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

Abstract

The application provides a method and system for normal mode dispersion modal decomposition and sound source depth estimation, wherein the method comprises the following steps: S1, obtaining a vertical array space-frequency domain signal; S2, obtaining each order space parameterization model; S3, obtaining a frequency parameterization model; S4, jointly establishing a space-frequency parameterization superposition model of the vertical array space-frequency domain signal; S5, optimizing and solving each order space-frequency parameter matrix; S6, reconstructing each order space modal function and each order dispersion modal response; and S7, constructing a sound source depth estimation index, and optimizing and solving a sound source depth value. The application jointly models the space modal function and the frequency modal response by parameterization, can simultaneously decompose complex normal mode dispersion modes in the space domain and the frequency domain, simultaneously reconstructs each order space modal function and frequency modal response, and can better utilize the rich information of normal modes in the space and frequency dimensions, and has a better modal decomposition effect compared with a traditional single frequency point modal decomposition method.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of underwater acoustic signal processing, in particular, to a method and system for normal mode dispersion modal decomposition and sound source depth estimation based on a vertical array, and particularly to a method and system for normal mode dispersion modal parameterization space-frequency joint decomposition and sound source depth estimation. BACKGROUND

[0002] In shallow water environment, the sound propagation process of transient sound source is superimposed by a series of normal mode modes, each of which has unique spatial modal function and dispersion phase characteristics. From the perspective of information content, the spatial modal function of each order normal mode contains the depth information of the sound source and the receiving hydrophone, so the modal function can be extracted by the vertical hydrophone array receiving signal, which provides theoretical support for sound source depth estimation. The dispersion characteristics in the phase of each order normal mode contain the sound source propagation distance information, which can be used for sound source distance estimation.

[0003] Normal mode dispersion modal decomposition plays a key role in the whole sound propagation research and sound source positioning system, and it is an effective way to separate and extract the spatial modal function and dispersion phase characteristics of each order normal mode. It plays a decisive role in improving the accuracy of sound source depth and distance estimation.

[0004] However, the current commonly used dispersion modal decomposition methods, including warping transformation, frequency-wavenumber transformation, singular value decomposition, etc., have certain limitations. Most of them can only extract dispersion phase with the help of a single hydrophone, or only decompose spatial modal function at a single frequency point, which leads to the inability to fully exploit the rich information in the frequency and spatial dimensions, and makes it difficult to achieve joint and simultaneous decomposition of spatial modal function and frequency domain dispersion phase.

[0005] In terms of sound source depth estimation, there are also many challenges. It often relies on a large amount of prior knowledge of the ocean environment and needs a dense vertical array covering the entire water layer. The high requirements for prior knowledge and equipment not only make the cost high, but also make the depth estimation accuracy easily disturbed by the matching degree of the actual modal function and the copy modal. Once the environmental parameters are mismatched, the performance of sound source depth estimation will be greatly reduced, ultimately resulting in low accuracy and poor stability of sound source depth estimation. The existence of these problems seriously restricts the application and development of normal mode dispersion modal decomposition technology in the field of sound source depth and distance estimation, and needs to be solved to promote the progress and improvement of related technology.

[0006] A search is conducted on patent documents and finds an invention patent with publication number CN117907998B, which discloses a shallow sea 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 sea floor for observation; dividing the received broadband signal into multiple frequency points; performing spatial Fourier transform on each frequency point signal to obtain a horizontal wave number amplitude spectrum; relating the energy size of each mode in the horizontal wave number amplitude spectrum to the estimation accuracy of the horizontal wave number value to obtain a mode energy proportion; setting a proportion threshold to filter out the horizontal wave number effective value of each frequency point signal; judging the mode symbol corresponding to the horizontal wave number effective value, and obtaining the distance ambiguity function using the horizontal wave number effective value and the mode symbol; obtaining the distance ambiguity function of the broadband sound source by summing and averaging the distance ambiguity function, and the distance corresponding to the peak value is the estimated distance of the broadband sound source. The patent mainly focuses on shallow sea broadband sound source ranging, does not involve parameterized space-frequency joint decomposition of normal mode dispersion mode, and cannot fully utilize the space and frequency information for sound source depth estimation, and lacks corresponding processing and optimization methods in terms of decomposition accuracy and depth estimation affected by environmental parameters.

