一种面向复杂问题的小样本建模方法研究  

Research of Modeling with Small Sample for Complex Problem

作　　者：冯国奇 崔东亮[1,3] 朱凯全 张琦[1] FENG Guo-qi;CUI Dong-liang;ZHU Kai-quan;ZHANG Qi(Signal&Communication Research Institute,China Academy of Railway Sciences,Beijing 100081,China;School of Business Administration,Northeastern University,Shenyang 110819,China;State Key Laboratory of Synthetical Automation for Process Industries,Northeastern University,Shenyang 110819,China;Air Traffic Management Bureau of Northeast China,Shenyang 110043,China)

机构地区：[1]中国铁道科学研究院通信信号研究所,北京100081 [2]东北大学工商管理学院,辽宁沈阳110819 [3]流程工业综合自动化国家重点实验室,辽宁沈阳110819 [4]民航东北地区空中交通管理局,辽宁沈阳110043

出　　处：《控制工程》2019年第11期2013-2018,共6页Control Engineering of China

基　　金：国家铁路智能运输系统工程技术研究中心开放课题（RITS2018KF03）;国家自然科学基金(U1834211,61790574)

摘　　要：科学研究中常因过高的试验成本导致机器学习的小样本问题,其难点在于数据集信息不足以描述原始问题的全部特征,因此需要根据学习算法特点精心安排试验以最大化小样本数据集的信息量。针对多元线性回归建模提出了一种样本选择方法:依托正交设计变量的水平特性,采用汉明距离评估试验样本相似性,以样本集最小汉明距离表征数据集的偏差;根据回归建模的样本量最低需求,采用深度优先算法建立最大最小汉明距离样本集以建立回归模型。最后以航空发动机高压涡轮盘为例验证该方法有效性,试验证明这种样本选择策略能在保证建模精度前提下降低试验费用。The problem of small sample size for machine learning is caused by the test cost of complex production,and experiment should be well designed to maximize the information under the size constraint of data set.This paper prompts a sample selection method for multiple linear regression(MLR):Hamming distance is used to evaluate the similarity of samples and depth-first strategy is employed to generate a data set with specified size by max-min Hamming distance,and the selected data set is used to evaluate the generalization performance.Finally a case of high pressure turbine disc design is used to verify this strategy,the result shows that the proposed strategy reduces experiment cost with necessary accuracy.

关 键 词：小样本学习 试验设计 汉明距离 泛化能力 

分 类 号：TP352[自动化与计算机技术—计算机系统结构]