A method for reconstructing marine environmental field based on multi-stage interpolation method

Abstract

The embodiment of the application provides a marine environment field reconstruction method based on a multi-stage interpolation method. The method is used for multi-source data fusion of low-resolution grid environment field output by a marine dynamic model and high-precision data observed by a mobile node, and a high-resolution and high-precision marine environment field is obtained through multi-stage interpolation reconstruction. The multi-source data fusion is always carried out in a uniform grid, first, the mobile node observation data is fused into the low-resolution grid field output by the marine dynamic model through a mean substitution method to obtain a fused grid field. Then, a radial basis function (RBF) grid interpolation model is constructed to extract grid features, and the fused grid field is expanded and the grid interpolation model is used to fill in the grid attribute values to obtain an expanded grid field. Finally, the foregoing steps are repeated, and the high-resolution reconstruction of the marine environment field is completed through multi-stage iteration. The application has potential application value in improving the resolution and precision of the environment field in the multi-source environment field data fusion scene in the marine information field.

Description

Technical Field

[0001] This application relates to the field of marine information technology, and in particular to a method for reconstructing marine environmental fields based on multi-level interpolation. Background Technology

[0002] Sound waves are an effective carrier of information in the ocean and an indispensable tool for probing the ocean's interior. However, variations in the speed of sound in seawater cause refraction during their journey, affecting their propagation. Therefore, to accurately understand the propagation characteristics of sound waves to meet the research needs of underwater acoustic detection, remote sensing, and underwater communication, it is essential to better capture the uncertainties in sound speed and obtain comprehensive knowledge of the ocean environmental field.

[0003] Environmental factors affecting sound speed in the ocean mainly include water temperature, salinity, and pressure. Sound speed can be calculated using empirical formulas by combining temperature, salinity, and depth data. Methods for obtaining sound speed include direct instrument observation, sound propagation model inversion, and ocean dynamics model calculation. However, each method has its advantages and disadvantages: direct observation provides high-precision and high-resolution data, but can only obtain local, short-term temperature, salinity, and depth data; sound propagation models can efficiently invert and obtain sound speed, but can only obtain the sound speed along the propagation path and are sensitive to noise and model parameter mismatch; ocean dynamics models can model large-scale environmental field forecasts based on ocean dynamic processes, but are difficult to predict small- to medium-scale environmental field changes. Therefore, leveraging the advantages of multi-source data to achieve high-resolution reconstruction of the ocean environmental field is a particularly important research topic. Summary of the Invention

[0004] This invention addresses the shortcomings of existing technologies by providing a multi-level interpolation algorithm that integrates ocean dynamic models and ocean mobile node observation data to achieve high-resolution interpolation reconstruction of the ocean environmental field. The multi-level interpolation algorithm implements: grid data fusion, grid feature extraction, grid expansion, and multi-level iteration to complete high-resolution reconstruction.

[0005] This application provides a method for reconstructing a marine environmental field based on multi-level interpolation, including the following steps:

[0006] Step (1): The observation data from the moving node is fused into the grid output by the ocean dynamics model;

[0007] Step (2): Construct a radial basis function (RBF) mesh interpolation model to extract mesh features;

[0008] Step (3): Expand the mesh and interpolate to fill in the mesh attribute values;

[0009] Step (4) involves multi-level iterations to complete the high-resolution environmental field reconstruction.

[0010] In some embodiments, step (1) specifically includes:

[0011] Suppose that the ocean dynamics model outputs environmental field forecast data for a certain sea area with a uniform grid, and the grid point set T = {(x i ,f i ), i = 1, 2, ..., n}, where x i f represents the spatial coordinates of the i-th grid point. i Let Z represent the attribute values ​​(temperature, salinity, etc.) of this grid point; the mobile node samples along the planned path in this sea area, acquiring data such as temperature, salinity, and depth along the path. The set of observation points is denoted as Z = {(x...} i ,f i ), i = 1, 2, ..., m}, where x i f represents the spatial coordinates of the i-th observation point. i These are the attribute values ​​(temperature, salinity, etc.) of the observation point;

[0012] The mobile node observation data is fused with the grid field output from the ocean dynamics model. The specific fusion method is as follows: for model output grid points T containing nodal observation data... k ={x k ,f k}, using the set of all observation points Z within this grid k ={(x ki ,f ki The mean of attribute values ​​for {i = 1, 2, ..., p}

[0013]

[0014] Replace the grid property value f k For grids that do not contain observation data, the original data values ​​are maintained; the final result is the grid point set T′={(x i ,f i ),i=1,2,…,n}.

