CN112784412A - Single hydrophone normal wave modal separation method and system based on compressed sensing - Google Patents
Single hydrophone normal wave modal separation method and system based on compressed sensing Download PDFInfo
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Abstract
The invention relates to the technical field of underwater acoustic signal processing, in particular to a method and a system for separating normal wave modes of a single hydrophone based on compressed sensing, wherein the method comprises the following steps: obtaining a horizontal wave value of the broadband normal wave according to the approximate modal dispersion relation; constructing a dictionary matrix of a sparse solution problem by using the horizontal wave number values based on a compressive sensing theory; according to the dictionary matrix and the broadband frequency domain sound pressure vector received by the single hydrophone, constructing a sparse signal model by adopting a compressive sensing theory, and solving and calculating by utilizing a compressed sensing implementation algorithm to obtain a sparse vector complex coefficient; and restoring each normal wave mode after separation according to the sparse vector complex coefficient and the dictionary matrix. The method is applicable to a wider scene, can be suitable for the condition that the refraction type and reflection type normal waves exist simultaneously under the negative gradient hydrological condition, and does not need to know the accurate sea water sound velocity profile and the sea bottom parameters.
Description
Technical Field
The invention relates to the technical field of underwater acoustic signal processing, in particular to a method and a system for separating normal wave modes of a single hydrophone based on compressed sensing.
Background
In shallow sea environments, normal wave theory is a powerful tool for modeling acoustic propagation of low frequency signals. According to the normal wave theory, far-field low-frequency signals are mainly composed of a few propagation normal wave modes which are superposed. The separation of each normal wave mode can be used for various applications of water acoustics, such as matched mode sound source positioning, earth sound parameter inversion and acoustic chromatography. Therefore, the separation method of normal wave modes in shallow sea is always a hot research point of water acoustics.
Compared with a method for extracting a normal wave mode based on a horizontal or vertical array signal, the mode separation method using a single hydrophone signal has the advantages of simple equipment layout and small mismatch of array parameters. Normal wave mode separation methods based on single hydrophones generally require the signal to be in the form of a pulse signal or a known frequency modulated signal. From the existing literature, the Warping transformation and the derivative form thereof are the main methods for realizing the modal separation of the single hydrophone, and are one of the most active research directions for the modal separation of the single hydrophone at present. Among them, the most widely used transform form is the time-domain Warping transform, which performs non-uniform resampling on the frequency dispersion signal received by the wideband. After the time domain Warping transformation, the modal components having a non-linear time-frequency structure are transformed into a plurality of single-frequency components. Thus, the respective modes can be more easily separated and filtered out from the time-frequency domain or the frequency domain. And restoring the separated modal components to the original time domain through inverse Warping, thereby obtaining the separated modal time domain signals of each order. The time domain Warping transformation is derived based on ideal waveguide conditions and is mainly suitable for reflection type normal waves (such as sea surface-seabed reflection normal waves). Another form of Warping transformation is derived based on waveguide invariants, and can be used for transformation of refraction-like normal waves under negative gradient hydrological conditions (such as normal waves inverted below sea surface). One of the main application limitations of the present Warping transform is that normal waves in the waveguide are either both reflective or both refractive, i.e. need to have the same mode type. If the mode contains both reflection-type and refraction-type normal waves, the separation performance of the Warping transformation is significantly reduced, because the two types of normal waves generate mutual interference after being transformed.
Disclosure of Invention
The invention provides a method and a system for separating normal wave modes of a single hydrophone based on compressed sensing, aiming at overcoming the technical defects and providing the method and the system for separating the normal wave modes of the single hydrophone based on compressed sensing.
In order to achieve the above object, embodiment 1 of the present invention provides a method for separating normal wave modes of a single hydrophone based on compressed sensing, where the method includes:
obtaining a horizontal wave value of the broadband normal wave according to the approximate modal dispersion relation;
constructing a dictionary matrix of a sparse solution problem by using the horizontal wave number values based on a compressive sensing theory;
according to the dictionary matrix and the broadband frequency domain sound pressure vector received by the single hydrophone, constructing a sparse signal model by adopting a compressive sensing theory, and solving and calculating by utilizing a compressed sensing implementation algorithm to obtain a sparse vector complex coefficient;
and restoring each normal wave mode after separation according to the sparse vector complex coefficient and the dictionary matrix.
