Prediction method of internal tide and internal solitary wave based on data of submerged buoy observation

Abstract

The application discloses an internal tide-internal solitary wave prediction method based on observation data of a submerged buoy and belongs to the technical field of ocean observation. In the internal tide prediction stage, a deep learning model is used to model the observation data in an end-to-end mode, long-period global dependence and local fine-grained features are effectively extracted through the combination of standardization processing, a sparse attention mechanism and a recurrent neural network, and the fast prediction of future multi-step internal tide sequences is realized; in the internal solitary wave prediction stage, a windowed statistical feature and a weighted logistic regression method are introduced, the predicted semidiurnal tide, diurnal tide and superposed tide sequences are converted into a statistical feature vector, and the prediction of internal wave occurrence in a future period is realized through a logistic regression model. The application can be widely applied to the fields of intelligent monitoring of ocean dynamic environment, internal wave prediction, engineering safety evaluation and the like, and provides an efficient and robust technical scheme for deep sea observation and rapid prediction.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of ocean observation, and particularly relates to an internal tide-internal solitary wave prediction method based on submerged buoy observation data. BACKGROUND

[0002] Internal tide is a periodic internal wave phenomenon in the ocean generated by the interaction of celestial body tide-generating force and complex seafloor topography, and is an important way of energy transmission in the vertical and horizontal directions. Its generation and propagation not only regulate the energy cascade and thermal-salinity structure of the ocean, but also affect the heat and material transport processes, and have a significant effect on the safety of ocean engineering facilities and the evolution of the climate system. Under the action of internal tide, strong nonlinear processes are often induced and further evolve into internal solitary waves. As a typical nonlinear internal wave, internal solitary wave has a steep wave shape and strong local transport capacity, and has an important influence on shipping safety, ocean engineering structures and military activities.

[0003] Internal solitary waves are characterized by strong burstiness, significant nonlinearity and complex spatiotemporal scales, making direct prediction extremely difficult. In contrast, internal tide has strong periodicity and regularity, and its occurrence and evolution characteristics are easier to capture and predict. Considering that internal tide is the energy background and triggering mechanism of internal solitary waves, accurate prediction of internal tide can further infer and predict the occurrence of internal solitary waves, providing a new approach to breaking through the technical difficulties of direct prediction of internal solitary waves. Therefore, constructing an internal tide wave-internal solitary wave coupled prediction framework not only has important scientific research significance, but also has outstanding engineering application value.

[0004] Existing internal tide prediction methods mainly include numerical model-based ocean dynamics simulation, harmonic analysis based on historical observation and empirical formula calculation. These methods generally have high dependence on the precision of environmental parameters, are complex in modeling, sensitive to parameters, and have large computational load, making it difficult to achieve efficient prediction in dynamic ocean environments. At the same time, most existing internal solitary wave prediction methods rely on numerical simulation or empirical criteria, lack effective coupling with internal tide processes, and fail to fully utilize the dynamic relationship between the two, thus limiting the prediction ability and application range.

[0005] With the development of ocean observation technology, a large amount of high-resolution temperature, salinity, flow rate and other observation data are continuously accumulated, which provides new opportunities for deeply mining the correlation mechanism of internal tides and internal solitary waves. However, at present, there is still a lack of a method that can fully utilize the potential rules of observation data and combine artificial intelligence technology to establish an internal tide wave-internal solitary wave prediction coupling framework. In view of this problem, it is urgent to develop an internal tide wave-internal solitary wave machine learning prediction method technology based on the observation data of the submerged buoy, so as to break through the limitations of traditional methods in calculation efficiency and prediction accuracy, deepen the understanding of the coupling mechanism of the two, and provide environmental warning support for ocean engineering safety and shipping, serve deep sea resource development and environmental assessment, and have important significance and broad prospects in scientific research and practical application. SUMMARY

[0006] The present application aims to solve the problems of existing internal tide prediction methods, such as complex calculation, low prediction efficiency, and high dependence on parameter accuracy, and to break through the limitations of internal solitary wave direct prediction, such as difficulty and lack of effective coupling with internal tide process. Therefore, an internal tide wave-internal solitary wave machine learning prediction method based on the observation data of the submerged buoy is proposed, which can predict different types of internal tide sequences in advance, and then use machine learning methods to establish the corresponding relationship between internal tide and internal solitary wave, so as to realize the indirect prediction of internal solitary wave occurrence.

[0007] In order to achieve the above purpose, the specific technical scheme provided by the present application is as follows:

[0008] An internal tide wave-internal solitary wave prediction method based on the observation data of the submerged buoy, comprising the following steps:

[0009] S1: Obtain high-resolution temperature, flow rate and other data at the observation station, complete preprocessing and generate standardized grid data;

[0010] S2: Extract three types of characteristic sequences of semidiurnal internal tide, diurnal internal tide and their superimposed synthetic internal tide based on the preprocessed data, as model input;

[0011] S3: Label the internal wave occurrence time period based on the environmental field observation data, and construct the corresponding 0 / 1 label sequence, where s represents that there is internal wave occurrence in the period;

[0012] S4: Construct a parallel prediction model (Fusion-IBFormer) that fuses a sparse attention encoder based on the Informer architecture and BiLSTM, which includes input encoding layer, sparse attention branch, BiLSTM branch, cross-branch feature fusion layer and prediction output layer in sequence;

[0013] S5: Input the three types of internal tide characteristic sequences into the model, and use end-to-end training combined with hyperparameter tuning to obtain a prediction model that can output the future three types of internal tide sequences simultaneously;

[0014] S6: Inference is performed on real-time observation data using the trained model to output semi-diurnal, diurnal and synthetic internal tide prediction sequences for future periods;

[0015] S7: A mapping relationship between the three types of internal tide feature sequences and internal wave occurrence is established using a logistic regression method in combination with the labeled internal wave occurrence sequences in S3 to form a logistic regression model;

[0016] S8: The three types of internal tide sequences predicted are input into the trained logistic regression model for discrimination to output the occurrence prediction results of internal solitary waves in future periods, realizing the coupling prediction of internal tide waves and internal solitary waves.

