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基于最小二乘法和支持向量机的海洋内孤立波传播速度反演模型

梁可达 刘滕飞 常哲 张猛 李志鑫 黄松松 王晶

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基于最小二乘法和支持向量机的海洋内孤立波传播速度反演模型

梁可达, 刘滕飞, 常哲, 张猛, 李志鑫, 黄松松, 王晶

Inversion models of internal solitary wave propagation speed in ocean based on least squares method and support vector machine

Liang Ke-Da, Liu Teng-Fei, Chang Zhe, Zhang Meng, Li Zhi-Xin, Huang Song-Song, Wang Jing
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  • 传播速度是内孤立波的重要参数之一, 如何通过光学遥感图像准确快速地获得内孤立波速度是目前需要解决的重要科学问题. 本文在实验室建立了模拟内孤立波光学遥感成像系统, 开展了系列综合实验, 获取实验数据库, 并利用最小二乘法和支持向量机两种方法分别建立基于单景光学遥感图像的内孤立波速度反演模型. 利用中国南海的MODIS图像和GF-4图像数据对速度反演模型进行精度检验. 研究结果表明: 最小二乘法内孤立波速度反演模型能够给出回归方程, 物理意义更为直观, 且在300—399 m水深范围精度更高, 而支持向量机内孤立波速度反演模型在水深400—1200 m和83—299 m的范围内精度高. 因此两种内孤立波速度反演模型各有优势, 都可以应用于真实海洋中内孤立波速度的反演.
    The propagation speed is one of the important parameters of the internal solitary wave (ISW). How to obtain the ISW speed through optical remote sensing images accurately and quickly is an important problem to be solved. In this paper, we simulate ISW optical remote sensing imaging, obtain an experimental database, and build the ISW speed inversion model based on a single-scene optical remote sensing image by using the least squares method and the support vector machine. The accuracy of the ISW speed inversion model is tested by using MODIS Image and GF-4 image data of the South China Sea. The study results are shown below. The least squares ISW speed inversion model can give the regression equation, which is more intuitive and has less accuracy in the water depth ranging from 300 m to 399 m, while the support vector machine ISW speed inversion model has high accuracy in the water depth ranging from 400 m to 1200 m and from 83 m to 299 m. Therefore, the two kinds of ISW speed inversion models have different advantages, and can be applied to the inversion of the ISW speed in the real ocean.
      通信作者: 王晶, wjing@ouc.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 61871353)资助的课题.
      Corresponding author: Wang Jing, wjing@ouc.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61871353).
    [1]

    Yang Y C, Huang X D, Zhao W, Zhou C, Huang S W, Zhang Z W, Tian J W 2021 J. Phys. Oceanogr. 51 3609Google Scholar

    [2]

    关晖, 苏晓冰, 田俊杰 2011 计算力学学报 28 60Google Scholar

    Guan H, Su X B, Tian J W 2011 Chin. J. Comp. Mech. 28 60Google Scholar

    [3]

    刘国涛, 尚晓东, 陈桂英, 卢著敏, 刘良钢, 程晓波 2007 中山大学学报(自然科学版) 46 167Google Scholar

    Liu G T, Shang X D, Chen G Y, Lu Z M, Liu L G, Cheng X B 2007 Acta Sci. Natur. Univ. Sunyatseni 46 167Google Scholar

    [4]

    汪超, 杜伟, 杜鹏, 李卓越, 赵森, 胡海豹, 陈效鹏, 黄潇 2022 力学学报 54 1921Google Scholar

    Wang C, Du W, Du P, Li Z Y, Zhao S, Hu H B, Chen X P, Huang X 2022 Chin. J. Theor. App. Mech. 54 1921Google Scholar

    [5]

    汪超, 杜伟, 李广华, 杜鹏, 赵森, 李卓越, 陈效鹏, 胡海豹 2022 中国舰船研究 17 102Google Scholar

    Wang C, Du W, LI G H, Du P, Zhao S, Li Z Y, Chen X P, Hu H B 2022 Chin. J. Ship Res. 17 102Google Scholar

    [6]

    刘秀全, 陈国明, 畅元江, 姬景奇, 傅景杰, 张浩 2017 石油学报 38 1448Google Scholar

    Liu X Q, Chen G M, Chang Y J, Ji J Q, Fu J J, Zhang H 2017 Acta Petro. Sin. 38 1448Google Scholar

    [7]

    Farrar J T, Zappa C J, Weller R A, Jessup A T 2007 J. Geophys. Res-Oceans 112 1Google Scholar

