Statistical characterization of in-service stress–frequency distributions for railway bogie frames

Estimation of stress–frequency distributions under in-service conditions is essential for assessing the structural integrity and fatigue safety of railway vehicle bogie frames, particularly at the design stage where actual measurement data are unavailable. This study aims to provide a simplified but effective approach to contribute fatigue life assessment or crack growth evaluation by generalizing and statistically characterizing stress–frequency distributions. A total of 113 measurement datasets were analyzed, obtained from eight types of bogies operated on nine conventional railway lines. Statistical evaluation showed a strong correlation between normalized stress, defined as the ratio to the maximum observed stress, and the logarithm of relative frequency normalized by total frequency. The slope of this relationship was found to follow a normal distribution, with a mean of 4.52 and a standard deviation of 0.66. Based on this result, two representative stress–frequency distributions with total frequencies of 10⁴ and 10⁵ cycles were assumed. For these distributions, equivalent running distances with respect to fatigue crack propagation were then evaluated in terms of percentile values. The findings indicate that the statistical representation of stress–frequency distributions provides a practical framework for estimating fatigue behavior in the absence of direct measurement data. Finally, potential applications of the proposed distributions were discussed, including approaches for estimating maximum stresses and effective utilization of the obtained statistical values in fatigue safety issues.