As an improvement of the above method, the method further comprises: arranging a single hydrophone in a region to be detected in shallow sea, wherein the distance between the single hydrophone and a sound source is rsThe frequency band of the sound source is [ f ]1,fF]。
As an improvement of the above method, the method further comprises: if the frequency band bandwidth of the sound source is larger than 40Hz, the frequency band is divided into a plurality of sub-frequency bands, and the bandwidth of each sub-frequency band is 20-40 Hz.
As an improvement of the above method, the horizontal wave value of the broadband normal wave is obtained according to the approximate modal dispersion relation; the method specifically comprises the following steps:
according to the shallow sea acoustic propagation theory, the phase velocity C of normal wave propagating in the waveguidepSatisfies the following formula:
Cw≤Cp≤Cb，
wherein, CwRepresenting the speed of sound of seawater CbRepresenting the seafloor acoustic velocity;
for frequency band f1,fF]First frequency point f1From the interval [2 π f1/Cb,2πf1/Cw]Uniformly sampling M horizontal wave numbers;
calculating the frequency band [ f ] according to the approximate modal dispersion relation1,fF]MF number of horizontal wave values krl(fj+1) Comprises the following steps:
wherein k isrlIs the real part of complex eigenvalue of the ith order normal wave, representing the horizontal wave number of the mode, j is frequency point, F is frequency band [ F1,fF]Upper limit of frequency point.
As an improvement of the above method, the dictionary matrix of the sparse solution problem is constructed from horizontal wave number values based on the compressed sensing theory; the method specifically comprises the following steps:
according to the distance r between a single hydrophone and a sound sourcesAnd frequency band [ f1,fF]MF number of horizontal wave values krl(fj+1) And calculating a dictionary matrix of the sparse signal model by the following formula
Comprises the following steps:
as an improvement of the method, a sparse signal model is constructed by adopting a compressive sensing theory according to a dictionary matrix and a broadband frequency domain sound pressure vector received by a single hydrophone, and a sparse vector complex coefficient is obtained by solving and calculating by using a compressed sensing implementation algorithm; the method specifically comprises the following steps:
according to a dictionary matrix
And a wideband frequency domain sound pressure vector y received by the hydrophone, and the sparse signal model constructed by the compressive sensing theory is as follows:
wherein n is a complex Gaussian noise vector
According to the sparse Bayesian learning algorithm, each element x of the sparse vector x to be solvedmAre subject to mean of zero and variance of gammam∈γ＝[γ1,…,γM]TComplex gaussian distribution of (a);
the maximum a posteriori probability estimate of the sparse vector x is calculated from
Comprises the following steps:
wherein H represents a conjugate transpose, and Γ ═ diag (γ)1,…,γM) And obtaining sparse vector complex coefficients for the diagonal covariance matrix.
As an improvement of the above method, restoring each normal wave mode after separation according to the sparse vector complex coefficient and the dictionary matrix; the method specifically comprises the following steps:
from sparse vector estimation
And corresponding dictionary vectors
Obtaining K separated frequency domain modal signals
Comprises the following steps:
wherein,
as a sparse vector
The first element of (A) is (B),
is composed of
The ith column vector of (1).
As an improvement of the above method, the method further comprises: and transforming the separated modal signals to a time domain.
A single hydrophone normal wave modal separation system based on compressed sensing, the system comprising: the device comprises a horizontal wave numerical value acquisition module, a dictionary matrix construction module, a sparse vector complex coefficient calculation module and a normal wave modal separation module; wherein,
the horizontal wave value acquisition module is used for acquiring a horizontal wave value of the broadband normal wave according to the approximate modal dispersion relation;
the dictionary matrix construction module is used for constructing a dictionary matrix of a sparse solution problem by using the horizontal wave number values based on a compressed sensing theory;
the sparse vector complex coefficient calculation module is used for constructing a sparse signal model by adopting a compressive sensing theory according to the dictionary matrix and the broadband frequency domain sound pressure vector received by the single hydrophone, and solving and calculating by utilizing a compressed sensing implementation algorithm to obtain a sparse vector complex coefficient;
and the normal wave mode separation module is used for recovering each separated normal wave mode according to the sparse vector complex coefficient and the dictionary matrix.
