Goodness vector calculation method for measuring modal filtering performance of vertical linear array

Abstract

The invention discloses a goodness vector calculation method for measuring modal filtering performance of a vertical linear array. The goodness vector calculation method comprises the following steps: (1) initializing marine environment parameters, line spectrum signal parameters emitted by a sound source and vertical receiving array parameters; (2) calculating each order normal wave mode function excited by a line spectrum signal emitted by a sound source and a receiving sound pressure value at each hydrophone depth of a vertical array by using a Kraken model, and establishing an array receiving sound pressure vector; (3) constructing a sampling mode function matrix, multiplying a pseudo-inverse matrix of the sampling mode function matrix by the sampling mode function matrix to obtain a mode filtering matrix, and calculating a relative attenuation coefficient of each order mode; (4) calculating to obtain a contribution degree matrix by using the modal filtering matrix and the relative attenuation coefficient of each order of modal, and taking out main diagonal element values of the contribution degree matrix to form a goodness vector; according to the method, the modal filtering performance can be quantitatively represented, and a quantitative analysis means is provided for measuring the modal filtering performance under the vertical linear array.

Description

Technical Field

[0001] This invention relates to a goodness vector calculation method for evaluating the performance of modal filtering of vertical linear arrays, belonging to the field of underwater acoustic target radiation noise line spectrum identification. Background Technology

[0002] Underwater acoustic target identification is a crucial support for underwater information acquisition and countermeasures, and is one of the important research directions in the field of underwater acoustics. Identifying whether an underwater acoustic target is located on the surface or underwater is of great guiding significance for ensuring one's own safety and attacking threatening enemy targets. The depth of an underwater target is one of the key characteristics of underwater acoustic target identification. Based on the target's depth information, targets can be distinguished into surface ships and underwater navigation equipment, allowing for different countermeasures. Compared to accurately estimating the target's depth, making a binary decision between surface and underwater targets simplifies the complex localization problem into a classification problem, thereby reducing reliance on prior acoustic field information.

[0003] Currently, underwater acoustic target depth identification techniques can be mainly divided into three categories: underwater acoustic target depth identification based on radiated noise characteristics, underwater acoustic target depth identification based on depth estimation, and underwater acoustic target depth identification based on channel characteristics. Channel characteristic-based underwater acoustic target depth identification does not require target depth estimation; it uses channel characteristics with high tolerance to environmental mismatch to identify target depth and has been widely used in recent years. For this type of technology, channel feature extraction is the key to achieving depth identification. Channel feature extraction is closely related to the array shape. Because vertical arrays have a larger aperture in the depth direction, they can collect changes in the sound field in the vertical direction. Using vertical arrays to extract channel features often achieves better classification results, making it particularly suitable for underwater acoustic target depth identification.

[0004] The modified modal scintillation index (MRSCI) based on vertical arrays is a statistical measure for depth identification of underwater acoustic targets. This statistic, grounded in modal filtering, utilizes the difference in normal mode amplitude fluctuations caused by depth variations in the target acoustic source to achieve binary identification of surface and underwater targets. This statistic is defined as a value independent of the target acoustic source level and distance, exhibiting high tolerance to environmental mismatch, but is limited by the performance of the modal filtering algorithm. When the number of hydrophones in the array is less than the normal mode order or the effective vertical aperture of the array is too small, the performance of the modal filtering algorithm degrades. Currently, there are few studies that quantitatively describe the performance of modal filtering. Whether the modified modal scintillation index can still be used for depth identification when the number of array elements is small and modal filtering performance degrades requires further investigation. Furthermore, in practical applications, the vertical arrays used by underwater unmanned platforms such as buoys and submersibles are usually sparse vertical arrays with a small number of array elements. Therefore, researching sound source depth identification methods under sparse vertical arrays is of great significance for the identification of underwater acoustic targets.

