A method for predicting propagation of internal solitary waves in the ocean based on an improved TimeXer model

Abstract

The application relates to the field of internal solitary wave prediction, and discloses a marine internal solitary wave propagation prediction method based on an improved TimeXer model, which comprises the following steps: constructing an improved TimeXer model; collecting and pre-processing remote sensing image data of a stationary orbit satellite GK-2A and a polar orbit satellite; extracting internal solitary wave parameters based on the remote sensing image data, combining with hydrological environment parameters to construct an internal solitary wave prediction data set, and training a model; obtaining remote sensing image data of the stationary orbit satellite GK-2A and the polar orbit satellite of a target sea area, pre-processing the remote sensing image data, inputting the remote sensing image data into a qualified model, and performing internal solitary wave prediction. The method disclosed by the application can effectively improve the precision and stability of marine internal solitary wave propagation prediction; the model adaptability to complex marine environments is enhanced by introducing an innovative module, and a reliable scheme is provided for accurate prediction of marine internal solitary waves.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of internal solitary wave prediction, and in particular to a method for predicting the propagation of ocean internal solitary waves based on an improved TimeXer model. BACKGROUND

[0002] Ocean internal solitary waves carry huge energy and can induce sudden strong currents and intense isopycnal wave motion, with a maximum amplitude of up to 240 m, posing a serious threat to the safety of submarine navigation. The maximum flow speed caused by internal solitary waves exceeds 2 m / s, which has a great impact on offshore oil platforms and engineering operations, and even causes them to move significantly, which has a huge impact on safety or operational performance during installation and operation. Therefore, the study of internal solitary waves is very important for ocean science, ocean engineering, and other fields, and accurate prediction of the propagation characteristics of internal solitary waves has important scientific value and application significance.

[0003] With the rapid development of deep learning, neural network models have been widely used in the study of internal solitary waves. In particular, existing satellite remote sensing images are becoming increasingly diverse, and the combination of satellite remote sensing and deep learning has become a hot topic in the study of ocean internal solitary waves. By utilizing the powerful learning ability of deep learning, the relationship between complex ocean background environment and internal solitary wave parameters can be deeply mined. Existing research can use optical remote sensing images and SAR remote sensing images to predict internal solitary wave amplitude, propagation speed and other parameter information using neural network models, and achieve internal solitary wave propagation prediction by combining physical mechanisms.

[0004] However, there are still some deficiencies in existing research that need to be improved. First, the real ocean environment is complex and variable, and traditional physical models can better describe the evolution of internal solitary waves under ideal conditions, but it is difficult to accurately obtain boundary conditions in real ocean environments, resulting in large prediction errors. The existing deep learning model does not sufficiently explore the coupling relationship between external variables (such as seabed topography, temperature and salinity data) and endogenous variables (such as propagation speed) for predicting the propagation of ocean internal solitary waves. Second, existing research mainly uses polar orbit satellite remote sensing data, which has a low time resolution and is difficult to capture the continuous dynamic change characteristics of internal solitary waves during propagation. SUMMARY

[0005] To solve the above technical problems, the present application provides a method for predicting the propagation of ocean internal solitary waves based on an improved TimeXer model, to effectively improve the accuracy and stability of the prediction of ocean internal solitary wave propagation.

[0006] To achieve the above purpose, the technical solution of the present application is as follows:

[0007] A method for predicting the propagation of ocean internal solitary waves based on an improved TimeXer model, comprising the following steps:

[0008] Step 1: Build the improved TimeXer model;

[0009] The improved TimeXer model includes an endogenous variable embedding layer, an adaptive spectrum module, a self-attention layer, a dynamic hyperbolic tangent module I, an interactive convolution module, a cross-attention layer, a dynamic hyperbolic tangent module II, a feedforward network layer, and a prediction layer.

[0010] Step 2, Model Training and Validation;

[0011] Collect remote sensing image data from geostationary satellite GK-2A and polar satellite, and preprocess the remote sensing image data;

[0012] Internal solitary wave parameters are extracted from remote sensing image data, and an internal solitary wave prediction dataset is constructed by combining hydrological environmental parameters. The constructed internal solitary wave prediction dataset is divided into a training set, a validation set, and a test set.

[0013] The training set is used to train the model, the validation set is used to validate the model, and the test set is used to test the model.

[0014] Step 3: Acquire remote sensing image data of the target sea area from the geostationary satellite GK-2A and polar satellite. After preprocessing the remote sensing image data, input it into the qualified model to perform internal solitary wave prediction.

[0015] In the above scheme, the adaptive spectrum module transforms the time-series data of the endogenous variable of the internal solitary wave from the time domain to the frequency domain through Fourier transform, thereby achieving the separation of signal and noise. Then, the adaptive mechanism is used to enhance key features and suppress redundant information.

