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

Abstract

The invention discloses a three-dimensional ocean sound velocity prediction method, and particularly relates to a three-dimensional ocean 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 area; determining an optimal primary function feature matrix set, wherein the optimal primary function feature matrix set comprises an optimal primary function feature matrix in the longitude direction, an optimal primary function feature matrix in the latitude direction and an optimal primary function feature matrix in the 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 primary function feature 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 of the second position. According to the invention, the precision of the three-dimensional ocean sound velocity prediction result can be improved.

Description

Technical Field

[0001] The present invention relates to a three-dimensional ocean sound speed prediction method, and in particular to a three-dimensional ocean sound speed prediction method and device based on tensor empirical orthogonal decomposition. Background Art

[0002] Acoustic signals are the main carrier of information in the ocean and are widely used in military and civilian fields such as marine engineering, underwater target detection, underwater navigation, and sonar tactical use. The propagation process of acoustic signals in the ocean is affected by many factors, among which the speed of sound propagation is the most critical factor. In a complex ocean environment, the speed of sound varies with temperature, salinity, and pressure, and the speed of sound at different times and geographical locations is different. In order to improve the ability and level of ocean acoustic information assurance, it is necessary to accurately obtain the temporal and spatial distribution of ocean sound speed. The traditional method of measuring sound speed in ocean mapping is time-consuming and costly, and it is impossible to quickly obtain large-scale three-dimensional sound speed data; although the ocean remote sensing method can obtain a large range of marine environmental data, it can only obtain ocean surface data, but cannot directly obtain sound speed data below the surface.

[0003] The existing technology usually uses the historical measurement data of the sea area of ​​interest to construct a parameterized mathematical model to characterize the three-dimensional sound speed in the sea area, and then predicts and calculates the three-dimensional sound speed distribution of the entire area based on the model combined with the sparsely measured sound speed data in the area. At present, the commonly used methods in the existing technology can be divided into two categories. One is to represent the sound speed data through empirical orthogonal functions. This method can effectively describe the sound speed with a small number of basis functions. Therefore, the prediction of the sound speed can be converted into the prediction of the coefficients corresponding to the basis functions, thereby greatly reducing the amount of calculation for the sound speed prediction. The other is a sound speed characterization and prediction method based on dictionary learning. Compared with the traditional empirical orthogonal function characterization method, this method can generate a dictionary basis function for sparse processing, represent the sound speed with the least atoms, enhance the description of the sound speed details, and improve the accuracy of sound speed prediction.

[0004] However, the variability of the actual ocean environment will cause irregularities and uncertainties in changes in seawater temperature, salinity and pressure. Although the above two methods commonly used in the prior art have good accuracy in predicting the ocean sound speed in the depth direction, they ignore the distribution of the ocean sound speed in the horizontal direction. Therefore, the ability to characterize the three-dimensional ocean sound speed is weak, resulting in poor accuracy in the prediction results, which is difficult to meet the needs of refined ocean acoustic information assurance. 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 characterization capabilities for three-dimensional ocean sound speed, resulting in poor accuracy of the prediction results, which is difficult to meet the needs of refined ocean acoustic information assurance. In order to solve the above-mentioned problem, the present invention provides a three-dimensional ocean sound speed prediction method and device based on tensor empirical orthogonal decomposition.

[0006] The content of the present invention includes:

[0007] In a first aspect, an embodiment of the present invention provides a three-dimensional ocean sound speed prediction method based on tensor empirical orthogonal decomposition, comprising:

[0008] Constructing a three-dimensional sound speed measurement tensor and a weight tensor based on the sound speed measurement data in the target area, wherein the position in the target area where the sound speed measurement data is located is a first position, and the position in the target area where the sound speed measurement data is not located is a second position, the value corresponding to the first position in the three-dimensional sound speed measurement tensor is the sound speed measurement value of the first position, the value corresponding to the second position in the three-dimensional sound speed measurement tensor is 0, the value corresponding to the first position in the weight tensor is 1, and the value corresponding to the second position in the weight tensor is 0;

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

[0010] Constructing a three-dimensional sound speed tensor prediction calculation function based on the three-dimensional sound speed measurement tensor, the weight tensor and the optimal basis function characteristic matrix set;

[0011] The three-dimensional sound speed tensor prediction calculation function is iteratively solved based on the tensor gradient descent method to obtain a predicted sound speed value at the second position.

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

[0013]

[0014] in, is the three-dimensional sound velocity measurement tensor, is the weight tensor, is the core tensor, the core tensor is The tensor composed of the projection coefficients on the optimal basis function feature matrix set, U Lon ′ is the optimal basis function characteristic matrix in the longitude direction, U Lat ′ is the optimal basis function characteristic matrix in the latitude direction, U Dep ′ is the optimal basis function feature matrix in the depth direction, is the regularization term, λ is the regularization parameter, ×1 represents the 1-mode product of the tensor and the matrix, ×2 represents the 2-mode product of the tensor and the matrix, and ×3 represents the 3-mode product of the tensor and the matrix. represents the Hadamard product, argmin represents the core tensor corresponding to the minimum value of the function, represents the Frobenius norm, ‖·‖ 2 Represents the square of the tensor's magnitude.

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

[0016] Determining an initial value of iteration of the core tensor;

[0017] Calculating the gradient of the three-dimensional sound speed tensor prediction calculation function with respect to the core tensor;

[0018] Perform multiple iterative calculations based on the gradient of the core tensor and the iteration initial value, obtain the core tensor of the kth iteration at the kth iteration, and calculate the predicted value of the kth iteration and the prediction error of the kth iteration based on the core tensor of the kth iteration and the optimal basis function feature matrix set;

[0019] When the number of iterations k is equal to the maximum number of iterations or the prediction error is less than or equal to a threshold, the prediction value of the kth iteration is determined as the predicted value of the sound speed at the second position, where k is a positive integer.

[0020] Optionally, the iteration initial value for:

[0021]

[0022] The gradient of the core tensor for:

[0023]

[0024] The core tensor obtained at the kth iteration for:

[0025]

[0026] The predicted value of the kth iteration for:

[0027]

[0028] The prediction error Err of the kth iteration is:

[0029]

[0030] Among them, α is the iteration step size.

[0031] Optionally, determining the optimal basis function feature matrix set includes:

[0032] Constructing a three-dimensional ocean sound speed prediction system, the three-dimensional ocean sound speed prediction system comprising an ocean sound speed tensor representation module, a tensor feature extraction module and a three-dimensional sound speed prediction calculation module;

[0033] Using training sample data to train the tensor feature extraction module and the three-dimensional sound speed prediction calculation module to obtain a trained three-dimensional ocean sound speed prediction system;

[0034] The trained three-dimensional ocean sound speed prediction system is tested using verification sample data, and 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 according to the prediction performance;

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

[0036] Optionally, the tensor feature extraction module and the three-dimensional sound speed prediction calculation module are trained using training sample data to obtain a trained three-dimensional ocean sound speed prediction system, including:

[0037] Acquire the training sample data and the verification sample data and store them in the ocean sound speed tensor representation module in tensor form;

[0038] Input the training sample data into the tensor feature extraction module to obtain a basis function feature matrix set and a model order set corresponding to the training sample data;

[0039] The basis function feature matrix set and the model order set corresponding to the training sample data are input into the three-dimensional sound speed prediction calculation module, and the sound speed is predicted by using the tensor gradient descent method in combination with the training sample data to obtain a prediction result.

