Three-dimensional ocean sound speed prediction method and device based on tensor empirical orthogonal decomposition

Abstract

The application discloses a three-dimensional marine sound velocity prediction method, in particular to a three-dimensional marine sound velocity prediction method and device based on tensor empirical orthogonal decomposition. The method comprises the following steps: constructing a three-dimensional sound velocity measurement tensor and a weight tensor based on sound velocity measurement data in a target region; determining an optimal base function characteristic matrix set, wherein the optimal base function characteristic matrix set comprises an optimal base function characteristic matrix in a longitude direction, an optimal base function characteristic matrix in a latitude direction and an optimal base function characteristic matrix in a depth direction; constructing a three-dimensional sound velocity tensor prediction calculation function based on the three-dimensional sound velocity measurement tensor, the weight tensor and the optimal base function characteristic matrix set; and iteratively solving the three-dimensional sound velocity tensor prediction calculation function based on a tensor gradient descent method to obtain a sound velocity prediction value at a second position. The application can improve the accuracy of a three-dimensional marine sound velocity prediction result.

Description

Technical Field

[0001] This invention relates to a three-dimensional ocean sound velocity prediction method, specifically a three-dimensional ocean sound velocity prediction method and apparatus based on tensor empirical orthogonal decomposition. Background Technology

[0002] Acoustic signals are the primary carriers of information in the ocean, with wide applications in military and civilian fields such as marine engineering, underwater target detection, underwater navigation, and tactical sonar use. The propagation of acoustic signals in the ocean is influenced by various factors, among which the speed of sound is the most critical. In complex marine environments, the speed of sound varies with temperature, salinity, and pressure, and differs at different times and geographical locations. To improve the capability and level of marine acoustic information support, it is necessary to accurately obtain the spatiotemporal distribution of ocean sound speed. Traditional marine mapping methods for measuring sound speed are time-consuming, costly, and unable to quickly obtain large-scale three-dimensional sound speed data; while marine remote sensing methods can obtain large-scale marine environmental data, they can only acquire surface data and cannot directly obtain sound speed data below the surface.

[0003] Existing techniques typically utilize historical measurement data of a sea area of ​​interest to construct a parameterized mathematical model representing the three-dimensional sound velocity within that area. Then, based on this model and sparsely measured sound velocity data for that region, the three-dimensional sound velocity distribution across the entire area is predicted and calculated. Currently, commonly used methods can be divided into two categories. One category uses empirical orthogonal functions to represent sound velocity data. This method can effectively describe sound velocity with a small number of basis functions, thus transforming sound velocity prediction into predicting the coefficients corresponding to the basis functions, significantly reducing the computational burden. The other category is a dictionary-based sound velocity representation and prediction method. Compared to traditional empirical orthogonal function representation methods, this method generates dictionary basis functions for sparse processing, representing sound velocity with the fewest atoms possible, enhancing the detailed description of sound velocity, and improving the accuracy of sound velocity prediction.

[0004] However, the variability of the actual marine environment causes irregularities and uncertainties in changes in seawater temperature, salinity, and pressure. While the two methods commonly used in existing technologies have good accuracy in predicting ocean sound speed in the depth direction, they ignore the distribution of ocean sound speed in the horizontal direction. Therefore, their ability to characterize three-dimensional ocean sound speed is weak, resulting in poor accuracy of the prediction results and making it difficult to meet the needs of refined ocean acoustic information support. Summary of the Invention

[0005] The technical problem to be solved by the present invention is that the above-mentioned methods commonly used in the prior art have weak ability to characterize three-dimensional ocean sound velocity, resulting in poor accuracy of the prediction results, which is difficult to meet the needs of refined ocean acoustic information protection. In order to solve the above problems, the present invention provides a three-dimensional ocean sound velocity prediction method and device based on tensor empirical orthogonal decomposition.

[0006] The content of this invention includes:

[0007] In a first aspect, embodiments of the present invention provide a three-dimensional ocean sound velocity prediction method based on tensor empirical orthogonal decomposition, comprising:

[0008] A three-dimensional sound velocity measurement tensor and a weight tensor are constructed based on the sound velocity measurement data within the target area. The location within the target area where the sound velocity measurement data is present is the first location, and the location within the target area where the sound velocity measurement data is absent is the second location. The value in the three-dimensional sound velocity measurement tensor corresponding to the first location is the sound velocity measurement value at the first location, and the value in the three-dimensional sound velocity measurement tensor corresponding to the second location is 0. The value in the weight tensor corresponding to the first location is 1, and the value in the weight tensor corresponding to the second location is 0.

[0009] Determine the optimal basis function feature matrix set, which includes the optimal basis function feature matrix in the longitude direction, the optimal basis function feature matrix in the latitude direction, and the optimal basis function feature matrix in the depth direction;

[0010] A three-dimensional sound velocity tensor prediction calculation function is constructed based on the three-dimensional sound velocity measurement tensor, the weight tensor, and the set of optimal basis function feature matrices.

[0011] The predicted sound velocity value at the second position is obtained by iteratively solving the three-dimensional sound velocity tensor prediction calculation function using the tensor gradient descent method.

[0012] Optionally, the three-dimensional sound velocity tensor prediction calculation function is:

[0013] ;

[0014] in, For the three-dimensional sound velocity measurement tensor, For the weight tensor, The core tensor is... The tensor formed by the projection coefficients onto the set of characteristic matrices of the optimal basis functions The optimal basis function characteristic matrix in the longitude direction, This is the optimal basis function characteristic matrix in the latitude direction. Let be the optimal basis function feature matrix in the depth direction. For regularization terms, For regularization parameters, This represents the 1-mode product of a tensor and a matrix. This represents the 2-mode product of a tensor and a matrix. This represents the 3-mode product of a tensor and a matrix. This represents the Hadamard product. The core tensor corresponding to the minimum value of the function. Denotes the Frobenius norm. This represents the square of the tensor modulus.

[0015] Optionally, the step of iteratively solving the three-dimensional sound velocity tensor prediction calculation function based on the tensor gradient descent method to obtain the sound velocity prediction value at the second position includes:

[0016] Determine the initial values ​​for the iteration of the core tensor;

[0017] Calculate the gradient of the three-dimensional sound velocity tensor prediction function with respect to the core tensor;

[0018] Based on the gradient of the core tensor and the initial value of the iteration, multiple iterative calculations are performed, and at the... In the nth iteration, we obtain the nth... The core tensor of the next iteration, and based on the first iteration The core tensor of the next iteration and the set of characteristic matrices of the optimal basis functions are used to calculate the first... The predicted value of the second iteration and the first iteration The prediction error of the next iteration;

[0019] The number of iterations When the number of iterations is equal to the maximum number of iterations or the prediction error is less than or equal to the threshold, the first iteration will be... The predicted value of the next iteration is determined as the predicted sound speed at the second position. It is a positive integer.

[0020] Optionally, the initial value of the iteration for:

[0021] ;

[0022] The gradient of the core tensor for:

[0023] ;

[0024] The first The core tensor obtained in the next iteration for:

[0025] ;

[0026] The first The predicted value of the next iteration for:

[0027] ;

[0028] The first Prediction error of the next iteration for:

[0029] ;

[0030] in, This is the iteration step size.