[0016] The adaptive spectrum module performs dynamic spectrum analysis using the following formula:

[0017] ;

[0018] ;

[0019] ;

[0020] ;

[0021] ;

[0022] ;

[0023] ;

[0024] in, For input signals; is a complex spectrum of the input signal after short-time Fourier transform; is the number of channels; is the frame length; is the energy distribution of the spectrum, which is used for subsequent threshold screening; is the significant spectrum after filtering low-frequency noise; is the energy threshold; represents element-wise multiplication; is the overall spectrum reserved by the global weight; is the key spectrum enhanced by the local weight; is the global weight; is the local weight; is the spectrum combining global and local information; is the enhanced time-domain signal after inverse Fourier transform, is the real signal at the time point.

[0025] In the above scheme, the interactive convolution module includes two parallel 1D convolution layers, Conv1 and Conv2, which use different sizes of convolution kernels to capture local features of different granularities respectively; and the cross-scale feature interaction is realized through an activation function + element multiplication, the features after interaction are summed, and then refined through a 1D convolution layer Conv3 to obtain the output of the interactive convolution module;

[0026] The interactive convolution module is realized by the following formula:

[0027] ;

[0028] ;

[0029] ;

[0030] wherein, is the input feature map; is the output enhanced feature; represents a nonlinear activation function, , , are three 1D convolution layers; is the first attention weight, highlighting important feature regions; is the second attention weight and the first attention weight, which are reversely interacted to capture complementary features.

[0031] In the above scheme, the dynamic hyperbolic tangent module one and the dynamic hyperbolic tangent module two realize feature normalization effect through the combination of a learnable scaling factor and a hyperbolic tangent function, and the mathematical expression is as follows:

[0032] ;

[0033] wherein a is a learnable scalar parameter dynamically adjusting the scaling range of the input; is a scaling parameter, is a translation parameter.

[0034] In the above scheme, the model retains the Transformer core component, and adopts a differentiated embedding strategy for endogenous variables and exogenous variables: the endogenous variables are divided into non-overlapping segments and converted into time tokens through linear projection, and the exogenous variables are converted into variable sub-tokens through linear projection; a learnable global token is introduced for each endogenous variable to associate the causal information of endogenous and exogenous variables, and to realize multi-source data integration; the endogenous variables include internal solitary wave position, propagation speed, propagation direction and wave peak line length, and the exogenous variables include water depth, temperature and salinity.

[0035] In the above scheme, the endogenous variable embedding layer is a double-layer representation that converts the endogenous variables of the ocean internal solitary wave to be predicted into patch-level time tokens and global tokens, each patch is converted into a time token through a trainable linear projection, and a position embedding is added to retain the time sequence order of the patch, and finally a patch-level token set is output; a learnable global token is introduced as a global trend representative of the endogenous variables, and the token learns the overall statistical characteristics of the endogenous variables through training.

[0036] In the above scheme, the self-attention layer performs self-attention between the patch-level tokens and the global tokens of the endogenous variables, while capturing the local temporal dependence between patches; the output of the endogenous embedding layer is taken as the input of the self-attention, and three types of interactions are realized through one self-attention calculation: patch-patch interaction, patch-global interaction, and global-patch interaction.

[0037] In the above scheme, the cross-attention layer takes the endogenous global token as the query, and the exogenous variable-level token as the key and value, to establish directional information transmission from the exogenous variable to the endogenous variable, and to realize on-demand injection of exogenous auxiliary information into the endogenous model; through cross-attention calculation, the global token selectively pays attention to the exogenous variables useful for internal solitary wave prediction, and only the endogenous global token pays attention to the exogenous variables, while the useful information is filtered through the global token and then transmitted to the patch.

[0038] In the above scheme, the feedforward network layer performs nonlinear transformation on the patch-level tokens and the global tokens updated by the cross-attention layer, strengthens the feature expression capability, and provides more abstract feature representation for the next layer module; the feedforward network layer adopts the standard structure of Transformer, including two linear transformations and a GELU activation function, and the patch-level tokens and the global tokens pass through the feedforward network layer respectively to ensure that the feature updates of the two do not interfere with each other.

[0039] In the scheme, the prediction layer maps the patch-level tokens and global tokens output by the TimeXer encoder into endogenous variable prediction results of the final internal solitary wave, and optimizes the model parameters through a loss function.