[0040] Optionally, inputting the training sample data into the tensor feature extraction module to obtain a basis function feature matrix set and a model order set corresponding to the training sample data includes:

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

[0042]

[0043] Among them, U Lon is the basis function feature matrix in the longitude direction corresponding to the training sample data, U Lat is the basis function feature matrix in the latitude direction corresponding to the training sample data, U Dep is the basis function feature matrix in the depth direction corresponding to the training sample data, It is the core tensor corresponding to the training sample data.

[0044] In a second aspect, an embodiment of the present invention provides a three-dimensional ocean sound speed prediction device based on tensor empirical orthogonal decomposition, comprising:

[0045] A first construction module is used to construct a three-dimensional sound speed measurement tensor and a weight tensor based on the sound speed measurement data in the target area, wherein the position in the target area where the sound speed measurement data is located is a first position, and the position in the target area where the sound speed measurement data is not located is a second position, the value corresponding to the first position in the three-dimensional sound speed measurement tensor is the sound speed measurement value of the first position, the value corresponding to the second position in the three-dimensional sound speed measurement tensor is 0, the value corresponding to the first position in the weight tensor is 1, and the value corresponding to the second position in the weight tensor is 0;

[0046] A determination module, used to determine an optimal basis function feature matrix set, wherein the optimal basis function feature matrix set includes an optimal basis function feature matrix in a longitude direction, an optimal basis function feature matrix in a latitude direction, and an optimal basis function feature matrix in a depth direction;

[0047] A second construction module is used to construct a three-dimensional sound speed tensor prediction calculation function based on the three-dimensional sound speed measurement tensor, the weight tensor and the optimal basis function characteristic matrix set;

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

[0049] In a third aspect, an embodiment of the present invention provides an electronic device, comprising: a memory, a processor, and a program stored in the memory and executable on the processor; the processor is used to read the program in the memory to implement the steps in the three-dimensional ocean sound speed prediction method based on tensor empirical orthogonal decomposition as described in the first aspect.

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

[0051] The beneficial effect of the present invention is that, in an embodiment of the present invention, a three-dimensional sound speed measurement tensor and a weight tensor are constructed based on the sound speed measurement data in the target area, and an optimal basis function feature matrix set is determined, and the optimal basis function feature matrix set includes an optimal basis function feature matrix in the longitude direction, an optimal basis function feature matrix in the latitude direction, and an optimal basis function feature matrix in the depth direction; a three-dimensional sound speed tensor prediction calculation function is constructed based on the three-dimensional sound speed measurement tensor, the weight tensor, and the optimal basis function feature matrix set; the three-dimensional sound speed tensor prediction calculation function is iteratively solved based on the tensor gradient descent method to obtain the sound speed prediction value of the second position. The method provided in an embodiment of the present invention uses a tensor to directly store three-dimensional ocean sound speed data, and obtains the basis function characteristics of the ocean sound speed in the longitude, latitude, and depth directions respectively through the tensor empirical orthogonal decomposition method, so as to alleviate the problem of insufficient characterization capability of the three-dimensional ocean sound speed distribution. On this basis, the three-dimensional ocean sound speed prediction is realized under the condition of sparse sound speed profile measurement data through the tensor gradient descent method, thereby improving the accuracy of sound speed prediction. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0054] Attached Figure 3 The three-dimensional ocean sound speed prediction result obtained based on the tensor empirical orthogonal decomposition;

[0055] Attached Figure 4 A comparison chart of the detection results of the three-dimensional ocean sound speed prediction method based on tensor empirical orthogonal decomposition provided in an embodiment of the present invention and the results of the EOF method;

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

[0057] Attached Figure 6A schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0058] In the embodiments of the present application, the term "and / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B may represent: A exists alone, A and B exist at the same time, and B exists alone. The character " / " generally indicates that the objects associated before and after are in an "or" relationship. In the embodiments of the present application, the term "multiple" refers to two or more, and other quantifiers are similar. The terms "first", "second", etc. in the specification and claims of the present application are used to distinguish similar objects, and are not used to describe a specific order or sequence. It should be understood that the terms used in this way can be interchangeable under appropriate circumstances, so that the embodiments of the present application can be implemented in an order other than those illustrated or described here, and the objects distinguished by "first" and "second" are generally of the same type, and the number of objects is not limited. For example, the first object can be one or more.

[0059] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work 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 those commonly understood by those skilled in the art to which this application belongs. The terms used herein are only for the purpose of describing the embodiments of this application and are not intended to limit this application.

[0061] The embodiments of the present application provide a three-dimensional ocean sound speed prediction method and device based on tensor empirical orthogonal decomposition, aiming to effectively explore the intrinsic essential characteristics of time-varying ocean sound speed distribution and improve the accuracy of three-dimensional ocean sound speed prediction.

[0062] See also Figure 1 , Figure 1 A schematic flow chart of a method for predicting three-dimensional ocean sound speed based on tensor empirical orthogonal decomposition provided in an embodiment of the present invention, wherein the method specifically comprises the following steps:

[0063] Step 101, constructing a three-dimensional sound speed measurement tensor and a weight tensor based on the sound speed measurement data in the target area, wherein the position in the target area where the sound speed measurement data is located is a first position, and the position in the target area where the sound speed measurement data is not located is a second position, the value corresponding to the first position in the three-dimensional sound speed measurement tensor is the sound speed measurement value of the first position, the value corresponding to the second position in the three-dimensional sound speed measurement tensor is 0, the value corresponding to the first position in the weight tensor is 1, and the value corresponding to the second position in the weight tensor is 0;

[0064] Step 102, determining an optimal basis function feature matrix set, wherein the optimal basis function feature matrix set includes an optimal basis function feature matrix in a longitude direction, an optimal basis function feature matrix in a latitude direction, and an optimal basis function feature matrix in a depth direction;

[0065] Step 103, constructing a three-dimensional sound speed tensor prediction calculation function based on the three-dimensional sound speed measurement tensor, the weight tensor and the optimal basis function characteristic matrix set;

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

[0067] In an embodiment of the present application, tensors are used to organize spatiotemporal multidimensional ocean sound speed data, and the tensor empirical orthogonal decomposition method is used to extract the basis function characteristic matrix in different latitudinal directions, thereby improving the characterization capability of spatiotemporal ocean sound speed data. At the same time, the tensor gradient descent method is used to realize the three-dimensional sound speed prediction function under the conditions of sparse sound speed profile measurement data, thereby improving the prediction accuracy.