[0031] Optionally, determining the optimal set of basis function characteristic matrices includes:

[0032] A three-dimensional ocean sound velocity prediction system is constructed, which includes an ocean sound velocity tensor representation module, a tensor feature extraction module, and a three-dimensional sound velocity prediction calculation module.

[0033] The tensor feature extraction module and the three-dimensional sound velocity prediction calculation module are trained using training sample data to obtain a trained three-dimensional ocean sound velocity prediction system.

[0034] The trained three-dimensional ocean sound velocity prediction system was tested using validation sample data, and the optimal basis function feature matrix in the longitude direction, the optimal basis function feature matrix in the latitude direction, and the optimal basis function feature matrix in the depth direction were determined based on the prediction performance.

[0035] The ocean sound velocity tensor representation module is used to store sound velocity measurement data in tensor form. The tensor feature extraction module is used to obtain a set of basis function feature matrices and a set of model orders. The set of basis function feature matrices includes basis function feature matrices in the longitude direction, basis function feature matrices in the latitude direction, and basis function feature matrices in the depth direction. The set of model orders includes model orders in the longitude direction, model orders in the latitude direction, and model orders in the depth direction. The three-dimensional sound velocity prediction calculation module is used to predict sound velocity based on the set of basis function feature matrices, the set of model orders, and the sound velocity measurement data.

[0036] Optionally, the step of training the tensor feature extraction module and the three-dimensional sound velocity prediction calculation module using training sample data to obtain the trained three-dimensional ocean sound velocity prediction system includes:

[0037] The training sample data and the validation sample data are acquired and stored in the ocean sound velocity tensor representation module in tensor form;

[0038] The training sample data is input into the tensor feature extraction module to obtain the set of basis function feature matrices and the set of model orders corresponding to the training sample data;

[0039] The set of basis function feature matrices and the set of model orders corresponding to the training sample data are input into the three-dimensional sound speed prediction calculation module. The tensor gradient descent method is used in conjunction with the training sample data to predict the sound speed and obtain the prediction result.

[0040] Optionally, the step of inputting the training sample data into the tensor feature extraction module to obtain the set of basis function feature matrices and the set of model orders corresponding to the training sample data includes:

[0041] The training sample data is subjected to tensor orthogonal decomposition, and the decomposed training sample data is obtained. for:

[0042] ;

[0043] in, The basis function feature matrix in the longitude direction corresponding to the training sample data, The basis function feature matrix in the latitudinal direction corresponding to the training sample data, The basis function feature matrix in the depth direction corresponding to the training sample data. This is the core tensor corresponding to the training sample data.

[0044] Secondly, embodiments of the present invention provide a three-dimensional ocean sound velocity prediction device based on tensor empirical orthogonal decomposition, comprising:

[0045] The first construction module is used to construct a three-dimensional sound velocity measurement tensor and a weight tensor based on sound velocity measurement data within a target area. The location within the target area where the sound velocity measurement data is present is a first location, and the location within the target area where the sound velocity measurement data is absent is a second location. The value in the three-dimensional sound velocity measurement tensor corresponding to the first location is the sound velocity measurement value at the first location, and the value in the three-dimensional sound velocity measurement tensor corresponding to the second location is 0. The value in the weight tensor corresponding to the first location is 1, and the value in the weight tensor corresponding to the second location is 0.

[0046] The determination module is used to determine the optimal basis function feature matrix set, which includes the optimal basis function feature matrix in the longitude direction, the optimal basis function feature matrix in the latitude direction, and the optimal basis function feature matrix in the depth direction;

[0047] The second construction module is used to construct a three-dimensional sound velocity tensor prediction calculation function based on the three-dimensional sound velocity measurement tensor, the weight tensor, and the set of optimal basis function feature matrices.

[0048] The solution module is used to iteratively solve the three-dimensional sound velocity tensor prediction calculation function based on the tensor gradient descent method to obtain the sound velocity prediction value at the second position.

[0049] Thirdly, embodiments of the present invention provide an electronic device, including: a memory, a processor, and a program stored in the memory and executable on the processor; the processor is configured to read the program in the memory to implement the steps in the three-dimensional ocean sound velocity prediction method based on tensor empirical orthogonal decomposition as described in the first aspect.

[0050] Fourthly, embodiments of the present invention provide a readable storage medium for storing a program, which, when executed by a processor, implements the steps in the three-dimensional ocean sound velocity prediction method based on tensor empirical orthogonal decomposition as described in the first aspect.

[0051] The beneficial effects of this invention are as follows: In the embodiments of this invention, a three-dimensional sound velocity measurement tensor and a weight tensor are constructed based on sound velocity measurement data within the target area. An optimal set of basis function feature matrices is determined, including optimal basis function feature matrices in the longitude direction, the latitude direction, and the depth direction. A three-dimensional sound velocity tensor prediction calculation function is constructed based on the three-dimensional sound velocity measurement tensor, the weight tensor, and the optimal basis function feature matrix set. The three-dimensional sound velocity tensor prediction calculation function is iteratively solved using the tensor gradient descent method to obtain the predicted sound velocity value at the second position. The method provided by this invention utilizes tensors to directly store three-dimensional ocean sound velocity data. It obtains the basis function features of ocean sound velocity in the longitude, latitude, and depth directions through the tensor empirical orthogonal decomposition method, alleviating the problem of insufficient characterization ability of three-dimensional ocean sound velocity distribution. Furthermore, the tensor gradient descent method is used to achieve three-dimensional ocean sound velocity prediction under sparse sound velocity profile measurement data conditions, improving the accuracy of sound velocity prediction. Attached Figure Description

[0052] Appendix Figure 1 A flowchart illustrating a three-dimensional ocean sound velocity prediction method based on tensor empirical orthogonal decomposition provided in an embodiment of the present invention;

[0053] Appendix Figure 2 The three-dimensional ocean sound velocity field distribution to be predicted under sparse observations;

[0054] Appendix Figure 3 The results are three-dimensional ocean sound velocity predictions obtained based on tensor empirical orthogonal decomposition.

[0055] Appendix Figure 4 This is a comparison chart of the detection results of the three-dimensional ocean sound velocity prediction method based on tensor empirical orthogonal decomposition provided in the embodiments of the present invention and the results of the EOF method.

[0056] Appendix Figure 5 A schematic diagram of a three-dimensional ocean sound velocity prediction device based on tensor empirical orthogonal decomposition provided in an embodiment of the present invention;

[0057] Appendix Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0058] In this application's embodiments, the term "and / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. The character " / " generally indicates that the preceding and following related objects have an "or" relationship. In this application's embodiments, the term "multiple" refers to two or more, and other quantifiers are similar. The terms "first," "second," etc., in the specification and claims of this application are used to distinguish similar objects and are not used to describe a specific order or sequence. It should be understood that such terms can be interchanged where appropriate so that embodiments of this application can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first" and "second" are generally of the same class, not limited to the number of objects. For example, the first object can be one or multiple.

[0059] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0060] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0061] This application provides a method and apparatus for predicting three-dimensional ocean sound velocity based on tensor empirical orthogonal decomposition, aiming to effectively mine the intrinsic essential characteristics of time-varying ocean sound velocity distribution and improve the accuracy of three-dimensional ocean sound velocity prediction.