[0040] Through the technical scheme, the ocean internal solitary wave propagation prediction method based on the improved TimeXer model has the following beneficial effects:

[0041] 1. Compared with the pure data-driven model in the prior art, which is difficult to capture the coupling relationship between exogenous variables (such as seabed topography) and endogenous variables (such as internal solitary wave propagation speed), and the defect that the physically informed model excludes key exogenous factors, the present application fuses multi-source satellite data (remote sensing images) and environmental variables (water depth, temperature, salinity, etc.) through a hybrid embedding strategy, introduces a learnable global token to aggregate the exogenous context through cross-attention, and effectively quantifies the exogenous-endogenous variable correlation.

[0042] 2. Compared with the prior art which relies on SAR remote sensing images with a long time interval, the present application uses 898 GEO-KOMPSAT-2A (GK-2A) AMI remote sensing images (10-minute time resolution, 500-meter spatial resolution) and 277 Terra / Aqua MODIS and SAR remote sensing images as core data, combined with WOA2023 temperature and salinity, GEBCO topography and other public environmental data. The high-frequency spatiotemporal observation capability of satellite data can realize continuous tracking of internal solitary wave trajectories (extracting 1378 internal solitary wave trajectories and 9987 feature points), improving the efficiency and spatiotemporal continuity of data processing.

[0043] 3. The present application replaces the traditional normalization layer of the Transformer with a dynamic hyperbolic tangent (DyT) module. Compared with the traditional normalization, which is difficult to handle the problem of extreme value fluctuation in internal solitary wave dynamics and distribution deviation of exogenous-endogenous variables, DyT can compress extreme values while preserving the local linearity of small amplitude fluctuations, which is more suitable for the nonlinear propagation characteristics of internal solitary waves, helps the model to learn complex data patterns, reduces the probability of falling into local optimum, and improves the optimization stability.

[0044] 4. The adaptive spectral (ASB) module integrated in the present application can suppress high-frequency noise generated by sensor measurement through a frequency domain analysis process, and enhance the low-frequency components of topography-induced wave modulation. Existing models do not specifically process frequency domain noise, which can easily lead to modeling errors in internal solitary wave speed and direction, while ASB can optimize the modeling accuracy of wave speed and direction, and improve the prediction stability in complex sea conditions.

[0045] 5、The traditional internal solitary wave prediction model often faces the problem of learning different scale features, and the integrated interactive convolution (ICB) module of the application captures local disturbance through 3x1 small kernel convolution, captures global propagation trend through 7x1 large kernel convolution, and realizes feature interaction. The design does not need to rely on the fixed terrain correction parameters of the traditional model, can dynamically modulate the influence of terrain on exogenous variables, effectively solves the problem of internal solitary wave propagation direction deflection caused by complex terrain, and ensures that the model extracts more accurate multi-scale features from data;

[0046] 6、Through comparison experiments with original TimeXer, LSTM and mainstream Transformer, the model of the application realizes 2.38km RMSE in 4-hour internal solitary wave position prediction, which is 50% lower than the baseline model TimeXer (4.77km), and is significantly better than LSTM (5.16km) and ordinary Transformer (4.86km). The model only needs to input satellite remote sensing images and environmental variables to complete high-precision prediction, which is an important supplement and optimization to existing internal solitary wave deep learning prediction technology;

[0047] 7、The application optimizes the variable fusion architecture of the model based on TimeXer: the internal solitary wave endogenous variables (internal solitary wave position, propagation speed, propagation direction and wave peak line length) are divided into non-overlapping segments and projected to time tokens, and the exogenous variables (water depth, temperature and salinity) are projected to variable tokens, and the dynamic dependence is captured through self-attention and cross-attention mechanism. The original TimeXer model has defects in variable granularity matching and time alignment, and the architecture design of the application solves the problems of granularity mismatch and time misalignment by aggregating exogenous context through global token, and at the same time cooperates with DyT, ASB and ICB modules to strengthen the feature expression ability. The adaptability of the application to the complex task of internal solitary wave propagation in Lombok Strait under complex sea conditions is significantly better than that of single architecture model. BRIEF DESCRIPTION OF DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the drawings needed to be used in the embodiment or prior art description will be briefly introduced below.

[0049] Figure 1 A flowchart of a marine internal solitary wave propagation prediction method based on an improved TimeXer model is disclosed in the embodiment of the application.

[0050] Figure 2 An improved TimeXer model structure diagram is shown.

[0051] Figure 3 An internal solitary wave propagation direction calculation diagram is shown.

[0052] Figure 4 Schematic diagram for calculating the internal solitary wave propagation speed;

[0053] Figure 5 SAR image of internal solitary wave on October 19, 2024 05:30;

[0054] Figure 6 Optical image of internal solitary wave on October 19, 2024 02:15;

[0055] Figure 7 Prediction result map of ocean internal solitary wave. DETAILED DESCRIPTION

[0056] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application.