[0068] It should be understood that the data expression form of three-dimensional ocean sound speed is a typical raster data, which is characterized by a multivariate time series cube data organization form composed of longitude, latitude, depth and time. Conventional data organization forms such as vectors and matrices are difficult to effectively store this type of high-dimensional data form. Tensors are the most natural expression form of high-dimensional data. Therefore, the data organization form based on tensors can be well compatible with multi-dimensional spatiotemporal ocean sound speed data, and has a unique advantage in expressing the spatiotemporal ocean sound speed field. For three-dimensional ocean sound speed data considering spatial longitude, latitude and depth It can be expressed as a third-order tensor Where I1, I2, and I3 represent the sound speed index range in longitude, latitude, and depth directions, respectively. The element a(i,j,d) corresponding to the index (i,j,d) represents the three-dimensional ocean sound speed value at latitude i, longitude j, and depth d. Based on the three-dimensional ocean sound speed representation of tensors, each dimension is independent of each other, and each dimension can correspond to a specific basis. The ocean sound speed data based on tensor representation can be retrieved and extracted through tensor operations. Furthermore, considering the ocean sound speed obtained at different times, the spatiotemporal ocean sound speed can be written as a fourth-order tensor form Where I4 represents the index range in the time direction.

[0069] When measuring the speed of sound in the target area, the speed of sound measurement data is obtained at some locations in the target area, but not at other locations. In this case, the measurement data obtained is sparsely measured speed of sound data. The location where the speed of sound measurement data is measured in the target area is taken as the first location, and the other location is taken as the second location. The second location is the location where the speed of sound 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 in the target area. 3D sound velocity measurement tensor In the example, according to the longitude and latitude coordinates of the sound speed measurement, the measured sound speed value is assigned to the location with sound speed measurement data, and zero is assigned to the location without sound speed measurement data (i.e. the location to be predicted). Then construct the weight tensor The dimension size of the weight tensor is Stay consistent, used to describe tensors The location where the speed of sound needs to be predicted, The element assignments in are as follows:

[0071]

[0072] It should be understood that the weight tensor Equivalent to measuring the three-dimensional sound speed tensor The data in the image is processed, the positions where data exists keep their values ​​unchanged, and the positions where no data exists are assigned zero.

[0073] In step 102, 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, and the specific method is not limited here. Optionally, in some embodiments, the step 102 includes:

[0074] Constructing a three-dimensional ocean sound speed prediction system, the three-dimensional ocean sound speed prediction system comprising an ocean sound speed tensor representation module, a tensor feature extraction module and a three-dimensional sound speed prediction calculation module;

[0075] Using training sample data to train the tensor feature extraction module and the three-dimensional sound speed prediction calculation module to obtain a trained three-dimensional ocean sound speed prediction system;

[0076] The trained three-dimensional ocean sound speed prediction system is tested using verification sample data, and 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 according to the prediction performance;

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

[0078] It should be understood that the ocean sound speed tensor representation module is used to store sound speed measurement data in tensor form, and output the sound speed measurement data after tensor representation to the tensor feature extraction module. The tensor feature extraction module is connected to the three-dimensional sound speed prediction and calculation module, and the tensor feature extraction module receives the sound speed measurement data in tensor form from the ocean sound speed tensor representation module, and uses the tensor empirical orthogonal decomposition method to construct a tensor feature representation model of the three-dimensional ocean sound speed, and transmits the basis function feature matrix set and the model order set in the ocean sound speed tensor feature representation model to the three-dimensional sound speed prediction and calculation module. The three-dimensional sound speed prediction and calculation module is connected to the tensor feature extraction module, receives the basis function feature matrix set and the model order set from the tensor feature extraction module, and uses the tensor gradient descent method to combine the sound speed profile data sparsely measured at the time to be predicted to calculate the three-dimensional ocean sound speed distribution, so as to realize the three-dimensional ocean sound speed prediction.

[0079] As a specific embodiment, a three-dimensional ocean sound speed prediction system based on tensor empirical orthogonal decomposition is constructed. First, the data set required for the ocean sound speed prediction system is constructed, and the data set is divided into training sample data, verification sample data and test sample data. Then the tensor feature extraction module and the three-dimensional sound speed prediction calculation module in the three-dimensional ocean sound speed prediction system are trained using the training sample data. After a round of training, the trained three-dimensional ocean sound speed prediction system is tested using the verification sample data, the model parameters with the best performance are selected, and the trainable modules (tensor feature extraction module and three-dimensional sound speed prediction calculation module) in the three-dimensional ocean sound speed prediction system are assigned to obtain the three-dimensional ocean sound speed prediction system with the best performance after training; finally, the three-dimensional ocean sound speed prediction system with the best performance after training is used in combination with the sound speed profile data of the sparse measurement in the sea area to perform three-dimensional ocean sound speed prediction, and the three-dimensional sound speed distribution in the sea area is obtained.

[0080] Optionally, the tensor feature extraction module and the three-dimensional sound speed prediction calculation module are trained using training sample data to obtain a trained three-dimensional ocean sound speed prediction system, including:

[0081] Acquire the training sample data and the verification sample data and store them in the ocean sound speed tensor representation module in tensor form;

[0082] Input the training sample data into the tensor feature extraction module to obtain a basis function feature matrix set and a model order set corresponding to the training sample data;

[0083] The basis function feature matrix set and the model order set corresponding to the training sample data are input into the three-dimensional sound speed prediction calculation module, and the sound speed is predicted by using the tensor gradient descent method in combination with the training sample data to obtain a prediction result.

[0084] As a specific embodiment, the Hycom dataset is used as training sample data, verification sample data, and test sample data. The Hycom dataset contains global ocean depth, salinity, temperature, flow field, sound speed and other marine environmental parameters. The horizontal spatial resolution is 1 / 12°×1 / 12°, and there are 50 layers in the depth direction, covering 0 to 5000 meters of water depth. The data is updated once a day. Specifically, the ocean sound speed in some areas of the South my country Sea (112°~114.4°E, 14.88°~19.6°N, depth 0-1500 meters) for T days in June 2020 was selected as sample data (i.e., sound speed samples). The number of sound speed samples is N×M×L, indicating that the sound speed ranges in longitude, latitude and depth directions have N, M and L spatial position points, respectively. Therefore, the total sample data used in this embodiment can be expressed as Will Recorded as data sample tensor.

