A Small Sample Prediction Method for Engineering p-S-N Curve

工程p-S-N曲线的小子样预测方法研究

School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China

Received: 3 September 2017

Abstract

Based on Non-intrusive Polynomial Chaos method, a small sample prediction method for engineering p-S-N curve that has a medium fatigue life is proposed. Parameters in Basquin model are calculated through optimization method based on small sample of observed fatigue life. We establish NIPC polynomials and obtain big sample parameters, obtaining probabilistic properties of parameters with the big sample EDF method. Then the relationship between statistics and stress level are fitted with least squares method. Some new samples are introduced to improve the accuracy of the method. The statistics are updated by Bayesian method. Samples parameters under any stress level are obtained to calculate corresponding fatigue life. Probabilistic properties of fatigue life are predicted, and the p-S-N curve is established. Test observations of aluminium alloy T-2024 are all located in the interval of 95% quantile, showing that the method can effectively predict probabilistic properties of medium fatigue life.

摘要

基于非嵌入多项式混沌（NIPC）展开及贝叶斯更新方法，提出一种中等寿命区p-S-N曲线的小子样预测方法。该方法运用较少应力水平下的小子样疲劳寿命数据样本，采用优化方法求解Basquin应力-寿命模型参数的样本数据；由此建立NIPC展开式并进行大子样抽样计算，通过大子样拟合优度检验，得其概率特性，继而拟合模型参数统计量与应力水平的关系。为改进模型参数统计量的预测精度，引入另一应力水平下的小子样试验数据，运用贝叶斯更新方法对模型参数统计量进行修正；由此通过Nataf变换对任意应力水平下模型参数进行抽样，代入模型计算获得疲劳寿命样本，进一步统计获得其概率分布，即完成基于小子样的p-S-N曲线预测。完成了铝合金2024-T3疲劳试验，各应力水平下试验寿命均落于预测概率疲劳寿命的上下95%分位数区间内，表明新方法得到的p-S-N曲线可有效预测疲劳寿命的概率特性。