A method for predicting the path of the kuroshio based on a hybrid deep learning model

Abstract

The present application relates to the technical field of marine information, in particular to a kind of Kuroshio path prediction method based on hybrid deep learning model, comprising the following steps: obtaining current data;Application improved feature line method identifies Kuroshio flow axis, and the Kuroshio flow axis identified is carried out sliding average and segmented interpolation;Deep learning model is constructed by orthogonal empirical function EOF, time domain convolution network TCN and long short-term memory network LSTM;The Kuroshio flow axis after segmented interpolation is divided into training set and test set;Training set is used to train the model constructed, and the Kuroshio path is predicted training;The Kuroshio path data before forecast time is input into the model trained, and the future Kuroshio path is predicted.The present application improves time series prediction performance;In the case of small data amount, relatively accurate prediction result is realized.

Description

Technical Field

[0001] This invention relates to the field of marine information technology, and in particular to a method for predicting the Kuroshio Current path based on a hybrid deep learning model. Background Technology

[0002] The Kuroshio Current originates from the North Equatorial Current and is influenced by intense solar radiation, resulting in high water temperature, high salinity, and rapid current. Its strength and location variations significantly impact the hydrological conditions and marine ecosystem of its downstream areas and adjacent waters. Therefore, research on the Kuroshio Current's path is of paramount importance.

[0003] The largest surface current velocity in the Kuroshio Current is found in the surface Kuroshio Current axis (hereinafter referred to as the Kuroshio Current axis). In 2004, Ambe et al. first proposed the method of characteristics to determine the Kuroshio Current axis using altimeter and buoy data. Since then, scholars have continuously improved this method and applied it to the identification of the Kuroshio Current axis. The method of characteristics has some problems: it is easily affected by surrounding eddies, fronts, and other phenomena, which can cause the position of the current axis to be offset; the identified current axis is not smooth enough and may contain local fluctuations or anomalies, etc.

[0004] While previous research has yielded fruitful results, many gaps remain in the study and prediction of the Kuroshio Current's path. Machine learning has become increasingly mature and widely accepted in the field of ocean forecasting; however, its potential in predicting the Kuroshio Current's path has not been fully explored. Therefore, this invention takes the Kuroshio Current's path as the research object, integrating mode decomposition methods and machine learning algorithms to systematically carry out feature extraction analysis and predictive modeling of the Kuroshio Current's path. Summary of the Invention

[0005] This invention provides a method for predicting the Kuroshio Current path based on a hybrid deep learning model, in order to solve the problems of unstable Kuroshio Current path identification and inaccurate prediction in the prior art.

[0006] This invention provides a method for predicting the Kuroshio Current path based on a hybrid deep learning model, comprising the following steps:

[0007] Step 1: Obtain ocean current data: Current velocity grid data at a fixed depth layer within a given ocean area;

[0008] Step 2: Apply the improved feature line method to identify the Kuroshio Current axis, and perform moving average and piecewise interpolation on the identified Kuroshio Current axis;

[0009] Step 3: Construct the deep learning model BiFuse-EOF-TCN-LSTM using the orthogonal empirical function EOF, the temporal convolutional network TCN, and the long short-term memory network LSTM.

[0010] Step 4: Divide the segmented interpolated Kuroshio Current axis into a training set and a test set;

[0011] The deep learning model BiFuse-EOF-TCN-LSTM was trained using the training set to predict the Kuroshio Current path.

[0012] Step 5: Input the Kuroshio Current path data before the forecast time into the trained deep learning model BiFuse-EOF-TCN-LSTM to predict the future Kuroshio Current path.

[0013] As a preferred technical solution, in step two, the method for identifying the Kuroshio Current axis using the improved feature line method is as follows:

[0014] Step S21, determine the starting point:

[0015] The point with the fastest current in the area through which the Kuroshio flows year-round was selected as the starting point.

[0016] Step S22: Draw an auxiliary line at the starting point that is perpendicular to the flow direction at that point and has a length of 140km.

[0017] Step S23, introduce a linear weighting function. Linear weighted interpolation of the flow direction is performed every 14 km along the auxiliary line, and the average flow direction at all interpolation points is calculated; where This indicates the calculation of the original weights, which is the first... The original weight value of each interpolation point is inversely proportional to the distance from that point to the center point; Representing the The position coordinates of the interpolation points Represents the position coordinates of the center point. The distance between the interpolation point on the auxiliary line and the center point; =140, satisfy , is the The final weight value of each interpolation point is the normalized result.

[0018] Step S24: Adjust the auxiliary line to be perpendicular to the average flow direction, and perform a second interpolation on the adjusted auxiliary line. The point with the fastest flow velocity on the new auxiliary line is defined as the position of the flow axis point.

[0019] Step S25, move the step size along the average flow direction. =10km to the next location; when moving along the average current direction into the extension area of ​​the Kuroshio Current, the step size will be... Increased to 50km;

[0020] Step S26: Repeat steps S22 to S25 to identify all current axis points; after identification, connect all current axis point positions to obtain a current axis of the Kuroshio Current; repeat step S26 to obtain multiple current axes of the Kuroshio Current corresponding to each month.

[0021] As a preferred technical solution, in step S26, for each new flow axis point identified, the distance between that point and all previously identified position points is calculated; when the distance is less than 0.01°, it is determined that the automatic identification process has fallen into a vortex, and the system automatically reverts to the position point before the vortex.

[0022] If outside the Kuroshio Current's extension zone, increase the forward step length. Up to 20km, with the average flow direction of the current location as the central axis, within an angle range of 30° on both sides, select the grid point for the next location;

[0023] If within the extended area of ​​the Kuroshio Current, then the distance forward is longer. The range remains at 50km, with the same restriction applied only to the area to which the vehicle can proceed.

[0024] As a preferred technical solution, in step two...