[0085] Specifically, in some embodiments, it is necessary to The specific method for deviation processing is as follows:

[0086] S1: data sample tensor Averaging along the time dimension Get the mean tensor of the three-dimensional sound speed distribution in the sea area

[0087] S2: Let i = 1, which means the three-dimensional sound speed sample tensor of the sea area on the i-th day is

[0088] S3: The three-dimensional sound speed sample tensor of the i-th day Subtract the mean tensor Right now represents the anomaly tensor of the sound speed sample tensor on the ith day;

[0089] S4: Let i = 1 + 1. If i ≤ T, execute S1. If i ≥ T, it means that the anomaly sample tensor of ocean sound speed has been constructed. The anomaly tensor of T days is written as a fourth-order tensor, recorded as Represents the anomaly tensor of all sound speed samples.

[0090] S5: The anomaly tensor of all sound speed samples The data is divided into training sample data, verification sample data and test sample data according to time.

[0091] The tensor feature extraction module is used to receive the sound speed tensor data from the ocean sound speed tensor representation module, and use the tensor empirical orthogonal decomposition method to construct a tensor feature representation model of the three-dimensional ocean sound speed, and obtain the basis function feature matrix of the three-dimensional ocean sound speed in the longitude, latitude and depth directions. Optionally, in some embodiments, the inputting of the training sample data into the tensor feature extraction module to obtain the basis function feature matrix set and 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 for:

[0093]

[0094] Among them, U Lon is the basis function feature matrix in the longitude direction corresponding to the training sample data, U Lat is the basis function feature matrix in the latitude direction corresponding to the training sample data, U Dep is the basis function feature matrix in the depth direction corresponding to the training sample data, U Time is the basis function feature matrix in the time direction corresponding to the training sample data, is the core tensor corresponding to the training sample data.

[0095] As a specific embodiment, its specific process can be expressed as follows:

[0096] Obtain the anomaly tensor of the training sample data For perform tensor empirical orthogonal decomposition, denoted as the training sound speed tensor Among them, in this embodiment, the training sound speed tensor can specifically be expressed as where ×1 represents the 1-mode product of a tensor and a matrix, ×2 represents the 2-mode product of a tensor and a matrix, ×3 represents the 3-mode product of a tensor and a matrix, ×4 represents the 4-mode product of a tensor and a matrix, U Lon is the basis function feature matrix in the longitude direction, U Lat is the basis function feature matrix in the latitude direction, U Dep is the basis function feature matrix in the depth direction, U Time is the basis function feature matrix in the time direction, is the core tensor, N1 < N, M1 < M, L1 < L, T1 < T, and is the training sound speed tensor is the tensor composed of the projection coefficients on the basis function feature matrix.

[0097] In this embodiment, through the above method, the sound speed tensor is decomposed into the product of a core tensor with a smaller dimension and four basis function feature matrices in four dimensions by applying tensor empirical orthogonal decomposition. Taking the training sound speed tensor as an example, the specific method of tensor empirical orthogonal decomposition is described as follows:

[0098] In the longitude direction: For the tensor perform matrix unfolding along the longitude direction to obtain a new matrix Specifically, take the longitude of the tensor as the columns of the new matrix with the number of columns being N, and the remaining dimensions as the rows of the new matrix with the number of rows being M×L×T (the product of all dimensions except the longitude dimension). Perform singular value decomposition on the unfolded matrix The formula is as follows:

[0099]

[0100] where U1 and V1 represent the left singular matrix and the right singular matrix, ∑ is the corresponding singular value matrix, and the superscript T in the formula represents the matrix transpose symbol. Take the first R Lon columns of U1 as the basis function feature matrix U Lon in the longitude direction, and R Lon is the model order in the longitude direction.

[0101] In the latitude direction: for the tensor Expand the matrix along the latitude direction to get a new matrix Specifically, the tensor The latitude of The number of columns is M, and the remaining dimensions are used as the new matrix The number of rows is N×L×T (the product of all dimensions except the latitude dimension). Perform singular value decomposition of the matrix, the formula is as follows:

[0102]

[0103] Among them, U2 and V2 represent the left singular matrix and the right singular matrix, ∑ is the corresponding singular value matrix, and the superscript T in the formula represents the transpose of the matrix. Lat As the basis function characteristic matrix U in the latitude direction Lat , R Lat is the model order in the latitude direction.

[0104] In the depth direction: for tensors Matrix expansion along the depth direction to obtain a new matrix The method is to convert the tensor The depth of The number of columns is L, and the remaining dimensions are used as the new matrix The number of rows is M×N×T (the product of all dimensions except the depth dimension). Perform singular value decomposition of the matrix, the formula is as follows:

[0105]

[0106] Among them, U3 and V3 represent the left singular matrix and the right singular matrix, ∑ is the corresponding singular value matrix, and the superscript T in the formula represents the transpose of the matrix. Dep The columns are used as the basis function feature matrix U in the depth direction Dep , U Dep is the model order in the depth direction.

[0107] In the time direction: for tensors Expand the matrix along the time direction to get the new matrix The method is to convert the tensor The depth of The number of columns is T, and the remaining dimensions are used as the new matrix The number of rows is M×N×L (the product of all dimensions except the depth dimension). Perform singular value decomposition of the matrix, the formula is as follows:

[0108]

[0109] Among them, U4 and V4 represent the left singular matrix and the right singular matrix, ∑ is the corresponding singular value matrix, and the superscript T in the formula represents the transpose of the matrix. Time The columns are used as the characteristic matrix U of the basis function in the time direction Time , R Time is the model order in the time direction.

[0110] The core tensor is calculated as follows:

[0111]

[0112] Save the basis function characteristic matrix U in the longitude direction Lon , the basis function characteristic matrix U in the latitude direction Lat And the basis function feature matrix U in the depth direction Dep , and the model order R in the longitude direction Lon , the model order R in the latitudinal direction Lat and the model order R in the depth direction Dep .

[0113] The three-dimensional sound speed prediction calculation module is combined with the basis function feature matrix set and model order received from the tensor feature extraction module, and the three-dimensional ocean sound speed distribution is calculated using the tensor gradient descent method combined with the sparsely measured sound speed profile data at the time to be predicted, to achieve three-dimensional ocean sound speed prediction. The specific implementation method is as follows:

[0114] Still taking the above specific embodiment as an example, K longitude and latitude positions are randomly selected in the sea area selected in the embodiment (112°~114.4°E, 14.88°~19.6°N) to measure the sound velocity profile, and the measurement result is the sound velocity distribution along the depth direction at the selected position, and the longitude and latitude coordinates of the measurement point are recorded at the same time;

[0115] Construct the three-dimensional sound speed measurement tensor corresponding to the training sample data and the weight tensor The specific construction method can refer to the description in step 101 and will not be repeated here.

[0116] Construct a three-dimensional sound speed tensor prediction calculation function to calculate the three-dimensional sound speed measurement tensor corresponding to the training sample data, as follows:

[0117]

[0118] in, represents the Hadamard product, represents the core tensor, ULon , U Lat and U Dep are respectively the basis function feature matrices in the longitude, latitude, and depth directions saved in the aforementioned steps. The second term is the regularization term, which is used to prevent overfitting of the function. λ is the regularization parameter, and argmin represents the core tensor corresponding to the minimum value of the function. denotes the Frobenius norm, ‖·‖ 2 represents the square of the tensor modulus.

