Method and system for normal wave frequency dispersion mode decomposition and sound source depth estimation

Abstract

The invention provides a normal wave frequency dispersion mode decomposition and sound source depth estimation method and system. The method comprises the following steps: S1, obtaining a vertical array space-frequency domain signal; s2, obtaining a parameterized model of each order of airspace; s3, obtaining a frequency domain parameterized model; s4, jointly establishing a space-frequency parameterization superposition model of the space-frequency domain signals of the vertical array; s5, optimizing and solving the space-frequency parameter matrix of each order; s6, reconstructing each order of space modal function and each order of frequency dispersion modal response; and S7, constructing a sound source depth estimation index, and performing optimization solution to obtain a sound source depth value. According to the method, parameterized joint modeling is carried out on the spatial modal function and the frequency domain modal response, a complex normal wave frequency dispersion mode can be jointly decomposed in the spatial domain and the frequency domain at the same time, meanwhile, the spatial modal function and the frequency domain modal response of each order are obtained through reconstruction, and compared with a traditional single-frequency-point modal decomposition method and the like, the method has the advantage that the method is more efficient. Rich information of normal waves in space and frequency dimensions can be better utilized, and the modal decomposition effect is better.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater acoustic signal processing, and in particular, to a method and system for simple normal wave dispersion modal decomposition and sound source depth estimation based on a vertical array, and in particular to a method and system for simple normal wave dispersion modal parameterized space-frequency joint decomposition and sound source depth estimation. Background Art

[0002] In shallow sea environments, the sound propagation process of transient sound sources is composed of a series of simple normal wave modes, each of which has a unique spatial modal function and dispersion phase characteristics. From the perspective of information inclusion, the spatial modal function of each order of simple normal waves contains the depth information of the sound source and the receiving hydrophone. Therefore, the modal function can be extracted by receiving the signal through the vertical hydrophone array, which provides theoretical support for the estimation of the sound source depth. The dispersion characteristics in the phase of each order of simple normal waves contain the sound source propagation distance information, which can be used to estimate the distance of the sound source.

[0003] Simple normal wave dispersion modal decomposition occupies a key position in the entire sound propagation research and sound source localization system. It is an effective way to separate and extract the spatial modal functions and dispersion phase characteristics of simple normal waves of various orders, and plays a decisive role in improving the accuracy of sound source depth and distance estimation.

[0004] However, the commonly used dispersion mode decomposition methods, including Warping transform, frequency-wavenumber transform, singular value decomposition, etc., all have certain limitations. Most of them can only realize dispersion phase extraction with the help of a single hydrophone, or only perform spatial mode function decomposition at a single frequency point, which makes it impossible to fully explore the rich information of frequency and spatial dimensions, and it is difficult to achieve the joint and simultaneous decomposition of spatial mode function and frequency domain dispersion phase.

[0005] There are also many challenges in sound source depth estimation. It often relies on a large amount of prior knowledge of the ocean environment and requires a dense vertical array covering the entire water layer. This high requirement for prior knowledge and equipment not only makes the cost high, but also the depth determination accuracy is easily affected by the degree of matching between the copied mode and the actual modal function. Once the environmental parameters are mismatched, the estimation performance of the sound source depth will drop significantly, ultimately resulting in low accuracy and poor stability in the sound source depth estimation. The existence of these problems has seriously restricted the application and development of simple normal wave dispersion mode decomposition technology in the field of sound source depth and distance estimation, and it is urgent to solve them to promote the advancement and improvement of related technologies.

[0006] By searching the patent literature, it was found that the invention patent with the publication number CN117907998B discloses a shallow water broadband sound source ranging method, medium and system, which includes the following steps: laying a horizontal line array parallel to the sea level at the bottom of the seabed for observation; dividing the received broadband signal into multiple frequency points; performing spatial Fourier transform on the signal of each frequency point to obtain a horizontal wavenumber amplitude spectrum; linking the energy size of each mode in the horizontal wavenumber amplitude spectrum with the estimated accuracy of the horizontal wavenumber value to obtain the modal energy proportion; setting a proportion threshold to filter out the horizontal wavenumber effective value of each frequency point signal; judging the modal sign corresponding to the horizontal wavenumber effective value, and using the horizontal wavenumber effective value and the modal sign to obtain the distance ambiguity function; obtaining the distance ambiguity function of the broadband sound source by summing and averaging the modulus value of the distance ambiguity function, and the distance corresponding to the peak value is the estimated broadband sound source distance. This patent mainly focuses on shallow water broadband sound source ranging, and does not involve the parametric space-frequency joint decomposition of simple normal wave dispersion modes. It cannot fully utilize the space-frequency domain information for sound source depth estimation, and lacks corresponding processing and optimization methods for the decomposition accuracy and depth estimation affected by environmental parameters.

[0007] In summary, the simple normal wave dispersion modal decomposition faces the dilemma of poor accuracy. It is difficult to fully explore and integrate the rich information in the spatial domain and the frequency domain to carry out joint decomposition. In addition, the sound source depth estimation link is significantly affected by environmental parameters, resulting in a large estimation error and other problems. In view of the above problems of the prior art, studying a method and system for simple normal wave dispersion modal decomposition and sound source depth estimation has become a key task that needs to be solved urgently. Summary of the invention

[0008] In view of the defects in the prior art, the object of the present invention is to provide a method and system for simple normal wave dispersion mode decomposition and sound source depth estimation.

