Underwater target depth attribute identification method under variation mode decomposition based on KRAKEN spectrum constraint

Abstract

The invention discloses an underwater target depth attribute recognition method under variation mode decomposition based on KRAKEN spectrum constraint, solves the problem of how to effectively extract target signals under the conditions of complex underwater sound environment and low signal-to-noise ratio, and belongs to the field of underwater sound field target recognition. The method comprises the steps that a KRAKEN model generates a reference signal, and the center frequency omega ref and the bandwidth delta omega k of a frequency spectrum are extracted; the method comprises the following steps: decomposing an original signal into K modal signal functions with different frequency components through variational modal decomposition, and establishing an objective function which enables the spectrum difference between the modal signal and the original signal to be minimum; introducing omega ref and delta omega k into a path weighted frequency spectrum constraint term of the target function, and ensuring that the frequency center omega k of the modal signal function is within a reference signal frequency spectrum range; solving the target function to obtain a group of modal signal functions, and obtaining an optimal reconstruction signal; and performing underwater target depth attribute identification according to the optimal reconstruction signal. The method is suitable for water surface and underwater target attribute discrimination.

Description

Technical Field

[0001] The present invention relates to a method for identifying the depth attribute of an underwater target based on variational mode decomposition with KRAKEN spectrum constraint, belonging to the field of underwater acoustic field target identification. Background Art

[0002] With the continuous deepening of ocean development and utilization, the demand for high-precision extraction and denoising of underwater acoustic field signals is increasing day by day. In many fields such as military, civilian, and scientific research, it is crucial to accurately and efficiently process underwater acoustic field signals. However, underwater signals are affected by complex factors such as multipath effects, background noise, and non-stationary characteristics during propagation, resulting in distortion of the time-frequency characteristics of the signals and affecting the accurate extraction of target signals. Therefore, how to effectively extract target signals under complex underwater acoustic environments and low signal-to-noise ratio conditions has become an urgent problem to be solved in the current field of underwater acoustic signal processing. Summary of the Invention

[0003] Aiming at the problem of how to effectively extract target signals under complex underwater acoustic environments and low signal-to-noise ratio conditions, the present invention provides a method for identifying the depth attribute of an underwater target based on variational mode decomposition with KRAKEN spectrum constraint.

[0004] A method for identifying the depth attribute of an underwater target based on variational mode decomposition with KRAKEN spectrum constraint of the present invention includes:

[0005] S1. The KRAKEN model generates a reference signal x sim (t), and further obtains the spectrum S sim (ω) of the reference signal. From the spectrum S sim (ω) of the reference signal, its center frequency ω ref and bandwidth Δω k are extracted;

[0006] S2. The original signal is decomposed into K modal signal functions with different frequency components through variational mode decomposition, and an objective function is established, which minimizes the spectrum difference between the modal signal and the original signal;

[0007] The objective function includes a time-domain smoothing term, a frequency-domain matching term, and a path-weighted spectrum constraint term;

[0008] The center frequency ω sim and bandwidth Δω ref of the spectrum S k of the reference signal are introduced into the path-weighted spectrum constraint term to ensure that the frequency center ω k of the modal signal function is within the spectrum range of the reference signal;

[0009] S3. The objective function is solved to obtain a set of modal signal functions u k(t);

[0010] S4. Denoise and reconstruct the obtained modal signal function to obtain the optimal reconstructed signal;

[0011] S5. Identify the depth attribute of the underwater target based on the optimal reconstructed signal.

[0012] Preferably, the objective function is:

[0013]

[0014] where, is the time-domain smoothing term;

[0015] is the frequency-domain matching term, F[·] represents the Fourier transform, and x(t) represents the original signal;

[0016] is the path-weighted spectrum constraint term, α is the regularization parameter, β is the overall constraint weight, w m is the energy weight of the m-th path, M represents the total number of paths, E m is the acoustic energy of the m-th path, I(·) is the indicator function, ω ref,m is the reference center frequency of the m-th path, ω ref is the global reference frequency, which is obtained by weighted averaging of ω ref,m of all paths.

