A sound velocity profile reconstruction method based on random basis

Abstract

The application discloses a sound velocity profile reconstruction method based on a random basis. Prior sound velocity disturbance probability density distribution is obtained by fitting and analyzing the distribution characteristics of sound velocity profile disturbances at different depths and sea areas; a random basis is constructed according to the prior sound velocity disturbance probability density distribution, and a super-complete dictionary is formed; a sound velocity profile is reconstructed by sparse processing of compressed sensing according to a sound velocity profile disturbance matrix and the super-complete dictionary, and a reconstructed sound velocity profile is obtained. The application reconstructs the sound velocity profile based on the random basis with certain universal applicability, effectively reduces the dependence on historical sound velocity profile data sets, and can better capture the slight disturbance of the sound velocity profile.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of ocean environment observation and parameterization technology, and relates to a seawater sound speed profile reconstruction method, in particular to a sound speed profile reconstruction method based on a random basis. BACKGROUND

[0002] The seawater sound speed profile refers to the variation of the sound speed with depth, and the estimation of the sound speed profile is a research focus in the fields of ocean science and ocean engineering. Due to the complexity of the seawater environment, the density, temperature distribution and dynamic processes such as tides, ocean currents and internal waves of seawater will affect the propagation of sound waves, so the sound speed profile will show different spatiotemporal variation characteristics in different sea areas of the world ocean.

[0003] Currently, the in-situ measurement of the seawater sound speed profile is mainly realized by using a CTD (Conductivity, Temperature, Depth), by measuring the temperature, salinity and other environmental parameters of seawater, and then calculating the seawater sound speed by combining with the empirical formula of sound speed. However, this method requires a high cost, and due to the vast area of the ocean, it is difficult to obtain a large amount of data in a short time, and it is difficult to obtain a complete sound speed profile.

[0004] Combining the insufficient in-situ measurement data with a parameterization model with universality to represent the seawater sound speed profile with wide coverage and high precision has become an important way to solve the above problems. Most of the current sound speed profile reconstruction methods use empirical orthogonal functions, model the sound speed profile as the sum of a known average sound speed profile and a sound speed profile disturbance, and expand the sound speed profile disturbance on a set of orthogonal bases. However, this method mainly aims to fully exploit the structural characteristics of the sound speed profile fluctuation, and reduce the number of basis functions required for the representation of the sound speed profile, so it relies on a large amount of historical data. The empirical orthogonal functions obtained in different seasons, different sea areas and different historical data amounts may have great differences, and the universality is poor, and part of the detailed features of the sound speed profile may be ignored. SUMMARY

[0005] The present application aims to solve the problem of severe dependence on historical data sets in the prior art, effectively reduce the dependence on historical sound speed profile data sets, and better capture the slight disturbance of the sound speed profile.

[0006] To achieve the above-mentioned purpose, the specific technical solutions provided by the present application are as follows:

[0007] Step 1: analyze the distribution characteristics of the sound speed profile disturbance of the world ocean with the depth of seawater, synthesize the similar characteristics of the sound speed profile disturbance with depth distribution in different sea areas and at different times, fit to obtain the prior sound speed disturbance probability density distribution, and use it as the prior information of the method, as shown in Figure 2 .

[0008] Step 2: generating a sound speed profile perturbation matrix and a random basis according to historical sound speed profile data sets combined with a priori sound speed perturbation probability density distribution, and the random basis constitutes an overcomplete dictionary;

[0009] Step 3: reconstructing a sound speed profile according to the sound speed profile perturbation matrix and the overcomplete dictionary through sparse processing of compressed sensing.

[0010] In the specific implementation of the step 1, in the process of fitting to obtain the priori sound speed perturbation probability density distribution, sound speed perturbations are mostly distributed in the range of -5 m / s to 5 m / s, and the place where the sound speed perturbation is 0 m / s accounts for more than 50 percent, which indicates that the sound speed profile perturbation has great sparsity.

[0011] The step 2 specifically includes the following steps:

[0012] Step 2.1: selecting M sound speed profiles from historical sound speed profile data sets, and the historical sound speed profile data set S is represented as Each sound speed profile is interpolated into K discrete points in depth, and the average sound speed profile s of all K discrete points is calculated mean , and the K discrete points are removed from the average sound speed profile s mean , and the sound speed profile perturbation matrix Y is obtained:

[0013]

[0014]

[0015] , wherein s i represents a sound speed profile, y i represents a sound speed profile perturbation, and M is the total number of sound speed profiles in the historical sound speed profile data set.

[0016] Step 2.2: generating a random basis according to the priori sound speed perturbation probability density distribution, and further constructing an overcomplete dictionary d represents a random basis, also known as a dictionary atom, N is the number of random bases, that is, the number of dictionary atoms, and N > K.

[0017] The random basis is generated according to the priori sound speed perturbation probability density distribution, and the overcomplete dictionary is constructed, specifically: the elements of the random basis are generated according to the priori sound speed perturbation probability density distribution of step 1, and all the elements of the random basis are combined to form an overcomplete dictionary with a size of KxN.