[0017] Further, the S1 comprises:

[0018] S1-1: The preprocessing comprises integrity checking and quality control of high-resolution data collected by the observation station, elimination of abnormal values and noise points, and filling of partial missing data through time interpolation and vertical interpolation.

[0019] S1-2: The preprocessed observation data are unified to a 5m vertical resolution and a fixed time step to generate a standard depth-time two-dimensional gridded observation matrix.

[0020] Further, in the S2: The internal tide signal extraction uses a frequency band separation method based on a Butterworth digital filter, calculates the sampling frequency according to the sampling interval of the observation sequence, designs low-pass and band-pass filters, and extracts main frequency band signals such as semi-diurnal tide, diurnal tide and inertial oscillation. The inertial oscillation frequency band is centered on the Coriolis frequency corresponding to the observation latitude ± 15%, is the angular velocity of the Earth's rotation, is the latitude of the observation point; and the filter transfer function is:

[0021] ,

[0022] wherein, is the cutoff frequency, is the filter order. Through the above filter design, semi-diurnal internal tide feature sequences and diurnal internal tide feature sequences can be obtained respectively; further, the two are superimposed to obtain synthetic internal tide feature sequences, and the three types of results are smoothed and reconstructed into complete internal tide feature sequences as the input of subsequent models.

[0023] Further, in S3, the internal wave occurrence time period is marked. First, according to the temperature field or flow velocity field data of the observation station, the profile of the time variation is drawn as a continuous time sequence graph. Then, the temperature field or background field image drawn is interpreted manually, and the internal wave occurrence time period is marked. The internal wave occurrence interval is marked as "1", and the internal wave-free interval is marked as "0", so as to construct a 0 / 1 label sequence corresponding to the observation data.

[0024] Further, S4 includes:

[0025] S4-1: input encoding layer, input tensor is organized as , wherein is the batch size, is the length of the historical time sequence, is the number of input feature channels. One-dimensional linear projection (Linear Projection) is used to map each channel to a unified feature dimension , and a fixed position encoding (PositionalEncoding) based on the sine / cosine function is added:

[0026] ;

[0027] ;

[0028] wherein represents the position index of the element in the input sequence, and the value range is ; represents the subscript index of the feature dimension, and the value range is , and each corresponds to a pair of sine and cosine encoding values. After the encoded tensor is added to the position encoding, the output tensor is obtained after normalization (LayerNorm) and regularization (Dropout) processing, and the shape of the output tensor is .

[0029] S4-2: build a sparse attention encoder branch, extract long-period global dependence features based on the Encoder design idea of Informer. The Encoder adopts a 2-layer encoder stack structure. Each layer of the encoder includes a sparse self-attention (ProbSparse Multi-Head Attention), a distilling convolution (Distilling), a feed-forward network (Feed-Forward Network, FFN), and a residual connection and layer normalization module.

[0030] The sparse self-attention calculates only important attention weights by screening query vectors with high probabilities, thereby reducing the computational complexity from , query (Q ), key (K ), value (V ) are computed as follows: , , where , is the attention scaling factor, , is the number of attention heads, and the attention output is:

[0031] ;

[0032] Distillation convolution uses one-dimensional convolution and pooling operations to halve the sequence length, highlighting long-period dependencies:

[0033] ;

[0034] The feedforward network has two fully connected mappings:

[0035] ;

[0036] where , , is the ReLU activation function. Each sub-layer output is processed through a residual connection and normalization, and the final output of the encoder stack is .

[0037] S4-3: Construct the BiLSTM branch, which receives the encoded time series , uses a two-layer bidirectional LSTM network to extract local fine-grained features and bidirectional time sequence dependencies. This branch includes a bidirectional LSTM stack layer, a normalization and regularization module, and a linear projection module for dimension alignment.

[0038] where the given input vector , the LSTM unit at time t is calculated as follows:

[0039]

[0040] where are the input gate, forget gate, and output gate, is the memory cell state, is the Sigmoid activation function, , .

[0041] In the bidirectional LSTM stack layer, the bidirectional structure is obtained by simultaneously propagating the LSTM forward and backward in time , and concatenating to get , is the one-way hidden dimension. The network stacks two layers, the second layer takes the output of the first layer as input, with Dropout and LayerNorm in between. The output of the stacked layers is: .

[0042] After stacking the BiLSTM, the output channel dimension is , which cannot be directly used with the sparse attention encoder branch output. The dimension is adjusted to by linear mapping, the mapping formula is as follows: The final output is: .

[0043] S4-4: Construct a cross-branch feature fusion layer to fuse the long-period global representation output by the sparse attention encoder with the local bidirectional context representation output by the BiLSTM branch, forming a unified representation with both global dependency and fine-grained temporal information. The fusion layer is designed based on multi-head attention mechanism and gated residual structure.

[0044] Take as Q, as K and V, project the two types of features into the multi-head attention space through the linear mapping matrix to get the input tensors Q, K, V of each attention head. Then calculate the cross-branch attention weight. Each attention head calculates the dot product similarity of Q and K in turn, and performs scaling and Softmax normalization:

[0045] ;

[0046] After concatenating the results of all attention heads, the cross-branch fusion feature is obtained through the output projection matrix .

[0047] The sparse attention encoder branch serves as the main query source, focusing on capturing long-period correlations in the sequence, while the BiLSTM branch provides fine-grained context to ensure that local change patterns are fully attended to.

[0048] Introduce a learnable gating coefficient to control the weighting ratio of the attention fusion result and the original BiLSTM feature. It is generated from the concatenated feature ; Z ] by a layer of multi-layer perceptron (MLP), and the fused representation is:

[0049] ;

[0050] Introduce a two-layer feedforward network to enhance the nonlinear modeling capability of the fusion representation. The first layer maps the dimension , the second layer maps back , with ReLU activation. The FFN output is added with the residual and normalized:

[0051] .

