王志勇,王崇倡,刘宇晨,金泽林,焦亚沁

• 1:辽宁工程技术大学测绘与地理科学学院
• 2:中国科学院南京地理与湖泊研究所
• 3:江苏海洋大学海洋技术与测绘学院

摘要(Abstract)：

针对传统线性模型通过拟合连续运行参考站(CORS)高程时间序列趋势项，使CORS站运动趋势单一化导致无法体现测站各自运动特性的问题，该文提出一种基于CORS高程时间序列本身的非线性趋势项定量识别与估计方法。首先，用K均值聚类整体经验模态分解方法对CORS站高程时间序列进行分解；其次，基于排列熵理论进行非线性趋势项的定量识别与合成；最后，采用正弦函数模型、线性多项式模型、傅里叶模型对非线性趋势项进行建模拟合并讨论拟合精度。实验结果表明：基于排列熵的非线性趋势项定量识别方法避免了人为判别误差，准确地反映了序列自身的变化趋势；3种模型中，傅里叶模型拟合效果最佳。

关键词(KeyWords)： CORS;非线性趋势项;K均值;排列熵;线性多项式模型;傅里叶模型;正弦函数模型

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金项目(41471351)

作者(Author): 王志勇,王崇倡,刘宇晨,金泽林,焦亚沁

DOI: 10.16251/j.cnki.1009-2307.2022.04.006

参考文献(References)：

• [1] 武曙光.区域CORS站坐标时间序列特征分析[D].武汉：武汉大学，2017.(WU Shuguang.Characteristics of coordinate time series from regional CORS stations[D].Wuhan:Wuhan University,2017.)
• [2] 姜卫平.GNSS基准站网数据处理方法与应用[M].武汉：武汉大学出版社，2017.(JIANG Weiping.GNSS reference network data processing method and application[M].Wuhan:Wuhan University Press,2017.)
• [3] 蒋志浩，张鹏，秘金钟，等.基于非线性运动分析的CGCS2000下我国CORS站运动特征[J].地球物理学报，2012,55(3):841-850.(JIANG Zhihao,ZHANG Peng,BEI Jinzhong,et al.Characteristics of the non-linear movement of CORS network in China based on the CGCS2000 frame[J].Chinese Journal of Geophysics,2012,55(3):841-850.)
• [4] 吉长东，吕广涵，张恒璟，等.一种CORS站高程序列噪声识别算法[J].测绘科学，2021,46(3):8-16.(JI Changdong,LYU Guanghan,ZHANG Hengjing,et al.A noise recognition algorithm of CORS station elevation series[J].Science of Surveying and Mapping,2021,46(3):8-16.)
• [5] 张恒璟，龙安森，文汉江.EEMDAN的CORS站高程时间序列分析方法[J].测绘科学，2020,45(2):29-34.(ZHANG Hengjing,LONG Ansen,WEN Hanjiang.Analysis method of CORS station height time series based on EEMDAN[J].Science of Surveying and Mapping,2020,45(2):29-34.)
• [6] 张恒璟，崔东东，程鹏飞.CORS站高程非线性速度场及方差波动模型构建方法[J].测绘学报，2019,48(9):1096-1106.(ZHANG Hengjing,CUI Dongdong,CHENG Pengfei.Height nonlinear velocity field and variance fluctuation model construction method for CORS stations[J].Acta Geodaetica et Cartographica Sinica,2019,48(9):1096-1106.)
• [7] 程鹏飞，成英燕，秘金钟.2000国家大地坐标系建立的理论与方法[M].北京：测绘出版社，2014.(CHENG Pengfei,CHENG Yingyan,BEI Jinzhong.Theory and method for establishment of the China geodetic coordinate system 2000[M].Beijing:Sino Maps Press,2014.)
• [8] 张鹏，蒋志浩，秘金钟，等.我国GPS跟踪站数据处理与时间序列特征分析[J].武汉大学学报(信息科学版),2007,32(3):251-254.(ZHANG Peng,JIANG Zhihao,BEI Jinzhong,et al.Data processing and time series analysis for GPS fiducial stations in China[J].Geomatics and Information Science of Wuhan University,2007,32(3):251-254.)
• [8] 张鹏，蒋志浩，秘金钟，等.我国GPS跟踪站数据处理与时间序列特征分析[J].测绘科学，2008(S2):10-13.(ZHANG Peng,JIANG Zhihao,BEI Jinzhong,et al.Data processing and time series analysis for GPS fiducial stations in China[J].Science of Surveying and Mapping,2008(S2):10-13.)