[0018] The step 3 specifically includes the following steps:

[0019] Step 3: under the framework of compressed sensing, the following objective equation is established according to the sound speed profile perturbation matrix and the overcomplete dictionary:

[0020]

[0021]

[0022]

[0023] Where X is a sparse coefficient matrix consisting of coefficient vectors, ||...|| F represents the norm calculation, x i represents the i-th coefficient vector in the sparse coefficient matrix X, ||x||0 represents the number of non-zero elements in each coefficient vector x, and T represents the sparsity constraint; a ij represents the element in the i-th row and j-th column of the matrix Y-DX, and M represents the total number of coefficients;

[0024] Solve the target equation to obtain the sparse coefficient matrix X of the overcomplete dictionary;

[0025] Step 3.1: Based on the coefficient vector x in the obtained coefficient matrix X, the reconstructed sound velocity profile is obtained according to the following formula:

[0026]

[0027] Among them, s i ' represents the reconstructed sound velocity profile.

[0028] In step 3, the orthogonal matching pursuit algorithm (OMP) is used to solve the target equation to obtain the sparse coefficient matrix X.

[0029] The present invention uses an overcomplete dictionary to replace traditional orthogonal basis functions under compressed sensing, providing great flexibility for signal adaptive sparse expansion. The overcomplete dictionary atoms do not need to meet the strict orthogonality condition, which can better achieve data set compression.

[0030] The present invention is based on the similarity of the distribution characteristics of different sound speed profile disturbance data with seawater depth. By fitting and analyzing the distribution characteristics of sound speed profile disturbances at different depths, sea areas and time seasons, the prior sound speed disturbance probability density distribution is obtained, and this probability density distribution is used as the prior information of the reconstruction method; a random basis is constructed according to the fixed disturbance distribution to form an overcomplete dictionary atom library; based on the sparse reconstruction algorithm, the sparse coefficient vectors of the overcomplete dictionary atoms are calculated to reconstruct the sound speed profile.

[0031] The beneficial effects of the present invention are:

[0032] 1. The method has universality and reduces dependence on historical sound speed profile data set by synthesizing distribution characteristics of different sound speed profile disturbances and reconstructing the sound speed profile by combining prior disturbance distribution only with historical average sound speed profile data.

[0033] 2. Compared with empirical orthogonal functions considering only overall structural characteristics of the sound speed profile, the random basis constructed by the method can better capture the minor disturbance part of the sound speed profile and accurately capture the sound speed profile with a small amount of historical sound speed profile data set. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 is a workflow diagram of the method;

[0035] Figure 2 is a schematic diagram of prior sound speed disturbance probability density distribution;

[0036] Figure 3 is a schematic diagram of shallow sea sound speed profile data set;

[0037] Figure 4 is a schematic diagram of deep sea sound speed profile data set;

[0038] Figure 5 is a schematic diagram of shallow sea sound speed profile disturbance;

[0039] Figure 6 is a schematic diagram of deep sea sound speed profile disturbance;

[0040] Figure 7 is a comparison diagram of shallow sea sound speed profile based on random basis and actual shallow sea sound speed profile;

[0041] Figure 8 is a comparison diagram of deep sea sound speed profile based on random basis and actual deep sea sound speed profile;

[0042] Figure 9 is a comparison diagram of reconstruction results of shallow sea sound speed profile based on random basis and empirical orthogonal function respectively;

[0043] Figure 10 is a comparison diagram of reconstruction results of deep sea sound speed profile based on random basis and empirical orthogonal function respectively;

[0044] Figure 11 is a comparison diagram of reconstruction results of twenty groups of sound speed profile data set based on random basis and empirical orthogonal function respectively. DETAILED DESCRIPTION

[0045] The application will be further described below in combination with the drawings and examples.

[0046] As Figure 1As shown, the implementation of the complete method according to the present application is as follows:

[0047] Step 1: The prior sound speed perturbation probability density distribution obtained after synthesizing the perturbations of different ocean sound speed profiles is shown in Figure 2 As shown, it can be seen that the perturbations of the sound speed profile are mostly distributed in the range of -5 m / s to 5 m / s, and the place where the perturbation is 0 m / s accounts for more than 50%, which indicates that the perturbation of the sound speed profile has great sparsity. This prior sound speed perturbation probability density distribution serves as the prior information for constructing all random bases.