    [8]

    蔡树群, 何建玲, 谢皆烁 2011 地球科学进展 26 703Google Scholar

    Cai S Q, He J L, Xie J H 2011 Adv. Earth Sci. 26 703Google Scholar

    [9]

    黄晓冬, 赵玮 2014 中国海洋大学学报(自然科学版) 44 19Google Scholar

    Huang X D, Zhao W 2014 Period. Ocean Univ. China 44 19Google Scholar

    [10]

    Cai S Q, Xie J S, He J L 2012 Surv. Geophys. 33 927Google Scholar

    [11]

    张涛, 张旭东 2020 海洋与湖沼 51 991Google Scholar

    Zhang T, Zhang X D 2020 Oceanologia Limnologia Sin. 51 991Google Scholar

    [12]

    邝芸艳, 王亚龙, 宋海斌, 关永贤, 范文豪, 龚屹, 张锟 2021 地球物理学报 64 597Google Scholar

    Kuang Y Y, Wang Y L, Song H B, Guan Y X, Fan W H, Ging Y, Zhang K 2021 Chin. J. Geophys. 64 597Google Scholar

    [13]

    孙丽娜, 张杰, 孟俊敏, 崔伟 2022 海洋学报 44 137Google Scholar

    Sun L N, Zhang J, Meng J M, Cui W 2022 Acta. Oceanol. Sin. 44 137Google Scholar

    [14]

    Alford M H, Lien R C, Simmons H, Klymak J, Ramp S, Yang Y J, Tang D, Chang M H 2010 J. Phys. Oceanogr. 40 1338Google Scholar

    [15]

    Huang X D, Chen Z H, Zhao W, Zhang Z W, Zhou C, Yang Q X, Tian J W 2016 Sci. Rep-UK. 6 30041Google Scholar

    [16]

    吕海滨, 何宜军, 申辉 2012 海洋科学 36 98Google Scholar

    LÜ H B, He Y J, Shen H 2012 Marine Sci. 36 98Google Scholar

    [17]

    Hong D B, Yang C S, Ouchi K 2015 Remote. Sens. Lett. 6 448Google Scholar

    [18]

    Meetei C, Nadimpalli J R, Dash M K, Barskar H 2020 Remote. Sens. Environ. 252 112123Google Scholar

    [19]

    Sun L N, Zhang J, Meng J M 2021 J. Oceanol. Limnol 39 14Google Scholar

    [20]

    Zhang M, Wang J, Li Z X, Liang K D, Chen X 2022 J. Geophys. Res-Oceans. 2 127Google Scholar

    [21]

    Wang J, Zhang M, Mei Y, Lu K X, Chen X 2020 IEEE. Geosci. Remote. S. 99 1Google Scholar

  • 图 1  内孤立波光学遥感仿真平台结构示意图

    Fig. 1.  Schematic diagram of simulation platform of the internal solitary wave optical remote sensing.

    图 2  实验室内孤立波参数示意图 (a) 内孤立波仿真遥感图像; (b)内孤立波波形图; (c)内孤立波灰度剖面图

    Fig. 2.  Schematic diagram of the internal solitary wave parameters in the laboratory: (a) Simulated remote sensing images; (b) the internal solitary wave waveform diagram; (c) the gray scale profiles.

    图 3  最小二乘法回归方程反演结果散点图 (a)最高幂次为2次方; (b)最高幂次为3次方

    Fig. 3.  Scatter plot of the inversion results of the least squares regression equation: (a) With the highest power of 2; (b) with the highest power of 3.

    图 4  SVR内孤立波速度反演模型测试集散点图

    Fig. 4.  Scatter plot of test set of solitary wave speed inversion model in SVR.

    图 5  多时间图像法示意图 (a) 2021年5月25日10:43 南海海域GF4光学遥感图像; (b) 2021年5月25日13:40南海海域 MODIS光学遥感图像

    Fig. 5.  Schematic diagram of the multi-time image method: (a) An optical remote sensing image of GF-4 in the South China Sea at 10:43 on May 25, 2021; (b) the MODIS optical remote sensing image of the South China Sea area is at 13:40 on May 25, 2021.

    图 6  最小二乘法内孤立波速度反演模型精度散点图 (a)校正前后最高幂次为2次方的最小二乘法回归方程的反演结果散点图, 黑色散点为校正前模型结果, 红色散点为校正后模型结果; (b)校正前后最高幂次为3次方的最小二乘法回归方程的反演结果散点图, 黑色散点为校正前模型结果, 红色散点为校正后模型结果.