[0062] Please see Figure 1 , Figure 1 This is a flowchart illustrating the three-dimensional ocean sound velocity prediction method based on tensor empirical orthogonal decomposition provided in an embodiment of the present invention. The method specifically includes the following steps:

[0063] Step 101: Construct a three-dimensional sound velocity measurement tensor and a weight tensor based on the sound velocity measurement data within the target area. The location within the target area where the sound velocity measurement data is present is the first location, and the location within the target area where the sound velocity measurement data is absent is the second location. The value in the three-dimensional sound velocity measurement tensor corresponding to the first location is the sound velocity measurement value at the first location, and the value in the three-dimensional sound velocity measurement tensor corresponding to the second location is 0. The value in the weight tensor corresponding to the first location is 1, and the value in the weight tensor corresponding to the second location is 0.

[0064] Step 102: Determine the optimal basis function feature matrix set, which includes the optimal basis function feature matrix in the longitude direction, the optimal basis function feature matrix in the latitude direction, and the optimal basis function feature matrix in the depth direction;

[0065] Step 103: Construct a three-dimensional sound velocity tensor prediction calculation function based on the three-dimensional sound velocity measurement tensor, the weight tensor, and the optimal basis function feature matrix set;

[0066] Step 104: Iteratively solve the three-dimensional sound velocity tensor prediction calculation function based on the tensor gradient descent method to obtain the sound velocity prediction value at the second position.

[0067] In this embodiment, tensors are used to organize spatiotemporal multidimensional ocean sound velocity data, and the basis function feature matrix in different latitudinal directions is extracted using the tensor empirical orthogonal decomposition method to improve the characterization ability of spatiotemporal ocean sound velocity data. At the same time, the tensor gradient descent method is used to realize the three-dimensional sound velocity prediction function under sparse sound velocity profile measurement data conditions, thereby improving the prediction accuracy.

[0068] It should be understood that the data representation of three-dimensional ocean sound velocity is typical raster data, characterized by a multivariate time-series cubic data organization consisting of longitude, latitude, depth, and time. Conventional data organization formats such as vectors and matrices are difficult to effectively store this type of high-dimensional data. Tensors are the most natural form of expression for high-dimensional data; therefore, tensor-based data organization is well-compatible with multidimensional spatiotemporal ocean sound velocity data and has unique advantages in representing spatiotemporal ocean sound velocity fields. This is particularly relevant for three-dimensional ocean sound velocity data considering spatial latitude, longitude, and depth. It can be expressed as a third-order tensor. ,in , ,and The tensor represents the range of sound speed indices in the longitude, latitude, and depth directions, respectively. The index is Corresponding elements Indicates latitude Longitude is Depth is The three-dimensional ocean sound velocity values ​​are obtained at a given location. Based on a tensor-based representation, the three-dimensional ocean sound velocity is independent of each other, and each dimension can correspond to a specific basis. Tensor operations can be used to retrieve and extract ocean sound velocity data based on the tensor representation. Furthermore, considering ocean sound velocities acquired at different times, the spatiotemporal ocean sound velocity can be written in fourth-order tensor form. ,in Indicates the index range for the time direction.

[0069] When measuring the speed of sound in a target area, sound speed data is obtained at some locations within the target area, while no sound speed data is obtained at other locations. This results in sparse sound speed data. The location within the target area where sound speed data was obtained is designated as the first location, and the other locations are designated as the second location. The second location is the location where the sound speed value needs to be predicted.

[0070] In step 101, a three-dimensional sound velocity measurement tensor is constructed based on the sound velocity measurement data within the target region. Three-dimensional sound velocity measurement tensor In the process, based on the latitude and longitude coordinates of the sound speed measurement, the measured sound speed value is assigned to locations with sound speed measurement data, while zero is assigned to locations without sound speed measurement data (i.e., locations to be predicted). Then, a weight tensor is constructed. The dimension size of the weight tensor and Maintaining consistency is used to describe tensors. The location where the speed of sound needs to be predicted. The elements in the array are assigned values ​​as follows:

[0071] ;

[0072] It should be understood that the weight tensor Equivalent to the three-dimensional sound velocity measurement tensor The data in the file has been processed; the positions containing data retain their values, while the positions without data are assigned a value of zero.

[0073] In step 102, the optimal basis function characteristic matrix in the longitude direction, the optimal basis function characteristic matrix in the latitude direction, and the optimal basis function characteristic matrix in the depth direction are determined. The specific method for this is not limited here. Optionally, in some embodiments, step 102 includes:

[0074] A three-dimensional ocean sound velocity prediction system is constructed, which includes an ocean sound velocity tensor representation module, a tensor feature extraction module, and a three-dimensional sound velocity prediction calculation module.

[0075] The tensor feature extraction module and the three-dimensional sound velocity prediction calculation module are trained using training sample data to obtain a trained three-dimensional ocean sound velocity prediction system.

[0076] The trained three-dimensional ocean sound velocity prediction system was tested using validation sample data, and the optimal basis function feature matrix in the longitude direction, the optimal basis function feature matrix in the latitude direction, and the optimal basis function feature matrix in the depth direction were determined based on the prediction performance.

[0077] The ocean sound velocity tensor representation module is used to store sound velocity measurement data in tensor form. The tensor feature extraction module is used to obtain a set of basis function feature matrices and a set of model orders. The set of basis function feature matrices includes basis function feature matrices in the longitude direction, basis function feature matrices in the latitude direction, and basis function feature matrices in the depth direction. The set of model orders includes model orders in the longitude direction, model orders in the latitude direction, and model orders in the depth direction. The three-dimensional sound velocity prediction calculation module is used to predict sound velocity based on the set of basis function feature matrices, the set of model orders, and the sound velocity measurement data.

[0078] It should be understood that the ocean sound velocity tensor representation module stores sound velocity measurement data in tensor form and outputs the tensor-represented sound velocity measurement data to the tensor feature extraction module. The tensor feature extraction module is connected to the 3D sound velocity prediction calculation module. It receives the tensor-form sound velocity measurement data from the ocean sound velocity tensor representation module, constructs a 3D ocean sound velocity tensor feature representation model using the tensor empirical orthogonal decomposition method, and transmits the set of basis function feature matrices and the model order set from the ocean sound velocity tensor feature representation model to the 3D sound velocity prediction calculation module. The 3D sound velocity prediction calculation module is connected to the tensor feature extraction module, receives the set of basis function feature matrices and the model order set from the tensor feature extraction module, and uses the tensor gradient descent method combined with sparsely measured sound velocity profile data at the time of prediction to calculate the 3D ocean sound velocity distribution, thus achieving 3D ocean sound velocity prediction.

[0079] As a specific implementation, a three-dimensional ocean sound velocity prediction system based on tensor empirical orthogonal decomposition was constructed. First, the dataset required for the ocean sound velocity prediction system was built, and the dataset was divided into training sample data, validation sample data, and test sample data. Then, the tensor feature extraction module and the three-dimensional sound velocity prediction calculation module of the three-dimensional ocean sound velocity prediction system were trained using the training sample data. After one round of training, the trained three-dimensional ocean sound velocity prediction system was tested using the validation sample data. The model parameters with the best performance were selected and assigned to the trainable modules (tensor feature extraction module and three-dimensional sound velocity prediction calculation module) of the three-dimensional ocean sound velocity prediction system, resulting in the best-performing trained three-dimensional ocean sound velocity prediction system. Finally, the best-performing trained three-dimensional ocean sound velocity prediction system was combined with sparsely measured sound velocity profile data of the sea area to predict the three-dimensional ocean sound velocity distribution of the sea area.

