Physical information fused sparse ocean sound velocity field tensor reconstruction method

Abstract

The invention discloses a sparse ocean sound velocity field tensor reconstruction method fusing physical information, and the method comprises the following steps: considering the distribution rule of a three-dimensional ocean sound velocity field, and building sparse ocean sound velocity tensor data of different sampling points at different depths; a temperature depth weight matrix is constructed based on ocean sound velocity physical information, and errors caused by pure tensor reconstruction are restrained through a space variable projection operator; applying smoothing to the sound velocity local gradient amplitude by adopting isotropic total variation, and establishing a marine sound velocity field reconstruction model based on a frame transformation tensor under physical information constraint; and inputting the sparse ocean sound velocity tensor data into the ocean sound velocity field reconstruction model for solving, and outputting a reconstructed three-dimensional ocean sound velocity field. According to spatial distribution characteristics of the ocean sound velocity field, high efficiency of data driving and interpretability of a physical model are fully utilized, sound velocity physical information is fused into the tensor model, three-dimensional reconstruction is carried out on the ocean sound velocity field of an unmeasured area, and the processing capacity of ocean basic information is improved.

Description

Technical Field

[0001] This invention belongs to the field of marine acoustic measurement, specifically a sparse marine sound velocity field tensor reconstruction method that integrates physical information. Background Technology

[0002] Ocean sound speed, as a fundamental physical parameter for sound wave propagation, has its spatial distribution—the sound speed field—that forms the basis for underwater integrated positioning, navigation, and timing. Ocean sound speed is closely related to seawater temperature, salinity, and pressure, and is often indirectly calculated using empirical formulas. Existing sound speed reconstruction methods can be mainly divided into three categories: direct measurement, indirect inversion, and model prediction. Direct measurement based on sound velocity profilers can obtain absolute sound speeds across the entire ocean depth, but it is inefficient and cannot cover unmeasured areas in the open ocean. Indirect inversion based on acoustic signal characteristics can provide sound field information for unmeasured areas, but it is difficult to reflect instantaneous sound speed changes and has significant errors in some areas. Model prediction based on artificial intelligence has high reconstruction accuracy, but it relies on high-quality training data and struggles to handle shallow wave conditions. Considering the significant spatiotemporal variation characteristics of the ocean sound speed field—multi-scale in the time dimension and three-dimensional heterogeneity in the spatial dimension—only partial ocean sound speed fields can be obtained, resulting in problems such as difficulty in reflecting instantaneous sound speeds, inability to cover unmeasured areas, and a lack of physical interpretability.

[0003] Relying on directly measured sound velocity is insufficient to provide information on the sound field in unmeasured deep-sea areas, while relying on indirect sound velocity reconstruction faces the problem of missing measured data. To improve the information acquisition and processing capabilities in ocean three-dimensional observation, and considering both the cost of sound velocity measurement and reconstruction accuracy, combining physical empirical models with indirect reconstruction methods is significant for reconstructing ocean sound velocity fields under sparse sampling. Summary of the Invention

[0004] Purpose of the invention: To address the problems of limited available sound velocity data and high measurement costs in ocean sound velocity reconstruction, this invention proposes a sparse ocean sound velocity field tensor reconstruction method that integrates physical information.

[0005] Technical solution: A sparse ocean sound velocity field tensor reconstruction method incorporating physical information, comprising the following steps:

[0006] Considering the distribution pattern of the three-dimensional ocean sound velocity field, sparse ocean sound velocity tensor data at different depths and sampling points are established;

[0007] A temperature-depth weight matrix is ​​constructed based on ocean sound velocity physical information, and the error caused by pure tensor reconstruction is constrained by a spatially variable projection operator.

[0008] An isotropic total variation is used to smooth the magnitude of the local gradient of sound velocity;

[0009] The application discloses a marine sound speed field reconstruction model based on frame transformation tensors under physical information constraints.

[0010] The marine sound speed data is input into the marine sound speed field reconstruction model for solving, and three-dimensional marine sound speed field data after reconstruction is output.