[0025] Moving average: The latitude and longitude of the points on the obtained flow axis are averaged to obtain the flow axis after moving average; where the moving window is 11 in the non-Kuroshio extension region and 3 in the Kuroshio extension region.

[0026] Segmented interpolation: Each complete current axis after moving average is divided into two segments of the Kuroshio Current path, namely the first segment and the second segment. The first segment of the Kuroshio Current path is the part with latitude between 23°N and 25.5°N, and longitude interpolation is performed with a latitude resolution of 1 / 12°. The second segment of the Kuroshio Current path is the part with longitude between 122°E and 141°E, and latitude interpolation is performed with a longitude resolution of 1 / 12°.

[0027] As a preferred technical solution, in step three, the deep learning model BiFuse-EOF-TCN-LSTM includes an EOF analysis unit and a TCN-LSTM prediction unit;

[0028] The EOF analysis unit decomposes the data from the two Kuroshio Current paths into spatial modes and time functions;

[0029] After piecewise interpolation, the data from the two segments of the Kuroshio path are used as the original data and are presented in matrix form:

[0030]

[0031] In the formula, This is the data matrix for the two segments of the Kuroshio path after piecewise interpolation. The number of points in space is called the spatial dimension. The number of time points or samples is called the time dimension.

[0032] As a preferred technical solution, the implementation steps of the EOF analysis unit are as follows:

[0033] Step 31, Data Standardization:

[0034] First calculate To obtain the time mean at each spatial point, we calculate the mean for each row of the data matrix for the two Kuroshio Current paths:

[0035]

[0036] in, This represents a column vector consisting of the time averages of all spatial points, with dimension 1. , This represents the number of interpolation points for latitude / longitude in the two Kuroshio Current paths. ,in, , indicating the first of the two Kuroshio paths The mean of longitude / latitude at each interpolated latitude / longitude spatial point. Indicates the first path corresponding to the Kuroshio Current. The interpolated latitude / longitude spatial point, the first Longitude / latitude values ​​at each point in time;

[0037] Secondly, calculate the standard deviation matrix. :

[0038]

[0039] in, The dimension is , ,in, , indicating the first of the two Kuroshio paths The standard deviation of longitude or latitude at each interpolated latitude or longitude point in space;

[0040] Then, the standardized data matrix is ​​obtained:

[0041]

[0042] in, The data matrix consists of two standardized segments of the Kuroshio Current path, each item of which is obtained through... The calculations show that the time series of each spatial point has a mean of 0 and a standard deviation of 1.

[0043] Step 32, calculate the covariance matrix:

[0044] The formula for calculating covariance is as follows:

[0045]

[0046] in, This is the standardized data matrix of the two Kuroshio Current paths. The number of time points, express The transpose of is used to obtain the covariance matrix of the two Kuroshio path data;

[0047] Step 33, for the covariance matrix Perform eigenvalue decomposition:

[0048] Find the eigenvalues ​​and eigenvectors of the covariance matrices for the two Kuroshio Current path data segments respectively:

[0049]

[0050] in, The eigenvector matrix of the covariance matrix of the two Kuroshio Current path data segments is... satisfy , This is a diagonal matrix, where the diagonal elements are the eigenvalues ​​of the covariance matrix of the two Kuroshio path data segments. The eigenvalues ​​and their corresponding eigenvectors are sorted from largest to smallest as follows:

[0051]

[0052] in, The value of is determined by the number of interpolation points of latitude or longitude in the two Kuroshio Current paths;

[0053] Step 34, Calculate the time coefficient:

[0054] Time coefficient It is achieved by standardizing the two segments of the Kuroshio Current path data matrix. Projected onto the corresponding eigenvector matrices What was obtained from:

[0055]

[0056] Among them, the eigenvector matrix That is, spatial modes. That is, the corresponding time coefficient;

[0057] Step 35, extract the principal components:

[0058] The two sections of the Kuroshio path Multiplying the eigenvector fields and their corresponding time coefficients yields a fitted field:

[0059]

[0060] in, That is, the standardized data matrix M represents the spatial dimension, and N represents the temporal dimension; To represent the fitted field matrix, use the first... The approximate matrix obtained by reconstructing the principal components is used to approximate... ; or This represents the eigenvector field matrix, taking the first... Each principal component corresponds to a feature vector, and each column is a feature vector (spatial mode), with a dimension of M×P; or Represents the time coefficient matrix, the first... The time coefficients corresponding to each principal component are shown in the figure. Each row is a sequence of coefficients of a principal component over time, with a dimension of P×N.

[0061] Then the first of the two Kuroshio paths Each eigenvector field pairs with the original field The contribution rate is:

[0062]

[0063] in, For the first eigenvector pairs The contribution rate represents the proportion of the original data variance that the principal component can explain. For the first The eigenvalues ​​corresponding to each principal component reflect the magnitude of the variance of the original data contained in that principal component. The sum of the eigenvalues ​​of all M principal components represents the original field. The total variance.

[0064] The two sections of the Kuroshio path Cumulative contribution rate of each eigenvector field for:

[0065]

[0066] in, Indicates the preceding The sum of the eigenvalues ​​of the principal components.

[0067] Step 36, significance test:

[0068] For the two Kuroshio Current paths, according to The magnitudes of the eigenvector fields are selected based on their physical significance, and a significance test is required:

[0069]

[0070] when When, it indicates that the two eigenvalues ​​are "separable", the first... Each mode is dominated by a significant signal.

[0071] As a preferred technical solution, the TCN-LSTM prediction unit includes a temporal convolutional network TCN and a long short-term memory network LSTM;

[0072] Deep learning models BiFuse-EOF-TCN-LSTM were constructed for the two Kuroshio Current paths, serving as prediction models for the first and second Kuroshio Current paths, respectively.