[0005] This invention proposes a goodness-of-performance vector calculation method for evaluating the modal filtering performance of a vertical linear array. The input signal is the received data of underwater acoustic target radiated noise sources at hydrophones at different depths, and the output is a goodness-of-performance vector evaluating the modal filtering performance of the vertical linear array. Simulation and sea trial data processing results show that this method can effectively reflect the performance of modal filtering and provides a quantitative analysis method for the depth identification performance of line spectrum sources under a vertical linear array.

[0006] The following prior art has been retrieved and compared with this application one by one, with the differences as follows:

[0007] I. Technical Comparison with Patent CN108562905B "A Weighted Underwater Target Detection Method Based on Modal Domain Subspace Detector"

[0008] 1. Patent CN108562905B utilizes a modal matrix of vertical linear arrays to construct modal subspace detectors (MSSDs) of various orders. Then, using the reciprocals of the attenuation exponents of each order of mode as weighting coefficients, the MSSDs of each order are weighted and superimposed to ultimately construct a weighted reconstructed modal spatial detector (WMSD). In contrast, this invention constructs a modal filtering matrix based on a modal matrix of vertical linear arrays, and then constructs a contribution matrix based on the relative attenuation coefficients of each order of mode. The main diagonal elements of the contribution matrix are used to form the final goodness vector. Therefore, although both utilize modal matrices and the attenuation characteristics of each order of mode, the construction principles and methods of their statistics are fundamentally different.

[0009] 2. The WMSD detection statistics constructed in patent CN108562905B aim to mitigate the impact of the poorly performing MSSD (low signal-to-noise ratio) on the final detector, thereby improving the passive detection probability of distant, unknown underwater targets. This patent represents a performance optimization of existing modal spatial detectors (MSDs), aiming to enhance the detection performance of underwater targets. In contrast, the goodness vector proposed in this invention aims to quantitatively characterize the performance of vertical linear array modal filtering. It is constructed based on existing modified modal scintillation index statistics and is used to measure under what conditions depth identification methods based on these statistics remain effective, focusing more on improving the depth identification performance of surface and underwater targets. Therefore, the technical problems addressed, the statistical systems relied upon, and the objectives of the two are different.

[0010] II. Technical Comparison with Patent CN110081964A "Joint Estimation Method of Underwater Sound Source Location and Power Spectrum Based on Sparse Spectrum Fitting"

[0011] 1. Patent CN110081964A constructs a sparse representation model of the received signal by performing distance-depth gridding on the experimental water area and transforming it to the frequency domain. It further establishes the correspondence between the frequency domain covariance matrix and the radiated noise power spectral density (PSD), and finally uses the sparse spectrum fitting (SpSF) method to jointly estimate the target spatial location and the radiated noise PSD. This method mainly solves the problems of locating sound sources at unknown locations and recovering the radiated noise power spectrum; its technical essence belongs to the category of target location and power spectrum estimation. In contrast, the core of this invention lies in quantitatively characterizing the performance of vertical linear array modal filtering to evaluate the effectiveness of depth identification methods based on modified modal scintillation index under different conditions; its essence belongs to the field of target depth identification. Therefore, it is evident that the two differ significantly in their technical focus and the technical fields they belong to.

[0012] 2. Patent CN110081964A calculates the sound field transfer function from each grid point to the array using acoustic parameters of the test water area and the Scooter & Fields model in the acoustic simulation software ActUP v2.2L. Based on this, it constructs the covariance matrix of the received signal, then vectorizes the covariance matrix and introduces regularization optimization to achieve sparse spectrum recovery. In contrast, this invention establishes the array's received sound pressure vector based on the Kraken model, obtains the modal filtering matrix and relative modal attenuation coefficients by constructing a sampling modal function matrix, further forms a contribution matrix, and uses its main diagonal as the goodness vector to measure modal filtering performance. Therefore, the sound field models and overall technical approaches used in the two inventions are different.