[0007] In summary, normal mode dispersion mode decomposition is faced with the problem of poor accuracy, it is difficult to fully exploit and integrate the rich information of space and frequency to carry out joint decomposition, and the sound source depth estimation link is significantly affected by environmental parameters, resulting in a series of problems such as large estimation error. In view of the problems of the prior art, it is a key task to study a method and system for normal mode dispersion mode decomposition and sound source depth estimation. SUMMARY

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

[0009] According to the method for normal mode dispersion mode decomposition and sound source depth estimation provided by the present application, the following steps are included:

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

[0011] Step S2: based on the vertical array space-frequency domain signal, the spatial mode function of each order normal mode is parameterized and characterized by a redundant Fourier basis function to obtain an air domain parameterization model of each order;

[0012] Step S3: frequency domain parameterization characterization is performed on each order dispersion mode response to obtain a frequency domain parameterization model, and the dispersion phase of each order dispersion mode response is obtained;

[0013] Step S4: coupling each order spatial parameterization model and frequency parameterization model, jointly establishing the spatial-frequency parameterization superposition model of vertical array spatial-frequency domain signal;

[0014] Step S5: constructing the joint decomposition optimization criterion of spatial-frequency parameterization superposition model, and optimizing and solving each order spatial-frequency parameter matrix;

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

[0016] Step S7: based on each order spatial modal function, each order frequency dispersion modal response and the dispersion phase of each order frequency dispersion modal response, constructing a sound source depth estimation index, and optimizing and solving to obtain the sound source depth value.

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

[0018]

[0019] Wherein, P(z,f) is the vertical array spatial-frequency domain signal, which is composed 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 is less than or equal to the depth of the seabed, f=f1,f2,…,f N represents discrete frequency points, and N is the number of frequency points; p m (z,f) is the mth order dispersion mode, and M is the order of the dispersion mode; represents residual noise and other high-order components; each order dispersion mode p m (z,f) is composed of the product of the spatial modal function Ψ m (z) and the frequency dispersion modal response q m (f).

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

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

[0022] Wherein, j 2 =-1 represents the imaginary symbol.

[0023] Preferably, in step S2, the spatial mode function of each order normal mode is as follows:

[0024]

[0025] wherein, is the 2K+1 spatial domain parameters of the mth order mode function, K is the order of the spatial domain redundant Fourier basis function; F0=1 / (2z g ) represents the basic resolution of the spatial domain redundant Fourier basis function,

[0026] Further, the spatial mode function of each order normal mode is converted into a matrix form of the spatial parameterization model:

[0027]

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

[0029]

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

[0031] Step S3.1: using a normal mode dispersion curve extraction method such as time-frequency transform, the group delay curve of each order dispersion mode is extracted from the hydrophone receiving signal, denoted as τ m (f), and the integral of each order group delay curve τ m (f) is carried out to obtain the dispersion phase φ m (f) of the response of each order dispersion mode:

[0032]

[0033] Step S3.2: the amplitude a m (f) of the response of each order dispersion mode is characterized by frequency domain parameterization using the redundant Fourier basis function:

[0034]

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

[0036] Step S3.3: Establishing the matrix form of the frequency domain parameterized model of each order dispersion modal response, i.e. bringing equation (6) and equation (7) into equation (2), and converting into the matrix form of the frequency domain parameterized model:

[0037]

[0038] wherein 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, and the expression is:

[0039]

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

[0041] Step S4.1: Coupling the mth order spatial domain parameterized model and the frequency domain parameterized model to establish the spatial-frequency parameterized model of the mth order dispersion modal:

[0042]

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

[0044] Step S4.2: Superimposing the spatial-frequency parameterized model of each order dispersion modal of equation (10) to jointly establish the spatial-frequency parameterized superimposed model of the vertical array spatial-frequency domain signal:

[0045]

[0046] wherein, is the matrix expression of the vertical array spatial-frequency domain signal;

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

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

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

[0050]

[0051] wherein, represents the square of the matrix F-norm, λ1and λ2are two regularization parameters;

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

[0053]