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

[0120] Step1: Initialize the loop variable k = 1 and determine the initial value of the iteration of the core tensor

[0121]

[0122] Step 2: Calculate the gradient of the function f with respect to the core tensor :

[0123]

[0124] is the tensor to be solved.

[0125] Step 3: Iteratively update the core tensor based on . The core tensor obtained in the k-th iteration is:

[0126]

[0127] where α is the iteration step size.

[0128] Step 4: Calculate the predicted value of the sound speed tensor:

[0129]

[0130] Step 5: Calculate the prediction error of the sound speed at the predicted position:

[0131]

[0132] Let k = k + 1. If the prediction error Err > ε or k < K_max, return to Step 2; otherwise, the predicted value of the three-dimensional ocean sound speed tensor is obtained from Step 4, where K_max represents the maximum number of iterations.

[0133] Through the above method, the tensor feature extraction module and the three-dimensional sound speed prediction calculation module have been trained using the training sample data to obtain a trained three-dimensional ocean sound speed prediction system; the prediction performance of the trained three-dimensional ocean sound speed prediction system is tested using the verification sample data, and the model parameters with the best prediction performance are retained as the parameters of the three-dimensional ocean sound speed prediction system. The parameters to be optimized are the model order R corresponding to the basis function feature matrix in the longitude, latitude and depth directions. Lon , R Lat and R Dep .

[0134] The specific process of testing the prediction performance of the trained three-dimensional ocean sound speed prediction system based on the validation sample data can be found in the description of the training sample data section above, which will not be described in detail here. Lon , R Lat and R Dep , and then obtain 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 specific process is as follows:

[0135] First, let R Lon =1, which is the model order reserved for the longitude direction basis function characteristic matrix. Then construct the longitude direction basis function characteristic matrix: U Lon ′=U Lon (1:R Lon ,:), that is, keep U Lon Front R Lon The column vectors form a new basis function feature matrix. The basis function feature matrices in latitude and depth directions are U Lat and U Dep The three-dimensional sound speed prediction calculation module receives the new basis function characteristic matrix in the longitude, latitude and depth directions, and uses the above method to calculate the three-dimensional sound speed tensor under the new basis function characteristic matrix. Calculate the current reconstruction error By traversing R Lon , find all R Lon The reconstruction error under the value is selected, and the R corresponding to the minimum reconstruction error is selected Lon As the model order of the optimal longitude direction basis function characteristic matrix, the corresponding longitude direction basis function characteristic matrix U Lon ′ is used as the optimal basis function feature matrix in the longitude direction.

[0136] Then, let R Lat =1, which is the model order reserved for the basis function feature matrix in the latitudinal direction. Construct the basis function feature matrix in the latitudinal direction: U Lat ′=U Lat (1:RLat ,:), that is, keep U Lat Front R Lat The column vectors form a new basis function feature matrix. The basis function feature matrices in the longitude and depth directions are U Lon ′ and U Dep The three-dimensional sound speed prediction calculation module receives the basis function feature matrices in the longitude, latitude and depth directions, which are U Lon ′、U Lat and U Dep , the three-dimensional sound velocity tensor under the new basis function characteristic matrix is ​​calculated using the above method And calculate the current reconstruction error By traversing R Lat , find all R Lat The reconstruction error under the value is selected, and the R corresponding to the minimum reconstruction error is selected Lat As the model order of the optimal latitudinal basis function characteristic matrix, the corresponding latitudinal basis function characteristic matrix U Lat ′ is used as the optimal basis function feature matrix in the latitude direction.

[0137] Finally, let R Dep =1, which is the model order reserved for the basis function feature matrix in the depth direction. Construct the basis function feature matrix in the latitude direction: U Dep ′=U Dep (1:R Dep ,:), that is, keep U Dep Front R Dep The column vectors form a new basis function feature matrix. The basis function feature matrices in the longitude and latitude directions are U Lon ′ and U Lat The three-dimensional sound speed prediction calculation module receives the basis function characteristic matrices in the longitude, latitude and depth directions, which are U Lon ′、U Lat ′ and U Dep , the three-dimensional sound velocity tensor under the new basis function characteristic matrix is ​​calculated using the above method And calculate the current reconstruction error By traversing R Dep , find all R Dep The reconstruction error under the value is selected, and the R corresponding to the minimum reconstruction error is selected Dep As the model order of the optimal depth-direction basis function feature matrix, the corresponding depth-direction basis function feature matrix U Dep ′ is used as the optimal basis function feature matrix in the depth direction.

[0138] It should be understood that the above is only an optional embodiment. In specific implementation, the order of determining 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 can be adjusted according to actual conditions and is not limited here.

[0139] The model order R of the optimal longitude direction basis function characteristic matrix can be determined by the above method. Lon , the model order R of the optimal latitudinal basis function characteristic matrix Lat and the model order R of the optimal depth-wise basis function feature matrix Dep , and the optimal basis function characteristic matrix U in the longitude direction Lon ′, optimal basis function characteristic matrix U in the latitude direction Lat ′ and the optimal basis function feature matrix U in the depth direction Dep ′.

[0140] In the specific implementation, U Lon ′、U Lat ′ and U Dep ′ is used as the basis function characteristic matrix selected by the three-dimensional ocean sound speed prediction system, and R Lon , R Lat , and R Dep The model order selected as the three-dimensional ocean sound speed prediction system is loaded into the three-dimensional ocean sound speed prediction system to obtain the trained three-dimensional ocean sound speed prediction system.

[0141] In this embodiment, a three-dimensional ocean sound speed prediction system is constructed that integrates an ocean sound speed tensor representation module, a tensor feature extraction module, and a three-dimensional sound speed prediction calculation module. The basis function feature matrix in the longitude, latitude, and depth directions is obtained through tensor representation and tensor empirical orthogonal decomposition methods, which can enhance the characterization capability of the three-dimensional ocean sound speed distribution and improve the prediction accuracy of the three-dimensional ocean sound speed.