[0057] The present application provides a method for predicting the propagation of ocean internal solitary waves based on an improved TimeXer model, as shown in Figure 1 The method comprises the following steps:

[0058] Step 1: Construct an improved TimeXer model;

[0059] The model retains the core components of the Transformer, and adopts a differentiated embedding strategy for endogenous variables (internal solitary wave position, propagation speed, propagation direction and wave crest line length) and exogenous variables (water depth, temperature, salinity): the endogenous variables are divided into non-overlapping segments and converted into time tokens through linear projection, and the exogenous variables are converted into variable sub-tokens through linear projection. A learnable global token is introduced for each endogenous variable to associate the causal information between endogenous and exogenous variables and realize multi-source data integration. In order to more effectively capture the complex nonlinear relationship between the factors affecting the propagation speed of internal solitary waves and their propagation speed, the DyT activation function is used in the model instead of the normalization layer in the original model. At the same time, an interactive convolution module (ICB) and an adaptive spectral module (ASB) are introduced to reduce the interference of noise on the prediction results and improve the robustness and prediction accuracy of the model.

[0060] The model structure is as shown in Figure 2The improved TimeXer model includes an endogenous embedding layer (Endogenous Embedding), an adaptive spectral module (ASB), a self-attention layer (Self-Attention), a dynamic hyperbolic tangent module (DyT), an interactive convolution module (ICB), a cross-attention layer (Cross-Attention), a dynamic hyperbolic tangent module (DyT), a feed-forward network layer (Feed-Forward), and a forecasting layer (Forecasting).

[0061] (1) Endogenous Embedding, which converts the endogenous variables of the ocean internal solitary wave to be predicted into a two-layer representation of "patch-level time tokens + global tokens", capturing both the local temporal dependence of the ocean internal solitary wave endogenous variables and the global trend information, laying the foundation for subsequent interaction with exogenous variables. Patch division and embedding: the input endogenous time series is divided into non-overlapping patches according to the preset patch length, each patch is converted into a time token through a trainable linear projection (PatchEmbed), and a position embedding is added to retain the temporal order of the patch. Finally, a set of patch-level tokens is output. A learnable global token is introduced as the "global trend representative" of the endogenous variables. This token does not depend on specific patches and learns the overall statistical characteristics of the endogenous variables through training, solving the problem of "patch-level representation only focusing on the local and lacking a global perspective".

[0062] (2) Adaptive Spectral Module (ASB), which first converts time-domain data (such as internal solitary wave propagation speed time series, latitude and longitude time series) to frequency domain through Fourier transform. At this time, high-frequency components correspond to noise, and low-frequency components correspond to the stable propagation characteristics of internal solitary waves, achieving adaptive frequency domain noise reduction. Internal solitary wave propagation is influenced by both "short-term local factors" (such as local sea current mutations) and "long-term global factors" (such as overall trends in seabed topography). Traditional models (such as LSTM and ordinary Transformer) are difficult to capture both types of dependencies. The global filter of ASB acts on the original frequency domain data, preserving the long-term global characteristics of internal solitary wave propagation; the local filter acts on the noise-reduced frequency domain data, capturing short-term local characteristics. Two sets of learnable filters are designed to extract features from the original frequency domain and filtered frequency domain, respectively. Perform IFFT on the fused frequency domain features to convert them back to time domain signals, ensuring that the output format is consistent with the original time series data, facilitating subsequent module processing.

[0063] The adaptive spectral module performs dynamic spectral analysis through the following formula:

[0064] ;

[0065] ;

[0066] ;

[0067] ;

[0068] ;

[0069] ;

[0070] ;

[0071] wherein, is the input signal; is the complex spectrum of the input signal after short-time Fourier transform; is the number of channels; is the frame length; is the energy distribution of the calculated spectrum, used for subsequent threshold screening; is the significant spectrum after filtering low-frequency noise; is the energy threshold; denotes element-wise multiplication; is the overall spectrum reserved by the global weight; is the key spectrum enhanced by the local weight; is the global weight; is the local weight; is the spectrum combining global and local information; is the enhanced time-domain signal after inverse Fourier transform, is the real signal at time point. ASB can optimize the modeling accuracy of wave speed and direction, and improve the prediction stability under complex sea conditions.