[0009] A method for normal wave dispersion mode decomposition and sound source depth estimation provided by the present invention comprises the following steps:

[0010] Step S1, using a vertical hydrophone array to receive the time domain propagation signal of a transient sound source in the shallow sea, and converting the time domain propagation signal of each array element of the vertical array into the space-frequency domain through Fourier transform to obtain a vertical array space-frequency domain signal;

[0011] Step S2: Based on the vertical array frequency domain signal, the spatial modal functions of each order of simple normal waves are characterized by spatial parameterization using redundant Fourier basis functions to obtain spatial parameterization models of each order;

[0012] Step S3: performing frequency domain parameterization on each order of dispersion modal response to obtain a frequency domain parameterized model, and simultaneously obtaining the dispersion phase of each order of dispersion modal response;

[0013] Step S4: coupling the spatial parameterized models and frequency domain parameterized models of various orders, and jointly establishing a spatial-frequency parameterized superposition model of the vertical array spatial frequency domain signal;

[0014] Step S5: constructing a joint decomposition optimization criterion for the space-frequency parameterized superposition model, and optimizing and solving the space-frequency parameter matrices of each order;

[0015] Step S6: decoupling each order of space-frequency parameter matrix, obtaining each order of space-domain parameter vector and each order of frequency-domain parameter vector, and simultaneously reconstructing each order of spatial modal function and each order of dispersion modal response;

[0016] Step S7: Based on each order of spatial mode function, each order of dispersion mode response and each order of dispersion mode response, a sound source depth estimation index is constructed, and the sound source depth value is obtained by optimization.

[0017] Preferably, in step S1, according to the simple normal wave theory, the weak dependence of the spatial modal function on the frequency is ignored, and the vertical array frequency domain signal is expressed as a superposition of a series of dispersive modes, and the expression is as follows:

[0018]

[0019] Where P(z,f) is the vertical array frequency domain signal, which is composed of the superposition of M-order dispersion modes and residual components, z = z1, z2, …, z g is the depth of each element of the vertical hydrophone array, g is the number of elements, z g Less than or equal to the seafloor depth, f=f1,f2,…,f N Represents discrete frequency points, N is the number of frequency points; p m (z,f) is the mth order dispersion mode, M is the order of the dispersion mode; Represents the residual noise and other high-order components; each order dispersion mode p m (z,f) is given by the spatial mode function Ψ m (z) and the dispersion modal response q m (f) is the product of

[0020] Preferably, in step S1, each order of dispersion modal response q m (f) contains the dispersion phase φ m (f) and amplitude a m (f), the expression is:

[0021] q m (f) = a m (f)exp(jφ m (f)) (2)

[0022] Among them, j 2 =-1 represents the imaginary number sign.

[0023] Preferably, in step S2, the spatial mode functions of each order of simple normal waves are as follows:

[0024]

[0025] in, are the 2K+1 spatial parameters of the m-th order modal function, K is the order of the spatial redundant Fourier basis function; F0 = 1 / (2z g ) represents the basic resolution of the spatial redundant Fourier basis function,

[0026] Then, the spatial modal functions of each order of simple normal waves are converted into spatial parameterized models in matrix form:

[0027]

[0028] Among them, ψ m =[ψ m (z1) ψ m (z2) … ψ m (z g )] T , The upper right corner T represents transpose; H represents the spatial redundant Fourier basis function matrix:

[0029]

[0030] Preferably, step S3 includes the following sub-steps:

[0031] Step S3.1: Use the time-frequency transform and other simple normal wave dispersion curve extraction methods to extract the group delay curves of each order dispersion mode from the hydrophone received signal, expressed as τ m (f), for each order group delay curve τ m (f) Integrate to obtain the dispersion phase φ of each order dispersion mode response m (f):

[0032]

[0033] Step S3.2: Calculate the amplitude a of each order of dispersion mode response m (f) Frequency domain parameterization using redundant Fourier basis functions:

[0034]

[0035] in, are the 2L+1 frequency domain parameters of the mth order dispersive modal response, L is the order of the frequency domain redundant Fourier basis function; T0 = 1 / (2f N ) represents the basic resolution of the redundant Fourier basis function in the frequency domain;

[0036] Step S3.3: Establish a frequency domain parameterized model in matrix form for each order of dispersion modal response, that is, substitute equation (6) and equation (7) into equation (2) and convert it into a frequency domain parameterized model in matrix form:

[0037]

[0038] Among them, q m =[q m (f1) q m (f2) … q m (f N )], Θ m Contains the product of the frequency domain basis function matrix and the dispersion phase, expressed as:

[0039]

[0040] Preferably, step S4 includes the following sub-steps:

[0041] Step S4.1: Couple the m-th order spatial domain parameterized model and the frequency domain parameterized model to establish the spatial-frequency parameterized model of the m-th order dispersion mode:

[0042]

[0043] in, is the mth order dispersion mode p m (z,f) at discrete points z=z1,z2,…,z g and f=f1,f2,…,f N The matrix expression of the value; It is called the space-frequency parameter matrix, which is the product of the space-domain parameter vector and the frequency-domain parameter vector;

[0044] Step S4.2: Superimpose the space-frequency parameterized models of each order dispersion mode in equation (10) to jointly establish the space-frequency parameterized superposition model of the vertical array space-frequency domain signal:

[0045]

[0046] in, It is the matrix expression of vertical array frequency domain signal;

[0047] Represents the matrix expression of residual noise and other high-order components; Ω = [Ω1Ω2…Ω M ] is called the overall space-frequency parameter matrix, which contains the space-frequency parameter matrices of each order; Θ = [Θ1Θ2…Θ M ] contains the basis function matrices of each order and the dispersion phase of each order of dispersion mode response.