[0013] III. Technical Comparison with Patent CN113704685B "A Deep-Sea Blind Deconvolution Method Based on Vertical Linear Array"

[0014] 1. Patent CN113704685B aims to solve the problem of channel impulse response estimation in deep-sea environments. This method is based on ray theory and uses the Bellhop model for sound field simulation calculations. Applicable conditions include a sound source depth greater than 200 m and a sound source signal bandwidth of not less than 300 Hz. In contrast, this invention focuses on solving the depth identification problem of narrowband line spectrum sources in shallow-sea environments, based on normal mode theory and using the Kraken model for sound field simulation. Furthermore, the sound source depth in shallow-sea environments is typically within 200 m, and the sound source type in this method is a narrowband line spectrum source. Therefore, it is evident that the two methods differ significantly in their underlying sound field propagation theories, simulation models, sound source parameters, and signal types.

[0015] 2. Patent CN113704685B optimizes the existing blind deconvolution (RBD) method based on ray theory. It introduces the time delay difference information between direct waves and sea-reflected waves in the conventional broadband beam output into the channel impulse response estimation process. It combines multipath time delay difference information with the beamformer output phase to construct a phase compensation term, thereby solving the performance degradation problem caused by insufficient array beam resolution and multipath aliasing in the RBD method. This method belongs to the field of marine channel estimation technology. In contrast, this invention is based on existing modal filtering methods. It obtains the modal filtering matrix and modal relative attenuation coefficients by constructing a sampling mode function matrix, further forming a contribution matrix and taking its main diagonal as the goodness vector to quantitatively characterize the modal filtering performance of a vertical linear array. This method belongs to the field of target identification technology. Therefore, the two methods rely on different existing theoretical foundations, adopt different technical routes, and address different technical problems. Summary of the Invention

[0016] The purpose of this invention is to address the problem of line spectrum source depth identification under vertical line arrays by providing a superiority vector calculation method for evaluating the modal filtering performance of vertical line arrays. This method establishes the array's received sound pressure vector based on the Kraken model; constructs a sampling mode function matrix and a mode filtering matrix; calculates the relative attenuation coefficients of each mode; calculates the contribution matrix; and extracts the diagonal elements of the contribution matrix to obtain the defined superiority vector. The output data can be further used to extract mode functions with high contributions, delineate the depth-identifiable region of line spectrum sources under vertical line arrays, etc.

[0017] To achieve the above objectives, the method employed in this invention is: a method for calculating the goodness-of-performance vector for evaluating the modal filtering performance of a vertical linear array, comprising the following steps:

[0018] (1) Initialize marine environmental parameters, line spectrum signal parameters emitted by the sound source, and vertical receiving array parameters;

[0019] (2) The Kraken model was used to calculate the mode functions of each normal mode excited by the line spectrum signal emitted by the sound source and the received sound pressure value at the depth of each hydrophone in the vertical array, and the array received sound pressure vector was established.

[0020] (3) Construct the sampling mode function matrix, multiply the pseudo-inverse matrix of the sampling mode function matrix with the sampling mode function matrix to obtain the mode filtering matrix, and calculate the relative attenuation coefficient of each mode.

[0021] (4) The contribution matrix is ​​calculated using the modal filtering matrix and the relative attenuation coefficients of each mode. The diagonal elements of the contribution matrix are then used to form the goodness vector.

[0022] As a further improvement of the present invention, step (1) specifically includes the following steps:

[0023] Initialize marine environmental parameters, setting underwater sound speed c, seawater density ρ, and sound source depth z. s The frequency f0 of the line spectrum signal emitted by the sound source, and the signal sampling rate f s Sampling time T s N is the number of vertical linear array hydrophones, and z is the depth of the i-th hydrophone. i Let i = 1, 2, ..., N, and r be the horizontal distance r from the vertical linear array hydrophone to the sound source. s .