[0072] (3) Self-Attention, is for the endogenous variable time series, through the "attention weight distribution" focus on the key features of time nodes. Traditional convolution or recurrent model can only capture local temporal relationship, self-attention layer through global calculation (calculate each time node and all other nodes associated), cover the long-range dependence of internal solitary wave propagation, avoid the prediction bias caused by local information missing. Perform self-attention between the "patch-level tokens + global tokens" of the endogenous variable of internal solitary wave, while capturing the local temporal dependence between patches; The association between patches and global trends strengthens the endogenous variable's own time series modeling ability. The output of the endogenous embedding layer is taken as the input of self-attention, and three types of interactions are realized through one self-attention calculation: Patch-to-Patch interaction: patch-level tokens pay attention to each other, capturing the local temporal dependence of endogenous variables (such as the correlation between Monday and Tuesday electricity load); Patch-to-Global interaction: each patch-level token pays attention to the global token, aligning local details with global trends (such as whether the load peak of a day conforms to the overall trend of the week); Global-to-Patch interaction: the global token pays attention to all patch-level tokens, aggregating local information to update the global trend.

[0073] (4) Dynamic hyperbolic tangent module one and dynamic hyperbolic tangent module two (DyT), is through the combination of "learnable scaling factor + hyperbolic tangent (tanh) function", to simulate the core role of the normalization layer, compress extreme values, stabilize the activation range, while avoiding the statistical aggregation operation of the normalization layer to calculate the mean and variance, realize more simple feature normalization effect, adapt to each layer of Transformer (attention block, feedforward network block, output layer).

[0074] The mathematical expression of DyT is as follows:

[0075] ;

[0076] Among them, a is a learnable scalar parameter, dynamically adjusting the scaling range of the input; is the scaling parameter, is the translation parameter, respectively used to control the gain and offset of the output.

[0077] (5) Interactive Convolution Block (ICB), which further refines the local features of time series through multi-scale convolution interaction, enhances the model's ability to capture complex time series patterns. For the influence of "local environmental mutations" on the propagation of internal solitary waves, small-size convolution kernels focus on short-term and small-space range feature changes; for the influence of "global environmental factors" on the propagation of internal solitary waves, large-size convolution kernels cover long-term / large-space range feature associations. Therefore, multi-scale convolution extraction allows the outputs of the two convolution groups to modulate each other, enhancing cross-scale feature associations, merging and modulating information through the final convolution layer, as the final features of the current TSLANet layer, and passing to the next layer.

[0078] The input of ICB is the time domain sequence processed by ASB, which has completed noise reduction and long and short range dependence capture, but still needs to further refine local complex patterns. ICB designs two parallel 1D convolution layers (Conv1 and Conv2) with different kernel sizes to capture local features of different granularities. Conv1 (small kernel convolution) has a kernel size k1 (k1=3) and an output channel number C (consistent with the input channel), which captures fine-grained local patterns. Conv2 (large kernel convolution) has a kernel size k2 (k2=7) and an output channel number C, which captures local long-range associations. To avoid multi-scale convolution features existing independently (leading to information fragmentation), ICB enables cross-scale feature interaction through an activation function + element multiplication, allowing small kernel features and large kernel features to modulate each other. After interaction, the features are summed and refined through a 1D convolution layer (Conv3) to obtain the output of ICB.

[0079] The interactive convolution module is implemented by the following formula:

[0080] ;

[0081] ;

[0082] ;

[0083] wherein, is the input feature map; is the output enhanced feature; represents a nonlinear activation function, , , are three 1D convolution layers; is the first attention weight, highlighting important feature areas; To capture complementary features, the second attention weight interacts with the first attention weight in the reverse direction. ICB can dynamically modulate the influence of terrain on exogenous variables, effectively solving the problem of internal solitary wave propagation direction deflection caused by complex terrain, and ensuring that the model extracts more accurate multi-scale features from the data.

[0084] (6) Cross-Attention, which is aimed at the influence of exogenous variables (such as water depth, temperature and salinity) on endogenous variables (such as internal solitary wave propagation speed and direction), calculates the key exogenous factors through attention weight calculation, such as internal solitary wave speed being more affected by water depth, and the cross-attention layer assigning higher weights to water depth variables and lower weights to wind speed variables that have less impact, achieving precise modeling of variable correlation. With "endogenous global token" as query, "exogenous variable level token" as key and value, directional information transmission from exogenous variables to endogenous variables is established, realizing "on-demand injection of exogenous auxiliary information into endogenous model". Through cross-attention calculation, the global token selectively pays attention to exogenous variables useful for internal solitary wave prediction. Only the endogenous global token pays attention to the exogenous variables, rather than allowing the patch-level token to directly interact with the exogenous, avoiding exogenous noise interference with local time series modeling, and at the same time, the useful information is filtered by the global token before being transmitted to the patch.

[0085] (7) The Feed-Forward network layer performs nonlinear transformation on the "patch-level token" and "global token" updated by the attention layer, strengthens the feature expression ability, and provides more abstract feature representation for the next layer module. The feed-forward network adopts the standard structure of Transformer, including two linear transformations and GELU activation function. The patch-level token and the global token pass through the feed-forward network respectively, ensuring that the feature updates of the two do not interfere with each other (patch-level focuses on local details, and global-level focuses on cross-variable information).