[0052] S4-5: Construct a prediction output layer to convert the integrated features output by the cross-branch attention fusion layer into an internal tide prediction sequence of a fixed time length in the future . The prediction output layer aggregates the historical features in the time dimension through a learnable attention aggregation strategy and directly regresses the future multi-step prediction results using a single-layer linear mapping.

[0053] The aggregation strategy introduces a learnable query vector as a time series aggregator to weight and aggregate in the time dimension. The features are mapped to the attention space through a linear projection matrix : , , The time dimension attention weight is calculated as follows: .

[0054] The aggregated prediction input features are calculated according to the weights: ;

[0055] The aggregated features are input into a single-layer linear mapping to directly output the prediction results of the future time steps, channels: + , where , , and finally the prediction results are reshaped to: .

[0056] Further, the S5 includes:

[0057] S5-1: Slide window slicing is performed on the internal tide feature sequence to generate samples, the training set, validation set and test set are divided in time sequence, and the features are normalized and standardized for preprocessing to ensure stable sample distribution.

[0058] S5-2: An end-to-end training strategy is adopted, and the Adam optimizer and learning rate scheduler are used for training; the model structure is optimized by adjusting the network depth, hidden unit dimension, attention head number and learning rate, etc.

[0059] ​S5-3: Evaluate the model performance based on the MSE, MAE indicators of the validation set, select the best weight parameter, save the model, and use it for subsequent prediction.

[0060] Further, the S6 uses the trained model to infer the current internal tide observation sequence, constructs the input data in the same sliding window manner as the training phase, and outputs the future multi-step prediction results at one time through the forward propagation of the model. After the prediction output is processed by inverse normalization and formatting, the three types of internal tide time series in the future time period are generated, realizing fast and accurate internal tide prediction.

[0061] Further, the S7 includes:

[0062] S7-1: Divide the time series of the three types of internal tides according to the preset window length, and each window corresponds to a fixed length of data; combine the labeled internal wave occurrence sequence, if there is an internal wave label in the window, it is defined as a positive class, otherwise it is defined as a negative class, and an input-output sample pair at the window level is established.

[0063] S7-2: For each window of the three types of internal tide sequences: semidiurnal internal tide sequence , diurnal internal tide sequence , and internal tide sequence superimposed by semidiurnal internal tide and diurnal internal tide , calculate the mean , standard deviation , linear slope , numerical range and energy statistical characteristics, the calculation formula is as follows:

[0064]

[0065]

[0066]

[0067]

[0068] ;

[0069] At the same time, in order to depict the interaction between different components, the Pearson correlation coefficient number is calculated for each pair of three types of internal tide sequences to represent the coupling relationship between components, and the calculation formula is as follows:

[0070] ;

[0071] Finally, each window can obtain an 18-dimensional feature vector:

[0072] ;

[0073] S7-3: Train the model using the weighted logistic regression method, and input the feature vector and the corresponding internal wave occurrence label into the logistic regression model to establish the discriminant function: , where is the feature weight vector, is the bias term. To alleviate the training bias caused by the uneven proportion of positive and negative samples, a class weighting mechanism is introduced: , where are the proportions of positive and negative samples in the training set, respectively.

[0074] The model training process is achieved by minimizing the weighted cross-entropy loss function:

[0075] ;

[0076] where , through the above method, the mapping relationship between the internal tide component features and the internal solitary wave occurrence can be learned more accurately under the condition of class imbalance.

[0077] S7-4: After the model training is completed, the performance of the output prediction probability is evaluated, and the precision (Precision), recall (Recall) and F1 value are calculated, and the calculation formula is as follows:

[0078]

[0079]

[0080] ;

[0081] where TP, FP, and FN represent the true positive, false positive, and missed detection number of the predicted positive class, respectively. The system calculates the corresponding F1 value in all candidate threshold ranges, and automatically selects the threshold value that makes F1 reach the maximum as the final discriminant threshold.

[0082] Further, the S8 divides the predicted three types of future internal tide feature sequences, i.e. semidiurnal tide, diurnal tide and superimposed tide time series, into windows in the same way as in the training stage, and extracts statistical features such as mean, standard deviation, slope, numerical range, energy and correlation coefficient to form the input feature vector.

[0083] Then the feature vector is input into a logistic regression model, the model calculates the internal wave occurrence probability in the future period based on the weight parameters and the discrimination threshold value determined in the training stage, and converts the probability result into a binary discrimination, outputs the prediction result of whether there is internal solitary wave in each time window in the future, so that the coupling prediction of internal tide wave and internal solitary wave is realized.

[0084] Compared with the prior art, the advantages and beneficial effects of the present application are:

[0085] The present application proposes an internal tide wave-internal solitary wave machine learning prediction method based on the observation data of a submerged buoy, aiming at the problems of traditional numerical mode such as dependence on high-precision physical parameters, complex calculation, and insufficient real-time performance, and a hybrid framework considering accuracy and efficiency is constructed. In the internal tide prediction stage, a deep learning model is used to model the observation data end to end, and through the combination of standardization processing, sparse attention mechanism and recurrent neural network, long-period global dependence and local fine-grained features are effectively extracted, realizing the rapid prediction of future multi-step internal tide sequences.

[0086] In the internal solitary wave prediction stage, the present application introduces windowed statistical features and weighted logistic regression method, converts the predicted semidiurnal tide, diurnal tide and superimposed tide sequences into a statistical feature vector, and realizes the prediction of internal wave occurrence in the future period through a logistic regression model. This method has good stability under the condition of class imbalance, and the model parameters have clear physical interpretability, overcoming the defect of insufficient interpretability of deep learning models.