[0024] As a further improvement of the present invention, step (2) specifically includes the following steps:

[0025] (2.1) The normal mode number M and the horizontal wave number k of the m-th mode excited by the line spectrum signal emitted by the sound source are calculated using the Kraken model. m m = 1, 2, …, M, hydrophone depth z i The m-th modal function value Ψ at point m (z i ), sound source depth z s The m-th modal function value Ψ at point m (z s );

[0026] (2.2) Calculate the received sound pressure value p(z) at each hydrophone depth. i , t k ):

[0027] ;

[0028] ;

[0029] Where ω0 = 2πf0, and S(ω0) is the value of the signal spectrum at frequency ω0. k = 0, 1, 2, …, T s f s -1, where j is the imaginary unit.

[0030] (2.3) Received sound pressure value p(z) at different hydrophone depths i , t k The array receives the sound pressure vector p(t). k ):

[0031] .

[0032] As a further improvement of the present invention, step (3) specifically includes the following steps:

[0033] (3.1) Construct an N×M dimensional sampling mode function matrix:

[0034] ;

[0035] (3.2) Construct the modal filtering matrix B:

[0036] ;

[0037] ;

[0038] Among them, Ψ + Let b be the pseudo-inverse matrix of Ψ. uv Let u,v be the elements of the modal filtering matrix B, where u,v = 1, 2, …, M;

[0039] (3.3) Calculate the first Relative attenuation coefficient of first mode :

[0040] .

[0041] As a further improvement of the present invention, step (4) specifically includes the following steps:

[0042] (4.1) Calculate the contribution matrix Q:

[0043] ;

[0044] ;

[0045] Where, q uv These are the elements of the contribution matrix Q;

[0046] (4.2) Take the main diagonal elements of the contribution matrix Q. Construct the excellence vector G:

[0047] ;

[0048] Among them, g m The value of satisfies: 0 ≤ g m ≤1;

[0049] (4.3) Calculate the true value of the excitation function and estimated value :

[0050] ;

[0051] ;

[0052] in, For the first First-order modal excitation function, For the first Estimates of the first-order modal excitation function;

[0053] (4.4) Calculate the true values ​​of each order of excitation function and estimated value relative error :

[0054] ;

[0055] (4.5) Utilizing relative error To measure the effectiveness of the goodness vector G, if the relative error of the m-th order activation function is... The smaller the value, the higher the corresponding order m of excellence. The larger the value, the better the proposed goodness vector can effectively measure the performance of modal filtering.

[0056] This invention discloses a method for calculating the dominance vector to measure the modal filtering performance of a vertical linear array. The method establishes the array's received sound pressure vector based on the Kraken model; constructs a sampling mode function matrix and a modal filtering matrix; calculates the relative attenuation coefficients of each mode; calculates the contribution matrix; and extracts the diagonal elements of the contribution matrix to obtain the defined dominance vector, providing a quantitative analytical means for measuring the modal filtering performance of a vertical linear array.

[0057] Beneficial effects:

[0058] Compared with existing technologies, the method disclosed in this invention has the following advantages: When the number of hydrophones in the vertical linear array is less than the normal mode order, the performance of modal filtering will significantly decrease, and it is uncertain whether the traditional modified modal scintillation index can continue to be used as an effective depth identification criterion. The goodness vector proposed in this invention can quantitatively characterize the performance of modal filtering, thereby clarifying under what conditions the line spectrum source depth identification method based on the modified modal scintillation index remains effective; at the same time, the goodness vector can also be used to extract the modal functions with large contributions, which is beneficial to the optimization of subsequent line spectrum source depth identification algorithms. Attached Figure Description

[0059] Figure 1 This is a flowchart illustrating the implementation of the method of the present invention.

[0060] Figure 2 This is a bubble diagram of the modal contribution matrix Q in Example 1.

[0061] Figure 3 This is the goodness curve of the modal excitation function in Example 1.

[0062] Figure 4 The curves showing the true and estimated values ​​of the modal excitation function in Example 1 are shown.

