基于样本信息重构的小子样P-S-N曲线拟合方法

Method of P-S-N Curve Fitting for Small Sample Based on Sample Information Reconstruction

为了在小子样条件下拟合出精度较高的P-S-N曲线,本文提出基于样本信息重构并符合疲劳寿命等效原理的极大似然法和基于样本信息重构的最小二乘法。样本信息重构有效解决了在部分相邻的应力水平下样本的对数寿命标准差与对数应力水平不呈线性关系的问题,同时该方法考虑了各应力水平下样本数量效应对整体样本分布的影响,有效降低了部分应力水平下小样本与异常样本对疲劳寿命均值与标准差的影响,保证疲劳寿命的等效精度。最后通过应用疲劳试验数据对本文提出的2种方法与传统的极大似然法和最小二乘法进行对比分析,结果表明基于样本信息重构并符合疲劳寿命等效原理的极大似然法拟合的P-S-N曲线精度高且偏于安全。

In order to fit P-S-N curves with high accuracy under the condition of small size sample,the paper presented two methods,the maximum likelihood method based on sample information reconstruction and the equivalence principle of fatigue life and the least-square method based on sample information reconstruction.The sample information reconstruction method effectively solved the problem that the logarithmic life standard deviation of the sample is not linearly related to the logarithmic stress level at the partial adjacent stress levels.Meanwhile,the method considered the impact of sample number effect on the global sample distribution at each stress level,which can effectively reduce the influence of small sample and abnormal sample on the average and standard deviation of fatigue life under partial stress levels,so as to ensure the equivalent accuracy of fatigue life.Finally,the two methods proposed in the paper were compared with the traditional maximum likelihood method and least-square method through fatigue life test data.The results show high accuracy and safety of the P-S-N curve fitted with maximum likelihood method based on sample information reconstruction and the equivalence principle of fatigue life.