[0087] The present application has high-precision prediction ability of deep learning model and lightweight and interpretable advantages of logistic regression model, which not only ensures the high consistency of the results and observations, but also considers the real-time performance and deployment flexibility. The method can be widely used in the fields of intelligent monitoring of marine dynamic environment, internal wave prediction, engineering safety evaluation, etc., and provides an efficient and robust technical solution for deep sea observation and rapid prediction. BRIEF DESCRIPTION OF DRAWINGS

[0088] Figure 1 It is the whole flow chart of the internal tide wave-internal solitary wave coupling prediction method described in the present application.

[0089] Figure 2 It is a data processing flowchart before inputting into the prediction model.

[0090] Figure 3 It is an internal solitary wave prediction model weighted logistic regression prediction flowchart.

[0091] Figure 4 It is an internal tide prediction model Fusion-IBFormer network structure and its principle schematic diagram.

[0092] Figure 5is a structural schematic diagram of a sparse attention branch module.

[0093] Figure 6 is a structural schematic diagram of a BiLSTM branch module.

[0094] Figure 7 is a structural schematic diagram of a feature fusion and prediction output module.

[0095] Figure 8 is a temperature field profile after preprocessing, in which the black curve represents the change of the 14.5℃ isotheral over time.

[0096] Figure 9 is a three-class internal tide feature sequence diagram extracted based on the isotheral sequence.

[0097] Figure 10 is a labeled internal solitary wave occurrence label sequence diagram, in which 0 represents no internal wave occurrence and 1 represents internal wave occurrence.

[0098] Figure 11 is a comparison diagram of three-class internal tide prediction results and real observation sequences, in which the yellow curve is the real internal tide sequence and the blue curve is the predicted sequence.

[0099] Figure 12 is a partial training set internal solitary wave prediction result schematic diagram, in which the diamond block is the measured internal solitary wave and the red line represents the predicted internal solitary wave occurrence interval.

[0100] Figure 13 is a test set internal solitary wave prediction result schematic diagram, in which the diamond block is the measured internal solitary wave and the red line represents the predicted internal solitary wave occurrence interval. DETAILED DESCRIPTION

[0101] The present application will be further explained and described below by specific embodiments in conjunction with the accompanying drawings, but the present application is not limited to the following specific embodiment descriptions.

[0102] Example 1:

[0103] As shown in Figure 1 , Figure 2 , Figure 3 , Figure 4 , a machine learning prediction method for internal tide waves and internal solitary waves based on subsurface buoy observation data includes the following steps:

[0104] Step 1: Collect high-resolution single-point continuous observation data obtained by the target sea area's subsurface buoy observation equipment, including but not limited to collection time t, observation depth d, temperature T, and flow rate (u, v), and other key marine environmental elements. First, unify and preliminarily quality control the collected raw observation data: unify time to UTC, remove duplicate timestamps and sort by time order; unify temperature to ℃; unify flow rate to m / s; depth is zero at sea level and positive downward; mark equipment downtime or offline segments as NaN. Correct flow rate data in combination with acoustic Doppler current profiler (ADCP) characteristics, consider the influence of shallow beam refraction, and mark flow rate above 50m as NaN to avoid system error affecting the prediction model.

[0105] For each variable , set a reasonable temperature and flow rate range according to the location and depth of the sea area. , mark as NaN if it exceeds the threshold range.

[0106] For the quality-controlled observation sequence, first resample along the time dimension to a fixed step size , then unify the depth to 5m layer spacing. Set the target time grid , the target depth grid , and use piecewise linear interpolation to complete the missing points.

[0107] Time interpolation, proceed by depth layer, set the adjacent valid observation points at depth d as , when , the calculation formula is as follows:

[0108] ;

[0109] Vertical interpolation, proceed by time, set the adjacent valid depth points at time t as , when , the calculation formula is as follows:

[0110] ;

[0111] If the continuous missing interval is greater than the preset threshold, do not extrapolate, keep NaN; do not extrapolate at the beginning and end of the time sequence and the vertical boundary, directly set the target points outside the outermost observation range to NaN.

[0112] Finally, for each variable , generate a regular grid matrix: , forming a standard "depth-time" two-dimensional observation matrix.

[0113] Step 2: Select and extract the internal tide signal in the standardized "depth-time" two-dimensional observation matrix obtained in step 1. First, select the appropriate isotherm variation sequence or fixed depth flow rate sequence as the analysis object in combination with the water depth of the study area and the quality of the observation data.

[0114] The internal tide signal extraction adopts a multi-frequency band separation strategy based on the Butterworth digital filter: calculate the sampling frequency according to the sampling interval Calculate the sampling frequency according to the sampling interval , design low-pass and band-pass filters, and extract the main frequency band signals such as semidiurnal tide, diurnal tide, and inertial oscillation. The inertial oscillation frequency band is the Coriolis frequency corresponding to the observation latitude ± 15%, is the angular velocity of the Earth's rotation, is the latitude of the observation point; the filter transfer function is:

[0115] ,

[0116] where, is the cutoff frequency, is the filter order. After smoothing the filtering results, the semidiurnal internal tide sequence , the diurnal internal tide sequence , the internal tide sequence superimposed by the semidiurnal internal tide and the diurnal internal tide are obtained, which are used as input for subsequent models.

[0117] Step 3: Divide the standardized "depth-time" two-dimensional observation matrix obtained in step 1 into "days" in sequence, and plot the data of each day as a time-depth profile. By observing the change characteristics of the profile, manually determine the time period of internal wave occurrence, mark the corresponding sequence position as "1" in the interval, and mark the interval without internal solitary wave occurrence as "0", thereby obtaining the internal solitary wave occurrence annotation sequence covering the entire observation period .

[0118] Step 4: Divide the three types of internal tide sequences obtained in step 2 into windows of a predetermined length, each window corresponding to a fixed length of data segment, and align with the manually annotated internal wave occurrence record obtained in step 3. If there is an internal wave marker in a window, it is defined as a positive class, otherwise it is a negative class, and the window-level input-output sample pairs are obtained.