[0073] The parameters are set as follows: the time backtracking window length is set to 6, the prediction step size is set to 3, the Adam optimizer is used, the decay rate is 0.5, and the initial learning rate is 0.001. The model decay period of the first Kuroshio path prediction model is 20, and the model decay period of the second Kuroshio path prediction model is 65.

[0074] As a preferred technical solution, Temporal Convolutional Network (TCN) is recommended.

[0075]

[0076] in, The time step is The output, For the input time series data, It is the size of Convolutional filters, For convolution operators, Convolutional filter The j-th weight parameter in the equation, The input values ​​are from past time steps. To capture long-range dependencies without increasing network depth, dilated convolutions are introduced, with the dilation factor set to [value missing]. Elements in the sequence dilated convolution operation Defined as:

[0077]

[0078] in, For dilated convolution operators, For the input sequence in the past The value of each time step;

[0079] Long Short-Term Memory (LSTM) network includes a forget gate, an input gate, and an output gate;

[0080] Forgotten Gate: ;

[0081] Input Gate: ;

[0082] A new candidate vector is created through the tanh layer, and this candidate vector is added to the cell state: ;

[0083] Update cell status: , This indicates element-wise multiplication;

[0084] Output gate: , ;

[0085] in, The input represents the current time step t. This represents the output of the forget gate at time step t. This indicates the output of the output gate at time step t. This represents the output of the input gate at time step t. This represents the hidden layer state at time step t. This represents the hidden layer output of the previous time step. This represents the hidden layer output at the previous time step. Concatenate it with the current input. The cell representing the current time step t, This indicates the cell status at the previous time step. Indicates the candidate values ​​for the cell status. This represents the sigmoid activation function of the gate. This represents the tanh activation function. , , , These represent the weight matrices for the forget gate, input gate, candidate cell generation state, and output gate, respectively. , , , These represent the bias terms for the forget gate, input gate, candidate cell generation state, and output gate, respectively.

[0086] As a preferred technical solution, in step four, the first segment of the Kuroshio Current path data in the training set is input into the first segment of the Kuroshio Current path prediction model. The EOF analysis unit in the model is used to perform spatiotemporal decomposition on the training set. The spatial modes with a cumulative variance contribution rate of 99% and their corresponding time functions are taken from the data of the first segment of the Kuroshio Current path and used as the input data for the TCN-LSTM prediction unit in the corresponding model. The TCN-LSTM prediction unit in the corresponding model is used to train and predict the first segment of the Kuroshio Current path prediction model.

[0087] The second segment of the Kuroshio Current path data in the training set is input into the second segment of the Kuroshio Current path prediction model. The EOF analysis unit in the model is used to perform spatiotemporal decomposition on the training set. The spatial modes with a cumulative variance contribution rate of 95% and their corresponding time functions are taken from the second segment of the Kuroshio Current path data and used as the input data for the TCN-LSTM prediction unit in the corresponding model. The TCN-LSTM prediction unit in the corresponding model is used to train and predict the second segment of the Kuroshio Current path prediction model.

[0088] As a preferred technical solution, in step five, the Kuroshio Current path data for the six months prior to the forecast time is input into the trained first and second Kuroshio Current path forecast models to predict the Kuroshio Current path data for the next three months, obtain the forecast time function results, and reshape the forecast results:

[0089]

[0090] in, The principal mode matrix, i.e., the eigenvector field matrix of the training set, is taken from the first... The eigenvectors corresponding to each principal component For the predicted time series, T denotes transpose. and These are the standard deviation and mean of the training set, respectively; finally, the reconstructed longitude and latitude prediction sequences are obtained: the predicted longitude sequence of the first Kuroshio path and the predicted latitude sequence of the second Kuroshio path;

[0091] The prediction results of the first Kuroshio path prediction model and the second Kuroshio path prediction model are recombined. If there is an intersection between the two models, the first Kuroshio path is completely retained, and the intersection of the second Kuroshio path is discarded, so that the starting longitude of the second Kuroshio path is not less than the longitude of the ending point of the first Kuroshio path.

[0092] This invention provides a Kuroshio Current path prediction method based on a hybrid deep learning model. Compared with existing technologies, it solves the problem of east-west oscillation of the Kuroshio Current path by segmenting the path for analysis. It adopts a hybrid model of TCN and LSTM, where TCN captures long-distance time dependencies in sequence data, while LSTM processes the dynamic changes in time series data. Combining the advantages of both structures improves the performance of time series prediction. It achieves relatively accurate prediction results even with small amounts of data. Attached Figure Description

[0093] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0094] Figure 1 This is a flowchart of the Kuroshio Current path prediction method based on a hybrid deep learning model according to the present invention;

[0095] Figure 2 The method of this invention is used to predict the Kuroshio Current path in October 2024;

[0096] Figure 3 The method of this invention is used to predict the Kuroshio Current path in November 2024;

[0097] Figure 4 The method of this invention is used to predict the Kuroshio Current path in December 2024. Detailed Implementation

[0098] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0099] Furthermore, the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article, unless otherwise specified, generally indicates that the preceding and following related objects have an "or" relationship.

[0100] The embodiments of the present invention will now be described in further detail with reference to the accompanying drawings.

[0101] See Figure 1 This invention provides a method for predicting the Kuroshio Current path based on a hybrid deep learning model, comprising the following steps:

[0102] Step 1: Obtain ocean current data: Current velocity grid data at a fixed depth layer within a given ocean area;

[0103] Step 2: Apply the improved feature line method to identify the Kuroshio Current axis, and perform moving average and piecewise interpolation on the identified Kuroshio Current axis;

[0104] Step 3: Construct the deep learning model BiFuse-EOF-TCN-LSTM using the orthogonal empirical function EOF, the temporal convolutional network TCN, and the long short-term memory network LSTM.

[0105] Step 4: Divide the segmented interpolated Kuroshio Current axis into a training set and a test set; use the training set to train the constructed deep learning model BiFuse-EOF-TCN-LSTM to predict the Kuroshio Current path.

