Quantitative analysis and prediction of the sound field convergence zone in mesoscale eddy environment based on data mining methods

Ming Li Yuhang Liu Yiyuan Sun Kefeng Liu

Ming Li, Yuhang Liu, Yiyuan Sun, Kefeng Liu. Quantitative analysis and prediction of the sound field convergence zone in mesoscale eddy environment based on data mining methods[J]. Acta Oceanologica Sinica. doi: 10.1007/s13131-024-2328-5
Citation: Ming Li, Yuhang Liu, Yiyuan Sun, Kefeng Liu. Quantitative analysis and prediction of the sound field convergence zone in mesoscale eddy environment based on data mining methods[J]. Acta Oceanologica Sinica. doi: 10.1007/s13131-024-2328-5

doi: 10.1007/s13131-024-2328-5

Quantitative analysis and prediction of the sound field convergence zone in mesoscale eddy environment based on data mining methods

Funds: The National Natural Science Foundation of China under contract Nos 41875061 and 41775165.
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    Corresponding author: E-mail: mingli152@163.com
  • These authors contributed equally to this work.
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    These authors contributed equally to this work.
  • Figure  1.  The sound speed profile of deep sea.

    Figure  2.  The convergence of sound rays in deep sea.

    Figure  3.  The technical route of CZ parameter modeling.

    Figure  4.  Different sound propagation scenarios.

    Figure  5.  Characteristics of sound propagation with a warm eddy: the sound propagation loss (a) and sound ray (b) distribution. In b, the red line represents the refracted sound, and the green line represents the reflected sound.

    Figure  6.  Characteristics of sound propagation with no eddy: the sound propagation loss (a) and sound ray (b) distribution. In b, the red line represents the refracted sound, and the green line represents the reflected sound.

    Figure  7.  The input and output of ML-based prediction model.

    Figure  8.  The technical process of ML-based prediction model.

    Figure  9.  The RE of the predicted CZ distance with RF.

    Figure  10.  The RE of the predicted CZ distance with GBDT.

    Figure  11.  The RE of the predicted CZ distance with SaD-ELM.

    Figure  12.  The RE of the predicted CZ width with RF.

    Figure  13.  The RE of the predicted CZ width with GBDT

    Figure  14.  The RE of the predicted CZ width with SaD-ELM

    Table  1.   The description of eddy parameters and sound source position

    Parameter Definition Setting
    Eddy intensity/(m · s−1) it is characterized by the sound velocity difference between the eddy center and the edge value range is –50 m/s to +50 m/s, gap is +5 m/s; + indicates warm eddy and – indicates cold eddy
    Eddy radius/km it is characterized by the horizontal distance between the eddy center and the edge value range is 20 km to 300 km, gap is 20 km
    Depth of sound source/m literal meaning value range is 100 m to 400 m, gap is 20 m
    Distance of sound source/km it is characterized by the horizontal distance of the sound source from the eddy center (vertical central axis) value range is 0 km to 150 km, gap is 15 km
    下载: 导出CSV

    Table  2.   Regression analysis between CZ distance and eddy intensity

    Model Depth/m Regression equation R2 F Sig. RMSE
    Linear regression model 100 y = 0.07615x + 53.15 0.992 14598.965 0 0.226
    200 y = 0.08775x + 49.94 0.998 19823.564 0 0.307
    300 y = 0.09979x + 47.14 0.988 10479.997 0 0.181
    Quadratic regression model 100 y = 0.00024x2 + 0.07615x + 52.92 0.999 13874.476 0 0.079
    200 y = 0.00032x2 + 0.08775x + 49.64 0.998 14462.807 0 0.121
    300 y = 0.00017x2 + 0.04979x + 46.98 0.996 9134.502 0 0.096
    下载: 导出CSV

    Table  3.   Regression analysis between CZ distance and eddy radius

    Model Depth/m Regression equation R2 F Sig. RMSE
    Linear regression model 100 y = 0.01253x + 54.59 0.752 1124.873 0 0.625
    200 y = 0.01651x + 51.37 0.839 1952.309 0 0.626
    300 y = 0.00886x + 48.02 0.793 1267.598 0 0.392
    Quadratic regression model 100 y = −0.00011x2 + 0.04102x + 52.93 0.963 11269.375 0 0.244
    200 y = −0.00012x2 + 0.04471x + 49.73 0.973 14633.754 0 0.261
    300 y = −0.00011x2 + 0.02719x + 46.96 0.979 15124.561 0 0.127
    下载: 导出CSV

    Table  4.   Regression analysis between CZ width and eddy intensity

    Model Depth/m Regression equation R2 F Sig. RMSE
    Linear regression model 100 y = −0.03299x + 5.979 0.973 12531.632 0 0.264
    200 y = −0.04228x + 9.829 0.978 13105.415 0 0.256
    300 y = −0.06683x + 14.51 0.184 / / 4.549
    Quadratic regression model 100 y = 0.00022x2 − 0.03299x + 5.77 0.942 9975.143 0 0.183
    200 y = 0.00017x2 − 0.04228x + 9.67 0.966 10132.472 0 0.211
    300 y = 0.00292x2 − 0.06683x + 11.68 0.454 / / 3.787
    Note: / indicates invalid value.
    下载: 导出CSV

    Table  5.   Regression analysis between the CZ width and eddy radius

    Model Depth/m Regression equation R2 F RMSE
    Linear regression model 100 y = −0.00197x + 5.022 0.411 / 0.254
    200 y = −0.00475x + 8.996 0.721 1024.143 0.256
    300 y = 0.00516x + 12.81 0.789 1322.219 0.231
    Quadratic regression model 100 y = 0.000032x2 − 0.01243x + 5.63 0.788 1387.458 0.133
    200 y = 0.000019x2 − 0.01103x + 9.36 0.789 1269.655 0.226
    300 y = −0.0000015x2 − 0.0054x + 12.82 0.787 1463.914 0.236
    Note: / indicates invalid value.
    下载: 导出CSV

    Table  6.   Parameters set of the three ML algorithms

    ML algorithm Parameter setting
    RF the number of decision trees, the maximum depth of each tree, and the number of node samples are set as 100, 30, and 10; the remaining parameters are left with the default values
    GBDT the maximum depth of the tree is 5; maximum iteration is 5; learning rate is 0.1; the remaining parameters are left with the default values
    SaD-ELM the number of hidden layers is 3; the number of neurons in each hidden layer is 10; the excitation function is “sig”; the population number, variation probability and crossover probability are set as 30, 0.5, and 0.4; the remaining parameters are left with the default values
    下载: 导出CSV

    Table  7.   Error measures of the predicted CZ parameters

    CZ parameter Assessing indicator RF GBDT SaD-ELM
    CZ distance RMSE 0.4412 0.1353 0.5182
    CC 0.9771 0.9982 0.9694
    NSE 0.9149 0.9829 0.9134
    CZ width RMSE 1.3345 1.3093 1.3642
    CC 0.8733 0.8782 0.8671
    NSE 0.6047 0.6231 0.5023
    下载: 导出CSV

    Table  8.   CZ parameters calculated by ML and simulation

    Eddy Distance of the first CZ/km Width of the first CZ/m
    GBDT BELLHOP GBDT BELLHOP
    Eddy A 56.3 63.9 9.2 4.8
    Eddy B 60.5 62.3 11.3 8.3
    Eddy C 57.1 59.3 9.5 5.2
    Eddy D 52.8 61.7 10.9 6.4
    Eddy E 55.6 63.8 12.1 7.2
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-12-08
  • 录用日期:  2024-04-03
  • 网络出版日期:  2024-05-13

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