[0086] (8) The Forecasting layer maps the "patch-level token + global token" output by the TimeXer encoder to the final endogenous variable prediction results of marine internal solitary wave, and optimizes the model parameters through the loss function. The encoder output is directly mapped to the prediction result without additional decoder, simplifying the model structure.

[0087] Step 2, model training and verification;

[0088] (1) Collect remote sensing image data of stationary orbit satellite GK-2A and polar orbit satellite, and preprocess the remote sensing image data.

[0089] According to the latitude and longitude lookup table specification document, the geometric correction and cutting of the optical image data of the stationary orbit satellite are realized by programming and software.

[0090] First, calculate the row and column numbers :

[0091] ;

[0092] ;

[0093] where, is the ratio of the circumference of a circle to its diameter, is the column number, is the row number, is the column offset, is the column scale factor, is the row offset, is the row scale factor.

[0094] The coefficients used in the following calculations are :

[0095] ;

[0096] ;

[0097] ;

[0098] ;

[0099] ;

[0100] where, is the distance from the center of the Earth to the center of the satellite, which is 42164 km, and represent the semi-major axis and semi-minor axis of the Earth, respectively, with values of 6378.137 km and 6356.7523 km.

[0101] Finally, calculate the latitude and longitude corresponding to the row and column numbers:

[0102] ;

[0103] ;

[0104] where, is the satellite's subpoint longitude.

[0105] After obtaining the latitude and longitude coordinates of the pixel points, a geographic location lookup table file (GLT) can be created, and geometric correction of the remote sensing image can be performed based on the GLT file.

[0106] (2) Extract the internal solitary wave parameters based on remote sensing image data, combine the hydrological environmental parameters to construct the internal solitary wave prediction dataset, and divide the constructed internal solitary wave prediction dataset into training set, validation set and test set;

[0107] The personnel with professional knowledge of internal solitary wave trained by the system use QGIS software to label the internal solitary wave. In order to accurately describe the direction, as shown in FIG. 2, each internal solitary wave sample point is given a direction value (such as N0, N1, N2, N3, N4), which represents the angle between the internal solitary wave propagation direction and the north direction, t0, t1, t2, t3 are the positions of the internal solitary wave at different times. When calculating the propagation speed of the internal solitary wave, a multi-time image comparison method is used, which analyzes the spatial position change of the internal solitary wave on remote sensing images at different times, and combines the corresponding time interval to calculate the propagation speed of the internal solitary wave, as shown in FIG. 3. Finally, the labeling results are matched with the extracted environmental parameters to complete the construction of the internal solitary wave prediction dataset of Longmeng Strait. The constructed dataset includes the position (latitude and longitude), propagation speed, propagation direction and peak line length of the internal solitary wave at different times, water depth, temperature and salinity. Figure 3 Figure 4

[0108] The constructed internal solitary wave prediction dataset is divided into training set, validation set and test set according to the ratio of 7:1.5:1.5. The training set is used for model parameter learning, the validation set is used for real-time evaluation and hyperparameter adjustment to prevent overfitting, and the test set is used for independent verification of generalization ability. The training set contains 6991 data, the validation set contains 1498 data, and the test set contains 1498 data.

[0109]

[0110] The endogenous variables, including the position (latitude and longitude), propagation speed, propagation direction and peak line length of the internal solitary wave, are input into the endogenous variable embedding layer, and the exogenous variables, including water depth, temperature and salinity, are input into the cross-attention layer. The model is trained. The position (latitude and longitude) reached by the internal solitary wave, the propagation speed and the propagation direction are used as the output of the model.

[0111] During training, the Adam optimizer is used for parameter update, the initial learning rate is set to 0.001 to balance the rapid convergence at the beginning of training and the fine adjustment at the later stage; the batch size is set to 64 to ensure the calculation efficiency while stabilizing the gradient estimation. The upper limit of the number of model training rounds is set to 100 rounds, and the early stopping method strategy is adopted, that is, when the RMSE on the validation set does not decrease for 10 consecutive rounds, the training is stopped and the optimal model parameters are saved.

[0112] ​​​The model test uses the test set data to input the optimal model obtained by training. The initial position of the internal solitary wave is taken as the input, and the time step is set to 30 minutes. The model is run to predict the propagation speed and direction of the internal solitary wave, and the predicted position of the internal solitary wave is calculated.