[0119] In each window, the statistical characteristics of the semi-diurnal tide, diurnal tide and superimposed synthetic internal tide are calculated, including mean, standard deviation, linear slope, numerical range and energy. The Pearson correlation coefficient between the three types of sequences is further calculated to describe the coupling relationship between the components. Finally, an 18-dimensional feature vector is obtained for each window .

[0120] In the modeling stage, the feature vector and the corresponding internal wave label are input into the logistic regression model to establish the mapping relationship between internal tide features and internal wave occurrence. The discriminant function of logistic regression is: During training, a class weighting mechanism is introduced to enable the model to learn the features of positive and negative samples more balanced. The weighted cross-entropy is used as the loss function of the model: Through the above mechanism, the model can still maintain the robust learning ability of internal tide features and internal wave occurrence under the condition of class imbalance, effectively improving the prediction performance.

[0121] After training, the performance is evaluated using the predicted probability results, and the precision, recall and F1 value are calculated. The threshold that maximizes the F1 value is automatically selected as the final discriminant condition. After model training and evaluation, the logistic regression model parameters are saved, which can be directly called in the subsequent prediction stage to realize the rapid discrimination of future internal tide feature sequence input and internal solitary wave occurrence prediction.

[0122] Step 5: Perform dataset construction and input encoding on the three types of internal tide feature sequences obtained in step 2 for deep learning model training. First, construct the sample dataset based on the time series sliding window strategy, set the historical input window length to , the prediction window length to , and the length of the continuous segment to on the complete signal. The input sample is obtained by sliding and intercepting, and the corresponding prediction label for the future steps is generated. After construction, the data is divided into training set, validation set and test set in proportion.

[0123] Then, each input segment is organized into a three-dimensional tensor input model according to the "batch size x time length x feature dimension ". Through a linear mapping layer, the feature channel is uniformly projected to a set dimension Based on the fixed time position coding constructed by sine and cosine functions, the model has the ability to capture the position relationship of the sequence. After coding, the tensor is normalized and regularized to form a uniform format input tensor , as the standard input for subsequent feature extraction and prediction modeling.

[0124] Step 6: The tensor output from Step 5 is fed into a designed parallel prediction model based on the Informer architecture's sparse attention encoder and BiLSTM, with detailed module structures as shown in Figs. Figure 5 , 6, and 7.

[0125] The sparse attention encoder branch adopts a two-layer stacked sparse self-attention encoder structure, with Pre-Norm design in each layer. The layer normalization is performed first, followed by sub-layer operations and feedback through residual connection. The attention module is based on the ProbSparse multi-head self-attention mechanism, which ranks the importance of query vectors by calculating the importance of query vectors, and only retains the attention of the top high importance queries, reducing the computational complexity from the traditional , while maintaining the global information capturing ability and reducing redundant calculations. A one-dimensional distillation convolution (Conv1D, kernel=3, stride=2) is introduced after the first layer encoder to reduce the time dimension resolution, suppress high-frequency noise, and highlight key long-period features; the second layer maintains the original time resolution to ensure alignment with other branch features. Each encoder contains two fully connected feedforward networks (FFN) to improve expression ability and prevent overfitting, combined with nonlinear activation, residual connection, and Dropout. The feature representation output by the two-layer encoder stack is the global long-period dependent representation .

[0126] The BiLSTM adopts a two-layer stacked bidirectional long short-term memory network (BiLSTM) structure, with Pre-Norm and residual connection design in each layer to ensure the stability and convergence speed of the deep network. The bidirectional structure of BiLSTM encodes the sequence through forward and backward recursion to obtain the context information of past and future time slices, making the model more accurate in describing the phase shift, amplitude change, and local disturbance features in the tidal signal. In the two-layer stack, the second layer takes the output of the first layer as input, with Dropout and LayerNorm inserted between each layer to alleviate overfitting and enhance generalization ability. The bidirectional hidden state is spliced to form a dimensional representation, consistent with the output of the sparse attention branch, and finally mapped to dimensions through a linear projection layer, outputting the local context feature matrix .

[0127] The features and output by the two branches are projected to a unified multi-head attention space through linear mapping, and the sparse attention encoder output ​BiLSTM outputs Query as Query As Key and Value, the cross-branch attention weights are calculated to capture the relevance between global and local features. The results of all attention heads are concatenated and projected linearly to generate the fused feature representation. A learnable gating mechanism is introduced to dynamically generate weight coefficients through a multi-layer perceptron (MLP), which weights the attention fusion results and the original BiLSTM features, thereby preserving the local change pattern while strengthening the dominant role of global features in prediction. The fused intermediate features are nonlinearly mapped through a feed-forward network (FFN), and residual connection and layer normalization are further combined to improve the expressiveness and training stability of the features, finally outputting a unified dimension of fused representation .

[0128] The prediction output layer uses a learnable query vector to realize time dimension aggregation, and through attention mechanism, it adaptively allocates the importance weight of each time slice feature in history to generate prediction input feature representation Finally, a single linear mapping is used to directly regress the prediction result matrix of fixed time length and fixed channel number .

[0129] In the process of model running, an end-to-end optimization strategy is adopted, and the mean square error (MSE) between the prediction result and the real observation sequence is taken as the loss function:

[0130] ;

[0131] Where is the batch index ; is the time index ; is the feature channel index, with a value range of .

[0132] The gradient is calculated by backpropagation: . The parameters are updated using the Adam optimizer, combined with the cosine annealing learning rate scheduling strategy, which converges quickly in the early stage and smoothly adjusts the learning rate in the later stage to improve the model accuracy. The calculation formula is as follows:

[0133] ;

[0134] ;

[0135] Where, and are the bias correction terms of the first and second moment estimates of the gradient, learning rate, , maximum learning rate and minimum learning rate. current iteration number, annealing period.