[0017] Preferably,

[0018]

[0019] where, W k (ω) is the weighted function for modal energy normalization, ω represents the angular frequency, ω max represents the maximum value of ω, ω min represents the minimum value of ω

[0020] Preferably, S3 includes:

[0021] Solve the objective function using the alternating direction method:

[0022] Update the modal signal function as:

[0023]

[0024] where, is the frequency-domain representation of the k-th modal signal function after the (n + 1)-th iteration, is the Fourier transform of the measured signal x(t), λ (n)$(\omega)$ is the frequency-domain representation of the Lagrange multiplier, and $n$ represents the number of iterations;

[0025] Update the center frequency:

[0026]

[0027] Preferably, S4 includes:

[0028] Calculate the energy of each mode, calculate the proportion of modal energy, remove the modes with energy less than the energy threshold, and complete denoising;

[0029] Reconstruct according to the denoised modal signal function to obtain the reconstructed signal

[0030] Select the reconstructed signal in the reconstructed signal sim with the highest correlation with the reference signal waveform $x$ best $(t)$ and the reconstruction order $k$ best , and obtain the optimal reconstructed signal according to the reconstruction order $k$

[0031] Preferably, calculate the Pearson correlation coefficient $r$ between the reconstructed signal sim and the reference analog signal $x$ k $(t)$:

[0032]

[0033] where is the mean value of all reconstructed signals , is the reconstructed signal of the $k$-th order part, and

[0034] is the mean value of the reference signal; k Select the reconstruction order $k$ best corresponding to the maximum Pearson correlation coefficient $r$;

[0035] Optimal reconstructed signal

[0036] The beneficial effects of the present invention are as follows. By introducing the spectral information of the reference waveform simulated by the KRAKEN model, the spectral center frequency and bandwidth of the reference signal are extracted and used as spectral constraints in the variational mode decomposition optimization problem, effectively optimizing the modal decomposition process of variational mode decomposition. In the signal reconstruction process, correlation analysis is used to select the best denoising result. Based on actual sea trial data, the recognition accuracy is improved from 85% to 95%. The present invention is applicable to the discrimination of the depth attributes of surface and underwater targets, especially in complex underwater acoustic environments, and can effectively improve the accuracy and stability of target recognition. Description of the Drawings

[0037] Figure 1 are the first two-order responses of sound pressure and vertical vibration velocity;

[0038] Figure 2 is the positive and negative variation law of the reactive component of the vertical sound intensity current;

[0039] Figure 3 is the positive and negative variation law of the reactive component of the vertical sound intensity current under 0 dB noise interference;

[0040] Figure 4 is the positive and negative variation law of the reactive component of the vertical sound intensity current after optimizing modal decomposition with the reference waveform spectrum information generated by introducing the KRAKEN model;

[0041] Figure 5 is the histogram of the target depth attribute determined by simulation based on the traditional vertical sound intensity current determination algorithm;

[0042] Figure 6 is the histogram of the target depth attribute determined by simulation based on the variational mode decomposition algorithm;

[0043] Figure 7 is the histogram of the target depth attribute determined by simulation based on the variational mode decomposition algorithm optimized by the KRAKEN model;

[0044] Figure 8 is the histogram of the target depth attribute classification of the actual sea trial data processed by the traditional vertical sound intensity current determination algorithm;

[0045] Figure 9 is the histogram of the target depth attribute classification of the actual sea trial data processed by the variational mode decomposition algorithm;

[0046] Figure 10 is the histogram of the target depth attribute classification of the actual sea trial data processed by the variational mode decomposition algorithm optimized by the KRAKEN model. Detailed Implementation Manner

[0047] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0048] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments may be combined with each other.

[0049] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but it is not intended to limit the present invention.