[0113] Ablation experiment: verify the effectiveness of the three core modules DyT, ICB and ASB in the TimeXer model and their synergistic effect;

[0114] The experiment sets 8 models to predict the position of the internal solitary wave after 4 hours of propagation. By comparing the performance of different module combinations, the role of each module is analyzed. The ablation experiment results are shown in Table 1. The original TimeXer model is the baseline model and does not contain DyT, ICB and ASB. The single-module experiment includes only DyT, only ICB, and only ASB. The double-module experiment includes DyT+ICB, ICB+ASB, and DyT+ASB. The complete model contains all three modules. Through this design, the individual effect of each module, the interaction between modules and the synergistic effect can be clearly analyzed.

[0115] Table 1 Ablation experiment results

[0116]

[0117] From the single-module effect, compared with the original TimeXer baseline model (RMSE = 4.760 km), the RMSE is reduced to 2.811 km when only the ASB module is introduced, with the most significant improvement. The RMSE is 3.299 km when only the ICB module is introduced, with the second best improvement. The RMSE is 4.187 km when only the DyT module is introduced, although the improvement is smaller, but still better than the baseline model, indicating that the three modules can effectively enhance the model performance when used alone, among which the contribution of ASB to reducing the prediction error is the most prominent.

[0118] From the synergistic effect between modules, in the double-module combination, the RMSE is 3.147 km when ICB and ASB are combined, which is better than using ICB alone (3.299 km), but slightly worse than using ASB alone (2.811 km), indicating that there is some synergy between the two but the effect is limited. The performance of the combination of DyT and ICB, DyT and ASB (3.863 km, 3.933 km) is not as good as ICB+ASB, indicating that the interaction of DyT with other modules depends on the joint action of the three.

[0119] When the three modules are introduced at the same time, the RMSE is reduced to 2.382 km, which is significantly lower than all single modules and double module combinations, and the error is reduced by more than 50% compared with the benchmark model, fully verifying the synergistic effect of DyT, ICB and ASB in capturing the propagation characteristics of internal solitary waves. The frequency domain noise reduction of ASB, the multi-scale feature extraction of ICB and the dynamic nonlinear fitting capability of DyT form a complement to each other, and together promote the model prediction accuracy to the optimal.

[0120] Step 3, obtain the remote sensing image data of the stationary orbit satellite GK-2A and the polar orbit satellite in the target sea area, and input the preprocessed remote sensing image data into the qualified model to predict the internal solitary wave.

[0121] To comprehensively evaluate the performance of the improved TimeXer model in the task of internal solitary wave propagation prediction, the improved TimeXer model is compared with the original TimeXer model, LSTM and Transformer model. As shown in Table 2, the RMSE of the improved TimeXer model is 2.382 km, which is significantly lower than other comparison models. Compared with the original TimeXer model (RMSE=4.760 km), the RMSE is reduced by about 50%, which verifies the improvement of the multi-scale feature extraction of the ICB module, the frequency domain noise reduction of the ASB module and the dynamic nonlinear fitting capability of the DyT activation function on the model performance, and indicates that the special improvement for the characteristics of internal solitary wave propagation effectively makes up for the insufficient adaptability of the original model in complex marine environment. The results prove that the method used in the present application is indeed feasible and effective. At the same time, using the real internal solitary wave position image of Longmu Strait observed by remote sensing, as shown in Figure 5 and Figure 6 , it is verified that the internal solitary wave position predicted based on the improved TimeXer model has good consistency, as shown in Figure 7 .

[0122] Table 2 Comparison of model results

[0123]

[0124] The above description of the disclosed embodiments enables one of ordinary skill in the art to make or use the application. Various modifications to these embodiments will be apparent to those skilled in the art, and the generic principles defined herein can be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting the propagation of internal solitary waves in the ocean based on an improved TimeXer model, characterized in that, Comprising the following steps: Step 1, constructing an improved TimeXer model; The improved TimeXer model comprises an endogenous variable embedding layer, an adaptive frequency spectrum module, a self-attention layer, a dynamic hyperbolic tangent module one, an interactive convolution module, a cross-attention layer, a dynamic hyperbolic tangent module two, a feedforward network layer, and a prediction layer; Step 2, model training and verification; Collecting remote sensing image data of stationary orbit satellite GK-2A and polar orbit satellite, and preprocessing the remote sensing image data; Based on the remote sensing image data, the internal solitary wave parameters are extracted, and the internal solitary wave prediction data set is constructed combined with the hydrological environment parameters, and the constructed internal solitary wave prediction data set is divided into a training set, a verification set and a test set; The training set is input into the model for training, the verification set is used to verify the model, and the test set is used to test the model; Step 3, obtaining the remote sensing image data of stationary orbit satellite GK-2A and polar orbit satellite in the target sea area, preprocessing the remote sensing image data, and inputting into the tested model to predict the internal solitary wave.