[0106] Step 5: Input the Kuroshio Current path data before the forecast time into the trained deep learning model BiFuse-EOF-TCN-LSTM to predict the future Kuroshio Current path.

[0107] Specifically, in step one, obtaining ocean current data includes downloading relevant data products and acquiring relevant data variables. Among these,

[0108] Download the relevant data products: The data source is the global multi-year physical ocean reanalysis product GLOBAL_MULTIYEAR_PHY_001_030 series, specifically cmems_mod_glo_phy_my_0.083deg_P1M-m and cmems_mod_glo_phy_myint_0.083deg_P1M-m, provided by the Copernicus Marine Environmental Monitoring Service (CMEMS) under the GLORYS12V1 global ocean reanalysis product. It covers data from January 1993 to December 2024, with a global data spatial scope.

[0109] Obtain relevant data variables: By downloading relevant data products, extract the eastward and northward flow velocity variables, with a spatial range of 110°E~160°E and 10°N~45°N. Vertically, select a 50m depth layer for single linear interpolation to obtain .mat data files of eastward flow velocity "uo" and northward flow velocity "vo" at the 50m layer from January 1993 to December 2024 (a total of 384 months).

[0110] In step two, the method for identifying the Kuroshio Current axis using the improved feature line method is as follows:

[0111] Step S21, determine the starting point:

[0112] The point with the fastest current in the area through which the Kuroshio flows year-round was selected as the starting point.

[0113] The region through which the Kuroshio Current passes annually is selected in this invention as the area east of a certain region through which the Kuroshio Current passes annually.

[0114] Step S22: Draw an auxiliary line at the starting point that is perpendicular to the flow direction at that point and has a length of 140km.

[0115] Step S23, introduce a linear weighting function. Linear weighted interpolation of the flow direction is performed every 14 km along the auxiliary line, and the average flow direction at all interpolation points is calculated; where This indicates the calculation of the original weights, which is the first... The original weight value of each interpolation point is inversely proportional to the distance from that point to the center point; Representing the The position coordinates of the interpolation points Represents the position coordinates of the center point. The distance between the interpolation point on the auxiliary line and the center point; =140, satisfy , is the The final weight value of each interpolation point is the normalized result.

[0116] Step S24: Adjust the auxiliary line to be perpendicular to the average flow direction, and perform a second interpolation on the adjusted auxiliary line. The point with the fastest flow velocity on the new auxiliary line is defined as the position of the flow axis point.

[0117] Step S25, move the step size along the average flow direction. =10km to the next location; when moving along the average current direction into the Kuroshio extension area (east of 141°E), the step length will be... Increased to 50km;

[0118] Step S26: Repeat steps S22 to S25 to identify all current axis points; after identification, connect all current axis point positions to obtain a current axis of the Kuroshio Current. Repeat step S26 to obtain multiple current axes of the Kuroshio Current corresponding to each month. In this embodiment, repeating step S26 yields a total of 384 current axes of the Kuroshio Current corresponding to each month.

[0119] For each new current axis point identified, the distance between that point and all previously identified locations is calculated. If the distance is less than 0.01° (approximately 1.11 km), the automatic identification process is considered to have entered a vortex. In this case, the system automatically retreats to the location before the vortex. If the location is outside the Kuroshio Current extension area, the forward step length is increased. Up to 20km, using the average flow direction at the current location as the central axis, within a 30° angle range on either side, select the next grid point; if within the Kuroshio extension area, the next step length is [not specified]. The limit remains at 50 km, with the same restriction applied only to the area through which the Kuroshio main axis passes during its forward flow.

[0120] Moving average: The latitude and longitude of the points on the obtained flow axis are averaged to obtain the flow axis after moving average; the moving average window is 11 in the non-Kuroshio extension area and 3 in the Kuroshio extension area.

[0121] Segmented interpolation: Each complete current axis after moving average is divided into two segments of the Kuroshio Current path, namely the first segment and the second segment. The first segment of the Kuroshio Current path is the part with latitude between 23°N and 25.5°N, and longitude interpolation is performed with a latitude resolution of 1 / 12°. The second segment of the Kuroshio Current path is the part with longitude between 122°E and 141°E, and latitude interpolation is performed with a longitude resolution of 1 / 12°.

[0122] In step three, the deep learning model BiFuse-EOF-TCN-LSTM includes an EOF analysis unit and a TCN-LSTM prediction unit.

[0123] The EOF analysis unit is used to reduce the dimensionality of data, extract the main spatiotemporal change patterns, and retain key information; it can be used to reduce the dimensionality of the original data and improve computational efficiency.

[0124] The TCN-LSTM prediction unit utilizes the dilated convolution of the temporal convolutional network TCN to expand the receptive field and the long short-term memory network LSTM to capture long-term dependencies, taking into account both local and global spatiotemporal information for training and prediction.

[0125] Furthermore, the EOF analysis unit decomposes the data from the two Kuroshio Current paths into spatial modes and time functions.

[0126] After piecewise interpolation, the data from the two segments of the Kuroshio path are used as the original data and are presented in matrix form:

[0127]

[0128] In the formula, This is the data matrix for the two segments of the Kuroshio path after piecewise interpolation. The number of points in space is called the spatial dimension. The number of time points or samples is called the time dimension.

[0129] In the matrix In the diagram, each column represents the spatial distribution at a specific point in time. For the first segment of the Kuroshio Current path, each column represents the longitude value at the interpolated latitude point at a specific point in time. For the second segment of the Kuroshio Current path, each column represents the latitude value at the interpolated longitude point at a specific point in time. Each row represents the time series value of a spatial point. For the first segment of the Kuroshio Current path, each row represents the longitude time series at a specific interpolated latitude point. For the second segment of the Kuroshio Current path, each row represents the latitude time series at a specific interpolated longitude point.