Compared with the prior art, the invention has the advantages that:
the method is applicable to a wider scene, can be suitable for the condition that the refraction type and reflection type normal waves exist simultaneously under the negative gradient hydrological condition, and does not need to know the accurate sea water sound velocity profile and the sea bottom parameters.
Drawings
Fig. 1 is a flowchart of a method for separating normal wave modes of a single hydrophone based on compressed sensing according to embodiment 1 of the present invention;
FIG. 2 is a simulation example 1 marine hydrological environment parameters and source-receiver position;
FIG. 3 shows the theoretical values of the pulse signal waveform and the first four-order modal signal of 90-120Hz obtained by numerical simulation in simulation example 1;
fig. 4(a) is a time domain signal after simulation example 1 adopted Warping transform;
fig. 4(b) is a time-frequency structure of a signal after the simulation example 1 adopts Warping transform;
fig. 4(c) is a frequency spectrum of a signal after the simulation example 1 employs Warping transform;
FIG. 5 is the result of simulation example 1 processing using the method of the present invention;
FIG. 6 is a graph comparing signals of the first four orders of modality separated by the method of the present invention using the Warping transformation in simulation example 1;
fig. 7(a) is a number 1 normal wave corresponding to the variation of correlation coefficient with the signal-to-noise ratio obtained by the method of the present invention using Warping transformation in simulation example 1;
fig. 7(b) is a number 2 normal wave corresponding to the variation of correlation coefficient with the signal-to-noise ratio obtained by the method of the present invention using Warping transformation in simulation example 1;
fig. 7(c) is a number 3 normal wave corresponding to the variation of correlation coefficient with the signal-to-noise ratio obtained by the method of the present invention using Warping transformation in simulation example 1;
fig. 7(d) is a number 4 normal wave corresponding to the variation of correlation coefficient with the signal-to-noise ratio obtained by the method of the present invention using Warping transformation in simulation example 1;
fig. 8(a) is a simulated example 2 refraction-like hydrographic sound velocity profile;
FIG. 8(b) is a phase velocity diagram of the first six-order normal wave theoretically calculated in simulation example 2;
fig. 9(a) is a time domain signal after simulation example 2 adopted Warping transform;
fig. 9(b) is a time-frequency structure of a signal after the simulation example 2 adopts Warping transform;
fig. 9(c) is a frequency spectrum of a signal after the simulation example 2 employs Warping transform;
FIG. 10(a) is the result of simulation example 2 processed using the method of the present invention;
fig. 10(b) is a comparison of the first four-order normal wave time domain signal separated by the method of the present invention and theoretical values in simulation example 2.
Detailed Description
Different from the conventional method for separating the normal wave modes by using Warping transformation, the invention provides a method for separating the normal wave modes of a single hydrophone based on compressed sensing in a frequency domain, which has a wider application range than the Warping transformation and can be applied to scenes in which reflection type normal waves and refraction type normal waves exist simultaneously under the condition of negative gradient hydrology. The compressive sensing theory can be used for recovering sparse signals, and mathematically solves an underdetermined equation set with sparse constraint. In addition to the fields of medical images, radar detection, communication and the like, in the field of underwater acoustics, compressed sensing is also applied to underwater acoustic target orientation estimation, underwater passive positioning, normal wave modal separation based on array signals and the like in recent years, and great application potential is shown. At present, compressed sensing has various realization algorithms to reconstruct sparse signals, such as basis tracking, matching orthogonal tracking, sparse Bayesian learning and the like. The sparse reconstruction algorithm can be theoretically used for solving the normal wave modal separation problem provided by the invention. In the following detailed description of the method of the present invention, the sparse bayesian method is taken as an example to solve the sparse signal recovery problem.
