基于支持向量回归的Bootstrap数据扩充方法及其在小子样可靠性评估中的应用  

A Bootstrap Data Expansion Method Based on SVR and Its Application In Small Sample Reliability Evaluation

作　　者：葛保聪 尚子涵 黄佳[1] 夏爱国[3] 王井科 秦飞[2] GE Baocong;SHANG Zihan;HUANG Jia;XIA Aiguo;WANG Jingke;QIN Fei(Research Institute of Aerospace Technology,Central South University,Changsha 410083,China;School of Astronautics NPU,Northwestern Polytechnical University,Xi'an 710072,China;Beijing Aeronautical Engineering Technical Research Center,Beijing 100076,China)

机构地区：[1]中南大学航空航天技术研究院,湖南长沙410083 [2]西北工业大学航天学院,陕西西安710072 [3]北京航空工程技术研究中心,北京100076

出　　处：《测控技术》2024年第9期58-66,共9页Measurement & Control Technology

基　　金：国家自然科学基金(52205177);航空发动机气动热力国防科技重点实验室基金(2022-JCJQ-LB-062-0409)。

摘　　要：针对航空发动机小子样特性下的可靠性评估问题,提出一种基于支持向量回归(Support Vector Regression, SVR)的Bootstrap数据扩充方法:建立并训练SVR模型,采用邻域抽样法构造输入集,输入训练好的模型中获得扩充样本。仿真结果表明,采用该方法获得的扩充样本较传统Bootstrap方法更接近真实分布,且有效拓展了样本取值区间。以某航空发动机涡轮盘小子样疲劳寿命试验数据为例:(1)非参数方法,采用两种方法获得的平均疲劳寿命十分接近,但新方法获得的置信区间更大,这与样本取值区间的拓展相关;(2)参数方法,对新方法扩充的样本进行参数估计得到的结果与参考值更为接近,最大相对偏差为-1.290 2%,而传统方法的最大相对偏差达到了29.477 6%,两种方法下计算得到的平均疲劳寿命与参考值均较接近,但新方法得到的置信区间与参考区间更为接近。综合来看,所提出的方法能够有效实现样本扩充,具有一定的应用价值。A Bootstrap data expansion method based on support vector regression(SVR)is proposed to address the reliability evaluation problem of aeroengine with small sample characteristicshe.The SVR model is estab-lished and trained,and the input set is constructed using neighborhood sampling.The augmented samples are obtained by inputting the trained model.The simulation results show that the expanded samples obtained by this method are closer to the true distribution than traditional Bootstrap methods,and effectively expand the range of sample values.Taking the fatigue life test data of a small sample of a certain aircraft engine turbine disk as an example:Non parametric method,the average fatigue life obtained by the two methods is very close,but the confidence interval obtained by the new method is larger,which is related to the expansion of the sample value range.②Theparameter method,theresultsobtained fromparameter estimationofthesamples expanded by the new method are closer to the reference values,with a maximum relative deviation of-1.2902%,while the maximum relative deviation of the traditional method reaches 29.4776%.The average fatigue life calculated by both methods is closer to the reference value,but the confidence interval obtained by the new method is closer to the reference interval.Overall,the proposed method can effectively achieve sample expan-sion and has certain application value.

关 键 词：支持向量回归 BOOTSTRAP方法 小子样 可靠性分析 航空发动机 

分 类 号：TP202.1[自动化与计算机技术—检测技术与自动化装置] V232.3[自动化与计算机技术—控制科学与工程]