[0015] In some embodiments, step (2) specifically includes:

[0016] After completing the grid data fusion, an RBF grid interpolation model is constructed to extract grid features; the RBF grid interpolation model is: given a function φ:R in space + →R, for the set of n uniform grid data points T′={(x i ,f i Given the sequence {i = 1, 2, ..., n}, we need to find a function:

[0017]

[0018] Make it satisfy the interpolation condition:

[0019]

[0020] Where x k Let f(x) be any coordinate point in space. k ) represents the attribute value f corresponding to that point. k , ||x k -x i ||2 represents any coordinate point x k To merge grid point x i The Euclidean distance between them, w i The coefficients of the linear combination are the weights; φ(||x k -x i ||2) is x k At the center point x i The corresponding RBF basis function at that point takes the form of a quadratic function:

[0021]

[0022] Where σ is the variable shape parameter of RBF;

[0023] For the weighting coefficient w in the interpolation formula i The calculation involves substituting the fused grid point set T′ from step (1) into formula (1) to obtain the grid feature extraction equation, i.e., the interpolation expression:

[0024]

[0025] Where φ ji =φ(||x j -x i 2). Let the basis function matrix Weight vector Attribute vector The interpolation expression can then be simplified as follows:

[0026] Φw=f, (6)

[0027] By inverting the matrix, the weight components corresponding to the basis functions of each grid point can be calculated:

[0028] w = Φ -1 f. (7).

[0029] In some embodiments, step (3) specifically includes:

[0030] After obtaining the RBF interpolation coefficients w by solving the interpolation expression, the grid point set T′ is uniformly expanded in each dimension to obtain the expanded grid point set T. 1 ={(x i ,f i ),i=1,2,…,n1}; Expand the grid coordinates x iSubstituting into the RBF interpolation equation (3), the attribute value f of the grid point is obtained. i This enables the expansion of the grid point set T. 1 Population of attribute values.

[0031] In some embodiments, step (4) specifically includes:

[0032] Steps (1), (2), and (3) have completed the first-level expansion of the initial mesh and obtained the first-level interpolated mesh field T. 1 The expanded mesh T 1 As the initial grid, steps (1), (2), and (3) are repeated sequentially to perform data fusion, grid feature extraction, and grid expansion, further utilizing more mobile node observation information and integrating it into the new grid T. 1 The grid is further expanded; through multiple iterations, the grid is continuously expanded to achieve high-resolution, high-precision multi-level interpolation reconstruction of the marine environmental field.

[0033] The beneficial effects of this invention include:

[0034] (1) The present invention can realize the fusion of marine environmental field data from different sources, especially the fusion of mobile node observation data and marine dynamic model output data.

[0035] (2) The present invention can integrate mobile node observation data and ocean dynamic model output data to achieve high-resolution and high-precision reconstruction of the ocean environment field, thereby improving the accuracy of model forecasts.

[0036] (3) The high-resolution, high-precision environmental field reconstructed by the present invention can be used in multiple marine engineering fields such as path planning and sound field calculation.

[0037] (4) The present invention can gradually fuse data and expand the grid by adopting a multi-level iterative approach. Each iteration will incorporate the mobile node observation information to a greater extent in a smaller grid, thereby making full use of the high-precision data of the mobile node observation.

[0038] (5) The RBF basis function in the RBF interpolation model constructed by the present invention when performing multi-level interpolation is the distance correlation function between the observation point and the point to be estimated, which can make good use of the spatial correlation between data points to improve the interpolation accuracy.

[0039] (6) When performing multi-level interpolation, the present invention can use different RBF bases, which enables the selection of RBF basis functions with better grid feature extraction effect under different reconstruction data or scenarios, so as to improve the interpolation reconstruction accuracy. Attached Figure Description

[0040] The accompanying drawings illustrate, by way of example and not limitation, the various embodiments discussed herein.