The key point of the compressed sensing-based single hydrophone modal separation is how to construct a sparse signal reconstruction mathematical model. In the invention, a single hydrophone broadband signal model is constructed by using a normal wave theory, and a sensing matrix is constructed by using a dispersion relation of horizontal wave numbers of normal waves among different frequencies, so that a sparse signal model based on the normal wave theory is established. The method provided by the invention can be suitable for low-frequency pulse signals with known sound source-receiver distance or signals in a known frequency modulation mode in a shallow sea environment without knowing accurate hydrological and seabed parameters, and is still suitable for the method when refraction type and reflection type normal waves exist simultaneously in a negative gradient hydrological environment, and the performance of the traditional Warping transformation method is seriously reduced.
The invention provides a normal wave modal separation method based on compressed sensing, aiming at a single hydrophone broadband signal in a shallow sea environment. And constructing a compressed sensing perception (dictionary) matrix by utilizing the approximate dispersion relation of the horizontal wave number of the normal waves among different frequencies and the normal wave signal model so as to construct a sparse signal model to be solved, and separating and recovering each order of normal wave modes by adopting a compressed sensing realization algorithm.
The following is a detailed description and derivation of the algorithm provided by the invention, including the construction of a sparse signal model based on the normal wave theory and a solution algorithm for separating the normal wave modes by using compressed sensing.
Sparse signal model based on normal wave theory:
according to the theory of normal waves, at spatial position (0, z)s) The sound field excited by the point source can be represented as superposition of multiple normal waves. At the receiver (r)s,zr) The sound pressure in the frequency domain can be expressed as the superposition of the L number normal wave:
wherein k isrlAnd krlRespectively the real part and the imaginary part of the eigenvalue of the complex of the ith order normal wave,representing the horizontal wavenumber and attenuation of the mode, respectively. Phi (z, k)rl) Is an eigenfunction or a depth function of the ith order normal wave. Formula (1) can be simplified as:
wherein,
recording the frequency domain broadband measurement signal as a vector
F is the number of frequency points. Equation (2) can be rewritten as an expression form of a matrix vector:
wherein,
Because of the number L of the normal wave and the horizontal wave number k of each normal waverlUnknown, based on the concept of compressed sensing, we extend the model of equation (4) to a sparse signal reconstruction model:
y＝Ax+n (6)
wherein, matrix A is represented by(5) Is/are as follows
In a different, expressed form
I.e. column number M > L and M > F of A, corresponding to the quantity to be solved
Is a sparse vector with only a few elements that are non-zero. To calculate equation (7), we first assume that at frequency f1M horizontal wave numbers krl(f1) 1,2, …, M; then, the entire frequency band [ f ] is calculated from the approximate dispersion relation of the following equation1,fF]MF number of horizontal wavenumbers above:
wherein, CwIs approximately the speed of sound of seawater. The advantage of using equation (8) is that the number of unknowns is greatly reduced, i.e., the MF unknown horizontal wavenumbers are generated using M unknowns. Using MF assumed horizontal wavenumbers krl(fj) 1,2, …, M, j 1,2, …, F, and the distance r of the sound source receiversThe perceptual matrix a can be calculated from equation (7). From this, we have constructed a sparse signal model. The signal model of the formula (6) is a typical sparse signal recovery problem, and can be solved by various implementation algorithms of compressed sensing.
Normal wave modal separation based on compressed sensing
The method is based on a sparse signal reconstruction model formula (6), takes a sparse Bayesian learning algorithm in compressed sensing as an example, and recovers sparse signals to realize normal wave modal separation.
Within the framework of a sparse Bayesian algorithm, each element x of a sparse vector x to be solvedmAre all obeyed to mean value of zero, squareThe difference is gammam∈γ＝[γ1,…,γM]TA complex Gaussian distribution of (i.e. corresponding to a prior probability of)
Wherein Γ ═ diag (γ)1,…,γM) Is a diagonal covariance matrix. It can be seen that the vector y is also sparse. The sparse bayesian algorithm transforms the estimate of the vector x into an estimate of the hyper-parameter set γ. Since the noise in equation (6) is gaussian, the likelihood function can be expressed as
Thereby to obtain
Therein, sigmay＝σ2IF+AΓAHFor covariance matrices, H denotes conjugate transpose. The hyperparameter γ can be solved by maximizing the equation (10), i.e.