2. The method according to claim 1, wherein, The adaptive frequency spectrum module converts the endogenous variable time series data of the internal solitary wave from time domain to frequency domain through Fourier transform, realizes the separation of signal and noise, and then strengthens the key features and suppresses the redundant information through an adaptive mechanism; The adaptive frequency spectrum module realizes dynamic spectrum analysis through the following formula: ； ； ； ； ； ； ； wherein, is the input signal; is the complex spectrum of the input signal after short-time Fourier transform; is the number of channels; is the frame length; is the energy distribution of the computed spectrum, used for subsequent threshold screening; is the significant spectrum after filtering low-frequency noise; is the energy threshold; denotes element-wise multiplication; is the overall spectrum with global weight preservation; is the key spectrum with local weight enhancement; is the global weight; is the local weight; is the spectrum combining global and local information; is the enhanced time-domain signal after inverse Fourier transform, is the real signal at time point.

3. The method according to claim 1, wherein, The interactive convolution module comprises two parallel 1D convolution layers, Conv1 and Conv2, which use different sizes of convolution kernels to capture local features of different granularities; And through the activation function + element multiplication, the cross-scale feature interaction is realized, the features after interaction are summed, and then a 1D convolution layer Conv3 is used for refining to obtain the output of the interactive convolution module; The interactive convolution module is realized through the following formula: ； ； ； wherein, is the input feature map; is the output enhanced feature; denotes a nonlinear activation function, , , are three 1D convolution layers; is the first attention weight, highlighting important feature regions; is the second attention weight, interacting reversely with the first attention weight, capturing complementary features.

4. The method of claim 1, wherein the method is characterized by, The dynamic hyperbolic tangent module one and the dynamic hyperbolic tangent module two realize feature normalization effect through the combination of learnable scaling factor and hyperbolic tangent function, and the mathematical expression is as follows: ； where a is a learnable scalar parameter that dynamically adjusts the scaling range of the input; is a scaling parameter, is a translation parameter.

5. The method of claim 1, wherein the method is characterized by, The model retains the core components of the Transformer, and adopts a differentiated embedding strategy for the endogenous variables and exogenous variables of the internal solitary wave: the endogenous variables are divided into non-overlapping segments and converted into time tokens through linear projection, and the exogenous variables are converted into variable sub-tokens through linear projection; a learnable global token is introduced for each endogenous variable to associate the causal information of the endogenous and exogenous variables, realizing the integration of multi-source data; the endogenous variables include internal solitary wave position propagation speed, propagation direction and peak line length, and the exogenous variables include water depth, temperature and salinity.

6. The method of claim 1, wherein the method is characterized by, The endogenous variable embedding layer converts the endogenous variables of the internal solitary wave to be predicted into a double-layer representation of patch-level time tokens and global tokens, each patch is converted into a time token through a trainable linear projection, and a position embedding is added to retain the time sequence order of the patch, and finally a set of patch-level tokens is output; a learnable global token is introduced as a global trend representative of the endogenous variables, which learns the overall statistical characteristics of the endogenous variables through training.

7. The method of claim 1, wherein the method is characterized by, The self-attention layer is to perform self-attention between patch-level tokens and global tokens of endogenous variables, while capturing local temporal dependencies between patches; the output of the endogenous embedding layer is taken as the input of the self-attention, and three types of interactions are realized through one self-attention calculation: patch-patch interaction, patch-global interaction, and global-patch interaction.

8. The method of claim 1, wherein the method is based on an improved TimeXer model. The cross-attention layer is to establish directional information transmission from exogenous variables to endogenous variables by taking endogenous global tokens as queries and exogenous variable-level tokens as keys and values, so as to realize on-demand injection of exogenous auxiliary information into the endogenous model; through cross-attention calculation, the global token selectively pays attention to the exogenous variable useful for the prediction of the internal solitary wave, and only the endogenous global token pays attention to the exogenous variable, while the useful information is filtered through the global token and then transmitted to the patch.

9. The method of claim 1, wherein, The feedforward network layer performs nonlinear transformation on the patch-level tokens and global tokens updated by the cross-attention layer, strengthens the feature expression capability, and provides more abstract feature representation for the next layer module. The feedforward network layer adopts the standard structure of the Transformer, including two linear transformations and a GELU activation function, and the patch-level tokens and the global tokens pass through the feedforward network layer respectively, ensuring that the feature updates of the two do not interfere with each other.

10. The method of claim 1, wherein the method is based on an improved TimeXer model for predicting the propagation of internal solitary waves in the ocean. The prediction layer maps the patch-level tokens and the global tokens output by the TimeXer encoder into the prediction results of the endogenous variables of the final ocean internal solitary wave, and optimizes the model parameters through a loss function.

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