[0080] Optionally, the step of training the tensor feature extraction module and the three-dimensional sound velocity prediction calculation module using training sample data to obtain the trained three-dimensional ocean sound velocity prediction system includes:

[0081] The training sample data and the validation sample data are acquired and stored in the ocean sound velocity tensor representation module in tensor form;

[0082] The training sample data is input into the tensor feature extraction module to obtain the set of basis function feature matrices and the set of model orders corresponding to the training sample data;

[0083] The set of basis function feature matrices and the set of model orders corresponding to the training sample data are input into the three-dimensional sound speed prediction calculation module. The tensor gradient descent method is used in conjunction with the training sample data to predict the sound speed and obtain the prediction result.

[0084] As a specific implementation, the Hycom dataset is used as training, validation, and test data. The Hycom dataset contains global ocean environmental parameters such as depth, salinity, temperature, current field, and sound speed. It has a horizontal spatial resolution of 1 / 12° × 1 / 12° and 50 depth layers, covering water depths from 0 to 5000 meters. This data is updated daily. Specifically, data from June 2020 is selected. T The ocean sound speed in a certain region of the sky is sample data (i.e., sound speed samples), and the number of sound speed samples is... N×M×L The ranges of sound speeds along the longitude, latitude, and depth directions are respectively: N , M and L There are 100 spatial location points. Therefore, the total sample data used in this embodiment can be represented as 100 spatial location points. ,Will Let it be denoted as the data sample tensor.

[0085] Specifically, in some embodiments, it is necessary to process the data sample tensor. The specific method for handling anomalies is as follows:

[0086] S1: Tensor of data samples Calculate the mean along the time dimension The mean tensor of the three-dimensional sound velocity distribution in this sea area was obtained. ;

[0087] S2: Order , indicating the first The three-dimensional sound velocity sample tensor of the Tiange sea area is ;

[0088] S3: The first Three-dimensional sound velocity sample tensor of the sky Subtract the mean tensor ,Right now , indicating the first The anomaly tensor of the celestial velocity sample tensor;

[0089] S4: Order ,like If, then execute S1; if This indicates that the anomaly sample tensor for ocean sound speed has been constructed. The anomaly tensor of the sky is written as a fourth-order tensor, denoted as , representing the anomaly tensor of all sound speed samples.

[0090] S5: Anomaly tensor of all sound speed samples Based on time, the data is divided into training sample data, validation sample data, and test sample data.

[0091] The tensor feature extraction module receives sound velocity tensor data from the ocean sound velocity tensor representation module, constructs a three-dimensional ocean sound velocity tensor feature representation model using the tensor empirical orthogonal decomposition method, and obtains the basis function feature matrices of the three-dimensional ocean sound velocity in the longitude, latitude, and depth directions. Optionally, in some embodiments, inputting the training sample data into the tensor feature extraction module to obtain the set of basis function feature matrices and the model order set corresponding to the training sample data includes:

[0092] The training sample data is subjected to tensor orthogonal decomposition, and the decomposed training sample data is obtained. for:

[0093] ;

[0094] in, The basis function feature matrix in the longitude direction corresponding to the training sample data, The basis function feature matrix in the latitudinal direction corresponding to the training sample data, The basis function feature matrix in the depth direction corresponding to the training sample data, The basis function feature matrix in the time direction corresponding to the training sample data. This is the core tensor corresponding to the training sample data.

[0095] As a specific embodiment, the specific process can be represented as follows:

[0096] Obtain the anomaly tensor of the training sample data ,right Perform tensor empirical orthogonal decomposition, denoted as the training sound velocity tensor. In this embodiment, the training sound velocity tensor can be specifically expressed as: ,in This represents the 1-mode product of a tensor and a matrix. This represents the 2-mode product of a tensor and a matrix. This represents the 3-mode product of a tensor and a matrix. This represents the 4-mode product of a tensor and a matrix. The basis function characteristic matrix in the longitude direction, The basis function characteristic matrix in the latitudinal direction, The basis function eigenma matrix in the depth direction, The characteristic matrix of the basis functions in the time direction, For the core tensor, , , , To train the sound speed tensor The tensor formed by the projection coefficients onto the eigenmatrix of the basis functions.

[0097] In this embodiment, the sound velocity tensor is decomposed into a core tensor with a smaller dimension and the product of four basis function feature matrices in four dimensions using the above method. The specific method of tensor empirical orthogonal decomposition is explained below using the training of the sound velocity tensor as an example:

[0098] In the longitude direction: for the tensor A new matrix is ​​obtained by matrix expansion along the longitude direction. Specifically, tensors Longitude as a new matrix The number of columns is The remaining dimensions are used as a new matrix. The number of rows is (The product of all dimensions except longitude). For the expanded matrix... The singular value decomposition of a matrix is ​​performed using the following formula:

[0099] ;

[0100] in, and Represent the left singular matrix and the right singular matrix. Let T be the corresponding singular value matrix, where the superscript T in the formula denotes the matrix transpose. (Truncation) forward The column serves as the characteristic matrix of the basis functions in the longitude direction. , This represents the model order in the longitude direction.

[0101] In the latitudinal direction: for tensor A new matrix is ​​obtained by matrix expansion along the latitudinal direction. Specifically, tensors latitude as a new matrix The number of columns is The remaining dimensions are used as a new matrix. The number of rows is (The product of all dimensions except the dimensional dimension). For the expanded matrix... The singular value decomposition of a matrix is ​​performed using the following formula:

[0102] ;

[0103] in, and Represent the left singular matrix and the right singular matrix. Let T be the corresponding singular value matrix, where the superscript T in the formula denotes the matrix transpose. (Truncation) forward Characteristic matrix of basis functions in the latitudinal direction , This represents the model order in the latitudinal direction.

[0104] In the depth direction: for tensors A new matrix is ​​obtained by matrix expansion along the depth direction. The method is to use tensors Depth as a new matrix The number of columns is The remaining dimensions are used as a new matrix. The number of rows is (The product of all dimensions except the depth dimension). For the expanded matrix... The singular value decomposition of a matrix is ​​performed using the following formula:

[0105]

[0106] in, and Represent the left singular matrix and the right singular matrix. Let T be the corresponding singular value matrix, where the superscript T in the formula denotes the matrix transpose. (Truncation) forward Columns as the basis function feature matrix in the depth direction , The depth is the model order.

[0107] In the time direction: for tensors A new matrix is ​​obtained by matrix expansion along the time direction. The method is to use tensors Depth as a new matrix The number of columns is The remaining dimensions are used as a new matrix. The number of rows is (The product of all dimensions except the depth dimension). For the expanded matrix... The singular value decomposition of a matrix is ​​performed using the following formula:

[0108]

[0109] in, and Represent the left singular matrix and the right singular matrix. Let T be the corresponding singular value matrix, where the superscript T in the formula denotes the matrix transpose. (Truncation) forward The column is the characteristic matrix of the basis function in the time direction. , The time order is the model order.