An updated iteration formula for the hyperparameter γ based on fixed-point iteration is thus obtained:
wherein, amIs the mth column of matrix a. Note the book
The submatrix composed of K columns extracted from the matrix A corresponds to the positions of K non-zero elements in gamma. We use the following noise covariance estimation formula:
wherein Tr represents the rank of the matrix, + represents the pseudo-inverse of the matrix, Sy＝yyHIs a sampled covariance matrix. Given the measurement data y and the perceptual matrix A, equations (12) and (13) are used to iteratively estimate γ and σ2. When gamma and sigma2After the estimation is completed, the maximum a posteriori estimate of the sparse vector x can be obtained:
note the book
The first column vector is
Sparse vectors
Wherein the first element is
The K frequency domain modal signals after separation can be calculated by the following formula:
the restored frequency domain modal signals of each order can be transformed from the frequency domain to the time domain by utilizing Fourier transform according to needs.
The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and examples.
Example 1
As shown in fig. 1, embodiment 1 of the present invention provides a method for separating normal wave modes of a single hydrophone based on compressed sensing, which includes the following specific steps:
1. according to shallow sea sound propagationTheory, phase velocity C of normal wave propagating in waveguidepShould satisfy Cw≤Cp≤CbIn which C iswRepresenting the speed of sound of seawater CbRepresenting the seafloor acoustic velocity. Thus, for frequency band [ f1,fF]First frequency point f1From the interval [2 π f1/Cb,2πf1/Cw]And uniformly sampling assumed values of M horizontal wave numbers. Since the sound velocity of sea water and sea bottom is not known in practical application, CwTaking the minimum sound velocity C over the depth of the seabTake an empirically large value, such as 2000 or 2500 m/s.
2. Giving the first frequency point f in the step 11And calculating MF horizontal wave values on the whole frequency band according to the following dispersion formula corresponding to the assumed values of the M horizontal wave numbers:
3. using known acoustic source-receiver distance rsAnd the assumed value k of MF horizontal wave numbers in the whole frequency band calculated in the step 2rl(fj+1) Calculating a dictionary matrix of the sparse signal model according to the following formula:
4. giving the dictionary matrix obtained by the 3 rd step of calculation
And the received broadband frequency domain signal y, and solving a sparse signal model by a compressed sensing realization algorithm (such as a sparse Bayesian algorithm)
Obtaining maximum a posteriori probability estimates for sparse vector x
5. Let K columns of dictionary matrix A constitute a subset of
Corresponding sparse vector estimation
K non-zero elements whose l column vector is noted
Sparse vectors
The first element of (A) is marked as
The K frequency domain modal signals after separation can be calculated by the following formula:
and the recovered modal signals of each order of frequency domain can be transformed to a time domain according to the requirement.
Note: the error of the horizontal wave number approximate dispersion formula in step 2 increases as the frequency band increases. Therefore, for a wider frequency band, we propose to divide the frequency band into a plurality of narrow sub-bands, each with a bandwidth of 20-40Hz, and process each sub-band according to the above steps 1-5, so as to obtain the result of mode separation over the whole wide frequency band.
The problem to be solved by the invention is normal wave modal separation by using a single hydrophone signal in a shallow sea environment. The sound source is a broadband signal, the receiver is a single hydrophone, and the signal transmitted by the sound source is transmitted through a shallow sea waveguide to generate a frequency dispersion effect. And carrying out modal separation on the received signals under the condition that the sea water sound velocity and the seabed parameters are not known exactly. The type of the sea water sound velocity profile, such as equal sound velocity, strong negative gradient and the like, determines whether the normal wave is refracted or reflected to a great extent. The advantages of the present invention are further illustrated by comparing the simulation examples in two different marine environments with the Warping transformation method.
Simulation example 1 reflection-like hydrological Environment
The reflection-type hydrological environment refers to that all orders of normal waves in the waveguide environment are reflected at the sea surface and the sea bottom, namely, no refraction-type normal waves exist in the waveguide. This hydrographic environment is simpler because all normal wave modes have the same characteristics, with reflections occurring at the sea surface and sea floor interfaces.