[0011] Further, the sparse marine sound speed tensor data of different depths and different sampling points is established by considering the distribution law of the three-dimensional marine sound speed field, and is expressed as: Wherein , and respectively represent the tangent planes perpendicular to the three-dimensional , and . The marine sound speed value of different depths and different sampling points is represented.

[0012] Further, the temperature-depth weight matrix is constructed based on the marine sound speed physical information, and specifically includes: Based on the marine sound speed physical information, the total gradient of the marine sound speed to temperature and depth is:

[0013] In the formula, , and respectively represent the marine sound speed, temperature and depth; the gradient derivative of the marine sound speed to temperature is , the gradient derivative of the marine sound speed to depth is , and the gradient derivative of the temperature to depth is . The weight matrix based on the marine sound speed physical information is used to constrain the update variable in the updating process and is applied to the updated tensor for correction so as to make the updated tensor comply with more actual physical laws; the tensor composed of the weight matrix based on the marine sound speed physical information is expressed as The expression is

[0014] In the formula, represents the Hadamard product; represents the sound speed correction vector, and the correction matrix is copied along the row direction to be a homomorphism matrix of the sound speed basic matrix , so that the sound speed basic matrix is obtained. is a strength constraint, and respectively represent a linearly decreasing column vector and a linearly decreasing row vector in two horizontal directions; represents the Kronecker product of two vectors; , The strength constraint is based on a physical empirical formula of sound speed.

[0015] Further, the error caused by the pure tensor reconstruction constrained by the spatially variable projection operator is represented as:

[0016] In the formula: The projection operator is represented as P, The prior ocean sound speed tensor is represented as C0; The weight constraint matrix composed of the sound speed physical empirical formula is represented as W, The prior ocean sound speed layer is represented as C0; The first-order forward difference operator of the ocean sound speed tensor in the water sound depth direction is represented as The first-order forward difference operator of the ocean sound speed tensor in the water sound depth direction is represented as The reconstructed layer.

[0017] Further, the isotropic total variation is used to impose smoothing on the local gradient amplitude of the sound speed, which is represented as:

[0018] In the formula: The isotropic total variation regularization constraint on the sound speed tensor is represented as The mixed norm based on and is represented as The norm calculation formula , The norm calculation formula is ; , and respectively represent the first-order forward difference operator of the ocean sound speed tensor along the three-dimensional , and directions. .

[0019] Further, the ocean sound speed field reconstruction model based on the frame transformation tensor under the physical information constraint is established, which is represented as:

[0020] In the formula: The tensor kernel norm based on the frame transformation is represented as The weight coefficient is represented as

[0021] Further, the sparse ocean sound speed tensor data is input into the ocean sound speed field reconstruction model for solving, and the reconstructed three-dimensional ocean sound speed field data is output, which specifically includes: The reconstruction model of ocean sound speed field is transformed into an unconstrained form as

[0022] where ; denotes the frame-transformed ocean sound speed tensor operator The two-dimensional sound speed field slice of the th layer is denoted as An auxiliary variable , and are introduced to perform variable separation, and we have

[0023] where is the mixed norm of the total variation tensor , where represents the operations on the horizontal , and vertical directions, respectively;

[0024] The above equation is transformed into the augmented Lagrangian function form as

[0025]

[0026] where denotes the Frobenius norm; , and denote the Lagrange multipliers, and where also represents the operations on the , , directions, respectively; , and denote the penalty parameters;

[0027] The variables, including the auxiliary variable of the ocean sound speed tensor and the auxiliary variable of the isotropic total variation tensor , are iteratively updated by the alternating direction method of multipliers (ADMM) as

[0028]

[0029]

[0030] The ocean sound speed tensor is updated as

[0031]

[0032] Isotropic total variation tensor Update to:

[0033]

[0034] Lagrange multiplier , and The update formula is:

[0035]

[0036] Iterative update of variables , , and Output the reconstructed three-dimensional ocean sound speed field tensor .