[0041] Figure 1 This is a flowchart of the multi-level interpolation environmental field reconstruction process of the present invention;

[0042] Figures 2A to 2C This is a simplified grid change diagram illustrating the multi-level interpolation algorithm flow of the present invention;

[0043] Figure 3A and Figure 3B These are illustrations of the dynamic mode ROMS output field, downsampled ROMS output field, and sampled data from 5 mobile nodes, respectively, based on the simulation of the multi-level interpolation algorithm of this invention.

[0044] Figure 4A and Figure 4B These are the simulation results and error diagrams of the four-level reconstruction using the multi-level interpolation algorithm of this invention. Detailed Implementation

[0045] In order to gain a more detailed understanding of the features and technical content of the embodiments of this application, the implementation of the embodiments of this application will be described in detail below with reference to the accompanying drawings. The accompanying drawings are for reference and illustration only and are not intended to limit the embodiments of this application.

[0046] The algorithm of this invention includes the following steps:

[0047] (1) Grid data fusion

[0048] Suppose that the ocean dynamics model outputs environmental field forecast data for a certain sea area with a uniform grid, and the grid point set T = {(x i ,f i ), i = 1, 2, ..., n}, where x i f represents the spatial coordinates of the i-th grid point. i This represents the attribute values ​​(temperature, salinity, etc.) of this grid point. The mobile node samples along a planned path within this sea area, acquiring data such as temperature, salinity, and depth along the path. The set of observation points is denoted as Z = {(x...} i ,f i ), i = 1, 2, ..., m}, where x i f represents the spatial coordinates of the i-th observation point. i This refers to the attribute values ​​(temperature, salinity, etc.) of the observation point.

[0049] The mobile node observation data is fused with the grid field output from the ocean dynamics model. The specific fusion method is as follows: for model output grid points T containing nodal observation data... k ={x k ,f k}, using the set of all observation points Z within this grid k ={(x ki ,f kiThe mean of attribute values ​​for {i = 1, 2, ..., p}

[0050]

[0051] Replace the grid property value f k For grids that do not contain observation data, the original data values ​​are maintained. The final result is the grid point set T′={(x i ,f i ),i=1,2,…,n}.

[0052] (2) Mesh feature extraction

[0053] After completing the grid data fusion, a radial basis function (RBF) grid interpolation model is constructed to extract grid features. The RBF grid interpolation model is: given a function φ:R in space... + →R, for the set of n uniform grid data points T′={(x i ,f i Given the sequence {i = 1, 2, ..., n}, we need to find a function:

[0054]

[0055] Make it satisfy the interpolation condition:

[0056]

[0057] Where x k Let f(x) be any coordinate point in space. k ) represents the attribute value f corresponding to that point. k , ||x k -x i ||2 represents any coordinate point x k To merge grid point x i The Euclidean distance between them, w i φ(||x) represents the linear combination coefficients, i.e., the weights. k -x i ||2) is x k At the center point x i The corresponding RBF basis function at that point takes the form of a quadratic function:

[0058]

[0059] Where σ is the variable shape parameter of RBF.

[0060] For the weighting coefficient w in the interpolation formula i The calculation involves substituting the fused grid point set T′ from step (1) into formula (1) to obtain the grid feature extraction equation, i.e., the interpolation expression:

[0061]

[0062] Where φ ji =φ(||x j -x i 2). Let the basis function matrix Weight vector Attribute vector The interpolation expression can then be simplified as follows:

[0063] Φw=f, (6)

[0064] By inverting the matrix, the weight components corresponding to the basis functions of each grid point can be calculated:

[0065] w = Φ -1 f. (7)

[0066] (3) Mesh expansion

[0067] After obtaining the RBF interpolation coefficients w by solving the interpolation expression, the grid point set T′ is uniformly expanded in each dimension (generally expanded to twice its original size) to obtain the expanded grid point set T. 1 ={(x i ,f i ),i=1,2,…,n1}. Expand the grid coordinates x i Substituting into the RBF interpolation equation (3), the attribute value f of the grid point is obtained. i This enables the expansion of the grid point set T. 1 Population of attribute values.