• [9] 刘宗强，党亚民，杨强，等.顾及共模误差的四川连续GPS基准站坐标时间序列噪声分析[J].大地测量与地球动力学，2018,38(5):510-515.(LIU Zongqiang,DANG Yamin,YANG Qiang,et al.Noise analysis of coordinate time series of Sichuan GPS reference stations with common mode error[J].Journal of Geodesy and Geodynamics,2018,38(5):510-515.)
• [10] HUANG N E,WU M L C,LONG S R,et al.A confidence limit for the empirical mode decomposition and Hilbert spectral analysis[J].Proceedings of the Royal Society of London Series A:Mathematical,Physical and Engineering Sciences,2003,459(2037):2317-2345.
• [11] WU Z H,HUANG N E.A study of the characteristics of white noise using the empirical mode decomposition method[J].Proceedings of the Royal Society of London Series A:Mathematical,Physical and Engineering Sciences,2004,460(2046):1597-1611.
• [12] 张锡越，朱照荣，曾艳艳，等.北京市CORS站坐标时间序列噪声分析[J].测绘科学，2021,46(3):48-54.(ZHANG Xiyue,ZHU Zhaorong,ZENG Yanyan,et al.Noise analysis of coordinate time series of Beijing CORS base station[J].Science of Surveying and Mapping,2021,46(3):48-54.)
• [13] 张恒璟，齐昕，文汉江.基于K均值聚类EEMD的CORS高程时间序列信号分析方法[J].大地测量与地球动力学，2019,39(10):1053-1057.(ZHANG Hengjing,QI Xin,WEN Hanjiang.Analytical method of CORS height time series based on K-means clustering EEMD[J].Journal of Geodesy and Geodynamics,2019,39(10):1053-1057.)
• [14] 冯辅周，饶国强，司爱威，等.排列熵算法的应用与发展[J].装甲兵工程学院学报，2012,26(2):34-38.(FENG Fuzhou,RAO Guoqiang,SI Aiwei,et al.Application and development of permutation entropy algorithm[J].Journal of Academy of Armored Forces Engineering,2012,26(2):34-38.)
• [15] 郑近德，程军圣，杨宇.改进的EEMD算法及其应用研究[J].振动与冲击，2013,32(21):21-26.(ZHENG Jinde,CHENG Junsheng,YANG Yu.Modified EEMD algorithm and its applications[J].Journal of Vibration and Shock,2013,32(21):21-26.)
• [16] 雷亚国，孔德同，李乃鹏，等.自适应总体平均经验模式分解及其在行星齿轮箱故障检测中的应用[J].机械工程学报，2014,50(3):64-70.(LEI Yaguo,KONG Detong,LI Naipeng,et al.Adaptive ensemble empirical mode decomposition and its application to fault detection of planetary gearboxes[J].Journal of Mechanical Engineering,2014,50(3):64-70.)
• [17] 李长伟，雷文平，庞博，等.基于EEMD的相关排列熵的滚动轴承故障诊断[J].组合机床与自动化加工技术，2020(8):1-4.(LI Changwei,LEI Wenping,PANG Bo,et al.Fault diagnosis of rolling element bearing of correlation coefficient and arrangement entropy based on EEMD[J].Modular Machine Tool & Automatic Manufacturing Technique,2020(8):1-4.)
• [18] 张恒璟.国家CORS基准站高程时间序列非线性时变研究[D].阜新：辽宁工程技术大学，2013.(ZHANG Hengjing.Nonlinear time-varying study of GPS height time series of national CORS stations[D].Fuxin:Liaoning Technical University,2013.)