[0048] Preferably, step S5 includes the following sub-steps:

[0049] Step S5.1: Constructing the joint decomposition optimization criterion of the space-frequency parameterized superposition model:

[0050]

[0051] in, represents the square of the matrix F-norm, λ1 and λ2 are two regularization parameters;

[0052] Step S5.2: Solve the joint decomposition optimization criterion to obtain the optimal solution of the overall space-frequency parameter matrix, as follows:

[0053]

[0054] Among them, I1 is the dimension and The same diagonal matrix, I2 has the same dimension as Θ T Θ is the same diagonal matrix; () -1 Represents the inverse operation of a matrix;

[0055] Step S5.3: Based on the optimal solution, according to the distribution position of each order space-frequency parameter matrix in the overall space-frequency parameter matrix, obtain From this, we can get the optimized space-frequency parameter matrices of each order in turn.

[0056] Preferably, step S6 includes the following sub-steps:

[0057] Step S6.1: Using the singular value decomposition principle, decouple the space-frequency parameter matrices of each order to obtain the space-domain parameter vectors of each order and the frequency-domain parameter vectors of each order, that is,

[0058]

[0059] in, is the spatial parameter vector to be solved, is the frequency domain parameter vector to be solved;

[0060] Step S6.2: Reconstruct the spatial modal functions of each order based on the spatial parameter vectors of each order:

[0061]

[0062] Step S6.3: Reconstruct the dispersion modal responses of each order based on the frequency domain parameter vectors of each order:

[0063]

[0064] Preferably, step S7 includes the following sub-steps:

[0065] Step S7.1: Reconstructed spatial mode function Not limited to the number and depth of vertical hydrophone array elements, according to the depth sampling points z = z1, z2, ..., z h , z h Less than or equal to the seabed depth (h is the number of depth sampling points), the value of the spatial modal function is obtained, and the sound source depth estimation index in the spatial frequency domain is constructed as follows:

[0066]

[0067] Among them, J(z,f) is the sound source depth estimation index, which is a two-dimensional distribution function of the spatial domain z and the frequency domain f; the dispersive modal response reconstructed at each order is multiplied by the dispersive phase of each order.

[0068] Step S7.2: Superimpose the square of J(z,f) along the frequency f and take the depth corresponding to the maximum value, which is the estimated value of the sound source depth The formula is as follows:

[0069]

[0070] The present invention also provides a system for normal wave dispersion mode decomposition and sound source depth estimation, comprising:

[0071] Module M1 uses a vertical hydrophone array to receive the time domain propagation signal of the transient sound source in the shallow sea, and converts the time domain propagation signal of each array element of the vertical array into the space-frequency domain through Fourier transform to obtain the vertical array space-frequency domain signal;

[0072] Module M2: Based on the vertical array frequency domain signal, the spatial modal functions of each order of simple normal waves are parameterized in the spatial domain using redundant Fourier basis functions to obtain parameterized models of each order in the spatial domain;

[0073] Module M3: Perform frequency domain parameterization on each order of dispersion modal response to obtain a frequency domain parameterized model and obtain the dispersion phase of each order of dispersion modal response;

[0074] Module M4: Couple the spatial parameterized models and frequency domain parameterized models of various orders to jointly establish the spatial-frequency parameterized superposition model of the vertical array spatial frequency domain signal;

[0075] Module M5: Construct the joint decomposition optimization criterion of the space-frequency parameterized superposition model and optimize the space-frequency parameter matrix of each order;

[0076] Module M6: Decouple the space-frequency parameter matrices of each order, obtain the space-domain parameter vectors of each order and the frequency-domain parameter vectors of each order, and simultaneously reconstruct the spatial modal functions of each order and the dispersion modal responses of each order;

[0077] Module M7: Based on the spatial modal functions of each order, the dispersion modal responses of each order and the dispersion phase of each order dispersion modal response, a sound source depth estimation index is constructed, and the sound source depth value is obtained by optimization.

[0078] Compared with the prior art, the present invention has the following beneficial effects:

[0079] 1. The present invention can jointly decompose complex simple normal wave dispersion modes in both the spatial domain and the frequency domain by performing parameterized joint modeling of the spatial modal function and the frequency domain modal response, and simultaneously reconstruct the spatial modal functions and frequency domain modal responses of various orders. Compared with traditional single-frequency point modal decomposition methods, it can better utilize the rich information of the simple normal wave in the spatial and frequency dimensions, and the modal decomposition effect is better.