[0142] In the specific implementation, the trained three-dimensional ocean sound speed prediction system can be used to perform three-dimensional sound speed prediction on the sparsely measured sound speed profile. Specifically, the sound speed measurement result in the target area is the sparsely measured sound speed profile. According to the relevant instructions of the aforementioned three-dimensional sound speed prediction calculation module, a three-dimensional sound speed measurement tensor is constructed. and the weight tensor

[0143] According to the final parameters of the trained three-dimensional ocean sound speed prediction system, the optimal basis function feature matrix set can be determined, and the three-dimensional sound speed tensor prediction calculation function is constructed using the optimal basis function feature matrix set. Optionally, the three-dimensional sound speed tensor prediction calculation function is:

[0144]

[0145] in, is the three-dimensional sound velocity measurement tensor, is the weight tensor, is the core tensor, the core tensor is The tensor composed of the projection coefficients on the optimal basis function feature matrix set, U Lon ′ is the optimal basis function characteristic matrix in the longitude direction, U Lat ′ is the optimal basis function characteristic matrix in the latitude direction, U Dep ′ is the optimal basis function feature matrix in the depth direction, is the regularization term, λ is the regularization parameter, ×1 represents the 1-mode product of the tensor and the matrix, ×2 represents the 2-mode product of the tensor and the matrix, and ×3 represents the 3-mode product of the tensor and the matrix. represents the Hadamard product, argmin represents the core tensor corresponding to the minimum value of the function, represents the Frobenius norm, ‖·‖ 2 Represents the square of the tensor's magnitude.

[0146] The three-dimensional sound speed tensor prediction calculation function is iteratively solved based on the tensor gradient descent method. Optionally, in some embodiments, the three-dimensional sound speed tensor prediction calculation function is iteratively solved based on the tensor gradient descent method to obtain the sound speed prediction value of the second position, including:

[0147] Determine the iteration initial value of the core tensor, the iteration initial value for:

[0148]

[0149] Calculate the gradient of the three-dimensional sound velocity tensor prediction calculation function to the core tensor, the gradient of the core tensor for:

[0150]

[0151] Perform multiple iterative calculations based on the gradient of the core tensor and the iteration initial value, obtain the core tensor of the kth iteration at the kth iteration, and calculate the predicted value of the kth iteration and the prediction error of the kth iteration based on the core tensor of the kth iteration and the optimal basis function feature matrix set; the core tensor obtained by the kth iteration for:

[0152]

[0153] The predicted value of the kth iteration for:

[0154]

[0155] The prediction error Err of the kth iteration is:

[0156]

[0157] Among them, α is the iteration step size.

[0158] When the number of iterations k is equal to the maximum number of iterations or the prediction error is less than or equal to a threshold, the prediction value of the kth iteration is determined as the predicted value of the sound speed at the second position, where k is a positive integer.

[0159] In this embodiment, the tensor gradient descent method is used to directly predict the three-dimensional ocean sound speed under sparse sound speed profile measurement conditions. There is no need to reduce the dimension of the ocean sound speed tensor to be reconstructed into a vector, which reduces the computational complexity, reduces the time for three-dimensional ocean sound speed prediction, and improves the real-time performance of three-dimensional ocean sound speed prediction.

[0160] The following takes the prediction results of a specific embodiment as an example to illustrate the effect of the three-dimensional ocean sound speed prediction method based on tensor empirical orthogonal decomposition provided by the embodiment of the present invention. This example selects the ocean sound speed of part of the South my country Sea (112°~114.4°E, 14.88°~19.6°N, depth 0-1500 meters) in the Hycom data for 30 days in June 2020 as sample data. The number of samples of the three-dimensional ocean sound speed distribution is 30×60×35, indicating that the sound speed ranges in the longitude, latitude and depth directions have 30, 60 and 35 spatial position points respectively. Therefore, the original sample data used in the embodiment of the present invention can be expressed as a tensor

[0161] The ocean sound speed data of the first 10 days were selected for training, and the tensor empirical orthogonal decomposition method was used to obtain the basis function feature matrix of ocean sound speed in longitude, latitude and depth. The ocean sound speed data of the 11th to 15th days were selected as the validation data set, and the optimal model order was selected using the validation set to obtain the final basis function feature matrix in longitude, latitude and depth. The ocean sound speed data of the 20th day was used as the test set, and the number of points for randomly measuring the sound speed profile was set to 200, which is far less than the 30×60=1800 grids in the horizontal direction (such as Figure 2 As shown), after the three-dimensional ocean sound speed prediction system of the present invention, the three-dimensional ocean sound speed prediction result is output, such as Figure 3 shown.

[0162] The root mean square error (RMSE) is further used as an indicator for evaluating the performance of the three-dimensional ocean prediction system. The smaller the RMSE value, the higher the prediction accuracy. The performance comparison of the three-dimensional ocean sound speed prediction algorithm with different numbers of measurement points randomly selected on the 20th day is shown in Table 1, and the performance is compared with the classic EOF ocean sound speed prediction method. It can be seen from the results in Table 1 that the three-dimensional ocean sound speed prediction method based on tensor empirical orthogonal decomposition provided by the present invention can obtain higher prediction accuracy than the classic EOF method in the prior art under different numbers of sparsely measured sound speed profiles. When the number of random measurement points in the sound speed profile is 200, a certain position (112°E, 15.04°N) is selected to draw the real sound speed profile and the prediction results of the two methods, as shown in Table 1. Figure 4 As shown. Figure 4 It can be seen that the prediction results of the EOF method deviate greatly from the actual sound speed profile, while the prediction results provided by the present invention are in good agreement with the actual sound speed profile, indicating the effectiveness of the three-dimensional ocean sound speed prediction method based on tensor empirical orthogonal decomposition provided by the present invention.

[0163] Table 1 Performance comparison of measurement points

[0164]

[0165] Under the condition that the number of random sound velocity profile measurement points is 200, the three-dimensional ocean sound velocity from day 21 to day 30 is predicted, and the results are shown in Table 2. From the results in Table 2, it can be seen that the three-dimensional ocean sound velocity prediction method based on tensor empirical orthogonal decomposition provided by the present invention can effectively predict the ocean sound velocity in the medium and long term.

[0166] Table 2 Comparison of prediction time performance

[0167]

[0168] See also Figure 5 The embodiment of the present invention further provides a three-dimensional ocean sound speed prediction device 500 based on tensor empirical orthogonal decomposition, comprising:

[0169] A first construction module 501 is used to construct a three-dimensional sound speed measurement tensor and a weight tensor based on the sound speed measurement data in the target area, wherein the position in the target area where the sound speed measurement data is located is a first position, and the position in the target area where the sound speed measurement data is not located is a second position, the value corresponding to the first position in the three-dimensional sound speed measurement tensor is the sound speed measurement value of the first position, the value corresponding to the second position in the three-dimensional sound speed measurement tensor is 0, the value corresponding to the first position in the weight tensor is 1, and the value corresponding to the second position in the weight tensor is 0;

[0170] A determination module 502 is used to determine an optimal basis function feature matrix set, wherein the optimal basis function feature matrix set includes an optimal basis function feature matrix in a longitude direction, an optimal basis function feature matrix in a latitude direction, and an optimal basis function feature matrix in a depth direction;

[0171] A second construction module 503 is used to construct a three-dimensional sound speed tensor prediction calculation function based on the three-dimensional sound speed measurement tensor, the weight tensor and the optimal basis function characteristic matrix set;

[0172] The solving module 504 is used to iteratively solve the three-dimensional sound speed tensor prediction calculation function based on the tensor gradient descent method to obtain the sound speed prediction value of the second position.