The waveguide environment shown in fig. 2 is a typical reflection-type hydrological environment, the sound velocity of seawater is equal to 1500m/s at the whole sea depth, the sea depth is 80m, the sea bottom is a semi-infinite liquid sea bottom model, and the sea bottom parameters are shown in fig. 2. The sound source depth is 10m, the receiver depth is 70m, and the distance between the sound source and the receiver is 10 km. The simulated signal has a frequency band of 90-120Hz and a frequency interval of 0.1 Hz.
Based on the marine environment parameters shown in fig. 2, the time domain pulse signal waveform obtained by using the normal wave model KRAKEN simulation calculation is shown in fig. 3 (the uppermost diagram in fig. 3). Meanwhile, modal signals of each order can be simulated and calculated, and the first four-order modal time domain signals are shown in figure 3. By using simulation comparison, the performance of the normal wave mode separation method can be checked.
Fig. 4 shows the result of the transformation process using Warping. A Warping transform is applied to the pulse signal received by the single hydrophone, and the time domain signal after the transform is shown in fig. 4 (a). The signal shown in fig. 4(a) was subjected to time-frequency analysis, and the result was shown in fig. 4 (b). It can be seen that after Warping conversion, the modal signals of each order are converted into superposition of a plurality of approximately single-frequency signals, and each number of normal waves has different characteristic frequencies. Within the frequency band of 90-120Hz, there are four orders of normal waves. Since the warp transformed signal is a superposition of a plurality of approximate single-frequency signals, we can calculate the corresponding frequency spectrum of the signal of fig. 4(a), as shown in fig. 4 (c). Because the waveguide is not an ideal waveguide, the signal after the warp transformation is not a strict single-frequency signal, and the peak on the frequency spectrum has a certain width.
For comparison, the normal wave modal separation method based on sparse bayesian learning provided by the present invention is applied to the same single hydrophone signal, and the result corresponding to the 90Hz frequency point is shown in fig. 5, where the horizontal axis is the assumed horizontal wave number and the vertical axis corresponds to the amplitude of γ. It can be seen that there are four sharp peaks corresponding to the fourth order normal wave modes.
For the Warping transformation, a band-pass filter is used for filtering four corresponding peaks in fig. 4(c) respectively, and then inverse Warping transformation is carried out, so that four-order normal wave time domain signals after separation can be obtained. For the sparse Bayes learning method, the frequency domain signals after normal wave modal separation are calculated by using the formulas (14) and (15), and then the frequency domain signals are transformed to the time domain through inverse Fourier transform, so that the time domain signals of the fourth-order normal waves are obtained. The time domain signals after normal wave separation based on the Warping transformation and the sparse bayesian learning method are shown in fig. 6. The modal signals of each order shown in fig. 6 are respectively correlated with the normal wave signals theoretically simulated in fig. 3, and corresponding correlation coefficients can be obtained. For the first four-order normal wave modes, correlation coefficients of the separation modes based on the Warping transformation are 0.876, 0.929, 0.957 and 0.926 respectively, and correlation coefficients corresponding to the separation modes based on the sparse Bayesian learning are 0.989, 0.998, 0.987 and 0.914 respectively. Therefore, the calculation result of the correlation coefficient shows that both the warp transformation and the sparse bayesian learning can obtain a good modal separation effect under the reflection-type hydrological environment condition, and the correlation coefficient of most modes is more than 0.9. We also examined the separation performance of the two methods under different SNR conditions, and the corresponding correlation coefficient results are shown in FIG. 7, wherein (a) (b) (c) (d) correspond to the fourth order normal wave respectively. It can be seen that under the condition of different signal-to-noise ratios, the separation performance of the method based on sparse Bayesian learning is slightly superior to that of the method based on Warping transformation.
Simulation example 2 downward refraction-like hydrological Environment (negative gradient hydrological Environment)
The 2 nd example is a downward refraction type hydrographic environment, i.e., a negative gradient hydrographic environment, which often occurs in summer with the seawater sound velocity gradually decreasing with depth. FIG. 8(a) shows a typical summer negative gradient hydronic velocity profile. The speed of sound drops from 1535m/s at the sea surface to 1498m/s near the sea floor. Other environmental parameters and settings of the sound source receiver are the same as in fig. 2. For this environment, the normal waves may reverse below the sea surface. FIG. 8(b) shows the phase velocity corresponding to the first six-order normal wave in the frequency band of 50-300Hz, wherein the dotted line represents the sound velocity at 1535m/s at the sea surface, and when the phase velocity is greater than 1535m/s, the normal wave is reflected at the sea surface, and the normal wave with the phase velocity less than 1535m/s is refracted below the sea surface. As can be seen from the figure, at some frequency bands, both reflection-type and refraction-type normal waves exist, and for this case, the Warping transformation is no longer applicable.
