北京航空航天大学学报 ›› 2016, Vol. 42 ›› Issue (9): 1911-1917.doi: 10.13700/j.bh.1001-5965.2015.0559

• 论文 • 上一篇    下一篇

基于小样本的试验系统可信度评估方法

吴云洁1,2, 王建敏2,3, 杨文光2,4   

  1. 1. 北京航空航天大学 虚拟现实技术与系统国家重点实验室, 北京 100083;
    2. 北京航空航天大学 自动化科学与电气工程学院, 北京 10008;
    3. 中国科学院空间应用工程与技术中心, 北京 10009;
    4. 北京航空航天大学 飞行器控制一体化技术重点实验室, 北京 100083
  • 收稿日期:2015-08-31 出版日期:2016-09-20 发布日期:2016-09-29
  • 通讯作者: 吴云洁,Tel.:010-82338716,E-mail:wyjmip@buaa.edu.cn E-mail:wyjmip@buaa.edu.cn
  • 作者简介:吴云洁,女,博士,教授,博士生导师。主要研究方向:智能控制理论、半实物仿真设备、系统仿真及评估。Tel.:010-82338716,E-mail:wyjmip@buaa.edu.cn;王建敏男,博士。主要研究方向:伺服控制、飞行器制导控制、灰色系统理论。E-mail:wjm123121@126.com;杨文光,男,博士研究生。主要研究方向:模糊控制、灰色系统理论。E-mail:wenguang6662003@aliyun.com
  • 基金资助:
    国家自然科学基金(91216304)

Approach of credibility evaluation for testing system with small samples

WU Yunjie1,2, WANG Jianmin2,3, YANG Wenguang2,4   

  1. 1. State Key Laboratory of Virtual Reality Technology and Systems, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
    2. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 10008;
    3. Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences, Beijing 10009;
    4. Science and Technology on Aircraft Control Laboratory, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
  • Received:2015-08-31 Online:2016-09-20 Published:2016-09-29
  • Supported by:
    National Natural Science Foundation of China (91216304)

摘要: 针对小样本试验数据信息匮乏、难以利用概率统计方法进行可信度评估的问题,将重抽样方法与小样本区间估计方法相融合,提出了小样本试验系统新型可信度评估方法。利用重抽样理论,获取多个具有相同样本量的相似小样本。根据灰色系统理论,提出了改进的灰色置信度及置信区间的定义及计算方法。并在此基础上通过求公共区间的方式计算原小样本数据的灰色置信区间。该置信区间在相同的置信度下,区间宽度更窄,精度更高。通过算例仿真,验证了上述方法的合理性、有效性,对工程试验中的小样本数据系统评估提供了一定的方法指导。

关键词: 小样本, 重抽样, 区间估计, 灰色系统, 置信度, 置信区间

Abstract: Aimed at the problem that the small sample test data are lack of information and it is difficult to use probability statistic method for interval estimation, a novel approach of credibility evaluation for small sample testing system is proposed by integrating the repeated sampling method and the small sample interval estimation method. Many similar small samples with the same sample size are obtained using the theory of repeated sampling. According to the grey system theory, an improved definition and calculation method for grey confidence level and grey confidence interval is proposed. On this basis, the common area of the grey confidence intervals of many small samples is calculated, which is the grey confidence interval for the original small sample data. Under the same confidence level, the above confidence interval has narrower interval width and higher precision. The rationality and validity of the above method is verified through example simulation, which provides certain method guidance for small sample data system evaluation in engineering test.

Key words: small sample, repeated sampling, interval estimation, grey system, confidence level, confidence interval

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