[0068] (4) Multi-level iterative reconstruction of the environmental field

[0069] In the previous steps, the first level of expansion of the initial mesh has been achieved. The expanded mesh T... 1 As the initial grid, steps (1), (2), and (3) are repeated sequentially to perform data fusion, grid feature extraction, and grid expansion, further utilizing more mobile node observation information and integrating it into the new grid T. 1 The grid is further expanded through multiple iterations to achieve high-resolution, high-precision multi-level interpolation reconstruction of the marine environmental field.

[0070] Example 1:

[0071] This embodiment describes the overall process of the present invention in practical application and performs simulation analysis.

[0072] like Figure 2A As shown in the grid and scatter plot, it is assumed that the ocean dynamics model outputs a two-dimensional low-resolution grid field T = {(x...i ,f i ), i=1,2,…,n}, where n=a×b; the set of observation points Z={(x i ,f i The mobile node observation data T is fused with the grid field Z output by the ocean dynamics model using a mean substitution algorithm. Specifically, for model output grid points T containing observation data from 3 mobile nodes... k ={x k ,f k}, using the set of all observation points Z within this grid k ={(x ki ,f ki The mean of attribute values ​​for {i = 1, 2, ..., p}

[0073]

[0074] Replace the grid property value f k For grid cells that do not contain observation data, the original data values ​​are maintained. The final result is as follows: Figure 2B The mesh field T′ after attribute fusion shown is T′={(x i ,f i ), i=1,2,…,n}, where the dark grid is the grid whose attribute value has been replaced. The data changes occur in the grid fields through which the moving node passes, in order to improve the accuracy of the current grid.

[0075] Construct the radial basis function (RBF) interpolation function:

[0076]

[0077] Make it satisfy the interpolation condition:

[0078]

[0079] Where x k Let f(x) be any coordinate point in space. k ) represents the attribute value f corresponding to that point. k , ||x k -x i ||2 represents any coordinate point x k To merge grid point x i The Euclidean distance between them, w i φ(||x) represents the linear combination coefficients, i.e., the weights. k -x i ||2) is x k At the center point x i The corresponding RBF basis function at that point takes the form of a quadratic function:

[0080]

[0081] Where σ is the variable shape parameter of RBF.

[0082] For any coordinate point x k To obtain the corresponding attribute estimate f k It is necessary to calculate all the weight components w of the RBF interpolation function. i Substitute the fused mesh field T′ into the RBF interpolation expression.

[0083]

[0084] Where φ ji =φ(||x j -x i 2). Let the basis function matrix Weight vector Attribute vector The interpolation expression can then be simplified as follows:

[0085] Φw=f, (6)

[0086] By solving the system of equations through matrix inversion, the weight components corresponding to the basis functions of each grid point can be calculated:

[0087] w = Φ -1 f. (7)

[0088] The merged mesh T′ is expanded in coordinates, doubling its original size in each dimension. In this example, the original a×b mesh T′ will be expanded into a new mesh field T of (2a-1)×(2b-1). 1 ={(x i ,f i ),i=1,2,…,n1}, where n1=(2a-1)×(2b-1). For the expanded grid field T 1 Each grid point x needs to be filled. i The attribute value f i Attribute value f i This can be achieved by expanding the grid coordinates x i The result is obtained by substituting into the RBF interpolation function (3).

[0089] At this point, the first level of mesh expansion has been completed. The process of data fusion, RBF interpolation model construction, mesh feature extraction, mesh expansion, and attribute value filling is repeated to achieve the second, third, ..., nth levels of expansion, until the desired result is obtained. Figure 2C The grid field shown meets the resolution requirements, at which point the environmental field reconstruction is complete. Further, as... Figure 1As shown, by comparing the reconstructed high-resolution environmental field with the real environmental field data, we can analyze the accuracy of the reconstructed field and the reconstruction performance of the multi-level interpolation algorithm.