[0130] The spatial modes do not change with time, while the time function depends only on time. The implementation steps of the EOF analysis unit are as follows:

[0131] Step 31, Data Standardization:

[0132] First calculate To obtain the time mean at each spatial point, we calculate the mean for each row of the data matrix for the two Kuroshio Current paths:

[0133]

[0134] in, This represents a column vector consisting of the time averages of all spatial points, with dimension 1. , This represents the number of interpolation points for latitude / longitude in the two Kuroshio Current paths. ,in, , indicating the first of the two Kuroshio paths The mean of longitude / latitude at each interpolated latitude / longitude spatial point. Indicates the first path corresponding to the Kuroshio Current. The interpolated latitude / longitude spatial point, the first Longitude / latitude values ​​at each point in time;

[0135] Secondly, calculate the standard deviation matrix. :

[0136]

[0137] in, The dimension is , ,in, , indicating the first of the two Kuroshio paths The standard deviation of longitude or latitude at each interpolated latitude or longitude point in space;

[0138] Then, the standardized data matrix is ​​obtained:

[0139]

[0140] in, The data matrix consists of two standardized segments of the Kuroshio Current path, each item of which is obtained through... The calculations show that the time series of each spatial point has a mean of 0 and a standard deviation of 1.

[0141] Step 32, calculate the covariance matrix:

[0142] The formula for calculating covariance is as follows:

[0143]

[0144] in, This is the standardized data matrix of the two Kuroshio Current paths. The number of time points, express The transpose of is used to obtain the covariance matrix of the two Kuroshio path data;

[0145] Step 33, for the covariance matrix Perform eigenvalue decomposition:

[0146] Find the eigenvalues ​​and eigenvectors of the covariance matrices for the two Kuroshio Current path data segments respectively:

[0147]

[0148] in, The eigenvector matrix of the covariance matrix of the two Kuroshio Current path data segments is... satisfy , This is a diagonal matrix, where the diagonal elements are the eigenvalues ​​of the covariance matrix of the two Kuroshio path data segments. The eigenvalues ​​and their corresponding eigenvectors are sorted from largest to smallest as follows:

[0149]

[0150] in, The value of is determined by the number of interpolation points (i.e., spatial dimensions) of latitude (or longitude) in the two Kuroshio paths;

[0151] Step 34, Calculate the time coefficient:

[0152] Time coefficient It is achieved by standardizing the two segments of the Kuroshio Current path data matrix. Projected onto the corresponding eigenvector matrices What was obtained from:

[0153]

[0154] Among them, the eigenvector matrix That is, spatial modes. That is, the corresponding time coefficient;

[0155] Step 35, extract the principal components:

[0156] The two sections of the Kuroshio path Multiplying the eigenvector fields and their corresponding time coefficients yields a fitted field:

[0157]

[0158] in, That is, the standardized data matrix M represents the spatial dimension, and N represents the temporal dimension; To represent the fitted field matrix, use the first... The approximate matrix obtained by reconstructing the principal components is used to approximate... ; or This represents the eigenvector field matrix, taking the first... Each principal component corresponds to a feature vector, and each column is a feature vector (spatial mode), with a dimension of M×P; or Represents the time coefficient matrix, the first... The time coefficients corresponding to each principal component are shown in the figure. Each row is a sequence of coefficients of a principal component over time, with a dimension of P×N.

[0159] Then the first of the two Kuroshio paths Each eigenvector field pairs with the original field The contribution rate is:

[0160]

[0161] in, For the first eigenvector pairs The contribution rate represents the proportion of the original data variance that the principal component can explain. For the first The eigenvalues ​​corresponding to each principal component reflect the magnitude of the variance of the original data contained in that principal component. The sum of the eigenvalues ​​of all M principal components represents the original field. The total variance.

[0162] The two sections of the Kuroshio path Cumulative contribution rate of each eigenvector field for:

[0163]

[0164] in, Indicates the preceding The sum of the eigenvalues ​​of the principal components.

[0165] Step 36, significance test:

[0166] For the two Kuroshio Current paths, according to The magnitudes of the eigenvector fields are selected based on their physical significance, and a significance test is required:

[0167]

[0168] when When, it indicates that the two eigenvalues ​​are "separable", the first... Each mode is dominated by a significant signal.

[0169] Furthermore, the TCN-LSTM prediction unit comprises a temporal convolutional network (TCN) and a long short-term memory network (LSTM), consisting of two convolutional layers with dilation factors, a fully connected layer, a GRU layer, and an output layer, with the ReLU activation function set. Deep learning models, BiFuse-EOF-TCN-LSTM, are constructed for the two Kuroshio Current paths, serving as prediction models for the first and second Kuroshio Current paths, respectively.

[0170] The parameters are set as follows: the time backtracking window length is set to 6, the prediction step size is set to 3, the Adam optimizer is used, the decay rate is 0.5, and the initial learning rate is 0.001. The model decay period of the first Kuroshio path prediction model is 20, and the model decay period of the second Kuroshio path prediction model is 65.

[0171] Temporal Convolutional Network (TCN):

[0172]

[0173] in, The time step is The output, For the input time series data, It is the size of Convolutional filters, For convolution operators, Convolutional filter The j-th weight parameter in the equation, The input values ​​are from past time steps. To capture long-range dependencies without increasing network depth, dilated convolutions are introduced, with the dilation factor set to [value missing]. Elements in the sequence dilated convolution operation Defined as:

[0174]

[0175] in, For dilated convolution operators, For the input sequence in the past The value of each time step;

[0176] Long Short-Term Memory (LSTM) network includes a forget gate, an input gate, and an output gate;

[0177] Forgotten Gate: ;

[0178] Input Gate: ;

[0179] A new candidate vector is created through the tanh layer, and this candidate vector is added to the cell state: ;

[0180] Update cell status: , This indicates element-wise multiplication;

[0181] Output gate: , ;

[0182] in, The input represents the current time step t. This represents the output of the forget gate at time step t. This indicates the output of the output gate at time step t. This represents the output of the input gate at time step t. This represents the hidden layer state at time step t. This represents the hidden layer output of the previous time step. This represents the hidden layer output at the previous time step. Concatenate it with the current input. The cell representing the current time step t, This indicates the cell status at the previous time step. Indicates the candidate values ​​for the cell status. This represents the sigmoid activation function of the gate. This represents the tanh activation function. , , , These represent the weight matrices for the forget gate, input gate, candidate cell generation state, and output gate, respectively. , , , These represent the bias terms for the forget gate, input gate, candidate cell generation state, and output gate, respectively.

