规则概率模型来选择具有更小样本的代表性轨道不规则集。为保证轨道不平顺数据的代表性，测量长达五千公里的轨道不平整度，以确保轨道不平整度的功率谱密度函数（PSD）的遍历性。此外，引入了一种快速准确的接触模型来提取轮轨接触面的应力分布。通过车轨动力学方法和随机模拟方法的有效结合，可以从统计的角度有效地量化轮轨接触应力的幅值和分布范围。