    Fig. 6.  Scatter plot of the solitary wave speed inversion model accuracy within least squares. (a) The scatter plot of inversion results of least squares regression equation with the highest power of 2 before and after correction. The black scatters are the model results before correction, and the red scatters are the model results after correction. (b) The scatter plot of the inversion results of the least squares regression equation with the highest power of 3 before and after correction. The black scatters are the model results before correction, and the red scatters are the model results after correction.

    图 7  内孤立波速度反演模型精度验证图 (a)—(d) 3种反演模型对400—1200 m、300—399 m、200—299 m、83—199 m水深范围的内孤立波的速度反演结果散点图; (e) 3种反演模型对83—1200 m水深范围的内孤立波的速度反演结果散点图; (a)—(e) 黑色散点为最高幂次为2次方的最小二乘法反演模型结果, 红色散点为最高幂次为3次方的最小二乘法反演模型结果, 蓝色散点为SVR反演模型结果; (f) 三种反演模型对400—1200 m、300—399 m、200—299 m、83—199 m水深范围的内孤立波的速度反演结果的平均绝对误差柱状图

    Fig. 7.  Precision validation diagram of the internal solitary wave velocity inversion model: (a)–(d) Scatter plots of inversion results of three inversion models for internal solitary waves speed in water depths of 400–1200 m, 300–399 m, 200–299 m and 83–199 m, respectively; (e) scatter plot of inversion results of three inversion models for internal solitary waves speed in water depths of 83–1200 m; (a)–(e) the black scattered points are the results of least squares inversion model with the highest power of 2, the red scattered points are the results of least squares inversion model with the highest power of 3, and the blue scattered points are the results of SVR inversion model; (f) the average absolute error histogram of the inversion results of the three inversion models for internal solitary waves speed in the water depths of 400–1200 m, 300–399 m, 200–299 m and 83–199 m.

    表 1  内孤立波实验设计表

    Table 1.  Design table of internal solitary wave experiment.

    组数总水深/cm上层水深/cm下层水深/cm上层密度/(g·cm–3)下层密度/(g·cm–3)塌陷高度/cm
    1444401.001.085, 10, 15, 20
    2445391.001.085, 10, 15, 20
    34410341.001.085, 10, 15, 20
    44412321.001.085, 10, 15, 20
    5655601.001.045, 10, 15, 20
    6655601.011.045, 10, 15, 20
    7655601.021.045, 10, 15, 20
    86510551.001.045, 10, 15, 20, 25
    9688.559.51.001.045, 10, 15, 20
    10688.559.51.001.065, 10, 15, 20
    11688.559.51.001.085, 10, 15, 20
    下载: 导出CSV

    表 2  内孤立波速度反演模型精度验证表

    Table 2.  Precision verification table of internal solitary wave velocity inversion model.

    水深
    范围/m
    数据V/
    (m·s–1)
    VZ2/
    (m·s–1)
    AEz2/
    (m·s–1)
    VZ3/
    (m·s–1)
    AEz3
    (m·s–1)
    VSVR/
    (m·s–1)
    AESVR/
    (m·s–1)
    400—1200数据12.221.730.491.710.511.850.37
    数据22.051.850.201.890.162.040.01
    数据91.521.770.251.770.251.930.41
    300—399数据11.601.690.091.620.021.800.20
    数据21.901.950.051.9001.720.18
    数据111.431.380.051.390.041.690.26
    200—299数据11.321.380.061.390.071.550.23
    数据21.441.620.181.450.011.480.04
    数据141.221.030.190.990.230.970.25
    83—199数据10.861.400.541.370.511.130.27
    数据21.271.330.061.290.021.060.21
    数据100.830.900.071.010.180.620.21
    注: V表示遥感实测速度, VZ2表示最小二乘法二次方速度反演模型反演值, VZ3表示最小二乘法三次方速度反演模型反演值, VSVR表示SVR速度反演模型反演值, AEZ2表示VZ2V的绝对误差, AEZ3 表示VZ3V的绝对误差, AESVR表示VSVRV的绝对误差.
    下载: 导出CSV
  • [1]

    Yang Y C, Huang X D, Zhao W, Zhou C, Huang S W, Zhang Z W, Tian J W 2021 J. Phys. Oceanogr. 51 3609Google Scholar

    [2]

    关晖, 苏晓冰, 田俊杰 2011 计算力学学报 28 60Google Scholar

    Guan H, Su X B, Tian J W 2011 Chin. J. Comp. Mech. 28 60Google Scholar

    [3]