[0183] In step four, the two segments of Kuroshio Current path data after segmented interpolation are divided into training and testing sets. The two segments of Kuroshio Current path data from the first 375 months are used as the training set and input into the deep learning model BiFuse-EOF-TCN-LSTM for Kuroshio Current path prediction training. The training set uses a rolling window strategy to construct training samples.

[0184] The two Kuroshio Current path data points from the last nine months were used as the test set. This test set is used to input data from April to September 2024 (a total of 6 months) into the trained deep learning model BiFuse-EOF-TCN-LSTM, which will then produce forecast results for October to December 2024 (a total of 3 months).

[0185] The first segment of the Kuroshio Current path data in the training set was input into the first segment of the Kuroshio Current path prediction model. The EOF analysis unit in this model was used to perform spatiotemporal decomposition on the training set. The spatial modes (i.e., the principal mode matrix) with a cumulative variance contribution rate of 99% and their corresponding time functions were selected from the first segment of the Kuroshio Current path data and used as the input data for the TCN-LSTM prediction unit in the corresponding model. The input data included the original data (original sequence and first-order difference sequence), achieving the fusion of dual features: absolute position and relative change of the flow axis.

[0186] The second segment of the Kuroshio Current path data in the training set was input into the second segment Kuroshio Current path prediction model. The EOF analysis unit in this model was used to perform spatiotemporal decomposition on the training set. The spatial modes (i.e., the principal mode matrix) with a cumulative variance contribution rate of 95% and their corresponding time functions were selected as the input data for the TCN-LSTM prediction unit in the corresponding model. The input data included the original data (the original sequence and the first-order difference sequence calculated from the original sequence), achieving the fusion of dual features: absolute position and relative change of the flow axis.

[0187] In step five, the Kuroshio Current path data for the six months prior to the forecast time is input into the trained first and second Kuroshio Current path prediction models. These models are applied to the first and second Kuroshio Current paths, respectively, to predict the Kuroshio Current path data for the next three months. The predicted time function results are obtained, and the prediction results are then reshaped.

[0188]

[0189] in, The principal mode matrix, i.e., the eigenvector field matrix of the training set, is taken from the first... The eigenvectors corresponding to each principal component For the predicted time series, T denotes transpose. and These are the standard deviation and mean of the training set, respectively; finally, the reconstructed longitude and latitude prediction sequences are obtained: the predicted longitude sequence of the first Kuroshio path and the predicted latitude sequence of the second Kuroshio path.

[0190] Finally, the prediction results of the first Kuroshio path prediction model and the second Kuroshio path prediction model are recombined. If there is an intersection between the two segments, the intersection of the second Kuroshio path is discarded while the first Kuroshio path is completely preserved, so that the starting longitude of the second Kuroshio path is not less than the longitude of the ending point of the first Kuroshio path.

[0191] The prediction performance evaluation criteria of this invention use RMSE and ACC as evaluation indicators for monthly prediction performance, as shown in the following formula:

[0192] Root mean square error:

[0193]

[0194] Spatial anomaly correlation coefficient:

[0195]

[0196] The number of grid points involved in the calculation. Indicates the first The grid point, the The actual value for the month, Indicates the first The grid point, the Monthly forecast, Indicates the first The average of the predicted values ​​for all grid points over the month. Indicates the first The average of all grid point observations for the month, predicted by the deep learning model BiFuse-EOF-TCN-LSTM, yielded RMSEs of 0.255, 0.310, and 0.351 for October, November, and December, respectively, and ACCs of 0.999969, 0.999951, and 0.999936, respectively. A comparison of the actual and predicted flow axes for October–December 2024 can be found in [link to data]. Figures 2 to 4 .

[0197] This invention provides a method for predicting the Kuroshio Current path based on a hybrid deep learning model. In the Kuroshio Current axis identification process, an improved feature line method is employed, combined with orthogonal empirical functions, temporal convolutional networks, and long short-term memory networks to construct a deep learning model for predicting the Kuroshio Current path. Compared with existing technologies, this method solves the problem of the east-west oscillation of the Kuroshio Current path in the eastern part of a certain region. It analyzes the Kuroshio Current path in segments, employs a hybrid TCN and LSTM model to capture the long-range temporal dependencies in the Kuroshio Current axis time series, extracts the dynamic change features of the Kuroshio Current axis, and improves the time series prediction performance; it achieves accurate prediction of the Kuroshio Current axis even with a small amount of data.

