论文:2022,Vol:40,Issue(5):1164-1171
引用本文:
宁小磊, 吴颖霞, 赵新, 赵军民, 张凯, 郝跳锋, 吕梅柏, 胡亚峰, 陈韵. 小样本概率关联度模型研究[J]. 西北工业大学学报
NING Xiaolei, WU Yingxia, ZHAO Xin, ZHAO Junmin, ZHANG Kai, HAO Tiaofeng, LYU Meibo, HU Yafeng, CHEN Yun. Research on small sample probability relational degree model[J]. Journal of Northwestern Polytechnical University

小样本概率关联度模型研究
宁小磊1, 吴颖霞1, 赵新1, 赵军民2, 张凯1, 郝跳锋1, 吕梅柏3, 胡亚峰1, 陈韵2
1. 中国华阴兵器试验中心, 陕西 华阴 714200;
2. 西安现代控制技术研究所, 陕西 西安 710065;
3. 西北工业大学 航天学院, 陕西 西安 710072
摘要:
针对小样本条件下多元时间序列之间的关联分析问题,提出了一种小样本概率关联度模型。使用样本函数或样本统计量代替样本构造累积经验分布函数并计算概率关联系数。当比较序列样本容量n<5,使用样本顺序统计量的经验分布函数计算概率关联系数;当比较序列样本容量n≥5,使用Bootstrap方法重抽样扩充样本后再构造经验分布函数计算概率关联系数,改进了概率关联度模型中关联系数的计算方法,解决了小样本条件下这一类多元数据关联分析问题。证明了小样本概率关联度模型满足的基本性质,给出了小样本概率关联分析的基本步骤,仿真案例和实际应用验证了文中模型的正确性和有效性。
关键词:    数据关联    概率关联度    小样本    多元时间序列    样本统计量   
Research on small sample probability relational degree model
NING Xiaolei1, WU Yingxia1, ZHAO Xin1, ZHAO Junmin2, ZHANG Kai1, HAO Tiaofeng1, LYU Meibo3, HU Yafeng1, CHEN Yun2
1. China Huayin Ordnance Test Center, Huayin 714200, China;
2. Xi'an Modern Control Technology Research Institute, Xi'an 710065, China;
3. School of Astronautics, Northwestern Polytechnical University, Xi'an 710072, China
Abstract:
The probability degree model is suitable for correlation analysis between multivariate time series, but its application effect is poor under the small sample condition. An improved probability degree model for small sample problem is proposed in this paper. Firstly, by using sample function or sample statistics instead of samples to construct cumulative empirical distribution function and calculate probability correlation coefficient, the framework of probability correlation degree model is developed and expanded. Secondly, the calculation method of correlation coefficient in the original model of probability correlation degree is improved. For the problem of sample size n<5, the empirical distribution function of sample order statistics is used to calculate the probability correlation coefficient; For the problem of comparison sequence sample size n≥5, the Bootstrap method is used to resample to construct the empirical distribution function to calculate the probability correlation coefficient. Thus, the problem of dynamic multivariate data association analysis under the condition of small samples is solved. It is proved that the small sample probability correlation degree model satisfies the correlation theorem and its basic properties. The basic steps of small sample probabilistic correlation analysis are given. At last simulation cases and practical application verify the rationality and effectiveness of the model and method.
Key words:    data association    probability correlation degree    small samples    multivariate time series    sample statistics   
收稿日期: 2021-12-21     修回日期:
DOI: 10.1051/jnwpu/20224051164
基金项目: 国防研究重大项目(16000102351)与基础加强计划重点基础研究项目(2020-JCJQ-ZD-076-00)资助
通讯作者: 赵新(1988-),中国华阴兵器试验中心工程师,主要从事常规兵器试验技术研究。e-mail:273579204@qq.com     Email:273579204@qq.com
作者简介: 宁小磊(1985—),中国华阴兵器试验中心工程师,主要从事常规兵器试验技术研究。
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