[0037] Beneficial effects: the application discloses a sparse ocean sound speed field tensor reconstruction method fusing physical information, considers the distribution law of three-dimensional ocean sound speed field, establishes sparse ocean sound speed tensor data of different depths and different sampling points; constructs a temperature-depth weight matrix based on sound speed physical information, and constrains the error caused by pure tensor reconstruction through a spatial variable projection operator; frame transformation is introduced in the tensor kernel norm for constraint, isotropic total variation is used to smooth the sound speed local gradient amplitude; an ocean sound speed field reconstruction model based on frame transformation tensor under the constraint of physical information is established, and the model is solved to complete the tensor reconstruction of three-dimensional ocean sound speed field. Although the distribution of the ocean sound speed field is different from that of the image data, the related idea of tensor reconstruction in the image processing field can provide strong reference for three-dimensional reconstruction of the ocean sound speed field. As a high-order extension of the matrix, the tensor can maintain the original structure of the data and represent and mine data with high-dimensional correlation characteristics, and can be used for ocean sound speed reconstruction based on the tensor drive. Through the above technical means, the application has the following advantages:

[0038] (1) Limited by the complex observation density of the ocean, the detection depth and the sampling cost, the application can reconstruct the sound speed of the missing sea area based on the sparse sampling sound speed data.

[0039] (2) The application introduces the tensor completion method into the ocean sound speed reconstruction, which can maintain the original structure of the ocean sound speed data and represent and mine data with high-dimensional correlation characteristics.

[0040] (3) The application considers the spatial and temporal dynamic changes of the ocean sound speed data and needs to maintain the physical interpretability, and performs three-dimensional reconstruction of the ocean sound speed field in the unmeasured area by fusing the sound speed physical information and the tensor model;

[0041] (4) The present application is directed to the characteristics of the spatial distribution of the ocean sound speed field, fully utilizes the high efficiency of data-driven and the interpretability of physical models, and through the fusion of sound speed physical information and tensor model, performs three-dimensional reconstruction of the ocean sound speed field in the unmeasured area, and improves the information acquisition and processing capability in the marine three-dimensional observation. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 A three-dimensional ocean sound speed field tensor reconstruction principle diagram fusing physical information is proposed for the present application;

[0043] Figure 2 A three-dimensional ocean sound speed field tensor missing reconstruction diagram fusing physical information is proposed for the present application;

[0044] Figure 3 A three-dimensional ocean sound speed field tensor depth reconstruction diagram fusing physical information is proposed for the present application. DETAILED DESCRIPTION

[0045] The technical solutions of the present application will be further described in combination with the drawings and embodiments.

[0046] The embodiment of the present application proposes a sparse ocean sound speed field tensor reconstruction method fusing physical information. Considering the problems of complex observation density, detection depth and sampling cost of the ocean, the sound speed reconstruction based on sparse data is difficult to depict the spatio-temporal dynamic change and lacks physical interpretability. The method fully utilizes the high efficiency of data-driven and the interpretability of physical models, and establishes a reconstruction model based on frame transformation tensor driven by fusing the ocean sound speed physical information. Specifically, the method includes the following steps:

[0047] Step 1: Establishing sparse ocean sound speed tensor data at different depths and different sampling points, constructing a temperature-depth weight matrix based on sound speed physical information, and constraining the error caused by pure tensor reconstruction through a spatially variable projection operator. Specifically, the method includes the following sub-steps:

[0048] S100: Model the three-dimensional ocean sound speed data as a tensor , wherein , and respectively represent the tangent planes perpendicular to the three-dimensional , and ; represents the ocean sound speed value at different positions underwater. The underwater sound depth direction is reconstructed based on the prior ocean sound speed layer to reconstruct the ocean sound speed of the deeper layer.

[0049] S110: The unknown depth can be effectively reconstructed based on the ocean sound speed tensor. To ensure the efficiency and interpretability of the model, a weight matrix based on the physical information of sound speed is introduced to constrain the result of each layer of the updated sound speed field.