Consider the 90-120Hz frequency band as an example. From fig. 8(b), it can be seen that there are five propagating normal waves in total, wherein the fifth normal wave is weaker in energy, the 1 st and 2 nd normal waves reverse below the sea surface, and the 3 rd and 4 th normal waves reverse at the sea surface. The received signal is processed by using Warping transform, and the time domain signal, time frequency structure and frequency spectrum after Warping respectively correspond to (a), (b) and (c) in fig. 9. As can be seen from fig. 9, the 3 rd and 4 th normal waves can be clearly separated, while the 1 st and 2 nd normal waves are mixed together and cannot be distinguished, so that the 1 st and 2 nd normal waves cannot be separated by using Warping transformation in this case. Then, the method based on sparse bayesian learning provided by the present invention is used to process the single hydrophone signal, and the obtained result is shown in fig. 10. Fig. 10(a) is a horizontal wave number spectrum of gamma amplitude at 90Hz, and it can be seen that the first four normal waves can be clearly separated, and the time domain waveform of the first four normal waves after separation can be obtained by using equations (14) and (15), see fig. 10 (b). In contrast, fig. 10(b) also shows the time domain waveforms of the first four-order normal waves obtained by theoretical calculation, and it can be seen that the waveforms of the first four-order normal waves are highly consistent, and the correlation coefficients of the first four-order normal waves are 0.978, 0.9909, 0.9893, and 0.8852, respectively. The result of the correlation coefficient shows that the method provided by the invention still has higher precision on the separation of the normal wave modes in the negative gradient hydrological environment, embodies the advantages of the method in the negative gradient hydrological environment, and can be simultaneously applied to the scenes in which the reflection type normal waves and the refraction type normal waves exist simultaneously.
Example 2
the horizontal wave value acquisition module is used for acquiring a horizontal wave value of the broadband normal wave according to the approximate modal dispersion relation;
the dictionary matrix construction module is used for constructing a dictionary matrix of a sparse solution problem by using the horizontal wave number values based on a compressed sensing theory;
the sparse vector complex coefficient calculation module is used for constructing a sparse signal model by adopting a compressive sensing theory according to the dictionary matrix and the broadband frequency domain sound pressure vector received by the single hydrophone, and solving and calculating by utilizing a compressed sensing implementation algorithm to obtain a sparse vector complex coefficient;
and the normal wave mode separation module is used for recovering each separated normal wave mode according to the sparse vector complex coefficient and the dictionary matrix.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and are not limited. Although the present invention has been described in detail with reference to the embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (9)
1. A method for separating normal wave modes of a single hydrophone based on compressed sensing comprises the following steps:
obtaining a horizontal wave value of the broadband normal wave according to the approximate modal dispersion relation;
constructing a dictionary matrix of a sparse solution problem by using the horizontal wave number values based on a compressive sensing theory;
according to the dictionary matrix and the broadband frequency domain sound pressure vector received by the single hydrophone, constructing a sparse signal model by adopting a compressive sensing theory, and solving and calculating by utilizing a compressed sensing implementation algorithm to obtain a sparse vector complex coefficient;
and restoring each normal wave mode after separation according to the sparse vector complex coefficient and the dictionary matrix.
2. The compressed sensing-based single hydrophone normal wave modal separation method of claim 1, further comprising: arranging a single hydrophone in a region to be detected in shallow sea, wherein the distance between the single hydrophone and a sound source is rsThe frequency band of the sound source is [ f ]1，fF]。
3. The compressed sensing-based single hydrophone normal wave modal separation method of claim 2, further comprising: if the frequency band bandwidth of the sound source is larger than 40Hz, the frequency band is divided into a plurality of sub-frequency bands, and the bandwidth of each sub-frequency band is 20-40 Hz.
