疲劳S-N曲线拟合的双加权最小二乘法

Double Weighted Least Square Method for Fatigue S-N Curve Fitting

为充分利用疲劳试验数据,获得较高精度的S-N曲线,本文提出一种融合成组疲劳试验数据和疲劳强度试验数据拟合S-N曲线的双加权最小二乘法。该方法充分考虑了疲劳试验方法、疲劳试验数据分散性和试验件样本容量对S-N曲线的影响。它首先考虑试验样本容量对试验结果分散性的影响,对S-N曲线进行第一次加权拟合。然后分别考虑疲劳寿命和疲劳强度的分散性以及试验件的数目的影响进行第二次加权拟合,从而得到材料或构件的S-N曲线。本文进行了大量的S-N曲线的统计分析,结果表明拟合得到的S-N曲线具有较高的精度和可信度。

In order to take full advantage of the fatigue data from both the group test and the staircase test and thus get S-N curves with higher accuracy,a S-N curve regression approach is proposed based on the double weighted least square method.In this approach,effects of fatigue test method,fatigue data dispersion and test sample size on S-N curves are included.Firstly the effect of test sample size of the group test on the dispersion of the fatigue life is considered,resulting in the length of the confidence interval of the mean value of fatigue life to be used for the first weighted fitting.Then effects of dispersion of fatigue life,dispersion of fatigue strength and test sample size are respeetively taken into account to implement the second weighted fitting.Finally S-N curves of materials or components are obtained.A lot of statistical analysis demonstrate the ability and rationality of the presented method.It is shown that the fitted S-N curves have higher accuracy and credibility.