The sufficiency and integrity of dynamic stress spectrum will affect the accuracy of the analysis result. It is necessary to extrapolate them from the short term to the long term while retaining the probability distribution characteristics. The stress spectrum extrapolation and fatigue life assessment of the bogie frame were studied, and a test point was taken as a case study. First, the optimal bandwidth determination in two-dimensional KDE (kernel density estimation) was studied. Second, the gray incidence degree analysis method was proposed to evaluate the proximity-incidence degree and similarity-incidence degree of the rain-flow matrices extrapolated before and after. Finally, a fatigue life assessment method, with a multi-sample dynamic stress spectrum extrapolated based on KDE, was proposed. Compared with the linear extrapolation, the relative error of fatigue life assessment result based on KDE extrapolation is −4.17%, which meets the accuracy requirements of engineering. It is more beneficial to ensure the vehicles' safe operation.

中文翻译：

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基于核密度估计法的列车转向架车架动应力谱外推

动态应力谱的充分性和完整性将影响分析结果的准确性。有必要将它们从短期外推到长期，同时保留概率分布特征。研究了转向架框架的应力谱外推和疲劳寿命评估，并以一个测试点为例进行了研究。首先，研究了二维 KDE（核密度估计）中的最佳带宽确定。其次，提出了灰色关联度分析方法来评价前后外推的雨流矩阵的接近度和相似度。最后，提出了一种基于KDE外推多样本动态应力谱的疲劳寿命评估方法。与线性外推法相比，基于KDE外推法的疲劳寿命评估结果相对误差为±4.17%，满足工程精度要求。更有利于保证车辆的安全运行。