[0050] Based on the physical information of ocean sound speed, the total gradient of ocean sound speed with respect to temperature and depth is:

[0051]

[0052] In the formula: , and respectively represent the ocean sound speed, temperature and depth. The gradient derivative of ocean sound speed with respect to temperature is , the gradient derivative of ocean sound speed with respect to depth is , and the gradient derivative of temperature with respect to is .

[0053] The weight matrix based on the physical information of sound speed is used to constrain the updated variable in the updating process and is applied to the updated tensor to correct it to comply with more realistic physical laws. The weight matrix based on the physical information of sound speed is composed of a tensor The expression is

[0054]

[0055] In the formula: represents the Hadamard product; represents the sound speed correction vector. The correction matrix is copied along the row direction to be the same type matrix of the sound speed base matrix , and the sound speed correction vector can be obtained. Among them, , is the intensity constraint, and respectively represent the linearly decreasing column vector and row vector in the horizontal direction; represents the Kronecker product of two vectors; , is the intensity constraint based on the physical empirical formula of sound speed.

[0056] The spatially variable projection operator used for constraint is

[0057]

[0058] In the formula: represents the projection operator; represents the prior ocean sound speed tensor; It represents a tensor composed of weight constraint matrices based on the physical empirical formula of sound speed. The reconstruction is more consistent with the sound speed field distribution by weight matrix constraint.

[0059] Step 2: Introduce frame transformation in the tensor kernel norm for constraint, and apply isotropic total variation to the local gradient amplitude of sound speed to impose smoothing, which includes the following steps:

[0060] S200: Introduce isotropic total variation regularization constraint of sound speed tensor to maintain the smoothness of the reconstructed sound speed field, and the introduced isotropic total variation regularization constraint is defined as follows:

[0061]

[0062] In the formula: represents the isotropic total variation regularization constraint of the sound speed tensor; represents the mixed norm based on and , wherein The norm calculation formula , The norm calculation formula is . , and respectively represent the first-order forward difference operator of the marine sound speed tensor along the three-dimensional , and directions are

[0063]

[0064] S210: The modulus of the gradient vector of marine sound speed at different positions represents the change of sound speed. By introducing isotropic total variation regularization, the modulus of the gradient vector of sound speed at each position is calculated, which can process sound speed data in any direction while preserving the characteristics of sound speed, and the distribution characteristics of sound speed are maintained to the greatest extent. Introducing isotropic total variation regularization as a constraint, the marine sound speed distribution tensor reconstruction model based on sound speed physical information is established as

[0065]

[0066] In the formula: represents the tensor kernel norm based on frame transformation; represents the weight coefficient.

[0067] Step 3: Establish marine sound speed field reconstruction model based on frame transformation tensor under physical information constraint, complete the tensor reconstruction of three-dimensional marine sound speed field, which includes the following steps:

[0068] S300: The ocean sound speed distribution tensor reconstruction model based on the sound speed physical information is converted into an unconstrained form as:

[0069]

[0070] wherein: ; represents the ocean sound speed tensor operator after frame transformation In the first layer, the two-dimensional sound speed field slice is obtained.

[0071] S310: Introducing auxiliary variables , and Variable separation can be obtained

[0072]

[0073] wherein: is the mixed norm of the total variation tensor , in which represents the operation on the horizontal , and vertical three directions respectively.

[0074] The above formula is converted into the augmented Lagrangian function form as

[0075]

[0076] wherein: represents the Frobenius norm; , and represent the Lagrange multipliers, in which also represent the operation on the , , three directions respectively; , and represent the penalty parameters.

[0077] S320: The variables are iteratively updated by the alternating direction multiplier method. The auxiliary variable of the ocean sound speed tensor and the auxiliary variable of the isotropic total variation tensor are updated to

[0078]

[0079] ​

[0080] Ocean acoustic velocity tensor is updated as

[0081]

[0082] Isotropic total variation tensor is updated as

[0083]

[0084] Lagrange multiplier , and is updated as

[0085]

[0086] is iteratively updated in sequence , , and , and the reconstructed three-dimensional ocean acoustic velocity tensor is output.