[0136] In the training process, the MSE and MAE of the validation set are monitored in real time. When the validation indicators do not improve significantly in consecutive training rounds, the early stopping mechanism (Early Stopping = 5) is enabled to terminate training and avoid overfitting.

[0137] ;

[0138] .

[0139] Step 7: Based on the deep learning model that has completed training and has the optimal verification performance, input the historical observation sequence with a length of before the prediction window into the model, and generate the prediction result sequence with a length of in one time through the forward inference of the model, which is directly mapped to the internal tide feature time series curve of the future time period, realizing the rapid prediction and visual display of the future internal tide information.

[0140] Step 8: Take the future internal tide prediction sequence obtained in step 7 as input and send it to the trained logistic regression model for discrimination, and then obtain the prediction result of the internal solitary wave in the time range of .

[0141] Example 2

[0142] This example is based on the method described in Example 1 and has been verified in practice. The experimental data is selected from the long-term continuous observation data of a mooring station in the South China Sea, with an observation time range from August 2, 2021 to August 29, 2022. The data set has a high time resolution, with a sampling interval of 3 minutes, covering the full water depth profile, and contains environmental factors such as temperature and flow rate. After preprocessing the original data as described in Example 1, a standardized "depth-time" two-dimensional matrix is constructed. Then, the processed data is divided into training set, validation set and test set in the ratio of 8:1:1, which is used for model training, tuning and performance evaluation.

[0143] In the internal tide sequence prediction process, the internal tide sequence of the past 2 days is used as input to predict the internal tide signal of the future 1 day. Due to the large amount of data throughout the year, in order to facilitate display, the observation data of October 2021 is selected for plotting in the training set.

[0144] The temperature data quality of this station is significantly better than the flow rate data, so the isotherm change curve is selected to extract the internal tide signal. As shown inFigure 8 Fig. 6 shows the temperature profile in October 2021, and the black curve represents the 14.5℃ isotherm changing over time. Based on the isotherm sequence, the main frequency band components are separated using the Butterworth digital filtering method described in Example 1, and signal reconstruction is performed to obtain three types of internal tide signal sequences. As shown in Fig. 7, the semidiurnal internal tide sequence, the diurnal internal tide sequence, and the superimposed internal tide sequence of the station in October 2021 are shown. The temperature-time profile is plotted by aggregating daily, and manual interpretation is performed to mark the time period of internal solitary wave occurrence, and a 0 / 1 label sequence is constructed. As shown in Fig. 8, the manual judgment label sequence of the station in October 2021 is given, where "1" represents the occurrence of internal solitary wave in the period, and "0" represents no internal wave. Figure 9 Figure 10

[0145] After aligning the three types of internal tide characteristic sequences with the corresponding internal wave label sequences, they are divided into fixed length 2-hour training windows, and a statistical feature vector is constructed for each window. Then, the feature vector and the label are input into the logistic regression model for training, and the model automatically learns the corresponding relationship between the internal tide characteristics and the occurrence of internal wave in the training set. After training, the performance is evaluated and the threshold is selected using the validation set, and the final model parameters are saved for subsequent test set prediction.

[0146] The three types of internal tide sequences are input into the model encoding layer, and after feature extraction, they are sent to the prediction network for training. In the training process, hyperparameter tuning is carried out synchronously, and the model weight with the best performance on the validation set is finally saved. To visually display the model effect, the observation data from July 28, 2022 to August 28, 2022 is selected from the test set for prediction analysis. Due to the setting of the input window, the actual prediction period is from July 30, 2022 to August 27, 2022.

[0147] As shown in Fig. 12, from top to bottom are the prediction results of the semidiurnal internal tide, the diurnal internal tide, and the superimposed internal tide of the station in August 2022, respectively. The yellow curve is the true observation sequence, and the blue curve is the model prediction sequence. The overall error evaluation shows that the mean square error (MSE) of the three types of internal tide prediction is 0.054, and the mean absolute error (MAE) is 0.157. The results show that the model can maintain high consistency with the true observation in terms of oscillation form and amplitude change, and can accurately depict the main dynamic characteristics of internal tide, verifying the effectiveness and reliability of the method in actual observation data. Figure 11

[0148] On this basis, the three types of internal tide sequences predicted are input into the logistic regression model as input features for discriminant analysis, and the occurrence of internal solitary wave in the future period is output. As shown in Fig. 13, the occurrence of internal solitary wave in the future period is shown, where "1" represents the occurrence of internal solitary wave, and "0" represents no internal wave. Figure 12 ​​​As shown, the comparison between the predicted internal solitary wave occurrence period and the actual observation in the training set from September to October 2021 shows that the model prediction is highly consistent with the actual occurrence period. The prediction result of the test set in August 2022 is shown in FIG. 6. Figure 13 As shown, the prediction period is also highly consistent with the actual occurrence period. The above results show that the method has successfully expanded to the prediction of internal solitary wave occurrence on the basis of high-precision internal tide prediction, completed the coupling application of internal tide wave and internal solitary wave, and verified the feasibility and effectiveness of the method through actual observation data.

[0149] In summary, the present application proposes an internal tide wave-internal solitary wave machine learning prediction method based on the observation data of a submerged buoy, which can realize efficient prediction of semidiurnal, diurnal and combined internal tides on the basis of full utilization of measured observation data, and further realize internal solitary wave occurrence prediction combined with a logistic regression model. The method has a significant improvement in prediction accuracy and computational efficiency compared with the traditional numerical model method, breaks through the limitations of high dependence on environmental parameters and large consumption of computing resources, and provides a new and feasible technical means for ocean dynamics research, real-time monitoring and early warning, engineering facility safety and deep sea resource development.

[0150] It should be noted that although the technical solutions of the present application are described in detail in combination with the drawings and specific embodiments, these embodiments are only used to illustrate the present application and should not be regarded as limiting the scope of protection. Those skilled in the art can make various equivalent modifications or improvements to the present application without departing from the spirit and essence of the present application, and these should all fall within the scope of protection of the present application.