[0080] 2. The sound source depth estimation of the present invention does not require any environmental parameters. The constructed sound source depth estimation index is derived from the spatial modal functions, dispersion modal responses and dispersion phases of various orders decomposed and reconstructed from actual data. It is a data-driven method and can accurately obtain the sound source depth estimation result without any environmental parameters. However, the sound source depth estimation of the traditional method needs to construct a matching field or matching mode according to good prior environmental parameters for matching processing, which is easily affected by the mismatch of environmental parameters, resulting in poor estimation accuracy.

[0081] 3. The sound source depth estimation index of the two-dimensional joint distribution of spatial and frequency domains constructed by the present invention has good visualization performance of the depth estimation result. In addition, the system does not need to evenly and densely deploy a large number of vertical hydrophone arrays, but only needs a small number of array elements to be sparsely deployed to obtain good depth estimation accuracy, and has strong automation and engineering practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0083] Figure 1 It is a flow chart of a method for parameterized space-frequency joint decomposition and sound source depth estimation of a simple normal wave dispersion mode in an embodiment of the present invention;

[0084] Figure 2 is a spatial frequency domain signal received by a 10-element vertical hydrophone array in an embodiment of the present invention;

[0085] Figure 3 is a short-frequency Fourier transform time-frequency diagram of the frequency domain signal of array element No. 1 in an embodiment of the present invention;

[0086] Figure 4 : The spatial mode functions of various orders reconstructed by parameterized space-frequency joint decomposition in an embodiment of the present invention: the black circles in the figure are the theoretical values ​​of the spatial mode functions of various orders at the depth of 10 array elements, and the black dotted lines are the spatial mode functions of various orders reconstructed by the present invention;

[0087] Figure 5 It is the dispersion modal response of each order of parameterized space-frequency joint decomposition and reconstruction in the embodiment of the present invention;

[0088] Figure 6 The embodiment of the present invention uses short-frequency Fourier transform to Figure 5 The results of time-frequency analysis of the reconstructed dispersion modal responses of each order can intuitively show that the reconstructed dispersion modal responses of each order have been completely decomposed, and the decomposed dispersion characteristics of each order modal are consistent with the theoretical group delay curve ( Figure 6 The white dotted line in the middle is consistent;

[0089] Figure 7 : is a two-dimensional joint distribution of the sound source depth estimation index constructed in the embodiment of the present invention in the spatial domain and the frequency domain (the white dotted line is a sound source depth-frequency estimation curve);

[0090] Figure 8 It is the sound source depth estimation result constructed in the embodiment of the present invention. DETAILED DESCRIPTION

[0091] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0092] Embodiment 1:

[0093] Figure 1 It is a flow chart of the method for space-frequency joint decomposition and sound source depth estimation of simple normal wave dispersion mode parameterization in an embodiment of the present invention.

[0094] like Figure 1 As shown, this embodiment provides a method for simple normal wave dispersion mode decomposition and sound source depth estimation, including the following steps:

[0095] Step S1, using a vertical hydrophone array to receive the time domain propagation signal of a transient sound source in the shallow sea, and converting the time domain propagation signal of each array element of the vertical array into the space-frequency domain through Fourier transform to obtain a vertical array space-frequency domain signal.

[0096] Specifically, according to the simple normal wave theory, ignoring the weak dependence of the spatial modal function on frequency, the vertical array frequency domain signal is expressed as the superposition of a series of dispersive modes, and the expression is as follows:

[0097]

[0098] Where P(z,f) is the vertical array frequency domain signal, which is composed of the superposition of M-order dispersion modes and residual components, z = z1, z2, …, z g is the depth of each element of the vertical hydrophone array (g is the number of elements, z is the number of elements, g less than or equal to the seabed depth), f=f1,f2,…,f N Represents discrete frequency points (N is the number of frequency points); p m (z,f) is the mth order dispersion mode, M is the order of the dispersion mode; Represents the residual noise and other high-order components; each order dispersion mode p m (z,f) is given by the spatial mode function Ψ m (z) and the dispersion modal response q m The product of (f) is formed. The dispersion modal response of each order q m (f) contains the dispersion phase φ m (f) and amplitude a m (f), the expression is:

[0099] q m (f) = a m (f)exp(jφ m (f)) (2)

[0100] Among them, j 2 =-1 represents the imaginary number sign.

[0101] Figure 2 is a spatial frequency domain signal received by a 10-element vertical hydrophone array in an embodiment of the present invention; Figure 3 It is a short-frequency Fourier transform time-frequency diagram of the frequency domain signal of array element No. 1 in an embodiment of the present invention.

[0102] Assume the ocean environment is as follows: the seabed depth is 100m, the speed of sound and density of seawater are 1500m / s and 1000kg / m respectively 3 , the seabed sound speed and density are 1700m / s and 2000kg / m 3 . A total of 10 elements of the vertical hydrophone array are sparsely deployed, with a deployment depth from 10m to 100m, and a vertical deployment depth interval of 10m. The vertical hydrophone array elements are numbered 1-10 from shallow to deep; the transient sound source is located at a water depth of 65m, and the horizontal distance from the receiving hydrophone array is 10000m. The vertical hydrophone array receiving signal is simulated, and the sampling frequency is set to 500Hz to obtain a 10-channel time domain receiving signal. The signal is Fourier transformed and converted to the space-frequency domain to obtain the vertical array space-frequency domain signal as shown in the figure. Figure 2 As shown; Then the frequency domain signal of array element 1 is short-frequency Fourier transformed to display the dispersion modes of each order of simple normal wave with typical dispersion characteristics, as shown in Figure 3 shown.