[0050] The method for identifying the depth attribute of an underwater target based on variational mode decomposition with KRAKEN spectrum constraint in this embodiment includes:

[0051] Step 1: Decompose the original signal into K modal signals with different frequency components by optimizing the variational problem. The optimization problem of variational mode decomposition is to minimize the difference between the frequency-domain representation of the signal and the frequency-domain representation of the modes, and solve a set of modal signal functions u k (t) and the corresponding frequency centers ω k such that the spectra of the modes and the spectrum of the original signal are as similar as possible. The specific objective function is:

[0052]

[0053] where: u k (t) is the k-th modal signal function, ω k is the center frequency of the k-th mode, α is the regularization parameter, F[·] represents the Fourier transform, and x(t) represents the original signal.

[0054] The second term of the objective function is the frequency-domain constraint, which aims to ensure that the spectrum of each mode approximates the spectrum of the original signal as much as possible, thereby improving the decomposition accuracy. Variational mode decomposition solves this optimization problem by variational method to obtain the modal signal function u k (t) and the center frequency ω k . However, relying on mathematical optimization still has problems such as modal frequency drift and unstable modal energy distribution. Therefore, physical constraints need to be introduced to further optimize the decomposition process.

[0055] In the underwater environment, the propagation of sound waves is affected by factors such as multipath effect, dispersion effect, and propagation loss, resulting in the spectrum characteristics of the signal being different from the ideal model in the case of free propagation. To solve this problem, this embodiment uses the KRAKEN acoustic field calculation model to generate a reference signal for the underwater target;

[0056] Step 2: The KRAKEN model generates a reference signal x sim (t), and further obtains the spectrum S sim (ω) of the reference signal:

[0057] S sim (ω) = |F[x sim (t)]| 2

[0058] This spectrum contains the main frequency components of the signal and the spectral distribution of the noise. By calculating its central frequency and bandwidth, it can be used to guide variational mode decomposition.

[0059] From the reference signal spectrum S sim (ω), extract its central frequency ω ref and bandwidth Δω k , which are used as spectral constraints in the decomposition process of guiding variational mode decomposition. The calculation of the central frequency of the reference signal is as follows:

[0060]

[0061] The calculation of the bandwidth of the reference signal (general method):

[0062]

[0063] To enhance the physical constraints of mode decomposition, a dynamic spectral constraint method can be used to adjust the modal central frequency ω k based on the KRAKEN reference spectrum.

[0064] The improved bandwidth calculation in this embodiment (considering the dynamic weight of multipath propagation):

[0065]

[0066] where W k (ω) is the weighted function of modal energy normalization:

[0067]

[0068] Step 3: Introduce the spectral information of the reference signal into the optimization problem of variational mode decomposition to ensure that the modal frequency ω k is within the reference spectral range. At the same time, the optimization objective function of variational mode decomposition includes minimizing the difference between the modal spectrum and the original signal spectrum, balancing the time-domain and frequency-domain constraints through a regularization parameter, and ensuring that the mode decomposition result conforms to the physical propagation characteristics of underwater signals through a path-weighted spectral constraint term. The objective function is optimized to include, in addition to the time-domain smoothing term and the frequency-domain matching term, a path-weighted spectral constraint term; introduce the central frequency ω sim and bandwidth Δω ref of the reference signal spectrum S k into the path-weighted spectral constraint term to ensure that the frequency center ω k of the modal signal function is within the reference signal spectrum range; the specific objective function is:

[0069]

[0070] where is the time-domain smoothing term to ensure the smoothness of the mode;

[0071] is the frequency-domain matching term to ensure that the spectrum of the mode is consistent with the original signal;

[0072] is the path-weighted spectrum constraint term to ensure that the center frequency of the mode conforms to the multi-path physical characteristics calculated by KRAKEN. α is the regularization parameter, β is the overall constraint weight, and w m is the energy weight of the m-th path, M represents the total number of paths, and E m is the acoustic energy of the m-th path, I(·) is the indicator function, ω ref,m is the reference center frequency of the m-th path, and ω ref is the global reference frequency, which is obtained by weighted averaging of ω of all paths ref,m .