[0087] The specific solving process is as follows:

[0088] 1. Fixing other variables, the variable is updated. Its closed-form solution is obtained by a singular value threshold algorithm as

[0089]

[0090] In the formula: .

[0091] 2. Fixing other variables, the variable is updated. The auxiliary variable is calculated as

[0092]

[0093] The derivative of the above formula is taken and set to 0, and

[0094]

[0095] In the formula: denotes the divergence operator. In the ocean acoustic velocity field, the divergence operator is the adjoint operator of the gradient operator, and . Therefore, , where ; denotes the tensor product; . The updated is obtained by solving the three-dimensional frequency response

[0096]

[0097] 3. Fixing other variables, updating variable . Convert it to matrix form by modulo-3 expansion, and based on the unitary extension principle, we can get

[0098]

[0099] In the formula: The sound velocity tensor of modulo-3 expansion . The derivative of the latter half is taken and set to zero to get

[0100]

[0101] Expanding the above formula to the back can get:

[0102]

[0103] Since It can be simplified to a unit matrix, and the updated sound velocity tensor is:

[0104]

[0105] 4. Fixing other variables, updating variable . Variable can be written as

[0106]

[0107] For each position , its optimal solution can be obtained by the shrinkage formula:

[0108]

[0109] In the formula: , , and respectively represent the first entry in the auxiliary variable. The Lagrange multiplier can be obtained by updating the slice in three directions respectively.

[0110] Iterative updating of variables , , and in turn can get the reconstructed ocean sound velocity tensor .

[0111] Figure 2 and Figure 3This demonstrates the reconstruction errors of the sound velocity field sampling rate and depth under different conditions according to embodiments of the present invention. Figure 2 The paper demonstrates the reconstruction errors of the sound velocity field at a depth of 90m with 10%, 30%, and 50% sampling. Verification shows that the method proposed in this embodiment of the invention has a good effect on the reconstruction of the sampled sound velocity field. The reconstruction errors at 10%, 30%, and 50% sampling are 0.154 m / s, 0.079 m / s, and 0.037 m / s, respectively. This is attributed to the utilization of the multi-scale nature of the three-dimensional tensor by wavelet frame transform and the smoothing effect of isotropic total variation in the reconstruction process. Therefore, this embodiment of the invention is effective in reconstructing the sound velocity field.

[0112] exist Figure 3 The paper demonstrates the reconstruction error of a 10m sound velocity field with a known prior depth. The errors in reconstructing the sound velocity field to a deeper depth of 10m are 0.863 m / s, 0.526 m / s, 0.615 m / s, and 0.834 m / s, respectively, given depths of 140m, 150m, 160m, and 170m. Although the error distribution is relatively stable, some differences still exist.

Claims

1. A sparse ocean sound velocity field tensor reconstruction method incorporating physical information, characterized in that: Includes the following steps: Considering the distribution pattern of the three-dimensional ocean sound velocity field, sparse ocean sound velocity tensor data at different depths and sampling points are established; A temperature-depth weight matrix is ​​constructed based on ocean sound velocity physical information, and the error caused by pure tensor reconstruction is constrained by a spatially variable projection operator. An isotropic total variation is used to smooth the magnitude of the local gradient of sound velocity; A model for reconstructing the ocean sound velocity field based on frame transform tensor under physical information constraints was established. Sparse ocean sound velocity tensor data are input into the ocean sound velocity field reconstruction model for solution, and the reconstructed three-dimensional ocean sound velocity field data is output.

2. The sparse ocean sound velocity field tensor reconstruction method fusing physical information according to claim 1, characterized in that: The aforementioned consideration of the distribution pattern of the three-dimensional ocean sound velocity field, establishing sparse ocean sound velocity tensor data at different depths and sampling points, is expressed as follows: ,in , and Representing perpendicular to three dimensions , and The cross-section; This represents the ocean sound velocity values ​​at different depths and sampling points.