[0063] Figure 5This is the relative error curve between the true value and the estimated value of the modal excitation function in Example 1. Detailed Implementation

[0064] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments:

[0065] This invention calculates the goodness vector for measuring modal filtering performance under a vertical linear array, and uses the relative error between the true and estimated values ​​of each order excitation function to help verify the effectiveness of the proposed goodness vector.

[0066] Example 1:

[0067] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments.

[0068] A method for calculating the goodness vector to measure the performance of modal filtering of vertical linear arrays, such as... Figure 1 , Figure 2 As shown, it includes the following steps:

[0069] Step (1) is as follows:

[0070] Initialize marine environmental parameters, setting the underwater sound speed c = 1500 m / s and the seawater density ρ = 1000 kg / m³. 3 Sound source depth z s = 5m, the frequency of the line spectrum signal emitted by the sound source is f0 = 100Hz, and the signal sampling rate is f s = 1000Hz, sampling time T s =100s, number of vertical linear array hydrophones N = 8, first element depth 11m, element spacing 11m, horizontal distance r from vertical linear array hydrophone to sound source s = 2km.

[0071] Step (2) specifically involves:

[0072] (2.1) Using the Kraken model, the normal mode number M = 13 excited by the line spectrum signal emitted by the sound source, and the horizontal wave number k of the m-th mode are calculated. m m = 1, 2, …, M, hydrophone depth z i The m-th modal function value Ψ at point m (z i ), sound source depth z s The m-th modal function value Ψ at point m (z s );

[0073] (2.2) Calculate the received sound pressure value p(z) at each hydrophone depth. i , t k ):

[0074] ;

[0075] ;

[0076] Where ω0 = 2πf0, and S(ω0) is the value of the signal spectrum at frequency ω0. k = 0, 1, 2, …, T s f s -1, where j is the imaginary unit.

[0077] (2.3) Received sound pressure value p(z) at different hydrophone depths i , t k The array receives the sound pressure vector p(t). k ):

[0078] .

[0079] Step (3) is as follows:

[0080] (3.1) Construct an N×M dimensional sampling mode function matrix:

[0081] ;

[0082] (3.2) Construct the modal filtering matrix B:

[0083] ;

[0084] ;

[0085] Among them, Ψ + Let b be the pseudo-inverse matrix of Ψ. uv Let u,v be the elements of the modal filtering matrix B, where u,v = 1, 2, …, M;

[0086] (3.3) Calculate the first Relative attenuation coefficient of first mode :

[0087] .

[0088] Step (4) is as follows:

[0089] (4.1) Calculate the contribution matrix Q:

[0090] ;

[0091] ;

[0092] Where, q uvThese are the elements of the contribution matrix Q;

[0093] (4.2) Take the main diagonal elements of the contribution matrix Q. Construct the excellence vector G:

[0094] ;

[0095] Among them, g m The value of satisfies: 0 ≤ g m ≤1;

[0096] (4.3) Calculate the true value of the excitation function and estimated value :

[0097] ;

[0098] ;

[0099] in, For the first First-order modal excitation function, For the first Estimates of the first-order modal excitation function;

[0100] (4.4) Calculate the true values ​​of each order of excitation function and estimated value relative error :

[0101] ;

[0102] (4.5) such as Figure 3 , Figure 4 as well as Figure 5 By comparing relative errors Goodness of the m-th order excitation function It can be observed that the relative error between the true and estimated values ​​of the first five activation functions is small, and their corresponding goodness is relatively high. All are greater than 0.5; significant deviations begin to appear in the sixth and seventh order excitation functions, with relative errors... Increase, corresponding to superiority The relative errors of the higher-order excitation functions decreased to 0.46 and 0.38 respectively; however, the relative errors of the higher-order excitation functions increased significantly, and their goodness of performance decreased. It also rapidly decreased to below 0.05. The above results show that the proposed goodness vector can accurately reflect the closeness of the estimated values ​​of each order of excitation function to the true values, thus verifying its effectiveness in measuring the performance of vertical linear array modal filtering.