[0173] Optionally, the three-dimensional sound velocity tensor prediction calculation function is:

[0174]

[0175] in, is the three-dimensional sound velocity measurement tensor, is the weight tensor, is the core tensor, the core tensor is The tensor composed of the projection coefficients on the optimal basis function feature matrix set, U Lon ′ is the optimal basis function characteristic matrix in the longitude direction, U Lat ′ is the optimal basis function characteristic matrix in the latitude direction, U Dep ′ is the optimal basis function feature matrix in the depth direction, is the regularization term, λ is the regularization parameter, ×1 represents the 1-mode product of the tensor and the matrix, ×2 represents the 2-mode product of the tensor and the matrix, and ×3 represents the 3-mode product of the tensor and the matrix. represents the Hadamard product, argmin represents the core tensor corresponding to the minimum value of the function, represents the Frobenius norm, ‖·‖ 2 Represents the square of the tensor's magnitude.

[0176] Optionally, the solution module 504 includes:

[0177] A first determining unit, used to determine an initial value of iteration of the core tensor;

[0178] A calculation unit, used for calculating the gradient of the three-dimensional sound speed tensor prediction calculation function with respect to the core tensor;

[0179] An iterative calculation unit, configured to perform multiple iterative calculations based on the gradient of the core tensor and the iteration initial value, obtain the core tensor of the kth iteration at the kth iteration, and calculate the predicted value of the kth iteration and the prediction error of the kth iteration based on the core tensor of the kth iteration and the optimal basis function feature matrix set;

[0180] The second determination unit is used to determine the predicted value of the kth iteration as the predicted value of the sound speed at the second position when the iteration number k is equal to the maximum iteration number or the prediction error is less than or equal to a threshold, where k is a positive integer.

[0181] Optionally, the iteration initial value for:

[0182]

[0183] The gradient of the core tensor for:

[0184]

[0185] The core tensor obtained at the kth iteration for:

[0186]

[0187] The predicted value of the kth iteration for:

[0188]

[0189] The prediction error Err of the kth iteration is:

[0190]

[0191] Among them, α is the iteration step size.

[0192] Optionally, the determining module 502 includes:

[0193] A construction unit, used to construct a three-dimensional ocean sound speed prediction system, wherein the three-dimensional ocean sound speed prediction system includes an ocean sound speed tensor representation module, a tensor feature extraction module, and a three-dimensional sound speed prediction calculation module;

[0194] A training unit, used to train the tensor feature extraction module and the three-dimensional sound speed prediction calculation module using training sample data to obtain a trained three-dimensional ocean sound speed prediction system;

[0195] A third determination unit is used to test the trained three-dimensional ocean sound speed prediction system using verification sample data, and determine 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 according to the prediction performance;

[0196] Among them, the ocean sound speed tensor representation module is used to store sound speed measurement data in tensor form, the tensor feature extraction module is used to obtain a basis function feature matrix set and a model order set, the basis function feature matrix set includes a basis function feature matrix in the longitude direction, a basis function feature matrix in the latitude direction and a basis function feature matrix in the depth direction, the model order set includes a model order in the longitude direction, a model order in the latitude direction and a model order in the depth direction, and the three-dimensional sound speed prediction calculation module is used to predict the sound speed based on the basis function feature matrix set, the model order set and the sound speed measurement data.

[0197] Optionally, the training unit is specifically used for:

[0198] Acquire the training sample data and the verification sample data and store them in the ocean sound speed tensor representation module in tensor form;

[0199] Input the training sample data into the tensor feature extraction module to obtain a basis function feature matrix set and a model order set corresponding to the training sample data;

[0200] The basis function feature matrix set and the model order set corresponding to the training sample data are input into the three-dimensional sound speed prediction calculation module, and the sound speed is predicted by using the tensor gradient descent method in combination with the training sample data to obtain a prediction result.

[0201] Optionally, inputting the training sample data into the tensor feature extraction module to obtain a basis function feature matrix set and a model order set corresponding to the training sample data includes:

[0202] The training sample data is subjected to tensor orthogonal decomposition, and the decomposed training sample data for:

[0203]

[0204] Among them, U Lon is the basis function feature matrix in the longitude direction corresponding to the training sample data, U Lat is the basis function feature matrix in the latitude direction corresponding to the training sample data, U Dep is the basis function feature matrix in the depth direction corresponding to the training sample data, U Time is the basis function feature matrix in the time direction corresponding to the training sample data, It is the core tensor corresponding to the training sample data.

[0205] The three-dimensional ocean sound speed prediction device 500 based on tensor empirical orthogonal decomposition provided in the embodiment of the present application can execute the above method embodiment, and its implementation principle and technical effect are similar, which will not be repeated in this embodiment.

[0206] It should be noted that the division of units in the embodiments of the present application is schematic and is only a logical function division. There may be other division methods in actual implementation. In addition, each functional unit in each embodiment of the present application may be integrated into a processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0207] If the integrated unit is implemented in the form of 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 the present application is essentially 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, and the computer software product is stored in a storage medium, including a number of instructions to enable a computer device (which can be a personal computer, server, or network device, etc.) or a processor (processor) to perform all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (Read-Only Memory, ROM), random access memory (Random Access Memory, RAM), disk or optical disk and other media that can store program codes.

[0208] like Figure 6 As shown, an embodiment of the present application provides an electronic device 600, comprising: 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 speed prediction method based on tensor empirical orthogonal decomposition as described above.

[0209] An embodiment of the present application also provides a readable storage medium, on which a program is stored. When the program is executed by a processor, the various processes of the above-mentioned three-dimensional ocean sound speed prediction method embodiment based on tensor empirical orthogonal decomposition are implemented, and the same technical effect can be achieved. To avoid repetition, it will not be repeated here. Among them, the readable storage medium can be any available medium or data storage device that can be accessed by the processor, including but not limited to magnetic storage (such as floppy disk, hard disk, magnetic tape, magneto-optical disk (MO), etc.), optical storage (such as compact disk (CD), digital video disk (DVD), Blu-ray Disc (BD), high-definition versatile disc (HVD), etc.), and semiconductor memory (such as read-only memory (ROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read only memory (EEPROM), non-volatile memory (NAND FLASH), solid-state drive (Solid State Disk or Solid State Drive, SSD)), etc.

[0210] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0211] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform, and of course by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, disk, CD), and includes a number of instructions for a terminal (which can be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in each embodiment of the present application.

[0212] The embodiments of the present application are described above in conjunction with the accompanying drawings, but the present application is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present application, ordinary technicians in this field can also make many forms without departing from the purpose of the present application and the scope of protection of the claims, all of which are within the protection of the present application.

