估计疲劳寿命三参数P—S—N曲线的新方法

NEW METHOD FOR ESTIMATING FATIGUE LIFE THREE-PARAMETER P—S—N CURVES

由于不同应力水平下对数疲劳寿命的方差不等,因而不同应力水平下的对数疲劳数据不满足最小二乘估计的Gauss-Markov假设条件,此时采用常规最小二乘法估计的三参数P—S—N曲线不是统计意义下的最佳线性无偏估计,而加权最小二乘法则可以给出异方差条件下的最佳线性无偏估计。为此基于加权最小二乘和Bootstrap方法提出一种疲劳寿命三参数P—S—N曲线估计方法,在所提方法中,Bootstrap方法被用来确定不同应力水平下疲劳试验寿命数据的协方差矩阵对角线元素,避免迭代确定加权最小二乘法中的权矩阵。对三种材料的四组疲劳试验寿命数据进行分析的结果表明,所提方法具有工程实用性,传统最小二乘法由于忽略了Gauss-Markov假设条件可能得到偏危险的结果,而由于所提方法得到的是最佳线性无偏估计,因而在子样容量增大时将趋于估计的真值,并且参数估计的方差将是最小的。

From the scatter nature of fatigue data at different stress levels, it is well known that the variances of fatigue life logarithms are different, which is out of Gauss-Markov assumptions. At the case, the conventional least square method （LSM） cannot provide an optimal estimation for three parameter P-S-N curves in statistics. The weighted least square method （WISM）, however, is a best linear unbiased estimator （BLUE） for this heterescedastic linear regression. Therefore, based on the WISM and Bootstrap method, a new method is presented to estimate the three parameter P-S-N curves of fatigue life. Bootstrap method is employed to determine the covar/ance matrix, which simplify the iterative procedure for computing weight matrix in WLSM. The applications in Aluminum alloy LY12CZ, 45 Carbon steel and 40CrNiMo steel show how the presented method is implemented. From the result comparison of the presented method and the conventional LSM, it is concluded that the conventional LSM might give a dangerous estimation due to ignoring the Gauss-Markov assumptions, but the presented method can give a rational estimation due to its BLUE, especially as the increase of the sample size, the mean estimation of the presented method converges to the real mean and the variances of regression coefficients are minimum.