4. The compressed sensing-based single hydrophone normal wave modal separation method of claim 2, wherein the horizontal wave value of the broadband normal wave is obtained according to an approximate modal dispersion relation; the method specifically comprises the following steps:
according to the shallow sea acoustic propagation theory, the phase velocity C of normal wave propagating in the waveguidepSatisfies the following formula:
Cw≤Cp≤Cb，
wherein, CwRepresenting the speed of sound of seawater CbRepresenting the seafloor acoustic velocity;
for frequency band f1，fF]First frequency point f1From the interval [2 π f1/Cb，2πf1/Cw]Uniformly sampling M horizontal wave numbers;
calculating the frequency band [ f ] according to the approximate modal dispersion relation1，fF]MF number of horizontal wave values krl(fj+1) Comprises the following steps:
wherein k isrlIs the real part of complex eigenvalue of the ith order normal wave, representing the horizontal wave number of the mode, j is frequency point, F is frequency band [ F1，fF]Upper limit of frequency point.
5. The compressed sensing-based normal wave modal separation method for the single hydrophone according to claim 4, wherein a dictionary matrix of a sparse solution problem is constructed by horizontal wave number values based on a compressed sensing theory; the method specifically comprises the following steps:
according to the distance r between a single hydrophone and a sound sourcesAnd frequency band [ f1，fF]MF number of horizontal wave values krl(fj+1) And calculating a dictionary matrix of the sparse signal model by the following formula
Comprises the following steps:
6. the method for separating the normal wave modes of the single hydrophone based on the compressed sensing as claimed in claim 5, wherein a sparse signal model is constructed by adopting a compressed sensing theory according to a dictionary matrix and a broadband frequency domain sound pressure vector received by the single hydrophone, and a sparse vector complex coefficient is obtained by solving and calculating by utilizing a compressed sensing implementation algorithm; the method specifically comprises the following steps:
according to a dictionary matrix
And a wideband frequency domain sound pressure vector y received by the hydrophone, and the sparse signal model constructed by the compressive sensing theory is as follows:
wherein n is a complex Gaussian noise vector;
according to the sparse Bayesian learning algorithm, each element x of the sparse vector x to be solvedmAre subject to mean of zero and variance of gammam∈γ＝[γ1，…，γM]TComplex gaussian distribution of (a);
the maximum a posteriori probability estimate of the sparse vector x is calculated from
Comprises the following steps:
wherein H represents a conjugate transpose, and Γ ═ diag (γ)1，…，γM) And obtaining sparse vector complex coefficients for the diagonal covariance matrix.
7. The method for separating the normal wave modes of the single hydrophone based on the compressed sensing as claimed in claim 6, wherein the normal wave modes after separation are recovered according to sparse vector complex coefficients and a dictionary matrix; the method specifically comprises the following steps:
training by sparse vectors
And corresponding dictionary vectors
Obtaining K separated frequency domain modal signals
Comprises the following steps:
wherein,
as a sparse vector
The first element of (A) is (B),
is composed of
The ith column vector of (1).
8. The compressed sensing-based single hydrophone normal wave modal separation method of claim 7, further comprising: and transforming the separated frequency domain modal signals to a time domain.
9. A compressed sensing-based single hydrophone normal wave modal separation system, the system comprising: the device comprises a horizontal wave numerical value acquisition module, a dictionary matrix construction module, a sparse vector complex coefficient calculation module and a normal wave modal separation module; wherein,
the horizontal wave value acquisition module is used for acquiring a horizontal wave value of the broadband normal wave according to the approximate modal dispersion relation;
the dictionary matrix construction module is used for constructing a dictionary matrix of a sparse solution problem by using the horizontal wave number values based on a compressed sensing theory;
the sparse vector complex coefficient calculation module is used for constructing a sparse signal model by adopting a compressive sensing theory according to the dictionary matrix and the broadband frequency domain sound pressure vector received by the single hydrophone, and solving and calculating by utilizing a compressed sensing implementation algorithm to obtain a sparse vector complex coefficient;
and the normal wave mode separation module is used for recovering each separated normal wave mode according to the sparse vector complex coefficient and the dictionary matrix.
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