[0054] wherein, I1is a diagonal matrix with the same dimension as Θ T Θ -1 represents the inverse operation of a matrix;

[0055] Step S5.3: Based on the optimal solution, according to the distribution positions of the spatial-frequency parameter matrices of each order in the overall spatial-frequency parameter matrix, obtaining from which the spatial-frequency parameter matrices of each order solved by optimization are obtained in sequence

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

[0057] Step S6.1: Using the singular value decomposition principle to decouple the spatial-frequency parameter matrices of each order to obtain the spatial-domain parameter vectors of each order and the frequency-domain parameter vectors of each order, i.e., there are:

[0058]

[0059] wherein, is the spatial-domain parameter vector solved, is the frequency-domain parameter vector solved;

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

[0061]

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

[0063]

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

[0065] Step S7.1: Reconstructed spatial modal 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 depth of the seabed (h is the number of depth sampling points), the numerical value of the spatial modal function is obtained, and the sound source depth estimation index in the space-frequency domain is constructed as follows:

[0066]

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

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

[0069]

[0070] The application also provides a normal wave dispersion modal decomposition and sound source depth estimation system, comprising:

[0071] Module M1 receives the time-domain propagation signal of the transient sound source in shallow water by using the vertical hydrophone array, and converts the time-domain propagation signal of each array element of the vertical array to the space-frequency domain by Fourier transform to obtain the space-frequency domain signal of the vertical array;

[0072] Module M2: Based on the space-frequency domain signal of the vertical array, the spatial modal function of each order of normal wave is characterized by using the redundant Fourier basis function for space parameterization to obtain the space parameterization model of each order;

[0073] Module M3: The frequency domain parameterization of the frequency dispersion modal response is characterized to obtain the frequency domain parameterization model, and the dispersion phase of the frequency dispersion modal response is obtained;

[0074] Module M4: Coupling the space parameterization model and the frequency domain parameterization model, the space-frequency parameterization superposition model of the space-frequency domain signal of the vertical array is jointly established;

[0075] Module M5: Constructing the joint decomposition optimization criterion of the space-frequency parameterization superposition model, optimizing and solving the space-frequency parameter matrix of each order;

[0076] Module M6: Decoupling the space-frequency parameter matrix of each order to obtain the space domain parameter vector of each order and the frequency domain parameter vector of each order, and simultaneously reconstructing the spatial modal function of each order and the frequency dispersion modal response of each order;

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

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

[0079] 1、The present application can simultaneously decompose complex normal mode dispersion in space and frequency domain by parameterizing joint modeling of spatial modal function and frequency domain modal response, and can simultaneously reconstruct each order spatial modal function and frequency domain modal response, which can better utilize the rich information of normal mode in space and frequency dimension, and has better modal decomposition effect compared with traditional single frequency point modal decomposition method.

[0080] 2、The sound source depth estimation of the present application does not require any environmental parameters, and the constructed sound source depth estimation index is derived from each order spatial modal function, frequency dispersion modal response and dispersion phase reconstructed from actual data, which belongs to a data-driven method and can accurately obtain sound source depth estimation result without any environmental parameters. The traditional method requires to construct a matching field or a matching modal for matching processing according to good prior environmental parameters, which is easily affected by environmental parameter mismatch, resulting in poor estimation accuracy.

[0081] 3、The sound source depth estimation index constructed by the present application has good depth estimation result visualization performance, and the present system does not require to uniformly and densely arrange a large number of vertical hydrophone arrays, but only needs a small number of sparse array elements to obtain good depth estimation accuracy, which has strong automation and engineering practicability. BRIEF DESCRIPTION OF DRAWINGS

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

[0083] Figure 1 The present application is a normal mode dispersion modal parameterization space-frequency joint decomposition and sound source depth estimation method flowchart in the embodiment of the present application;

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

[0085] Figure 3 The present application is a short frequency Fourier transform time-frequency diagram of the frequency domain signal of the 1st array element in the embodiment of the present application;

[0086] Figure 4 The present application is each order spatial modal function reconstructed by parameterization space-frequency joint decomposition in the embodiment of the present application: the black circles in the figure are the theoretical values of each order spatial modal function at the depth of the 10-element array, and the black dotted line is each order spatial modal function reconstructed by the present application.