[0090] Example: To verify the effectiveness of the marine environmental field interpolation reconstruction algorithm based on multi-level interpolation, a two-dimensional simulation analysis of the marine environmental field is performed below. Figure 3A The image shows a 321*321 temperature grid field for a certain sea area output by the Regional Ocean Model System (ROMS). N(1,0.25) Gaussian noise (unit: °C) was added to this field, and then downsampled to obtain a 21*21 ROMS downsampled field, which was used as the model output data. The original ROMS field was used for comparison with the multi-level interpolated reconstructed field. The navigation paths of five mobile nodes were simulated and planned within the original ROMS grid field, and the temperature values ​​of the corresponding grid points along the paths were sampled as high-precision observation data. Figure 3B This demonstrates the downsampled ROMS field and simulated moving node sampled scatter temperature values. Using a multi-level interpolation reconstruction algorithm, data fusion is first performed, RBF basis is constructed to extract mesh features, the mesh is expanded, and temperature values ​​are interpolated. After four levels of iterative mesh expansion (the number of mesh points changes sequentially from 21*21→41*41→81*81→161*161→321*321), the reconstructed temperature restored field is shown below. Figure 4A As shown, the temperature restoration field is compared with the original ROMS output temperature field. Figure 4B The absolute values ​​of the temperature reconstruction field error are shown. It can be seen that the reconstruction field error is significantly lower and the reconstruction effect is better near the sampling path of the moving node. Further along the moving node path, the amount of high-resolution, high-precision information provided by the observation point is reduced due to the greater distance from the observation point, resulting in a higher reconstruction error. Overall, the multi-level interpolation algorithm of this invention performs well in this example, especially in the reconstruction of the grid near the observation path of the moving node.

[0091] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of disclosure in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described concept. For example, the above features may be formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A method for reconstructing marine environmental fields based on multi-level interpolation, characterized in that, Includes the following steps: Step (1): The observation data from the mobile node is fused into the grid output by the ocean dynamics model; Step (2): Construct a radial basis function (RBF) mesh interpolation model to extract mesh features; Step (3): Expand the mesh and interpolate to fill in the mesh attribute values; Step (4) involves multi-level iterations to complete the high-resolution environmental field reconstruction; Step (1) specifically includes: Assuming the ocean dynamics model outputs environmental field forecast data for a certain sea area with a uniform grid, the grid point set... ,in For the first The spatial coordinates of each grid point The attribute values ​​for this grid point include temperature and salinity. The mobile node samples along a planned path within this sea area, acquiring temperature, salinity, and depth data along the path. The set of observation points is denoted as […]. ,in For the first The spatial coordinates of each observation point These are the attribute values ​​for the observation point, including temperature and salinity. The mobile node observation data is fused with the grid field output from the ocean dynamics model. The specific fusion method is as follows: for model output grid points containing nodal observation data... Use the set of all observation points within this grid mean of attribute values ，（1） Alternate grid points attribute values For grids that do not contain observation data, the original data values ​​are maintained; finally, the grid point set after attribute value fusion is obtained. .

2. The marine environmental field reconstruction method based on multi-level interpolation as described in claim 1, characterized in that, Step (2) specifically includes: After completing the grid data fusion, an RBF grid interpolation model is constructed to extract grid features; the RBF grid interpolation model is: given a function in space For the fusion obtained in step (1) A set of uniform grid data points We need to find a function: ， （2） Make it satisfy the interpolation condition: ，（3） in For any coordinate point in space, The value is this The attribute value corresponding to the point , Represents any coordinate point To merge grid points Euclidean distance between them These are the coefficients of the linear combination, i.e., the weights; for At the center point The corresponding RBF basis function at that point takes the form of a quadratic function: ， （4）. in For the variable shape parameters of RBF; For the weighting coefficients in the interpolation formula The calculation will merge the grid point set in step (1). Substituting into formula (1), we obtain the grid feature extraction equation, i.e., the interpolation expression: （5） in Let the basis function matrix... Weighted components Attribute vector The interpolation expression is then simplified to: ,（6） By inverting the matrix, the weight components corresponding to the basis functions of each grid point can be calculated: （7）。 3. The marine environmental field reconstruction method based on multi-level interpolation as described in claim 2, characterized in that, Step (3) specifically includes: The RBF weight components are obtained by solving the interpolation expression. Then, the grid point set The grid points are expanded by uniformly dividing and expanding the grid in each dimension to obtain the expanded grid point set. Expand the grid coordinates Substituting the values ​​into the RBF interpolation equation (3) yields the attribute values ​​of the grid point. This enables the expansion of the grid point set. Population of attribute values.

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