基于灰色系统理论的小样本P-S-N曲线拟合方法

兰州理工大学学报 ›› 2026, Vol. 52 ›› Issue (1): 63-67.

基于灰色系统理论的小样本P-S-N曲线拟合方法

张震^*1, 刘俭辉², 程玲玲¹, 牛富超¹

1.河南驼人医疗器械研究院有限公司, 河南新乡 453000;
2.兰州理工大学机电工程学院, 甘肃兰州 730050

收稿日期:2023-03-21 出版日期:2026-02-28 发布日期:2026-03-05
通讯作者: 张震(1994-),男,河南睢县人,硕士.Email:zhangz0618@163.com
基金资助:
国家自然科学基金(52365016)

A small sample P-S-N curve fitting method based on grey system theory

ZHANG Zhen¹, LIU Jian-hui², CHENG Ling-ling¹, NIU Fu-chao¹

1. Henan Camel Medical Device Research Institute Co. Ltd., Xinxiang 453000, China;
2. School of Mechanical Electrical Engineering, Journal of Lanzhou University of Technology, Lanzhou 730050, China

Received:2023-03-21 Online:2026-02-28 Published:2026-03-05

摘要/Abstract

摘要： Bootstrap法在处理小样本疲劳试验数据时,只能在原始数据中进行抽样,所得数据信息有限.为此,引入灰色系统理论对小样本数据进行处理,建立数据的灰微分方程,并挖掘原始数据的隐藏关系,得到更多数据的潜在信息.首先,借助灰色系统理论处理原始数据;其次,通过Bootstrap法对已处理的数据进行抽样得到再生样本;最后,对再生样本进行处理得到小样本数据的P-S-N曲线.结果表明,与Bootstrap法相比,通过灰色Bootstrap法处理所得小样本P-S-N曲线精度更高.

关键词: 小样本, Bootstrap法, 灰色系统理论, P-S-N曲线

Abstract: The traditional Bootstrap method, when applied to small-sample fatigue test data, is limited by the fact that it can only resample from the original data, thereby constraining the amount of available information. To overcome this limitation, it is proposed to introduce grey system theory to process small-sample data by establishing grey differential equations that uncover hidden relationships within the original data, thus extracting additional implicit information. First, the original data are processed using grey system theory. Secondly, the bootstrap method is used to sample the processed data to obtain regenerated samples. Finally, the P-S-N curve of the small sample data was obtained by reprocessing the regenerated data. Through validation analysis, compared with the Bootstrap method, the grey Bootstrap method proposed in this paper has higher accuracy in processing the small sample P-S-N curve.

Key words: small samples, Bootstrap method, gray system theory, P-S-N curve

中图分类号:

TH114

张震, 刘俭辉, 程玲玲, 牛富超. 基于灰色系统理论的小样本P-S-N曲线拟合方法[J]. 兰州理工大学学报, 2026, 52(1): 63-67.

ZHANG Zhen, LIU Jian-hui, CHENG Ling-ling, NIU Fu-chao. A small sample P-S-N curve fitting method based on grey system theory[J]. Journal of Lanzhou University of Technology, 2026, 52(1): 63-67.

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