Claims

1. A three-dimensional ocean sound speed prediction method based on tensor empirical orthogonal decomposition, characterized in that: include: Constructing a three-dimensional sound speed measurement tensor and a weight tensor based on the sound speed measurement data in the target area, wherein the position in the target area where the sound speed measurement data is located is a first position, and the position in the target area where the sound speed measurement data is not located is a second position, the value corresponding to the first position in the three-dimensional sound speed measurement tensor is the sound speed measurement value of the first position, the value corresponding to the second position in the three-dimensional sound speed measurement tensor is 0, the value corresponding to the first position in the weight tensor is 1, and the value corresponding to the second position in the weight tensor is 0; Determine an optimal basis function feature matrix set, wherein the optimal basis function feature matrix set includes an optimal basis function feature matrix in a longitude direction, an optimal basis function feature matrix in a latitude direction, and an optimal basis function feature matrix in a depth direction; Constructing a three-dimensional sound speed tensor prediction calculation function based on the three-dimensional sound speed measurement tensor, the weight tensor and the optimal basis function characteristic matrix set; The three-dimensional sound speed tensor prediction calculation function is iteratively solved based on the tensor gradient descent method to obtain a predicted sound speed value at the second position.

2. The method according to claim 1, characterized in that: The three-dimensional sound velocity tensor prediction calculation function is: in, is the three-dimensional sound velocity measurement tensor, is the weight tensor, is the core tensor, the core tensor is The tensor composed of the projection coefficients on the optimal basis function feature matrix set, U Lon ′ is the optimal basis function characteristic matrix in the longitude direction, U Lat ′ is the optimal basis function characteristic matrix in the latitude direction, U Dep ′ is the optimal basis function feature matrix in the depth direction, is the regularization term, λ is the regularization parameter, ×1 represents the 1-mode product of the tensor and the matrix, ×2 represents the 2-mode product of the tensor and the matrix, and ×3 represents the 3-mode product of the tensor and the matrix. represents the Hadamard product, argmin represents the core tensor corresponding to the minimum value of the function, represents the Frobenius norm, ‖·‖ 2 Represents the square of the tensor's magnitude.

3. The method according to claim 2, characterized in that: The iteratively solving the three-dimensional sound speed tensor prediction calculation function based on the tensor gradient descent method to obtain the sound speed prediction value of the second position includes: Determining an initial value of iteration of the core tensor; Calculating the gradient of the three-dimensional sound speed tensor prediction calculation function with respect to the core tensor; Perform multiple iterative calculations based on the gradient of the core tensor and the iteration initial value, obtain the core tensor of the kth iteration at the kth iteration, and calculate the predicted value of the kth iteration and the prediction error of the kth iteration based on the core tensor of the kth iteration and the optimal basis function feature matrix set; When the number of iterations k is equal to the maximum number of iterations or the prediction error is less than or equal to a threshold, the prediction value of the kth iteration is determined as the predicted value of the sound speed at the second position, where k is a positive integer.

4. The method according to claim 3, characterized in that: The initial value c0 of the iteration is: The gradient of the core tensor for: The core tensor obtained at the kth iteration for: The predicted value of the kth iteration for: The prediction error Err of the kth iteration is: Among them, α is the iteration step size.

5. The method according to claim 1, characterized in that: The step of determining the optimal basis function feature matrix set comprises: Constructing a three-dimensional ocean sound speed prediction system, the three-dimensional ocean sound speed prediction system comprising an ocean sound speed tensor representation module, a tensor feature extraction module and a three-dimensional sound speed prediction calculation module; Using training sample data to train the tensor feature extraction module and the three-dimensional sound speed prediction calculation module to obtain a trained three-dimensional ocean sound speed prediction system; The trained three-dimensional ocean sound speed prediction system is tested using verification sample data, and 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 according to the prediction performance; Among them, the ocean sound speed tensor representation module is used to store sound speed measurement data in tensor form, the tensor feature extraction module is used to obtain a basis function feature matrix set and a model order set, the basis function feature matrix set includes a basis function feature matrix in the longitude direction, a basis function feature matrix in the latitude direction and a basis function feature matrix in the depth direction, the model order set includes a model order in the longitude direction, a model order in the latitude direction and a model order in the depth direction, and the three-dimensional sound speed prediction calculation module is used to predict the sound speed based on the basis function feature matrix set, the model order set and the sound speed measurement data.

6. The method according to claim 5, characterized in that: The method of using the training sample data to train the tensor feature extraction module and the three-dimensional sound speed prediction calculation module to obtain a trained three-dimensional ocean sound speed prediction system includes: Acquire the training sample data and the verification sample data and store them in the ocean sound speed tensor representation module in tensor form; Input the training sample data into the tensor feature extraction module to obtain a basis function feature matrix set and a model order set corresponding to the training sample data; The basis function feature matrix set and the model order set corresponding to the training sample data are input into the three-dimensional sound speed prediction calculation module, and the sound speed is predicted by using the tensor gradient descent method in combination with the training sample data to obtain a prediction result.

7. The method according to claim 6, characterized in that: The step of inputting the training sample data into the tensor feature extraction module to obtain a basis function feature matrix set and a model order set corresponding to the training sample data includes: The training sample data is subjected to tensor orthogonal decomposition, and the decomposed training sample data for: Among them, U Lon is the basis function feature matrix in the longitude direction corresponding to the training sample data, U Lat is the basis function feature matrix in the latitude direction corresponding to the training sample data, U Dep is the basis function feature matrix in the depth direction corresponding to the training sample data, It is the core tensor corresponding to the training sample data.

8. A three-dimensional ocean sound speed prediction device based on tensor empirical orthogonal decomposition, characterized in that: include: A first construction module is used to construct a three-dimensional sound speed measurement tensor and a weight tensor based on the sound speed measurement data in the target area, wherein the position in the target area where the sound speed measurement data is located is a first position, and the position in the target area where the sound speed measurement data is not located is a second position, the value corresponding to the first position in the three-dimensional sound speed measurement tensor is the sound speed measurement value of the first position, the value corresponding to the second position in the three-dimensional sound speed measurement tensor is 0, the value corresponding to the first position in the weight tensor is 1, and the value corresponding to the second position in the weight tensor is 0; A determination module, used to determine an optimal basis function feature matrix set, wherein the optimal basis function feature matrix set includes an optimal basis function feature matrix in a longitude direction, an optimal basis function feature matrix in a latitude direction, and an optimal basis function feature matrix in a depth direction; A second construction module is used to construct a three-dimensional sound speed tensor prediction calculation function based on the three-dimensional sound speed measurement tensor, the weight tensor and the optimal basis function characteristic matrix set; A solution module is used to iteratively solve the three-dimensional sound speed tensor prediction calculation function based on the tensor gradient descent method to obtain the sound speed prediction value of the second position.

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

10. A readable storage medium for storing a program, characterized in that: When the program is executed by a processor, the steps of the three-dimensional ocean sound speed prediction method based on tensor empirical orthogonal decomposition as claimed in any one of claims 1 to 7 are implemented.

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