3. The sparse ocean sound velocity field tensor reconstruction method fusing physical information according to claim 2, characterized in that: The aforementioned construction of a temperature-depth weighting matrix based on ocean sound velocity physical information specifically includes: Based on physical information about ocean sound speed, the total gradient of ocean sound speed with respect to temperature and depth is: In the formula: , and Let represent the ocean's sound speed, temperature, and depth, respectively; the derivative of the ocean's sound speed with respect to temperature is... The gradient derivative of ocean sound speed with respect to depth is The gradient derivative of temperature with respect to depth is ; The weight matrix based on ocean sound velocity physical information constrains the updated variables during the update process and applies it to the updated tensor to correct it to conform to more realistic physical laws. The tensor composed of the weight matrix based on ocean sound velocity physical information... The expression is In the formula: Represents the Hadamard product; Represents the sound speed correction vector, correction matrix Copy as the sound speed fundamental matrix along the row direction From the same type of matrix, we obtain the fundamental matrix of the speed of sound. , For strength constraints, and These represent column vectors and row vectors that decrease linearly in the horizontal direction, respectively. Represents the Kronecker product of two vectors; , This is a strength constraint based on the empirical formula for the speed of sound.

4. The sparse ocean sound velocity field tensor reconstruction method incorporating physical information according to claim 3, characterized in that: The method of constraining the error caused by pure tensor reconstruction using the spatially variable projection operator is expressed as follows: In the formula: Represents the projection operator. Represents the a priori ocean sound velocity tensor; This represents a tensor composed of weight constraint matrices based on empirical formulas for the speed of sound. This represents the a priori oceanic sound velocity layer. Indicates the direction of underwater acoustic depth Based on prior ocean sound velocity layer Reconstructed layer.

5. The sparse ocean sound velocity field tensor reconstruction method fusing physical information according to claim 4, characterized in that: The method of applying smoothing to the local gradient magnitude of sound velocity using isotropic total variation is expressed as follows: In the formula: This represents the isotropic total variational regularization constraint on the sound velocity tensor; Indicates based on and The mixture norm, where Norm calculation formula , The formula for calculating the norm is: ; , and Represent the ocean sound speed tensor along three dimensions , and The first-order forward difference operator in the direction is 。 6. The sparse ocean sound velocity field tensor reconstruction method incorporating physical information according to claim 5, characterized in that: The aforementioned model for reconstructing the ocean sound velocity field based on the frame transform tensor under physical information constraints is expressed as follows: In the formula: Represents the tensor nuclear norm based on frame transform; This represents the weighting coefficient.

7. The sparse ocean sound velocity field tensor reconstruction method fusing physical information according to claim 6, characterized in that: The process of inputting sparse ocean sound velocity tensor data into an ocean sound velocity field reconstruction model for solution, and outputting reconstructed three-dimensional ocean sound velocity field data, specifically includes: The ocean sound velocity field reconstruction model is transformed into an unconstrained form as follows: In the formula: ; Represents the ocean sound velocity tensor operator after frame transformation In the Two-dimensional sound velocity field slice of the layer; Introducing auxiliary variables , and By separating the variables, we can obtain In the formula: For total variation tensors The mixed norm, middle Representatives respectively on the level , and vertical Operate in three directions; The above equation can be transformed into the augmented Lagrange function form as follows: In the formula: Denotes the Frobenius norm; , and Representing Lagrange multipliers, in middle Similarly, they represent respectively... , , Operate in three directions; , and Indicates the penalty parameter; The variables are iteratively updated using the alternating direction multiplier method, including the ocean sound speed tensor. Auxiliary variables and isotropic total variation tensor Auxiliary variables Updated to Ocean sound speed tensor Updated to: Isotropic total variation tensor Updated to: Lagrange multipliers , and Updated to: Variables in turn , , and Perform iterative updates and output the reconstructed three-dimensional ocean sound velocity field tensor. .

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