[0087] Figure 5 for the parametric spatial-frequency joint decomposition of the reconstructed modal responses of each order of dispersion in the embodiments of the present application;

[0088] Figure 6 for the time-frequency analysis of the reconstructed modal responses of each order of dispersion in the embodiments of the present application using the short frequency Fourier transform, Figure 5 the results of which can intuitively show that the reconstructed modal responses of each order of dispersion have been completely decomposed, and the dispersion characteristics of the decomposed modal responses of each order are consistent with the theoretical group delay curve (white dotted line in the figure). Figure 6

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

[0090] Figure 8 for the constructed sound source depth estimation results in the embodiments of the present application. DETAILED DESCRIPTION

[0091] The present application will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the present application, but do not limit the present application in any form. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present application. These are within the scope of protection of the present application.

[0092] Example 1:

[0093] Figure 1 for the normal mode dispersion modal parameterized spatial-frequency joint decomposition and sound source depth estimation method flowchart in the embodiments of the present application.

[0094] As shown in the figure, the present embodiment provides a normal mode dispersion modal decomposition and sound source depth estimation method, which comprises the following steps: Figure 1

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

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

[0097]

[0098] ​​where P(z,f) is the vertical array's spatial-frequency domain signal, which is composed 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 is less than or equal to the depth of the seabed, f=f1,f2,…,f N represents discrete frequency points (N is the number of frequency points); p m (z,f) is the m-order dispersion mode, and M is the order of the dispersion mode. represents residual noise and other high-order components; each order of dispersion mode p m (z,f) is composed of the product of the spatial mode function Ψ m (z) and the dispersion mode response q m (f). Each order of dispersion mode response q m (f) contains the dispersion phase φ m (f) and the amplitude a m (f), and the expression is:

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

[0100] where j 2 =-1 represents the imaginary symbol.

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

[0102] Assume that the ocean environment is as follows: the depth of the seabed is 100 m, the sound speed and density of seawater are 1500 m / s and 1000 kg / m 3 respectively, the sound speed and density of the seabed are 1700 m / s and 2000 kg / m 3 respectively. The sparse vertical hydrophone array has 10 elements, which are arranged at depths from 10 m to 100 m at an interval of 10 m, and the elements of the vertical hydrophone array are numbered as 1-10 from shallow to deep; the transient sound source is located at a water depth of 65 m and has a horizontal distance of 10000 m from the receiving hydrophone array. The simulation is performed on the received signal of the vertical hydrophone array, the sampling frequency is set to 500 Hz, 10 channels of time domain received signals are obtained, and the signals are converted into the spatial-frequency domain by Fourier transform, and the vertical array spatial-frequency domain signal is obtained as shown in Figure 2 Then, the short frequency Fourier transform is performed on the frequency domain signal of the No. 1 element, and the dispersion modes of each order of normal mode with typical dispersion characteristics are displayed as shown in Figure 3 .

[0103] Step S2: Based on the vertical array spatial domain signal, the spatial mode function Ψ m (z) of each order normal mode is obtained.

[0104] Specifically, the spatial mode function of each order normal mode is as follows:

[0105]

[0106] wherein, is the 2K+1 spatial parameters of the mth order mode 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. The boundary effect problem introduced by the conventional Fourier basis function in approximating non-periodic functions can be effectively avoided, so that the spatial mode function of each order is better characterized.

[0107] Further, the spatial mode function of each order normal mode in formula (3) is converted into a matrix form of the spatial parameterization model:

[0108]

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

[0110]

[0111] Step S3: The frequency domain parameterization characterization is performed on the frequency dispersion mode response q m (f) of each order, and the frequency domain parameterization model is obtained, and the dispersion phase of the frequency dispersion mode response of each order is obtained.