Claims

1. A method for predicting internal tidal waves and internal solitary waves based on submerged buoy observation data, characterized in that, Includes the following steps: S1: Acquire high-resolution temperature and flow velocity data from the observation station, complete preprocessing, and generate standardized grid data; S2: Based on the preprocessed data, extract three types of feature sequences: semi-diurnal tide, full-diurnal tide, and composite intra-diurnal tide (the superposition of the two), and use them as model input; S3: Based on environmental field observation data, mark the time periods of internal wave occurrence and construct the corresponding 0 / 1 label sequence, where 1 indicates that internal waves occur during that time period; S4: Construct a parallel prediction model that integrates a sparse attention encoder based on the Informer architecture and a BiLSTM. The model includes an input encoding layer, a sparse attention branch, a BiLSTM branch, a cross-branch feature fusion layer, and a prediction output layer. S5: Input the three types of endocytic feature sequences from S2 into the parallel prediction model, use end-to-end training and combine hyperparameter tuning to obtain a prediction model that can simultaneously output the three types of endocytic sequences in the future. S6: Use the trained parallel prediction model to infer from real-time observation data and output the half-day, full-day and synthetic endocytic prediction sequences for future time periods; S7: Combining the internal wave generation sequences already labeled in S3, the logistic regression method is used to establish the mapping relationship between the three types of internal tide characteristic sequences and internal wave generation, forming a logistic regression model; S8: Input the intidal prediction sequence obtained from S6 into the trained logistic regression model for discrimination, and output the prediction results of the occurrence of isolated waves in the future time period, so as to realize the coupled prediction of intidal wave-intra-isolated wave.

2. The method for predicting internal tidal waves and internal solitary waves as described in claim 1, characterized in that, S1 includes: S1-1: The preprocessing includes integrity checks and quality control of the high-resolution data collected from the observation stations, removal of outliers and noise points, and supplementation of some missing data through time interpolation and vertical interpolation. S1-2: Unify the preprocessed observation data to a 5m vertical resolution and a fixed time step to generate a standard depth-time two-dimensional gridded observation matrix.

3. The method for predicting internal tidal waves and internal solitary waves as described in claim 1, characterized in that, In S2: the internal tide signal extraction employs a frequency band separation method based on Butterworth digital filters. The sampling frequency is calculated according to the sampling interval of the observation sequence. Low-pass and band-pass filters are designed to extract the semi-diurnal tide, diurnal tide, and inertial oscillation frequency band signals, respectively. The inertial oscillation frequency band uses the Coriolis frequency corresponding to the observation latitude. ±15% of the center This is the Earth's rotational angular velocity. The latitude of the observation point is given; the filter transfer function is: in, The cutoff frequency, denoted as the filter order; through the above filter design, the semi-diurnal tidal characteristic sequence and the full-diurnal tidal characteristic sequence are obtained respectively, and the two are superimposed to obtain the synthetic tidal characteristic sequence. After smoothing the three types of results, the complete tidal characteristic sequence is reconstructed.

4. The method for predicting internal tidal waves and internal solitary waves as described in claim 1, characterized in that, In S3: the time period of internal wave occurrence is marked. First, based on the temperature field or velocity field data of the observation station, the profile of its change over time is drawn as a continuous time series diagram. Then, the drawn temperature field or background field image is manually interpreted, and the time period of internal wave occurrence is marked. The interval of internal wave occurrence is marked as "1", and the interval without internal wave is marked as "0", thereby constructing a 0 / 1 label sequence corresponding to the observation data.