[0198] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A method for predicting the Kuroshio Current path based on a hybrid deep learning model, characterized in that, Includes the following steps: Step 1: Obtain ocean current data: Current velocity grid data at a fixed depth layer within a given ocean area; Step 2: Apply the improved feature line method to identify the Kuroshio Current axis, and perform moving average and piecewise interpolation on the identified Kuroshio Current axis; Step 3: Construct the deep learning model BiFuse-EOF-TCN-LSTM using the orthogonal empirical function EOF, the temporal convolutional network TCN, and the long short-term memory network LSTM. Step 4: Divide the segmented interpolated Kuroshio Current axis into a training set and a test set; The deep learning model BiFuse-EOF-TCN-LSTM was trained using the training set to predict the Kuroshio Current path. Step 5: Input the Kuroshio Current path data before the forecast time into the trained deep learning model BiFuse-EOF-TCN-LSTM to predict the future Kuroshio Current path; In step three, the deep learning model BiFuse-EOF-TCN-LSTM includes an EOF analysis unit and a TCN-LSTM prediction unit; The EOF analysis unit decomposes the data from the two Kuroshio Current paths into spatial modes and time functions; After piecewise interpolation, the data from the two segments of the Kuroshio path are used as the original data and are presented in matrix form: In the formula, This is the data matrix for the two segments of the Kuroshio path after piecewise interpolation. The number of points in space is called the spatial dimension. The number of time points or samples is called the time dimension; The TCN-LSTM prediction unit comprises a temporal convolutional network (TCN) and a long short-term memory network (LSTM). Deep learning models BiFuse-EOF-TCN-LSTM were constructed for the two Kuroshio Current paths, serving as prediction models for the first and second Kuroshio Current paths, respectively. The parameter settings are as follows: time backtracking window length is set to 6, prediction step size is 3, Adam optimizer is used, decay rate is 0.5, and initial learning rate is... 0.001, where the model decay period of the first Kuroshio track prediction model is 20, and the model decay period of the second Kuroshio track prediction model is 65; Temporal Convolutional Network (TCN): in, The time step is The output, For the input time series data, It is the size of Convolutional filters, For convolution operators, Convolutional filter The j-th weight parameter in the equation, The input values ​​are from past time steps. To capture long-range dependencies without increasing network depth, dilated convolutions are introduced, with the dilation factor set to [value missing]. Elements in the sequence dilated convolution operation Defined as: in, For the dilated convolution operator, For the input sequence in the past The value of each time step; Long Short-Term Memory (LSTM) network includes a forget gate, an input gate, and an output gate; Forgotten Gate: ; Input Gate: ; A new candidate vector is created through the tanh layer, and this candidate vector is added to the cell state: ; Update cell status: , This indicates element-wise multiplication; Output gate: , ; in, This represents the input at the current time step t. This represents the output of the forget gate at time step t. This indicates the output of the output gate at time step t. This represents the output of the input gate at time step t. This represents the hidden layer state at time step t. This represents the output of the hidden layer at the previous time step. This represents the hidden layer output at the previous time step. Concatenate it with the current input. The cell representing the current time step t, This indicates the cell status at the previous time step. Indicates the candidate values ​​for the cell status. This represents the sigmoid activation function of the gate. This represents the tanh activation function. , , , These represent the weight matrices for the forget gate, input gate, candidate cell generation state, and output gate, respectively. , , , These represent the bias terms for the forget gate, input gate, candidate cell generation state, and output gate, respectively.

2. The Kuroshio Current path prediction method based on a hybrid deep learning model according to claim 1, characterized in that, In step two, the method for identifying the Kuroshio Current axis using the improved feature line method is as follows: Step S21, determine the starting point: The point with the fastest current in the area through which the Kuroshio flows year-round was selected as the starting point. Step S22: Draw an auxiliary line at the starting point that is perpendicular to the flow direction at that point and has a length of 140km. Step S23, introduce a linear weighting function. Linear weighted interpolation of the flow direction is performed every 14 km along the auxiliary line, and the average flow direction at all interpolation points is calculated; where This indicates the calculation of the original weights, which is the first... The original weight value of each interpolation point is inversely proportional to the distance from that point to the center point; Representing the The position coordinates of the interpolation points Represents the position coordinates of the center point. The distance between the interpolation point on the auxiliary line and the center point; =140, satisfy , is the The final weight value of each interpolation point is the normalized result. Step S24: Adjust the auxiliary line to be perpendicular to the average flow direction, and perform a second interpolation on the adjusted auxiliary line. The point with the fastest flow velocity on the new auxiliary line is defined as the position of the flow axis point. Step S25, move the step size along the average flow direction. =10km to the next location; when moving along the average current direction into the extension area of ​​the Kuroshio Current, the step size will be... Increased to 50km; Step S26: Repeat steps S22 to S25 to identify all current axis points; after identification, connect all current axis point positions to obtain a current axis of the Kuroshio Current; repeat step S26 to obtain multiple current axes of the Kuroshio Current corresponding to each month.

3. The method for predicting the Kuroshio Current path based on a hybrid deep learning model according to claim 2, characterized in that, In step S26, for each new flow axis point identified, the distance between that point and all previously identified position points is calculated; when the distance is less than 0.01°, it is determined that the automatic identification process has fallen into a vortex, and the system automatically reverts to the position point before the vortex. If outside the Kuroshio Current's extension zone, increase the forward step length. Up to 20km, with the average flow direction of the current location as the central axis, within an angle range of 30° on both sides, select the grid point for the next location; If within the extended area of ​​the Kuroshio Current, then the distance forward is longer. The range remains at 50km, with the same restriction applied only to the area to which the vehicle can proceed.

4. The Kuroshio Current path prediction method based on a hybrid deep learning model according to claim 1, characterized in that, In step two, Moving average: The latitude and longitude of the points on the obtained flow axis are averaged to obtain the flow axis after moving average; where the moving window is 11 in the non-Kuroshio extension region and 3 in the Kuroshio extension region. Segmented interpolation: Each complete current axis after moving average is divided into two segments of the Kuroshio Current path, namely the first segment and the second segment. The first segment of the Kuroshio Current path is the part with latitude between 23°N and 25.5°N, and longitude interpolation is performed with a latitude resolution of 1 / 12°. The second segment of the Kuroshio Current path is the part with longitude between 122°E and 141°E, and latitude interpolation is performed with a longitude resolution of 1 / 12°.