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

[0113] Step S3.1: A normal mode dispersion curve extraction method such as time-frequency transform is adopted to extract the group delay curve of each order dispersion mode from the hydrophone receiving signal, which is represented as τ m (f), and the integration is performed on each order group delay curve τ m (f) to obtain the dispersion phase φ m (f) of the frequency dispersion mode response:

[0114]

[0115] Step S3.2: the amplitude a of each order dispersion modal response m (f) the frequency domain parameterization representation is carried out by using a redundant Fourier basis function:

[0116]

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

[0118] Step S3.3: the frequency domain parameterization model of each order dispersion modal response is established in a matrix form, that is, formula (6) and formula (7) are brought into formula (2), and the frequency domain parameterization model in a matrix form is converted:

[0119]

[0120] wherein, 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, and the expression is:

[0121]

[0122] Step S4: coupling the space domain parameterization model and the frequency domain parameterization model of each order, a space-frequency parameterization superposition model of the vertical array space-frequency domain signal is jointly established.

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

[0124] Step S4.1: coupling the mth order space domain parameterization model and the frequency domain parameterization model, establishing the space-frequency parameterization model of the mth order dispersion modal:

[0125]

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

[0127] Step S4.2: superimpose the parametric models of each order dispersion mode of formula (10) to jointly establish a parametric superimposed model of the vertical array's spatial-frequency domain signal:

[0128]

[0129] wherein, is a matrix expression form of the vertical array's spatial-frequency domain signal;

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

[0131] Step S5: construct a joint decomposition optimization criterion of the parametric superimposed model to optimize and solve each order spatial-frequency parameter matrix.

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

[0133] Step S5.1: construct a joint decomposition optimization criterion of the parametric superimposed model:

[0134]

[0135] wherein, represents the square of the matrix F-norm, and 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 spatial-frequency parameter matrix, as follows:

[0137]

[0138] wherein, I1 is a diagonal matrix with the same dimension as , and I2 is a diagonal matrix with the same dimension as Θ T ; represents the inverse operation of the matrix. -1

[0139] Step S5.3: based on the optimal solution, according to the distribution position of each order spatial-frequency parameter matrix in the overall spatial-frequency parameter matrix, obtain from which the optimized and solved each order spatial-frequency parameter matrix

[0140] Step S6: decouple each order spatial-frequency parameter matrix to obtain each order spatial parameter vector and each order frequency parameter vector, and simultaneously reconstruct each order spatial mode function and each order dispersion mode response. ​

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

[0142] Step S6.1: Using the singular value decomposition principle, decouple each order spatial-frequency parameter matrix to obtain each order spatial parameter vector and each order frequency parameter vector, i.e.

[0143]

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

[0145] Step S6.2: Reconstruct each order spatial modal function based on each order spatial parameter vector:

[0146]

[0147] The reconstruction results of the first 6 orders of spatial modal functions are shown in Figure 4 : the black circles are the theoretical values of each order of spatial modal function at the depth of 10 array elements, and the resolution is low; and the black dotted line is the value of each order of spatial modal function decomposed and reconstructed by the application, and the black dotted line has higher depth resolution, because the reconstructed spatial modal function can calculate the spatial modal function value at finer depth sampling points z=z1, z2, …, z h (here, the z value is 1, 2, 3, …, 100 m in turn) so that the depth resolution is better, which lays a solid foundation for improving the accuracy of sound source depth estimation in the next step.

[0148] Step S6.3: Reconstruct each order of frequency dispersion modal response based on each order of frequency parameter vector:

[0149]

[0150] The reconstruction results of the first 6 orders of frequency dispersion modal responses are shown in Figure 5 : it can be clearly found that the cutoff frequency of each order of frequency dispersion modal increases in turn as the order increases. In order to visually display the effectiveness and accuracy of the decomposition and reconstruction results of each order of frequency dispersion modal response, the short frequency Fourier transform is performed on each order of frequency dispersion modal to obtain the time-frequency diagram of each order of frequency dispersion modal, as shown in Figure 6 : it intuitively shows that each order of frequency dispersion modal response has been completely decomposed, and the frequency dispersion characteristics of each order of decomposed modal are consistent with the theoretical group delay curve (the white dotted line in Figure 6 ), which fully verifies the effectiveness and accuracy of the joint decomposition method of the application.

[0151] Step S7: constructing a sound source depth estimation index based on the spatial modal functions, the dispersion modal responses, and the dispersion phases of the dispersion modal responses, and optimizing to obtain a sound source depth value.