    刘国涛, 尚晓东, 陈桂英, 卢著敏, 刘良钢, 程晓波 2007 中山大学学报(自然科学版) 46 167Google Scholar

    Liu G T, Shang X D, Chen G Y, Lu Z M, Liu L G, Cheng X B 2007 Acta Sci. Natur. Univ. Sunyatseni 46 167Google Scholar

    [4]

    汪超, 杜伟, 杜鹏, 李卓越, 赵森, 胡海豹, 陈效鹏, 黄潇 2022 力学学报 54 1921Google Scholar

    Wang C, Du W, Du P, Li Z Y, Zhao S, Hu H B, Chen X P, Huang X 2022 Chin. J. Theor. App. Mech. 54 1921Google Scholar

    [5]

    汪超, 杜伟, 李广华, 杜鹏, 赵森, 李卓越, 陈效鹏, 胡海豹 2022 中国舰船研究 17 102Google Scholar

    Wang C, Du W, LI G H, Du P, Zhao S, Li Z Y, Chen X P, Hu H B 2022 Chin. J. Ship Res. 17 102Google Scholar

    [6]

    刘秀全, 陈国明, 畅元江, 姬景奇, 傅景杰, 张浩 2017 石油学报 38 1448Google Scholar

    Liu X Q, Chen G M, Chang Y J, Ji J Q, Fu J J, Zhang H 2017 Acta Petro. Sin. 38 1448Google Scholar

    [7]

    Farrar J T, Zappa C J, Weller R A, Jessup A T 2007 J. Geophys. Res-Oceans 112 1Google Scholar

    [8]

    蔡树群, 何建玲, 谢皆烁 2011 地球科学进展 26 703Google Scholar

    Cai S Q, He J L, Xie J H 2011 Adv. Earth Sci. 26 703Google Scholar

    [9]

    黄晓冬, 赵玮 2014 中国海洋大学学报(自然科学版) 44 19Google Scholar

    Huang X D, Zhao W 2014 Period. Ocean Univ. China 44 19Google Scholar

    [10]

    Cai S Q, Xie J S, He J L 2012 Surv. Geophys. 33 927Google Scholar

    [11]

    张涛, 张旭东 2020 海洋与湖沼 51 991Google Scholar

    Zhang T, Zhang X D 2020 Oceanologia Limnologia Sin. 51 991Google Scholar

    [12]

    邝芸艳, 王亚龙, 宋海斌, 关永贤, 范文豪, 龚屹, 张锟 2021 地球物理学报 64 597Google Scholar

    Kuang Y Y, Wang Y L, Song H B, Guan Y X, Fan W H, Ging Y, Zhang K 2021 Chin. J. Geophys. 64 597Google Scholar

    [13]

    孙丽娜, 张杰, 孟俊敏, 崔伟 2022 海洋学报 44 137Google Scholar

    Sun L N, Zhang J, Meng J M, Cui W 2022 Acta. Oceanol. Sin. 44 137Google Scholar

    [14]

    Alford M H, Lien R C, Simmons H, Klymak J, Ramp S, Yang Y J, Tang D, Chang M H 2010 J. Phys. Oceanogr. 40 1338Google Scholar

    [15]

    Huang X D, Chen Z H, Zhao W, Zhang Z W, Zhou C, Yang Q X, Tian J W 2016 Sci. Rep-UK. 6 30041Google Scholar

    [16]

    吕海滨, 何宜军, 申辉 2012 海洋科学 36 98Google Scholar

    LÜ H B, He Y J, Shen H 2012 Marine Sci. 36 98Google Scholar

    [17]

    Hong D B, Yang C S, Ouchi K 2015 Remote. Sens. Lett. 6 448Google Scholar

    [18]

    Meetei C, Nadimpalli J R, Dash M K, Barskar H 2020 Remote. Sens. Environ. 252 112123Google Scholar

    [19]

    Sun L N, Zhang J, Meng J M 2021 J. Oceanol. Limnol 39 14Google Scholar

    [20]

    Zhang M, Wang J, Li Z X, Liang K D, Chen X 2022 J. Geophys. Res-Oceans. 2 127Google Scholar

    [21]

    Wang J, Zhang M, Mei Y, Lu K X, Chen X 2020 IEEE. Geosci. Remote. S. 99 1Google Scholar

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  • 收稿日期:  2022-08-16
  • 修回日期:  2022-10-09
  • 上网日期:  2022-11-01
  • 刊出日期:  2023-01-20

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