5. The method for predicting the Kuroshio Current path based on a hybrid deep learning model according to claim 1, characterized in that, The implementation steps of the EOF analysis unit are as follows: Step 31, Data Standardization: First calculate To obtain the time mean at each spatial point, we calculate the mean for each row of the data matrix for the two Kuroshio Current paths: in, This represents a column vector consisting of the time averages of all spatial points, with dimension 1. , This represents the number of interpolation points for latitude / longitude in the two Kuroshio Current paths. ,in, , indicating the first of the two Kuroshio paths The mean of longitude / latitude at each interpolated latitude / longitude point in space. Indicates the first path corresponding to the Kuroshio Current. The interpolated latitude / longitude spatial point, the first Longitude / latitude values ​​at each point in time; Secondly, calculate the standard deviation matrix. : in, The dimension is , ,in, , indicating the first of the two Kuroshio paths The standard deviation of longitude or latitude at each interpolated latitude or longitude point in space; Then, the standardized data matrix is ​​obtained: in, The data matrix consists of two standardized segments of the Kuroshio Current path, each item of which is obtained through... The calculations show that the time series of each spatial point has a mean of 0 and a standard deviation of 1. Step 32, calculate the covariance matrix: The formula for calculating covariance is as follows: in, This is the standardized data matrix of the two Kuroshio Current paths. The number of time points, express The transpose of is used to obtain the covariance matrix of the two Kuroshio path data; Step 33, for the covariance matrix Perform eigenvalue decomposition: Find the eigenvalues ​​and eigenvectors of the covariance matrices for the two Kuroshio Current path data segments respectively: in, The eigenvector matrix of the covariance matrix of the two Kuroshio Current path data segments is... satisfy , This is a diagonal matrix, where the diagonal elements are the eigenvalues ​​of the covariance matrix of the two Kuroshio path data segments. The eigenvalues ​​and their corresponding eigenvectors are sorted from largest to smallest as follows: in, The value of is determined by the number of interpolation points of latitude or longitude in the two Kuroshio Current paths; Step 34, Calculate the time coefficient: Time coefficient It is achieved by standardizing the two segments of the Kuroshio Current path data matrix. Projected onto the corresponding eigenvector matrices What was obtained from: Among them, the eigenvector matrix That is, spatial modes. That is, the corresponding time coefficient; Step 35, extract the principal components: The two sections of the Kuroshio path Multiplying the eigenvector fields and their corresponding time coefficients yields a fitted field: in, That is, the standardized data matrix M represents the spatial dimension, and N represents the temporal dimension; To represent the fitted field matrix, use the first... The approximate matrix obtained by reconstructing the principal components is used to approximate... ; or This represents the eigenvector field matrix, taking the first... The matrix has M×P dimensions and consists of eigenvectors corresponding to each principal component, with each column representing an eigenvector and corresponding to a spatial mode. or Represents the time coefficient matrix, the first... The time coefficients corresponding to each principal component are shown in the figure. Each row is a sequence of coefficients of a principal component over time, with a dimension of P×N. Then the first of the two Kuroshio paths Each eigenvector field pairs with the original field The contribution rate is: in, For the first eigenvector pairs The contribution rate represents the proportion of the original data variance that the principal component can explain. For the first The eigenvalues ​​corresponding to each principal component reflect the magnitude of the variance of the original data contained in that principal component. The sum of the eigenvalues ​​of all M principal components represents the original field. The total variance; The two sections of the Kuroshio path Cumulative contribution rate of each eigenvector field for: in, Indicates the preceding The sum of the eigenvalues ​​of the principal components; Step 36, significance test: For the two Kuroshio Current paths, according to The magnitudes of the eigenvector fields are selected based on their physical significance, and a significance test is required: when When, it indicates that the two eigenvalues ​​are "separable", the first... Each mode is dominated by a significant signal.

6. The method for predicting the Kuroshio Current path based on a hybrid deep learning model according to claim 1, characterized in that, In step four, the first segment of the Kuroshio Current path data in the training set is input into the first segment of the Kuroshio Current path prediction model. The EOF analysis unit in the model is used to perform spatiotemporal decomposition on the training set. The spatial modes with a cumulative variance contribution rate of 99% and their corresponding time functions are taken from the data of the first segment of the Kuroshio Current path and used as the input data for the TCN-LSTM prediction unit in the corresponding model. The TCN-LSTM prediction unit in the corresponding model is then used to train and predict the first segment of the Kuroshio Current path prediction model. The second segment of the Kuroshio Current path data in the training set is input into the second segment of the Kuroshio Current path prediction model. The EOF analysis unit in the model is used to perform spatiotemporal decomposition on the training set. The spatial modes with a cumulative variance contribution rate of 95% and their corresponding time functions are taken from the second segment of the Kuroshio Current path data and used as the input data for the TCN-LSTM prediction unit in the corresponding model. The TCN-LSTM prediction unit in the corresponding model is used to train and predict the second segment of the Kuroshio Current path prediction model.

7. The Kuroshio Current path prediction method based on a hybrid deep learning model according to claim 1, characterized in that, In step five, the Kuroshio Current path data for the six months prior to the forecast time is input into the trained first and second Kuroshio Current path prediction models. Forecasts are then performed on the Kuroshio Current path data for the next three months, obtaining the predicted time function results, and the prediction results are then reshaped. in, The principal mode matrix, i.e., the feature vector field matrix of the training set, is taken from the first... The eigenvectors corresponding to each principal component For the predicted time series, T denotes transpose. and These are the standard deviation and mean of the training set, respectively; finally, the reconstructed longitude and latitude prediction sequences are obtained: the predicted longitude sequence of the first Kuroshio path and the predicted latitude sequence of the second Kuroshio path; The prediction results of the first Kuroshio path prediction model and the second Kuroshio path prediction model are recombined. If there is an intersection between the two models, the first Kuroshio path is completely retained, and the intersection of the second Kuroshio path is discarded, so that the starting longitude of the second Kuroshio path is not less than the longitude of the ending point of the first Kuroshio path.

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