[0110] The core tensor is calculated as follows:

[0111] .

[0112] Preserving the basis function characteristic matrix of longitude direction , latitudinal basis function characteristic matrix and depth direction basis function characteristic matrix And the model order in the longitude direction. Model order in the latitudinal direction Model order in the depth direction .

[0113] The 3D sound velocity prediction calculation module combines the set of basis function feature matrices and the model order received from the tensor feature extraction module. It then uses the tensor gradient descent method, combined with sparsely measured sound velocity profile data at the time of prediction, to calculate the 3D ocean sound velocity distribution, thus achieving 3D ocean sound velocity prediction. The specific implementation is as follows:

[0114] Taking the aforementioned specific embodiment as an example, K longitude and latitude locations are randomly selected within the sea area selected in the embodiment to measure the sound speed profile. The measurement result is the sound speed distribution along the depth direction at the selected location, and the longitude and latitude coordinates of the measurement point are recorded at the same time.

[0115] Construct the three-dimensional sound velocity measurement tensor corresponding to the training sample data and weight tensor For details on how to construct the system, please refer to the description in step 101. We will not repeat it here.

[0116] A three-dimensional sound velocity tensor prediction calculation function is constructed to calculate the three-dimensional sound velocity measurement tensor corresponding to the training sample data, as follows:

[0117] ;

[0118] in," " represents the Hadamard product, Represents the core tensor. , and These are the basis function feature matrices for longitude, latitude, and depth directions saved in the preceding steps, respectively. The second term... This is a regularization term used to prevent overfitting of the function. For regularization parameters, The core tensor corresponding to the minimum value of the function. Denotes the Frobenius norm. This represents the square of the tensor modulus.

[0119] The tensor gradient descent method is used for iterative solution, as follows:

[0120] Step 1: Initialize the loop variable =1, determining the initial value for iteration of the core tensor. :

[0121] ;

[0122] Step 2: Calculate the function For core tensor gradient:

[0123] ;in, Let be the tensor to be determined.

[0124] Step 3: In Iteratively update the core tensor based on the previous iterations, the first... The core tensor obtained in the next iteration for:

[0125] ;

[0126] in, This is the iteration step size.

[0127] Step 4: Calculate the predicted value of the sound speed tensor:

[0128] ;

[0129] Step 5: Calculate the prediction error of the sound velocity at the predicted location:

[0130] ;

[0131] make If the prediction error or If not, return to Step 2; otherwise, obtain the predicted value of the three-dimensional ocean sound velocity tensor from Step 4. This indicates the maximum number of iterations.

[0132] The tensor feature extraction module and the three-dimensional sound velocity prediction calculation module have been trained using training sample data to obtain a trained three-dimensional ocean sound velocity prediction system. The prediction performance of the trained three-dimensional ocean sound velocity prediction system has been tested using validation sample data. The model parameters with the best prediction performance have been retained as the parameters of the three-dimensional ocean sound velocity prediction system. The parameters that need optimization are the model orders corresponding to the basis function feature matrices in the longitude, latitude, and depth directions. , and .

[0133] The specific process for testing the prediction performance of the trained 3D ocean sound velocity prediction system based on validation sample data can be found in the aforementioned description of the training sample data section, and will not be repeated here. The following section details the determination... , and The process of obtaining the optimal basis function characteristic matrix in the longitude direction, the optimal basis function characteristic matrix in the latitude direction, and the optimal basis function characteristic matrix in the depth direction is explained in detail below:

[0134] First of all, let =1, which represents the model order reserved for the basis function characteristic matrix in the longitude direction. Then, the basis function characteristic matrix in the longitude direction is constructed: That is, to retain forward The column vectors form a new basis function feature matrix, and the basis function feature matrices in the dimensional and depth directions are respectively... and The three-dimensional sound velocity prediction calculation module receives new basis function feature matrices in the longitude, latitude, and depth directions, and calculates the three-dimensional sound velocity tensor under the new basis function feature matrices using the aforementioned method. Calculate the current reconstruction error By traversing Find all The reconstruction error is selected based on the value of the minimum reconstruction error. The model order is used as the optimal longitude direction basis function characteristic matrix, and the corresponding longitude direction basis function characteristic matrix is ​​also used. As the characteristic matrix of the optimal basis function in the longitude direction.

[0135] Then, let =1, which represents the model order reserved for the basis function feature matrix in the latitudinal direction. Construct the basis function feature matrix in the latitudinal direction: That is, to retain forward The column vectors form a new basis function feature matrix, and the basis function feature matrices in the longitude and depth directions are respectively... and The 3D sound velocity prediction calculation module receives the basis function feature matrices in the longitude, latitude, and depth directions, respectively. , and The three-dimensional sound velocity tensor under the new basis function characteristic matrix is ​​calculated using the aforementioned method. And calculate the current reconstruction error. By traversing Find all The reconstruction error is selected based on the value of the minimum reconstruction error. The model order is used as the optimal latitudinal direction basis function characteristic matrix, and the corresponding latitudinal direction basis function characteristic matrix is ​​also used. As the characteristic matrix of the optimal basis function in the latitudinal direction.

[0136] Finally, let =1, representing the model order reserved for the basis function feature matrix in the depth direction. Constructing the basis function feature matrix in the dimensional direction: That is, to retain forward The column vectors form a new basis function feature matrix, and the basis function feature matrices in the longitude and latitude directions are respectively... and The 3D sound velocity prediction calculation module receives the basis function feature matrices in the longitude, latitude, and depth directions, respectively. , and The three-dimensional sound velocity tensor under the new basis function characteristic matrix is ​​calculated using the aforementioned method. And calculate the current reconstruction error. By traversing Find all The reconstruction error is selected based on the value of the minimum reconstruction error. The model order is used as the optimal depth-direction basis function feature matrix, and the corresponding depth-direction basis function feature matrix is ​​also used. The feature matrix is ​​the optimal basis function in the depth direction.

[0137] It should be understood that the above is only one optional embodiment. In specific implementation, the order in which the optimal basis function feature matrix in the longitude direction, the optimal basis function feature matrix in the latitude direction, and the optimal basis function feature matrix in the depth direction are determined can be adjusted according to the actual situation, and is not limited here.

[0138] The optimal model order of the longitude direction basis function characteristic matrix can be determined using the method described above. The model order of the optimal latitudinal direction basis function characteristic matrix The model order of the optimal depth-direction basis function eigenma. And the optimal basis function characteristic matrix in the longitude direction. Optimal basis function characteristic matrix in the latitudinal direction Optimal basis function feature matrix in the depth direction .

[0139] In the specific implementation, , and As the selected basis function characteristic matrix for the three-dimensional ocean sound velocity prediction system, , ,and The selected model order is used to predict the speed of sound in the three-dimensional ocean, and then loaded into the three-dimensional ocean sound prediction system to obtain the trained three-dimensional ocean sound prediction system.