[0073] This objective function forces the modal frequencies outside the reference spectrum range to be excluded. The frequency constraint term ensures that the frequency of each mode is limited to the KRAKEN reference spectrum range, but allows a certain degree of dynamic variation through Δω k .

[0074] Step 4: Use the alternating direction method (ADMM) to solve the objective function to obtain a set of modal signal functions u k (t);

[0075] Update the modal signal function. Using the Lagrange multiplier method and Fourier transform, the update formula of the modal signal function is:

[0076]

[0077] where: is the frequency-domain representation of the k-th modal signal function after the (n + 1)-th iteration, is the Fourier transform of the measured signal x(t), and λ (n) (ω) is the frequency-domain representation of the Lagrange multiplier, and n represents the number of iterations;

[0078] Update the center frequency:

[0079]

[0080] Step 5: Denoise and reconstruct the obtained modal signal function to obtain the best reconstructed signal, including:

[0081] Step 51: Noise modes usually have lower energy. Calculate the energy of each mode, calculate the proportion of modal energy, and remove the modes with energy less than the energy threshold:

[0082]

[0083] Then, by calculating the proportion of modal energy:

[0084]

[0085] If E k <γ (such as γ < 5%), it is determined as a low - energy noise mode. Then, this mode is removed.

[0086] Step 52: Reconstruct according to the denoised modal signal function to obtain the reconstructed signal

[0087] By retaining the modes that conform to the reference spectrum characteristics, reconstruct the denoised signal Superimpose the modes that meet the conditions to obtain the denoised signal. Assume that the first K' modes are retained, and the reconstructed signal is:

[0088]

[0089] Step 53: Introduce correlation analysis. During the reconstruction process, calculate the Pearson correlation coefficient r between the reconstructed signal sim and the reference simulation signal x k :

[0090]

[0091] where, is the mean value of all reconstructed signals , is the reconstructed signal of the k - th order part, is the mean value of the reference signal;

[0092] Through the correlation analysis of the reconstructed signals of different orders, select the reconstructed order k k corresponding to the maximum Pearson correlation coefficient r best , and the best - reconstructed signal

[0093] Step 6: Identify the depth attribute of the underwater target according to the best - reconstructed signal.

[0094] Table 1

[0095]

[0096] Table 1 is a comparison table of the recognition rates of simulation and sea - trial experiments based on the traditional vertical sound intensity current algorithm, variational mode decomposition algorithm, and KRAKEN - optimized variational mode decomposition algorithm.

[0097] This embodiment uses the reference waveform generated by the KRAKEN model to provide an ideal underwater acoustic field interference waveform, providing spectral information guidance for the variational mode decomposition process. By introducing the spectral constraint of the KRAKEN model to optimize the variational mode decomposition, the denoising effect is significantly improved, and a high-quality reconstructed signal is obtained by combining correlation analysis, thereby improving the accuracy of target depth attribute discrimination. The prior art can only determine the target depth attribute at a relatively high signal-to-noise ratio, while the present invention combines the shallow water interference theory and the mode decomposition theory, and uses the KRAKEN model to improve the denoising performance of the variational mode decomposition, realizing the effective identification of surface and underwater targets at a low signal-to-noise ratio. This not only overcomes the limitations of the prior art, but also promotes the development of the surface and underwater target identification technology of a single vector hydrophone to a wider application field.

[0098] Although the invention has been described herein with reference to particular embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. It should thus be understood that numerous modifications may be made to the exemplary embodiments, and other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the features described herein may be combined in different ways than those described in the original claims. It should also be understood that the features described in connection with separate embodiments may be used in other described embodiments.