[0103] Step S2: Based on the vertical array frequency domain signal, the spatial mode function Ψ of each order of simple normal wave is calculated. m (z) Redundant Fourier basis functions are used to perform spatial parameterization characterization to obtain spatial parameterization models of various orders.

[0104] Specifically, the spatial mode functions of each order of simple normal waves are as follows:

[0105]

[0106] in, are the 2K+1 spatial parameters of the m-th order modal function, K is the order of the spatial redundant Fourier basis function; F0 = 1 / (2z g ) represents the basic resolution of the spatial redundant Fourier basis function. It can effectively avoid the boundary effect problem introduced by the conventional Fourier basis function approximation of non-periodic functions, thereby better characterizing the spatial modal functions of various orders.

[0107] Then, the spatial modal functions of each order of simple normal waves in equation (3) are converted into spatial parameterized models in matrix form:

[0108]

[0109] Among them, ψ m =[ψ m (z1) ψ m (z2) … ψ m (z g )] T , The upper right corner T represents transpose; H represents the spatial redundant Fourier basis function matrix:

[0110]

[0111] Step S3: For each order of dispersion mode response q m (f) Perform frequency domain parametric characterization to obtain a frequency domain parametric model and obtain the dispersion phase of each order of dispersion mode response.

[0112] Specifically, step S3 includes the following sub-steps:

[0113] Step S3.1: Use the time-frequency transform and other simple normal wave dispersion curve extraction methods to extract the group delay curves of each order dispersion mode from the hydrophone received signal, expressed as τ m (f), for each order group delay curve τ m (f) Integrate to obtain the dispersion phase φ of each order dispersion mode response m (f):

[0114]

[0115] Step S3.2: Calculate the amplitude a of each order of dispersion mode response m (f) Frequency domain parameterization using redundant Fourier basis functions:

[0116]

[0117] in, are the 2L+1 frequency domain parameters of the mth order dispersive modal response, L is the order of the frequency domain redundant Fourier basis function; T0 = 1 / (2f N ) represents the basic resolution of the redundant Fourier basis function in the frequency domain.

[0118] Step S3.3: Establish a frequency domain parameterized model in matrix form for each order of dispersion modal response, that is, substitute equation (6) and equation (7) into equation (2) and convert it into a frequency domain parameterized model in matrix form:

[0119]

[0120] Among them, q m =[q m (f1) q m (f2) … q m (f N )], Θ m Contains the product of the frequency domain basis function matrix and the dispersion phase, expressed as:

[0121]

[0122] Step S4: coupling the spatial parameterized models and frequency domain parameterized models of various orders, and jointly establishing a spatial-frequency parameterized superposition model of the vertical array spatial frequency domain signal.

[0123] Specifically, step S4 includes the following sub-steps:

[0124] Step S4.1: Couple the m-th order spatial domain parameterized model and the frequency domain parameterized model to establish the spatial-frequency parameterized model of the m-th order dispersion mode:

[0125]

[0126] in, is the mth order dispersion mode p m (z,f) at discrete points z=z1,z2,…,z g and f=f1,f2,…,f N The matrix expression of the value; It is called the space-frequency parameter matrix, which is the product of the space domain parameter vector and the frequency domain parameter vector.

[0127] Step S4.2: Superimpose the space-frequency parameterized models of each order dispersion mode in equation (10) to jointly establish the space-frequency parameterized superposition model of the vertical array space-frequency domain signal:

[0128]

[0129] in, It is the matrix expression of vertical array frequency domain signal;

[0130] Represents the matrix expression of residual noise and other high-order components; Ω = [Ω1Ω2…Ω M ] is called the overall space-frequency parameter matrix, which includes the space-frequency parameter matrices of each order; Θ = [Θ1Θ2…Θ M ] contains the basis function matrices of each order and the dispersion phase of each order of dispersion mode response.

[0131] Step S5: construct a joint decomposition optimization criterion for the space-frequency parameterized superposition model to optimize and solve the space-frequency parameter matrices of each order.

[0132] Specifically, step S5 includes the following sub-steps:

[0133] Step S5.1: Constructing the joint decomposition optimization criterion of the space-frequency parameterized superposition model:

[0134]

[0135] in, represents the square of the matrix F-norm, λ1 and λ2 are two regularization parameters.

[0136] Step S5.2: Solve the joint decomposition optimization criterion to obtain the optimal solution of the overall space-frequency parameter matrix, as follows:

[0137]

[0138] Among them, I1 is the dimension and The same diagonal matrix, I2 has the same dimension as Θ T Θ is the same diagonal matrix; () -1 Represents the matrix inversion operation.

[0139] Step S5.3: Based on the optimal solution, according to the distribution position of each order space-frequency parameter matrix in the overall space-frequency parameter matrix, obtain From this, we can get the optimized space-frequency parameter matrices of each order in turn.

[0140] Step S6: Decouple each order of space-frequency parameter matrix to obtain each order of space-domain parameter vector and each order of frequency-domain parameter vector, and simultaneously reconstruct each order of spatial modal function and each order of dispersion modal response.