[0140] In this embodiment, a three-dimensional ocean sound velocity prediction system is constructed, which integrates an ocean sound velocity tensor representation module, a tensor feature extraction module, and a three-dimensional sound velocity prediction calculation module. The system obtains the basis function feature matrices in the longitude, latitude, and depth directions through tensor representation and tensor empirical orthogonal decomposition methods, which can enhance the characterization ability of the three-dimensional ocean sound velocity distribution and improve the prediction accuracy of the three-dimensional ocean sound velocity.

[0141] In practical implementation, the trained 3D ocean sound velocity prediction system can be used to predict the 3D sound velocity from the sparse measured sound velocity profile. Specifically, the sound velocity measurement results within the target area constitute the sparse measured sound velocity profile. Based on the aforementioned description of the 3D sound velocity prediction calculation module, a 3D sound velocity measurement tensor is constructed. and weight tensor .

[0142] Based on the final parameters of the trained 3D ocean sound velocity prediction system, the optimal set of basis function feature matrices can be determined. This optimal set of basis function feature matrices is then used to construct a 3D sound velocity tensor prediction calculation function. Optionally, the 3D sound velocity tensor prediction calculation function is:

[0143] ;

[0144] in, For the three-dimensional sound velocity measurement tensor, For the weight tensor, The core tensor is... The tensor formed by the projection coefficients onto the set of characteristic matrices of the optimal basis functions The optimal basis function characteristic matrix in the longitude direction, This is the optimal basis function characteristic matrix in the latitude direction. Let be the optimal basis function feature matrix in the depth direction. For regularization terms, For regularization parameters, This represents the 1-mode product of a tensor and a matrix. This represents the 2-mode product of a tensor and a matrix. This represents the 3-mode product of a tensor and a matrix. This represents the Hadamard product. The core tensor corresponding to the minimum value of the function. Denotes the Frobenius norm. This represents the square of the tensor modulus.

[0145] The three-dimensional sound velocity tensor prediction calculation function is solved iteratively using the tensor gradient descent method. Optionally, in some embodiments, the iterative solution of the three-dimensional sound velocity tensor prediction calculation function based on the tensor gradient descent method to obtain the sound velocity prediction value at the second position includes:

[0146] Determine the initial value for the iteration of the core tensor, the initial value for the iteration for:

[0147] ;

[0148] Calculate the gradient of the three-dimensional sound velocity tensor prediction function with respect to the core tensor, and the gradient of the core tensor. for:

[0149] ;

[0150] Based on the gradient of the core tensor and the initial value of the iteration, multiple iterative calculations are performed, and at the... In the nth iteration, we obtain the nth... The core tensor of the next iteration, and based on the first iteration The core tensor of the next iteration and the set of characteristic matrices of the optimal basis functions are used to calculate the first... The predicted value of the second iteration and the first iteration The prediction error of the first iteration; the first iteration The core tensor obtained in the next iteration for:

[0151] ;

[0152] The first The predicted value of the next iteration for:

[0153] ;

[0154] The first Prediction error of the next iteration for:

[0155] ;

[0156] in, This is the iteration step size.

[0157] The number of iterations When the number of iterations is equal to the maximum number of iterations or the prediction error is less than or equal to the threshold, the first iteration will be... The predicted value of the next iteration is determined as the predicted sound speed at the second position. It is a positive integer.

[0158] In this embodiment, the tensor gradient descent method is used to directly predict the three-dimensional ocean sound velocity under sparse sound velocity profile measurement conditions. This eliminates the need to reduce the dimension of the ocean sound velocity tensor to be reconstructed into a vector, thereby reducing computational complexity, shortening the prediction time of the three-dimensional ocean sound velocity, and improving the real-time performance of the prediction.

[0159] The following example, using a specific embodiment, illustrates the effectiveness of the three-dimensional ocean sound velocity prediction method based on tensor empirical orthogonal decomposition provided by this invention. This example selects ocean sound velocity data from a portion of the Hycom data for 30 days in June 2020 as sample data. The three-dimensional ocean sound velocity distribution sample size is 30×60×35, representing 30, 60, and 35 spatial locations for sound velocity ranges in longitude, latitude, and depth, respectively. Therefore, the original sample data used in this embodiment can be represented as a tensor. .

[0160] Ocean sound velocity data from the first 10 days were selected for training. Tensor empirical orthogonal decomposition was used to obtain the basis function feature matrices of ocean sound velocity in the longitude, latitude, and depth directions. Ocean sound velocity data from days 11-15 were selected as the validation dataset. The optimal model order was selected using the validation set to obtain the final basis function feature matrices in the longitude, latitude, and depth directions. Ocean sound velocity data from day 20 was used as the test set. The number of randomly measured sound velocity profile points was set to 200, far fewer than the 30×60=1800 grid points in the horizontal space (e.g., ...). Figure 2 As shown), the three-dimensional ocean sound velocity prediction system of this invention outputs a three-dimensional ocean sound velocity prediction result, such as... Figure 3 As shown.

[0161] The root mean square error (RMSE) is further used as the performance evaluation index for the three-dimensional ocean prediction system. A smaller RMSE value indicates higher prediction accuracy. Table 1 shows the performance comparison of the three-dimensional ocean sound velocity prediction algorithm with different numbers of measurement points randomly selected on day 20, and compares its performance with the classic EOF ocean sound velocity prediction method. The results in Table 1 show that the three-dimensional ocean sound velocity prediction method based on tensor empirical orthogonal decomposition provided by this invention achieves higher prediction accuracy than the classic EOF method under different numbers of sparse measured sound velocity profiles. When the number of randomly measured sound velocity profiles is 200, a real sound velocity profile and the prediction results of the two methods are plotted at a selected location, as shown below. Figure 4 As shown. From Figure 4 As can be seen, the prediction results of the EOF method deviate significantly from the actual sound velocity profile, while the prediction results provided by this invention match the actual sound velocity profile very well, demonstrating the effectiveness of the three-dimensional ocean sound velocity prediction method based on tensor empirical orthogonal decomposition provided by this invention.

[0162] Table 1 Comparison of Measurement Point Count and Performance

[0163]

[0164] With 200 random sound velocity profile measurement points, the three-dimensional ocean sound velocity for days 21-30 was predicted, and the results are shown in Table 2. As can be seen from Table 2, the three-dimensional ocean sound velocity prediction method based on tensor empirical orthogonal decomposition provided by this invention can effectively predict ocean sound velocity over medium to long-term timeframes.

[0165] Table 2 Comparison of Prediction Time Performance

[0166]

[0167] Please see Figure 5 This invention also provides a three-dimensional ocean sound velocity prediction device 500 based on tensor empirical orthogonal decomposition, comprising:

[0168] The first construction module 501 is used to construct a three-dimensional sound velocity measurement tensor and a weight tensor based on sound velocity measurement data within a target area. The location within the target area where the sound velocity measurement data is present is a first location, and the location within the target area where the sound velocity measurement data is absent is a second location. The value in the three-dimensional sound velocity measurement tensor corresponding to the first location is the sound velocity measurement value at the first location, and the value in the three-dimensional sound velocity measurement tensor corresponding to the second location is 0. The value in the weight tensor corresponding to the first location is 1, and the value in the weight tensor corresponding to the second location is 0.