[0048] Step 2: To prove the effectiveness of the sound speed profile reconstruction method based on random bases, shallow and deep sea sound speed profile data sets are selected respectively: the shallow sea data is the sound speed profile data measured in the Asian Ocean International Underwater Experiment in the East China Sea from May 28 to June 9, 2001, the sound speed profile depth is 106 meters, and there are M = 200 sound speed profiles, each sound speed profile has K = 106 discrete points in depth; the deep sea data comes from the global ocean Argo data set, which is the sound speed profile data in the Indian Ocean area from 16.5°S to 18.5°S and 60.5°E to 62.5°E from 2006 to 2015 every August, the sound speed profile depth is 1975 meters, and there are M = 90 sound speed profiles, each sound speed profile has K = 58 discrete points in depth. The historical sound speed profile data set can be expressed as As shown in Figure 3 and Figure 4 The average sound speed profile is expressed as s mean , and the zero-mean sound speed profile perturbation matrix is obtained after removing the average profile As shown in Figure 5 and Figure 6 , wherein,

[0049]

[0050] According to the prior sound speed perturbation probability density distribution, a random basis is generated, and an overcomplete dictionary is constructed, expressed as N is the number of random bases, i.e. the number of dictionary atoms, and N > K.

[0051] Step 3: Based on the orthogonal matching pursuit (OMP) algorithm, the sparse coefficient vector of the overcomplete dictionary atom is calculated, and under the theory of compressed sensing, the target equation is as follows:

[0052]

[0053] , wherein, is a matrix composed of the coefficient vector, and T is the number of non-zero elements in the coefficient vector x, i.e. the sparsity.

[0054] Step 4: Calculate the sound speed profile according to the obtained coefficient vector x:

[0055]

[0056] According to the coefficient vector obtained in step 3, the sound speed profile can be reconstructed using formula (3).

[0057] The sound speed profile reconstructed based on the random basis is compared with the actual sound speed profile, where the number of atoms in the overcomplete dictionary in step 2 is set to N = 2500, and the sparsity of the orthogonal matching pursuit algorithm in step 3 is set to T = 15. The reconstruction results are shown in Figure 7 and Figure 8 It can be seen that the error between the random basis model fitting value and the true value is small, indicating the effectiveness of the method for reconstructing the sound speed profile.

[0058] The method is compared with the traditional method based on empirical orthogonal functions. In the random basis-based method, the number of atoms in the overcomplete dictionary is set to N = 2500, and the sparsity T is set to 15. In the EOF-based method, the first five orthogonal basis functions are used.

[0059] The reconstruction results are shown in Figure 9 and Figure 10 It can be seen that the average error of the two methods is small. Figure 11 Further comparison of the average reconstruction error of twenty groups of sound speed profile data sets shows that the reconstruction error using random basis is close to that using five-order EOF, also indicating the feasibility of the method.

Claims

1. A random basis-based sound velocity profile reconstruction method, characterized by, The method comprises the following steps: Step 1: fitting a prior sound speed disturbance probability density distribution by synthesizing similar features of the sound speed profile disturbance distribution with depth in different sea areas and at different times; Step 2: generating a sound speed profile disturbance matrix and a random basis according to a historical sound speed profile data set combined with the prior sound speed disturbance probability density distribution, and the random basis is used to form an overcomplete dictionary; Step 3: performing sparse processing and reconstructing the sound speed profile according to the sound speed profile disturbance matrix and the overcomplete dictionary in the compressive sensing; The step 2 comprises the following specific steps: Step 2.1: Select M sound speed profiles from the historical sound speed profile dataset, the historical sound speed profile dataset S is represented as Each sound speed profile is interpolated to K discrete points in depth, and the average sound speed profile s of all K discrete points is calculated mean The K discrete points are removed from the average sound speed profile s mean The sound speed profile perturbation matrix Y is obtained where s i represents the sound speed profile, y i represents the sound speed profile perturbation, M is the total number of sound speed profiles in the historical sound speed profile dataset; Step 2.2: Generate random bases according to the prior sound speed perturbation probability density distribution, and then construct an overcomplete dictionary d represents a random base, also called a dictionary atom, N is the number of random bases, and N > K.

2. The method of claim 1, wherein: The random basis is generated according to the prior sound speed disturbance probability density distribution, and then the overcomplete dictionary is constructed, specifically: the elements of the random basis are generated according to the prior sound speed disturbance probability density distribution in step 1, and all the elements of the random basis are used to form the overcomplete dictionary.

3. The method of claim 1, wherein: The step 3 comprises the following specific steps: Step 3: in the compressive sensing framework, the following objective equation is established according to the sound speed profile disturbance matrix and the overcomplete dictionary: where X is a sparse coefficient matrix composed of coefficient vectors, ||...||0 F denotes norm calculation, x i denotes the i-th coefficient vector in the sparse coefficient matrix X, ||x||0denotes the number of non-zero elements in each coefficient vector x, T denotes sparsity constraint; ij denotes the element in the i-th row and j-th column in the matrix Y-DX, M denotes the total number of coefficient vectors; Solving the objective equation to obtain a sparse coefficient matrix X; Step 3.1: according to the coefficient vector x in the obtained coefficient matrix X, the following formula is used to process to obtain the reconstructed sound speed profile: where s i denotes the reconstructed sound speed profile.

4. The random basis-based sound velocity profile reconstruction method of claim 1, wherein: In the step 3, the orthogonal matching pursuit algorithm is used to solve the objective equation to obtain the sparse coefficient matrix X.

Images