[0141] Specifically, step S6 includes the following sub-steps:

[0142] Step S6.1: Using the singular value decomposition principle, decouple the space-frequency parameter matrices of each order to obtain the space-domain parameter vectors of each order and the frequency-domain parameter vectors of each order, that is,

[0143]

[0144] in, is the spatial parameter vector to be solved, is the frequency domain parameter vector to be solved.

[0145] Step S6.2: Reconstruct the spatial modal functions of each order based on the spatial parameter vectors of each order:

[0146]

[0147] The reconstruction results of the first 6 order spatial mode functions are as follows: Figure 4 As shown: the black circles are the theoretical values ​​of the spatial mode functions of each order at the depth of 10 array elements, and their resolution is relatively low; while the black dotted lines are the values ​​of the spatial mode functions of each order decomposed and reconstructed by the present invention, and the black dotted lines have a higher depth resolution because the reconstructed spatial mode functions It can be calculated at finer depth sampling points z = z1, z2, ..., z h The spatial modal function value (the z value here is 1, 2, 3, ..., 100m), so that the depth resolution is better, laying a solid foundation for the next step to improve the accuracy of sound source depth estimation.

[0148] Step S6.3: Reconstruct the dispersion modal responses of each order based on the frequency domain parameter vectors of each order:

[0149]

[0150] The reconstruction results of the first 6 order dispersive modal responses are as follows: Figure 5 As shown in the figure, it can be clearly found that as the order increases, the cutoff frequency of each order of dispersion mode increases successively. In order to visualize the effectiveness and accuracy of the decomposition and reconstruction results of each order of dispersion mode response, a short-frequency Fourier transform is performed on each order of dispersion mode to obtain the time-frequency diagram of each order of dispersion mode, as shown in Figure 6 As shown, it is intuitively shown that the modal responses of each order of dispersion have been completely decomposed, and the decomposed modal dispersion characteristics of each order are consistent with the theoretical group delay curve ( Figure 6 The white dotted line in the figure is consistent, which fully verifies the effectiveness and accuracy of the combined decomposition method of the present invention.

[0151] Step S7: Based on each order of spatial mode function, each order of dispersion mode response and each order of dispersion mode response, a sound source depth estimation index is constructed, and the sound source depth value is obtained by optimization.

[0152] Specifically, step S7 includes the following sub-steps:

[0153] Step S7.1: Reconstructed spatial mode function Not limited to the number and depth of vertical hydrophone array elements, according to the depth sampling points z = z1, z2, ..., z h , z h Less than or equal to the seabed depth (h is the number of depth sampling points), obtain the value of the spatial modal function (here the z value is 1, 2, 3, ..., 100m in sequence), and construct the sound source depth estimation index in the space-frequency domain as follows:

[0154]

[0155] Among them, J(z,f) is the sound source depth estimation index, which is a two-dimensional distribution function of the spatial domain z and the frequency domain f; multiplying the reconstructed dispersion mode response of each order by the dispersion phase of each order is equivalent to demodulating the phase of each order dispersion mode, so that the above index has a maximum value when a certain depth sampling point is close to the actual sound source depth.

[0156] Step S7.2: Superimpose the square of J(z,f) along the frequency f and take the depth corresponding to the maximum value, which is the estimated value of the sound source depth The formula is as follows:

[0157]

[0158] In equations (17) and (18), some order dispersion modes are selected from the M-order dispersion modes to construct the sound source depth index, and some frequency bands can also be selected to superimpose J(z,f) to obtain the maximum value to estimate the sound source depth. The above indicators have the function of selecting the modal order and frequency band, which can allow the operator to have a better understanding of the sound source depth estimation results and its influencing factors.

[0159] like Figure 7 The figure shows the two-dimensional joint distribution of the sound source depth estimation index in the spatial domain and the frequency domain. It can be clearly seen that the curve of the sound source depth estimation value changing with frequency ( Figure 7 Furthermore, the square sum of the sound source depth estimation index is performed along the frequency dimension, and the maximum value of the index is found as the sound source depth estimation result, such as Figure 8 As shown, the sound source depth estimation result is 64m, which is consistent with the actual value of 65m, and the depth estimation error is about 1.5%, which verifies that the present invention has a high estimation accuracy in sound source depth estimation.

[0160] Embodiment 2:

[0161] The present invention also provides a system for simple normal wave dispersion modal decomposition and sound source depth estimation. The system for simple normal wave dispersion modal decomposition and sound source depth estimation can be implemented by executing the process steps of the method for simple normal wave dispersion modal decomposition and sound source depth estimation, that is, those skilled in the art can understand the method for simple normal wave dispersion modal decomposition and sound source depth estimation as a preferred implementation of the system for simple normal wave dispersion modal decomposition and sound source depth estimation.