[0169] The determination module 502 is used to determine the optimal basis function feature matrix set, which includes the optimal basis function feature matrix in the longitude direction, the optimal basis function feature matrix in the latitude direction, and the optimal basis function feature matrix in the depth direction;

[0170] The second construction module 503 is used to construct a three-dimensional sound velocity tensor prediction calculation function based on the three-dimensional sound velocity measurement tensor, the weight tensor, and the set of optimal basis function feature matrices.

[0171] The solver module 504 is used to iteratively solve the three-dimensional sound velocity tensor prediction calculation function based on the tensor gradient descent method to obtain the sound velocity prediction value at the second position.

[0172] Optionally, the three-dimensional sound velocity tensor prediction calculation function is:

[0173] ;

[0174] in, For the three-dimensional sound velocity measurement tensor, For the weight tensor, The core tensor is... The tensor formed by the projection coefficients onto the set of characteristic matrices of the optimal basis functions The optimal basis function characteristic matrix in the longitude direction, This is the optimal basis function characteristic matrix in the latitude direction. Let be the optimal basis function feature matrix in the depth direction. For regularization terms, For regularization parameters, This represents the 1-mode product of a tensor and a matrix. This represents the 2-mode product of a tensor and a matrix. This represents the 3-mode product of a tensor and a matrix. This represents the Hadamard product. The core tensor corresponding to the minimum value of the function. Denotes the Frobenius norm. This represents the square of the tensor modulus.

[0175] Optionally, the solution module 504 includes:

[0176] The first determining unit is used to determine the initial iteration value of the core tensor;

[0177] The calculation unit is used to calculate the gradient of the three-dimensional sound velocity tensor prediction calculation function with respect to the core tensor;

[0178] The iterative calculation unit is used to perform multiple iterative calculations based on the gradient of the core tensor and the initial value of the iteration, in the... In the nth iteration, we obtain the nth... The core tensor of the next iteration, and based on the first iteration The core tensor of the next iteration and the set of characteristic matrices of the optimal basis functions are used to calculate the first... The predicted value of the second iteration and the first iteration The prediction error of the next iteration;

[0179] The second determining unit is used in the iteration number. When the number of iterations is equal to the maximum number of iterations or the prediction error is less than or equal to the threshold, the first iteration will be... The predicted value of the next iteration is determined as the predicted sound speed at the second position. It is a positive integer.

[0180] Optionally, the initial value of the iteration for:

[0181] ;

[0182] The gradient of the core tensor for:

[0183] ;

[0184] The first The core tensor obtained in the next iteration for:

[0185] ;

[0186] The first The predicted value of the next iteration for:

[0187] ;

[0188] The first Prediction error of the next iteration for:

[0189] ;

[0190] in, This is the iteration step size.

[0191] Optionally, the determining module 502 includes:

[0192] A construction unit is used to construct a three-dimensional ocean sound velocity prediction system, which includes an ocean sound velocity tensor representation module, a tensor feature extraction module, and a three-dimensional sound velocity prediction calculation module.

[0193] The training unit is used to train the tensor feature extraction module and the three-dimensional sound velocity prediction calculation module using training sample data to obtain the trained three-dimensional ocean sound velocity prediction system.

[0194] The third determining unit is used to test the trained three-dimensional ocean sound speed prediction system using verification sample data, and to determine the optimal basis function feature matrix in the longitude direction, the optimal basis function feature matrix in the latitude direction, and the optimal basis function feature matrix in the depth direction based on the prediction performance.

[0195] The ocean sound velocity tensor representation module is used to store sound velocity measurement data in tensor form. The tensor feature extraction module is used to obtain a set of basis function feature matrices and a set of model orders. The set of basis function feature matrices includes basis function feature matrices in the longitude direction, basis function feature matrices in the latitude direction, and basis function feature matrices in the depth direction. The set of model orders includes model orders in the longitude direction, model orders in the latitude direction, and model orders in the depth direction. The three-dimensional sound velocity prediction calculation module is used to predict sound velocity based on the set of basis function feature matrices, the set of model orders, and the sound velocity measurement data.

[0196] Optionally, the training unit is specifically used for:

[0197] The training sample data and the validation sample data are acquired and stored in the ocean sound velocity tensor representation module in tensor form;

[0198] The training sample data is input into the tensor feature extraction module to obtain the set of basis function feature matrices and the set of model orders corresponding to the training sample data;

[0199] The set of basis function feature matrices and the set of model orders corresponding to the training sample data are input into the three-dimensional sound speed prediction calculation module. The tensor gradient descent method is used in conjunction with the training sample data to predict the sound speed and obtain the prediction result.

[0200] Optionally, the step of inputting the training sample data into the tensor feature extraction module to obtain the set of basis function feature matrices and the set of model orders corresponding to the training sample data includes:

[0201] The training sample data is subjected to tensor orthogonal decomposition, and the decomposed training sample data is obtained. for:

[0202] ;

[0203] in, The basis function feature matrix in the longitude direction corresponding to the training sample data, The basis function feature matrix in the latitudinal direction corresponding to the training sample data, The basis function feature matrix in the depth direction corresponding to the training sample data, The basis function feature matrix in the time direction corresponding to the training sample data. This is the core tensor corresponding to the training sample data.

[0204] The three-dimensional ocean sound velocity prediction device 500 based on tensor empirical orthogonal decomposition provided in this application embodiment can execute the above method embodiment, and its implementation principle and technical effect are similar, so it will not be described again here.

[0205] It should be noted that the division of units in the embodiments of this application is illustrative and only represents one logical functional division. In actual implementation, other division methods may be used. Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated units described above can be implemented in hardware or as software functional units.

[0206] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a processor-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0207] like Figure 6 As shown, this application provides an electronic device 600, including: a memory 602, a processor 601, and a program stored in the memory 602 and executable on the processor 601; the processor 601 is used to read the program in the memory 602 to implement the steps in the three-dimensional ocean sound velocity prediction method based on tensor empirical orthogonal decomposition as described above.

[0208] This application also provides a readable storage medium storing a program that, when executed by a processor, implements the various processes of the above-described embodiments of the three-dimensional ocean sound velocity prediction method based on tensor empirical orthogonal decomposition, and achieves the same technical effect. To avoid repetition, it will not be described again here. The readable storage medium can be any available medium or data storage device that the processor can access, including but not limited to magnetic storage (such as floppy disks, hard disks, magnetic tapes, magneto-optical disks (MOs), etc.), optical storage (such as compact discs (CDs), digital video discs (DVDs), Blu-ray discs (BDs), high-definition versatile discs (HVDs), etc.), and semiconductor storage (such as read-only memory (ROMs), erasable programmable read-only memory (EPROMs), electrically erasable programmable read-only memory (EEPROMs), non-volatile memory (NAND flash), solid-state disks (SSDs), etc.).

[0209] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0210] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, disk, optical disk) and includes several instructions to cause a terminal (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0211] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of this application.