5. The method for predicting internal tidal waves and internal solitary waves as described in claim 1, characterized in that, S4 includes: S4-1: Input encoding layer, which converts the input tensor... The organization is , in For batch size, The length of the historical time series. The input feature channel number is used; a one-dimensional linear projection is employed to map each channel to a unified feature dimension. And add fixed-position encoding based on sine / cosine functions: in This represents the position index of an element in the input sequence, with a value range of 1. ; The index represents the feature dimension, and its value ranges from 1 to 2. Each Corresponding to a pair of sine and cosine encoded values; the encoded tensor is added to the positional encoding, then normalized; and regularized; the processed tensor is then output. Shape ; S4-2: Construct a sparse attention encoder branch and extract long-period global dependency features based on the Informer encoder design idea; the encoder is composed of two stacked encoders, each of which contains sparse self-attention, distilled convolution, feedforward network and residual connection and layer normalization module; Sparse self-attention reduces computational complexity by filtering query vectors with higher probabilities and calculating only the most important attention weights. Query ( ),key( ),value( The evidence calculation is as follows: , , ,in , It is the attention scaling factor. , This refers to the number of attention heads, and the attention output is: ； Distillation convolution uses one-dimensional convolution and pooling operations to halve the sequence length, highlighting long-period dependencies: ； Two-layer fully connected mapping of feedforward network: ； in , , The ReLU activation function is used. The output of each sub-layer is processed through residual connections and normalization. The final output after the encoders are stacked is... ; S4-3: Construct the BiLSTM branch to receive the encoded time series. It employs a two-layer bidirectional LSTM network to extract local fine-grained features and bidirectional temporal dependencies. This branch includes a bidirectional LSTM stacked layer, a normalization and regularization module, and a linear projection module for dimension alignment. Given an input vector The LSTM cell is calculated at time t as follows: in These are the input gate, forget gate, and output gate, respectively. For the state of the memory unit, It is the Sigmoid activation function. , ; In a bidirectional LSTM stack, the bidirectional structure is obtained by simultaneously recursively iterating along both the forward and backward time directions of the LSTM. spliced ​​together , It is a one-way hidden dimension; the network is stacked with two layers, the second layer takes the output of the first layer as input, and Dropout and LayerNorm are added in between; the output after stacking is: ; After stacking bidirectional LSTMs, the resulting output channel dimension is: Adjusting the dimension to using a linear mapping The mapping formula is as follows: Final output: ; S4-4: Construct a cross-branch feature fusion layer to integrate the long-period global representation output by the sparse attention encoder. Local bidirectional context representation of BiLSTM branch output The fusion layer is designed based on a multi-head attention mechanism and a gated residual structure to form a unified representation that simultaneously possesses global dependencies and fine-grained temporal information. Will As Q, As K and V, through the linear mapping matrix The two types of features are projected into the multi-head attention space to obtain the input tensors Q, K, and V for each attention head; then, the cross-branch attention weights are calculated; for each attention head, the dot product similarity between Q and K is calculated sequentially, and then scaled and normalized using Softmax. ； After concatenating all attention head results, the projection matrix is ​​output. Obtain cross-branch fusion features The sparse attention encoder branch serves as the primary query source, focusing on capturing long-term correlations in the sequence, while the BiLSTM branch provides fine-grained context to ensure that local change patterns are given sufficient attention. Introducing learnable gating coefficients Used to control the weighting ratio of the attention fusion result to the original BiLSTM features; through a multilayer perceptron (MLP) layer from [ Generated from the splicing features of ; Z ], and represented after fusion as: ； A two-layer feedforward network is introduced to enhance the nonlinear modeling capability of the fused representation, where the first layer maps the dimension. The second layer is mapped back. ReLU activation is used; the output after FFN is summed with the residuals and normalized. ； S4-5: Construct a prediction output layer that integrates the combined features output from the cross-branch attention fusion layer. Converted into a future fixed-time-length endocrine prediction sequence The prediction output layer summarizes historical features in the time dimension through a learnable attention aggregation strategy and uses a single-layer linear mapping to directly regress the future multi-step prediction results. Aggregation strategies introduce learnable query vectors As a time series aggregator, Weighted summation is performed along the time dimension using a linear projection matrix. Map the features to the attention space: , , The attention weights in the time dimension are calculated as follows: ; The aggregated predicted input features are calculated based on the weights: ; Aggregated features Input a single-layer linear mapping, directly output the future Time step, Channel prediction results: + ,in , Finally, the prediction results Remodeled as: .

6. The method for predicting internal tidal waves and internal solitary waves as described in claim 1, characterized in that, S5 includes: S5-1: Slide the endocrine feature sequence through a sliding window to generate samples, divide the training set, validation set and test set in chronological order, and perform normalization and standardization preprocessing on the features to ensure stable sample distribution; S5-2: An end-to-end training strategy is adopted, using the Adam optimizer and learning rate scheduler for training; the model structure is optimized by adjusting the network depth, hidden unit dimension, number of attention heads, and learning rate hyperparameters; S5-3: Evaluate model performance based on MSE and MAE metrics of the validation set, select the best-performing weight parameters, save the model, and use it for subsequent predictions.

7. The method for predicting internal tidal waves and internal solitary waves as described in claim 1, characterized in that, In step S6, the trained model is used to infer the current intidal observation sequence. Input data is constructed using the same sliding window method as in the training phase. The model forward propagates and outputs the prediction results for multiple future steps at once. After the prediction output is processed by inverse normalization and formatting, three types of intidal time series for a certain period of time in the future are generated, so as to achieve fast and accurate intidal prediction.

8. The method for predicting internal tidal waves and internal solitary waves as described in claim 1, characterized in that, S7 includes: S7-1: Divide the time series of the three types of internal tides into a preset window length, with each window corresponding to a data segment of fixed duration; combine the labeled internal wave occurrence sequence, define the internal wave as positive if there is an internal wave marker within the window, otherwise define it as negative, and establish window-level input-output sample pairs; S7-2: For the three types of endocrine sequences within each window: semi-diurnal endocrine sequences , full-day internal tide sequence Intratidal sequence consisting of superimposed semi-diurnal and diurnal tides Calculate the mean respectively Standard deviation linear slope Numerical range and energy The statistical characteristics, including those included, are calculated using the following formula: At the same time, in order to characterize the interaction between different components, Calculate the Pearson correlation coefficients for each pairwise sequence of the three types of endorheic sequences. The following formula is used to characterize the coupling relationship between components: ； Ultimately, each window yields an 18-dimensional feature vector: ； S7-3: Use weighted logistic regression for training, and then use the feature vectors... Corresponding internal wave generation label Input the logistic regression model and establish the discriminant function: , in For the feature weight vector, This is the bias term; to mitigate the training bias caused by the imbalance between positive and negative samples, a class weighting mechanism is introduced: , in These represent the proportions of positive and negative samples in the training set, respectively. The model training process is achieved by minimizing the weighted cross-entropy loss function: ； in ; S7-4: After the model training is completed, the performance of the output predicted probabilities is evaluated by calculating precision, recall, and F1 score. The calculation formulas are as follows: Wherein, TP, FP, and FN represent the number of true positives, false positives, and missed detections predicted as positive, respectively; the system calculates the corresponding F1 value within all candidate threshold ranges and automatically selects the threshold that maximizes F1 as the final discrimination threshold.

9. The method for predicting internal tidal waves and internal solitary waves as described in claim 1, characterized in that, S8 divides the predicted three types of future intidal feature sequences—namely, semi-diurnal tides, diurnal tides, and superimposed tides—into windows in a manner consistent with the training phase, and extracts statistical features such as mean, standard deviation, slope, numerical range, energy, and correlation coefficient to form an input feature vector. Then, the feature vector is input into a logistic regression model. The model calculates the probability of intidal wave occurrence within future time periods based on the weight parameters and discrimination thresholds determined during the training phase, and converts the probability results into binary discrimination, outputting the prediction results of whether there are intidal isolated waves in each future time window, thereby realizing the coupled prediction of intidal wave-intidal isolated wave.

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