[0162] The system for normal wave dispersion mode decomposition and sound source depth estimation includes:

[0163] Module M1 uses a vertical hydrophone array to receive the time domain propagation signal of the transient sound source in the shallow sea, and converts the time domain propagation signal of each array element of the vertical array into the space-frequency domain through Fourier transform to obtain the vertical array space-frequency domain signal;

[0164] Module M2: Based on the vertical array frequency domain signal, the spatial modal functions of each order of simple normal waves are parameterized in the spatial domain using redundant Fourier basis functions to obtain parameterized models of each order in the spatial domain;

[0165] Module M3: Perform frequency domain parameterization on each order of dispersion modal response to obtain a frequency domain parameterized model and obtain the dispersion phase of each order of dispersion modal response;

[0166] Module M4: Couple the spatial parameterized models and frequency domain parameterized models of various orders to jointly establish the spatial-frequency parameterized superposition model of the vertical array spatial frequency domain signal;

[0167] Module M5: Construct the joint decomposition optimization criterion of the space-frequency parameterized superposition model and optimize the space-frequency parameter matrix of each order;

[0168] Module M6: Decouple the space-frequency parameter matrices of each order, obtain the space-domain parameter vectors of each order and the frequency-domain parameter vectors of each order, and simultaneously reconstruct the spatial modal functions of each order and the dispersion modal responses of each order;

[0169] Module M7: Based on the spatial modal functions of each order, the dispersion modal responses of each order and the dispersion phase of each order dispersion modal response, a sound source depth estimation index is constructed, and the sound source depth value is obtained by optimization.

[0170] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0171] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A method for normal wave dispersion mode decomposition and sound source depth estimation, characterized in that: The steps include: Step S1, using a vertical hydrophone array to receive the time domain propagation signal of a transient sound source in the shallow sea, and converting the time domain propagation signal of each array element of the vertical array into the space-frequency domain through Fourier transform to obtain a vertical array space-frequency domain signal; Step S2: Based on the vertical array spatial frequency domain signal, the spatial modal functions of each order of simple normal waves are characterized by spatial parameterization using redundant Fourier basis functions to obtain spatial parameterization models of each order; Step S3: performing frequency domain parameterization on each order of dispersion modal response to obtain a frequency domain parameterized model, and simultaneously obtaining the dispersion phase of each order of dispersion modal response; Step S4: coupling the spatial parameterized models of each order and the frequency domain parameterized models to jointly establish a spatial-frequency parameterized superposition model of vertical array spatial frequency domain signals; Step S5: constructing a joint decomposition optimization criterion of the space-frequency parameterized superposition model to optimize and solve space-frequency parameter matrices of various orders; Step S6: decoupling the space-frequency parameter matrices of each order, obtaining space-domain parameter vectors of each order and frequency-domain parameter vectors of each order, and simultaneously reconstructing spatial modal functions of each order and dispersion modal responses of each order; Step S7: constructing a sound source depth estimation index based on the spatial modal functions of each order, the dispersion modal responses of each order, and the dispersion phases of the dispersion modal responses of each order, and optimizing and solving to obtain the sound source depth value.

2. The method for normal wave dispersion modal decomposition and sound source depth estimation according to claim 1, characterized in that: In step S1, according to the simple normal wave theory, the weak dependence of the spatial modal function on the frequency is ignored, and the vertical array frequency domain signal is expressed as a superposition of a series of dispersion modes, and the expression is as follows: Where P(z,f) is the vertical array frequency domain signal, which is composed of the superposition of M-order dispersion modes and residual components, z = z1, z2, …, z g is the depth of each element of the vertical hydrophone array, g is the number of elements, z g Less than or equal to the seafloor depth, f=f1,f2,…,f N Represents discrete frequency points, N is the number of frequency points; p m (z,f) is the mth order dispersion mode, M is the order of the dispersion mode; Represents the residual noise and other high-order components; each order dispersion mode p m (z,f) is given by the spatial mode function Ψ m (z) and the dispersion modal response q m (f) is the product of 3. The method for normal wave dispersion modal decomposition and sound source depth estimation according to claim 2, characterized in that: In step S1, each order of dispersion modal response q m (f) contains the dispersion phase φ m (f) and amplitude a m (f), the expression is: q m (f)=a m (f)exp(jφ m (f)) (2) Among them, j 2 =-1 represents the imaginary number sign.

4. The method for normal wave dispersion modal decomposition and sound source depth estimation according to claim 3, characterized in that: In step S2, the spatial modal functions of the simple normal waves of each order are as follows: in, are the 2K+1 spatial parameters of the m-th order modal function, K is the order of the spatial redundant Fourier basis function; F0 = 1 / (2z g ) represents the basic resolution of the spatial redundant Fourier basis function, Then, the spatial modal functions of the simple normal waves of each order are converted into spatial parameterized models in matrix form: Among them, ψ m =[ψ m (z1) ψ m (z2) … ψ m (z g )] T , The upper right corner T represents transpose; H represents the spatial redundant Fourier basis function matrix:

5. The method for normal wave dispersion modal decomposition and sound source depth estimation according to claim 4, characterized in that: The step S3 includes the following sub-steps: Step S3.1: Use the time-frequency transform and other simple normal wave dispersion curve extraction methods to extract the group delay curves of each order dispersion mode from the hydrophone received signal, expressed as τ m (f), for each order group delay curve τ m (f) Integrate to obtain the dispersion phase φ of each order dispersion mode response m (f): Step S3.2: Calculate the amplitude a of each order of the dispersion modal response m (f) Frequency domain parameterization using redundant Fourier basis functions: in, are the 2L+1 frequency domain parameters of the mth order dispersive modal response, L is the order of the frequency domain redundant Fourier basis function; T0 = 1 / (2f N ) represents the basic resolution of the redundant Fourier basis function in the frequency domain; Step S3.3: Establish a frequency domain parameterized model in matrix form for each order of the dispersion modal response, that is, substitute equation (6) and equation (7) into equation (2) and convert it into a frequency domain parameterized model in matrix form: Among them, q m =[q m (f1) q m (f2) … q m (f N )], Θ m Contains the product of the frequency domain basis function matrix and the dispersion phase, expressed as:

6. The method for normal wave dispersion modal decomposition and sound source depth estimation according to claim 5, characterized in that: The step S4 includes the following sub-steps: Step S4.1: Coupling the m-th order spatial domain parameterized model and the frequency domain parameterized model to establish a spatial frequency parameterized model of the m-th order dispersion mode: in, is the mth order dispersion mode p m (z,f) at discrete points z=z1,z2,…,z g and f=f1,f2,…,f N The matrix expression of the value; It is called the space-frequency parameter matrix, which is the product of the space-domain parameter vector and the frequency-domain parameter vector; Step S4.2: Superimpose the space-frequency parameterized models of each order dispersion mode in equation (10) to jointly establish the space-frequency parameterized superposition model of the vertical array space-frequency domain signal: in, It is the matrix expression of vertical array frequency domain signal; Represents the matrix expression of residual noise and other high-order components; Ω = [Ω1Ω2…Ω M ] is called the overall space-frequency parameter matrix, which contains the space-frequency parameter matrices of each order; Θ = [Θ1Θ2…Θ M ] contains the basis function matrices of each order and the dispersion phase of each order of dispersion mode response.

7. The method for normal wave dispersion modal decomposition and sound source depth estimation according to claim 6, characterized in that: The step S5 comprises the following sub-steps: Step S5.1: constructing a joint decomposition optimization criterion for the space-frequency parameterized superposition model: in, represents the square of the matrix F-norm, λ1 and λ2 are two regularization parameters; Step S5.2: Solve the joint decomposition optimization criterion to obtain the optimal solution of the overall space-frequency parameter matrix, as follows: Among them, I1 is the dimension and The same diagonal matrix, I2 has the same dimension as Θ T Θ is the same diagonal matrix; () -1 Represents the inverse operation of a matrix; Step S5.3: Based on the optimal solution, according to the distribution position of each order space-frequency parameter matrix in the overall space-frequency parameter matrix, obtain From this, we can get the optimized space-frequency parameter matrices of each order in turn.

8. The method for normal wave dispersion modal decomposition and sound source depth estimation according to claim 7, characterized in that: The step S6 comprises the following sub-steps: Step S6.1: Using the singular value decomposition principle, decouple the space-frequency parameter matrices of each order to obtain space-domain parameter vectors of each order and frequency-domain parameter vectors of each order, that is, in, is the spatial parameter vector to be solved, is the frequency domain parameter vector to be solved; Step S6.2: Reconstructing spatial modal functions of various orders based on the spatial parameter vectors of various orders: Step S6.3: Reconstruct the dispersion modal responses of each order based on the frequency domain parameter vectors of each order:

9. The method for normal wave dispersion modal decomposition and sound source depth estimation according to claim 8, characterized in that: The step S7 includes the following sub-steps: Step S7.1: Reconstructed spatial mode function Not limited to the number and depth of vertical hydrophone array elements, according to the depth sampling points z = z1, z2, ..., z h , z h Less than or equal to the seabed depth, h is the number of depth sampling points, the value of the spatial modal function is obtained, and the sound source depth estimation index in the space-frequency domain is constructed as follows: Among them, J(z,f) is the sound source depth estimation index, which is a two-dimensional distribution function of the spatial domain z and the frequency domain f; the reconstructed dispersion modal response of each order is multiplied by the dispersion phase of each order; Step S7.2: Superimpose the square of J(z,f) along the frequency f and take the depth corresponding to the maximum value, which is the estimated value of the sound source depth The formula is as follows:

10. A system for normal wave dispersion mode decomposition and sound source depth estimation, characterized in that: include: Module M1 uses a vertical hydrophone array to receive the time domain propagation signal of the transient sound source in the shallow sea, and converts the time domain propagation signal of each array element of the vertical array into the space-frequency domain through Fourier transform to obtain the vertical array space-frequency domain signal; Module M2: Based on the vertical array spatial frequency domain signal, the spatial modal functions of each order of simple normal waves are parameterized in the spatial domain using redundant Fourier basis functions to obtain spatial parameterized models of each order; Module M3: Perform frequency domain parameterization on each order of dispersion modal response to obtain a frequency domain parameterized model and obtain the dispersion phase of each order of dispersion modal response; Module M4: coupling the spatial parameterized models of each order and the frequency domain parameterized models to jointly establish a spatial-frequency parameterized superposition model of vertical array spatial frequency domain signals; Module M5: constructing a joint decomposition optimization criterion for the space-frequency parameterized superposition model, and optimizing and solving the space-frequency parameter matrices of each order; Module M6: decouple the space-frequency parameter matrices of each order, obtain space-domain parameter vectors of each order and frequency-domain parameter vectors of each order, and simultaneously reconstruct space modal functions of each order and dispersion modal responses of each order; Module M7: Based on the spatial modal functions of each order, the dispersion modal responses of each order and the dispersion phases of the dispersion modal responses of each order, a sound source depth estimation index is constructed, and the sound source depth value is obtained by optimization.

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