Claims

1. An underwater target depth attribute recognition method based on variational mode decomposition with KRAKEN spectrum constraint, characterized in that, Including: S1. The KRAKEN model generates a reference signal x sim (t), and further obtains the reference signal spectrum S sim (ω). From the reference signal spectrum S sim (ω), its center frequency ω ref and bandwidth Δω k are extracted; S2. Decompose the original signal into K modal signal functions with different frequency components through variational mode decomposition, and establish an objective function that minimizes the spectral difference between the modal signals and the original signal; The objective function includes a time-domain smoothing term, a frequency-domain matching term, and a path-weighted spectrum constraint term; Introduce the center frequency ω sim (ω) of the reference signal spectrum S ref and the bandwidth Δω k into the path weighted spectrum constraint term to ensure that the frequency center ω k of the modal signal function is within the range of the reference signal spectrum; S3. Solve the objective function to obtain a set of modal signal functions u k (t); S4. Denoise and reconstruct the obtained modal signal functions to obtain the optimal reconstructed signal; S5. Identify the depth attribute of the underwater target based on the optimal reconstructed signal.

2. The method for identifying the depth attribute of an underwater target based on variational mode decomposition with KRAKEN spectrum constraint according to claim 1, characterized in that, The objective function is: Among them, is the time-domain smoothing term; is a frequency-domain matching term, F[·] represents the Fourier transform, and x(t) represents the original signal; is the path-weighted spectrum constraint term, α is the regularization parameter, β is the overall constraint weight, and w m is the energy weight of the m-th path, M represents the total number of paths, and E m is the acoustic energy of the m-th path, and I(·) is the indicator function, ω ref,m is the reference center frequency of the m-th path, and ω ref is the global reference frequency, which is obtained by weighted averaging of ω of all paths ref,m ​ 3. The method for identifying the depth attribute of an underwater target based on variational mode decomposition with KRAKEN spectrum constraint according to claim 2, characterized in that Among them, W k (ω) is the weighted function for modal energy normalization, ω represents the angular frequency, ω max represents the maximum value of ω, ω min represents the minimum value of ω.

4. The underwater target depth attribute recognition method based on variational mode decomposition with KRAKEN spectrum constraint according to claim 3, characterized in that S3 Including: Solve the objective function using the alternating direction method: Update the modal signal function as: Among them, is the frequency-domain representation of the k-th modal signal function after the (n + 1)-th iteration, is the Fourier transform of the measured signal x(t), and λ (n) (ω) is the frequency-domain representation of the Lagrange multiplier, and n represents the number of iterations; Update the central frequency:

5. The method for identifying the depth attribute of an underwater target by variational mode decomposition based on KRAKEN spectrum constraint according to claim 1, characterized in that, S4 includes: Calculate the energy of each mode, calculate the proportion of modal energy, and remove the modes with energy less than the energy threshold to complete denoising; Reconstruct according to the denoised modal signal function to obtain the reconstructed signal Select the reconstructed signal with the largest correlation with the reference signal waveform x sim (t) among the reconstruction orders k best , and according to this reconstruction order k best obtain the optimal reconstructed signal 6. The method for identifying the depth attribute of an underwater target based on variational mode decomposition with KRAKEN spectrum constraint according to claim 5, characterized in that Calculate the reconstructed signal and the Pearson correlation coefficient r sim with the reference analog signal x k : Among them, is the mean of all reconstructed signals , is the reconstructed signal of the k-th order part, is the mean of the reference signal; Select the Pearson correlation coefficient r k The reconstruction order k corresponding to the maximum best ; Optimal reconstructed signal 7. A computer-readable storage device storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method for identifying the depth attribute of an underwater target based on variational mode decomposition with KRAKEN spectrum constraint as described in any one of claims 1 to 6.

8. An underwater target depth attribute recognition device based on variational mode decomposition with KRAKEN spectrum constraint, comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor, characterized in that, The processor executes the computer program to implement the steps of the method for identifying the depth attribute of an underwater target based on variational mode decomposition with KRAKEN spectrum constraint as described in any one of claims 1 to 6.

9. A computer program product comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method for identifying the depth attribute of an underwater target based on variational mode decomposition with KRAKEN spectrum constraint as described in any one of claims 1 to 6.

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