[0152] Specifically, step S7 includes the following substeps:

[0153] Step S7.1: reconstructing the spatial modal functions Without being limited to the number and depth of the vertical hydrophone array elements, the spatial modal functions are reconstructed according to the depth sampling points z = z1, z2, …, z h , z h < h (h is the number of depth sampling points) to obtain the numerical values of the spatial modal functions (here, the z values are taken as 1, 2, 3, …, 100 m in turn), and constructing the sound source depth estimation index in the space-frequency domain as follows:

[0154]

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

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

[0157]

[0158] In formula (17) and formula (18), part of the orders of the dispersion modal is selected from the M orders of the dispersion modal to construct the sound source depth index, and part of the frequency bands can also be selected to superimpose J(z, f) to estimate the sound source depth. The above index has the selection function of the modal order and the frequency band, and can enable the operator to have a better understanding of the sound source depth estimation result and its influencing factors.

[0159] As shown in Figure 7 , it is the two-dimensional joint distribution of the sound source depth estimation index in the space and the frequency domain, and the curve of the change of the sound source depth estimation value with the frequency (the white dotted line in Figure 7 ) can be clearly found; further, the square sum of the sound source depth estimation index along the frequency dimension is found to find the maximum value of the index as the sound source depth estimation result, as shown in Figure 8 , the sound source depth estimation result is 64 m, which is consistent with the actual value 65 m, and the depth estimation error is about 1.5%, which verifies that the present application has high estimation accuracy in the sound source depth estimation.

[0160] Example 2:

[0161] The present invention also provides a system for normal mode dispersion mode decomposition and sound source depth estimation. The system for normal mode dispersion mode decomposition and sound source depth estimation can be implemented by performing the process steps of the method for normal mode dispersion mode decomposition and sound source depth estimation. That is, those skilled in the art can understand the method for normal mode dispersion mode decomposition and sound source depth estimation as a preferred embodiment of the system for normal mode dispersion mode decomposition and sound source depth estimation.

[0162] The system for normal mode 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 a transient sound source in shallow sea, and converts the time-domain propagation signal of each element of the vertical array to the spatial frequency domain through Fourier transform to obtain the vertical array spatial frequency domain signal.

[0164] Module M2: Based on the vertical array spatial frequency domain signal, the spatial mode functions of each order normal wave are characterized by spatial parameterization using redundant Fourier basis functions to obtain spatial parameterization models of each order.

[0165] Module M3: Performs frequency domain parameterization characterization on the dispersion modal responses of each order to obtain the frequency domain parameterization model, and simultaneously obtains the dispersion phase of the dispersion modal responses of each order;

[0166] Module M4: Couples spatial and frequency parameterization models of various orders to jointly establish a spatial-frequency parameterization superposition model of vertical array spatial-frequency signals;

[0167] Module M5: Constructs a joint decomposition optimization criterion for the spatial frequency parameterized superposition model, and optimizes the solution of spatial frequency parameter matrices of each order;

[0168] Module M6: Decouples the space-frequency parameter matrices of each order to obtain the spatial parameter vectors and frequency parameter vectors of each order, and simultaneously reconstructs the spatial mode functions and dispersion mode responses of each order.

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

[0170] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0171] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for normal mode dispersion mode decomposition and sound source depth estimation, characterized in that, Includes the following steps: Step S1: Receive the time-domain propagation signal of the transient sound source in the shallow sea using a vertical hydrophone array, and convert the time-domain propagation signal of each element of the vertical array to the spatial frequency domain through Fourier transform to obtain the vertical array spatial frequency domain signal. Step S2: Based on the vertical array spatial frequency domain signal, the spatial mode functions of each order normal wave are characterized by spatial parameterization using redundant Fourier basis functions to obtain the spatial parameterization model of each order. Step S3: Perform frequency domain parameterization characterization on the dispersion modal responses of each order to obtain the frequency domain parameterization model, and at the same time obtain the dispersion phase of each order dispersion modal response; Step S4: Couple the spatial parameterization models of each order and the frequency parameterization models to jointly establish a spatial-frequency parameterization superposition model of the vertical array spatial-frequency domain signal; Step S5: Construct the joint decomposition optimization criterion for the space frequency parameterized superposition model, and optimize the solution of space frequency parameter matrices of each order; Step S6: Decouple the space-frequency parameter matrices of each order to obtain the spatial parameter vectors and frequency parameter vectors of each order, and simultaneously reconstruct the spatial mode functions and dispersion mode responses of each order. Step S7: Based on the reconstructed spatial mode functions of each order, the reconstructed dispersion mode responses of each order, and the dispersion phase of the reconstructed dispersion mode responses of each order, construct a sound source depth estimation index and optimize the solution to obtain the sound source depth value.

