小子样疲劳寿命分散系数置信区间随应力的变化规律研究

Research on Law of Confidence Interval of Scatter Factor Based on Small Sample Fatigue Life Versus Test Stress

针对疲劳寿命样本小子样统计分析问题,采用Bootstrap方法模拟母体标准差的抽样分布,并结合纠偏的百分位法估算母体标准差的置信区间,着重估计了疲劳分散系数的置信区间。首先利用Bootstrap方法在参数区间估计方面的优越性能,对已知疲劳寿命母体分布的模拟试验数据进行了疲劳分散系数置信区间的估计,通过与真值的对照分析,验证了结合纠偏百分位思想的Boot-strap方法进行疲劳分散系数区间估计的可信性。然后利用此方法对航空材料的140个钢合金试件和295个铝合金试件的真实疲劳寿命试验数据进行了疲劳寿命分散系数的区间估计,并研究了疲劳分散系数置信区间随疲劳试验应力的变化规律,为在工程实际中分析疲劳寿命试验数据提供了参考方法。

For the statistical analysis of the small sample fatigue life, the sampling distribution of the population standard deviation is simulated by the Bootstrap method, then the confidence interval of the population standard deviation is estimated by the percentile method with rectification and the confidence interval of the fatigue scatter factor is estimated especially. Firstly, for the test data sampling from the known population distribution of the fatigue life, owing to the superiority of the Bootstrap method on the interval estimate of the parameters, the confidence interval of the fatigue scatter factor is estimated and compared with its true value. The result validates the creditability of the Bootstrap method combined with rectification percentile method for the interval estimate of the fatigue scatter factor. Afterward, for the actual fatigue life test data of aeronautical material on 140 steel-alloy test pieces and 295 aluminum-alloy test pieces, the confidence interval of the fatigue scatter factor is estimated by the above method and the law of the confidence interval with the fatigue test stress is studied also, and, an alternative method for analyzing fatigue life test data in the engineering practice has been provided.