Claims

1. A three-dimensional ocean sound velocity prediction method based on tensor empirical orthogonal decomposition, characterized in that, include: A three-dimensional sound velocity measurement tensor and a weight tensor are constructed based on the sound velocity measurement data within the target area. The location within the target area with sound velocity measurement data is designated as the first location, and the location within the target area without sound velocity measurement data is designated as the second location. The value corresponding to the first location in the three-dimensional sound velocity measurement tensor is the sound velocity measurement value at the first location, and the value corresponding to the second location in the three-dimensional sound velocity measurement tensor is 0. The value corresponding to the first location in the weight tensor is 1, and the value corresponding to the second location in the weight tensor is 0. The optimal set of basis function feature matrices is determined through the following steps: Constructing a three-dimensional ocean sound velocity prediction system, which includes an ocean sound velocity tensor representation module, a tensor feature extraction module, and a three-dimensional sound velocity prediction calculation module; Training the tensor feature extraction module and the three-dimensional sound velocity prediction calculation module using training sample data to obtain the trained three-dimensional ocean sound velocity prediction system; Testing the trained three-dimensional ocean sound velocity prediction system using validation sample data, and determining the optimal set of basis function feature matrices based on the prediction performance; The ocean sound velocity tensor representation module stores sound velocity measurement data in tensor form; the tensor feature extraction module obtains the set of basis function feature matrices and the model order set; the set of basis function feature matrices includes basis function feature matrices in the longitude, latitude, and depth directions; the set of model orders includes model orders in the longitude, latitude, and depth directions; the three-dimensional sound velocity prediction calculation module performs sound velocity prediction based on the set of basis function feature matrices, the model order set, and the sound velocity measurement data; the optimal set of basis function feature matrices includes... , , , represent the optimal basis function feature matrices in the longitude, latitude, and depth directions, respectively; A three-dimensional sound velocity tensor prediction calculation function is constructed based on the three-dimensional sound velocity measurement tensor, weight tensor, and the set of feature matrices of the optimal basis functions. ； For the three-dimensional sound velocity measurement tensor, For weight tensors, For the core tensor, is The tensor formed by the projection coefficients onto the set of characteristic matrices of the optimal basis functions. For regularization terms, For regularization parameters, , , These represent the 1-mode product, 2-mode product, and 3-mode product of a tensor and a matrix, respectively. This represents the Hadamard product. The core tensor corresponding to the minimum value of the function. Describing the Frobenius norm, Represents the square of the tensor modulus; The predicted sound velocity value at the second position is obtained by iteratively solving the three-dimensional sound velocity tensor prediction calculation function using the tensor gradient descent method.

2. The method as described in claim 1, characterized in that, The step of iteratively solving the three-dimensional sound velocity tensor prediction calculation function based on the tensor gradient descent method to obtain the sound velocity prediction value at the second position includes: Determine the initial value for the iteration of the core tensor; Calculate the gradient of the three-dimensional sound velocity tensor prediction function with respect to the core tensor; Based on the gradient of the core tensor and the initial value of the iteration, multiple iterative calculations are performed, and at the... In the nth iteration, we obtain the nth... The core tensor of the next iteration, and based on the first iteration The core tensor of the next iteration and the set of characteristic matrices of the optimal basis functions are used to calculate the first... The predicted value of the second iteration and the first iteration The prediction error of the next iteration; The number of iterations When the number of iterations equals the maximum number of iterations or the prediction error is less than or equal to the threshold, the first iteration will be... The predicted value of the next iteration is determined as the predicted sound speed at the second position. It is a positive integer.

3. The method as described in claim 2, characterized in that, The initial value of the iteration for: ； The gradient of the core tensor for: ； The first The core tensor obtained in the next iteration for: ； The first The predicted value of the next iteration for: ； The first Prediction error of the next iteration for: ； in, This is the iteration step size.

4. The method as described in claim 1, characterized in that, The tensor feature extraction module and the three-dimensional sound velocity prediction calculation module are trained using training sample data to obtain a trained three-dimensional ocean sound velocity prediction system, including: The training sample data and the validation sample data are acquired and stored in the ocean sound velocity tensor representation module in tensor form; The training sample data is input into the tensor feature extraction module to obtain the set of basis function feature matrices and the set of model orders corresponding to the training sample data; The set of basis function feature matrices and the set of model orders corresponding to the training sample data are input into the three-dimensional sound speed prediction calculation module. The tensor gradient descent method is used in conjunction with the training sample data to predict the sound speed and obtain the prediction result.

5. The method as described in claim 4, characterized in that, The step of inputting the training sample data into the tensor feature extraction module to obtain the set of basis function feature matrices and the set of model orders corresponding to the training sample data includes: The training sample data is subjected to tensor orthogonal decomposition, and the decomposed training sample data is obtained. for: ； in, The basis function feature matrix in the longitude direction corresponding to the training sample data, The basis function feature matrix in the latitudinal direction corresponding to the training sample data, The basis function feature matrix in the depth direction corresponding to the training sample data. This is the core tensor corresponding to the training sample data.

6. A three-dimensional ocean sound velocity prediction device based on tensor empirical orthogonal decomposition, characterized in that, include: The first construction module is used to construct a three-dimensional sound velocity measurement tensor and a weight tensor based on sound velocity measurement data within a target area. The location within the target area where the sound velocity measurement data is present is a first location, and the location within the target area where the sound velocity measurement data is absent is a second location. The value in the three-dimensional sound velocity measurement tensor corresponding to the first location is the sound velocity measurement value at the first location, and the value in the three-dimensional sound velocity measurement tensor corresponding to the second location is 0. The value in the weight tensor corresponding to the first location is 1, and the value in the weight tensor corresponding to the second location is 0. The determination module is used to determine the optimal basis function feature matrix set, which includes the optimal basis function feature matrix in the longitude direction, the optimal basis function feature matrix in the latitude direction, and the optimal basis function feature matrix in the depth direction; The second construction module is used to construct a three-dimensional sound velocity tensor prediction calculation function based on the three-dimensional sound velocity measurement tensor, the weight tensor, and the set of optimal basis function feature matrices. The solution module is used to iteratively solve the three-dimensional sound velocity tensor prediction calculation function based on the tensor gradient descent method to obtain the sound velocity prediction value at the second position. The three-dimensional sound velocity tensor prediction calculation function is as follows: ； in, For the three-dimensional sound velocity measurement tensor, For the weight tensor, The core tensor is... The tensor formed by the projection coefficients onto the set of characteristic matrices of the optimal basis functions The optimal basis function characteristic matrix in the longitude direction, This is the optimal basis function characteristic matrix in the latitude direction. Let be the optimal basis function feature matrix in the depth direction. For regularization terms, For regularization parameters, This represents the 1-mode product of a tensor and a matrix. This represents the 2-mode product of a tensor and a matrix. This represents the 3-mode product of a tensor and a matrix. This represents the Hadamard product. The core tensor corresponding to the minimum value of the function. Describing the Frobenius norm, Represents the square of the tensor modulus; The three-dimensional ocean sound velocity prediction device based on tensor empirical orthogonal decomposition is used to implement the method as described in claim 1.

7. An electronic device, comprising: A memory, a processor, and a program stored in the memory and executable on the processor; characterized in that the processor is configured to read the program from the memory to implement the steps in the three-dimensional ocean sound velocity prediction method based on tensor empirical orthogonal decomposition as described in any one of claims 1 to 5.

8. A readable storage medium for storing a program, characterized in that, When the program is executed by the processor, it implements the steps in the three-dimensional ocean sound velocity prediction method based on tensor empirical orthogonal decomposition as described in any one of claims 1 to 5.

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