2. The method for normal mode dispersion mode decomposition and sound source depth estimation according to claim 1, characterized in that, In step S1, based on normal mode theory, ignoring the weak frequency dependence of the spatial mode function, the vertical array spatial frequency domain signal is expressed as a superposition of a series of dispersion modes, as shown in the following expression: (1) in, P ( z , f () is a vertical array spatial frequency domain signal, composed of M The frequency dispersion mode and residual components are superimposed to form the frequency dispersion mode. z=z 1, z 2,…, z g The depth of each element in the vertical hydrophone array. g The number of array elements z g Less than or equal to the depth of the seabed f=f 1, f 2, …, f N Representing discrete frequency points, N The number of frequency points; p m ( z , f ) is the first m First-order dispersion mode, M Let be the order of the dispersion mode; Represents residual noise and other higher-order components; each dispersion mode p m ( z , f ) by spatial mode function Ψ m ( z and dispersive modal response q m ( f It is composed of the product of ).

3. The method for normal mode dispersion mode decomposition and sound source depth estimation according to claim 2, characterized in that, In step S1, the dispersive mode responses of each order q m ( f Includes dispersive phase ϕ m ( f ) and amplitude a m ( f The expression is: (2) in, j 2 =-1 represents the imaginary number sign.

4. The method for normal mode dispersion mode decomposition and sound source depth estimation according to claim 3, characterized in that, In step S2, the spatial mode functions of each normal mode are as follows: （3） in,{ } is the first m 2nd order mode function K +1 spatial parameters, K The order of the spatially redundant Fourier basis functions; F 0 = 1 / (2 z g ) represents the fundamental resolution of the spatially redundant Fourier basis functions. Furthermore, the spatial mode functions of each normal mode are converted into a matrix-form spatial parameterized model: (4) in, , The upper right corner T indicates transpose; H represents the spatially redundant Fourier basis function matrix: （5）。 5. The method for normal mode dispersion mode decomposition and sound source depth estimation according to claim 4, characterized in that, Step S3 includes the following sub-steps: Step S3.1: Using the time-frequency transform normal mode dispersion curve extraction method, extract the group delay curves of each dispersion mode from the hydrophone received signal, represented as follows: τ m ( f ( ), for the delay curves of each order group τ m ( f Integrating, the dispersion phase of each order dispersion mode response is obtained. ϕ m ( f ): (6) Step S3.2: Measure the amplitude of each dispersive mode response. a m ( f Frequency domain parameterization is performed using redundant Fourier basis functions: （7） in,{ } is the first m 2nd order dispersion mode response L +1 frequency domain parameter, L The order of the frequency-domain redundant Fourier basis functions; T 0 = 1 / (2 f N ) represents the fundamental resolution of the frequency domain redundant Fourier basis functions; Step S3.3: Establish a matrix-form frequency domain parameterized model for each order of dispersion mode response, that is, substitute equations (6) and (7) into equation (2) and convert it into a matrix-form frequency domain parameterized model: （8） in, , , The product of the frequency domain basis function matrix and the dispersion phase is expressed as: （9）。 6. The method for normal mode dispersion mode decomposition and sound source depth estimation according to claim 5, characterized in that, Step S4 includes the following sub-steps: Step S4.1: Coupling the first m The first-order spatial domain parameterization model and the frequency domain parameterization model are used to establish the second-order spatial domain parameterization model. m Spatial frequency parameterization model of the first dispersion mode: （10） in, It is the first m First-order dispersion mode p m ( z , f At discrete points z=z 1, z 2, …, z g and f=f 1, f 2, …, f N The matrix representation of the values; It is called the space-frequency parameter matrix, which is the product of the spatial domain parameter vector and the frequency domain parameter vector; Step S4.2: Superimpose the space-frequency parameterization models of each order dispersion mode in equation (10) to jointly establish the space-frequency parameterization superposition model of the vertical array space-frequency domain signal: （11） in, This is the matrix representation of the vertical array spatial frequency domain signal; A matrix representation of residual noise and other higher-order components; This is called the overall space frequency parameter matrix, which contains space frequency parameter matrices of various orders; It includes the basis function matrices of each order and the dispersion phase of the dispersion mode response of each order.