[0103] The above embodiments demonstrate that the goodness vector proposed in this invention can accurately characterize the degree of closeness between the estimated values ​​of each order of excitation function and the true values, providing a quantitative means for measuring the modal filtering performance under vertical linear arrays.

[0104] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A method for computing an optimality vector for measuring the performance of a vertical linear array modal filter, the method comprising: The method comprises the following steps: (1) initializing marine environment parameters, line spectrum signal parameters emitted by a sound source, and vertical receiving array parameters; (2) calculating each order normal wave mode function excited by the line spectrum signal emitted by the sound source and the receiving sound pressure value at the depth of each hydrophone of the vertical array by using a Kraken model, and establishing an array receiving sound pressure vector; (3) constructing a sampling mode function matrix, multiplying the pseudo-inverse matrix of the sampling mode function matrix with the sampling mode function matrix to obtain a mode filtering matrix, and calculating the relative attenuation coefficients of each order mode; (4) calculating a contribution degree matrix by using the mode filtering matrix and the relative attenuation coefficients of each order mode, and taking the main diagonal element values of the contribution degree matrix to form a goodness vector.

2. The method for calculating the performance of a vertical linear array modal filter according to claim 1, wherein, Step (1) specifically comprises the following steps: Initialize the ocean environment parameters, set the underwater sound speed c, seawater density p, sound source depth z s , the frequency f0of the line spectrum signal emitted by the sound source, the signal sampling rate f s , the sampling time T s , the number of vertical linear array hydrophones N, the depth z i of the i-th hydrophone, i=1,2,…, N, the horizontal distance r s from the sound source to the vertical linear array hydrophone.

3. The method for calculating the performance of a vertical linear array modal filter according to claim 1, wherein, Step (2) specifically comprises the following steps: (2.1) Calculate the number of normal modes M excited by the line spectrum signal emitted by the sound source using the Kraken model, the horizontal wave number k of the mth mode m , m = 1, 2, …, M, the mth mode function value Ψ i (z m ) at the depth z of the hydrophone i , the mth mode function value Ψ s (z m ) at the depth z of the sound source s ; (2.2) Calculate the received sound pressure value p(z i , t k ) at each hydrophone depth ； ； where ω0= 2πf0, S(ω0) is the value of the signal spectrum at the frequency ω0, , k = 0, 1, 2, … s f s -1, j is the imaginary unit; (2.3) The received sound pressure values p(z i , t k ) at different hydrophone depths constitute an array received sound pressure vector p(t k ): 。 4. The method for calculating the performance of a vertical linear array modal filter according to claim 1, wherein, Step (3) specifically comprises the following steps: (3.1) constructing an N*M-dimensional sampling mode function matrix: ； (3.2) constructing a mode filtering matrix B: ； ； where Ψ + is the pseudo-inverse of Ψ, b uv are elements of the modal filter matrix B, u, v = 1, 2, …, M; (3.3) calculating the relative attenuation coefficient of the mode : 。 5. The method for calculating the performance of a vertical linear array modal filter according to claim 1, wherein, Step (4) specifically comprises the following steps: (4.1) calculating a contribution degree matrix Q: ； ； where q uv is an element of the contribution matrix Q; (4.2) Take the main diagonal elements of the contribution matrix Q Construct the goodness vector G: ； wherein g m takes a value satisfying: 0≤g m ≤1; (4.3) Compute the true values of the excitation function and the estimated values : ； ； wherein is the order modal excitation function, is the estimate of the order modal excitation function; (4.4) Relative error of the real value of each order excitation function and the estimated value :​ ； (4.5) The effectiveness of the goodness vector G is measured by the relative error of the mth order excitation function, i.e., if the relative error of the mth order excitation function is smaller, then the corresponding mth order goodness is larger, thus it can be shown that the proposed goodness vector can effectively measure the performance of the modal filter.

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