7. The method for normal mode dispersion mode decomposition and sound source depth estimation according to claim 6, characterized in that, Step S5 includes the following sub-steps: Step S5.1: Construct the joint decomposition optimization criteria for the space-frequency parameterized superposition model: （12） in, Denotes the square of the F-norm of a matrix. λ 1 and λ 2 represents 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: （13） in, I 1 is the dimension and The same diagonal matrix, I 2 is the dimension and Same diagonal matrix; () -1 Represents the matrix inversion operation; Step S5.3: Based on the optimal solution, according to the distribution position of each order of space frequency parameter matrix in the overall space frequency parameter matrix, obtain... From this, the space frequency parameter matrices of each order obtained by optimization solution are obtained sequentially. .

8. The method for normal mode dispersion mode decomposition and sound source depth estimation according to claim 7, characterized in that, Step S6 includes the following sub-steps: Step S6.1: Using the singular value decomposition principle, the space-frequency parameter matrices of each order are decoupled to obtain the spatial parameter vectors and frequency parameter vectors of each order, i.e.: （14） in, To solve for the spatial parameter vector, The frequency domain parameter vector to be solved; Step S6.2: Reconstruct the spatial mode functions of each order based on the spatial parameter vectors of each order: （15） Step S6.3: Reconstruct the dispersion mode response of each order based on the frequency domain parameter vectors of each order: （16）。 9. The method for normal mode dispersion mode decomposition and sound source depth estimation according to claim 8, characterized in that, Step S7 includes the following sub-steps: Step S7.1: Reconstructed Spatial Mode Functions Including the number and depth of vertical hydrophone array elements, according to depth sampling points z=z 1, z 2, …, z h ，z h For depths less than or equal to the seabed depth, where h is the number of depth sampling points, the spatial modal function values ​​are obtained, and the following spatial frequency domain sound source depth estimation index is constructed: （17） in, J ( z , f () is a sound source depth estimation index, which is a spatial domain z and frequency domain f The two-dimensional distribution function; multiply the reconstructed dispersion mode response of each order by the dispersion phase of each order; Step S7.2: For J ( z , f The square of the frequency f The depth corresponding to the maximum value after superposition is the estimated depth of the sound source. The formula is as follows: （18）。 10. A system for normal mode 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 a transient sound source in shallow sea, and converts the time-domain propagation signal of each element of the vertical array to the spatial frequency domain through Fourier transform to obtain the vertical array spatial frequency domain signal. Module M2: Based on the vertical array spatial frequency domain signal, the spatial mode functions of each order normal wave are characterized by spatial parameterization using redundant Fourier basis functions to obtain spatial parameterization models of each order. Module M3: Performs frequency domain parameterization characterization on the dispersion modal responses of each order to obtain the frequency domain parameterization model, and simultaneously obtains the dispersion phase of the dispersion modal responses of each order; Module M4: Couples the spatial parameterization models of each order and the frequency parameterization model to jointly establish a spatial-frequency parameterization superposition model of the vertical array spatial-frequency domain signal; Module M5: Constructs the joint decomposition optimization criterion for the space-frequency parameterized superposition model, and optimizes the solution of space-frequency parameter matrices of each order; Module M6: Decouples the space-frequency parameter matrices of each order to obtain the spatial parameter vectors and frequency parameter vectors of each order, and simultaneously reconstructs the spatial mode functions and dispersion mode responses of each order. Module M7: Based on the reconstructed spatial mode functions of each order, the reconstructed dispersion mode responses of each order, and the dispersion phase of the reconstructed dispersion mode responses of each order, a sound source depth estimation index is constructed, and the sound source depth value is obtained by optimizing the solution.

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