A ship radiated noise line spectrum estimation method based on multi-snapshot sparse Bayesian learning

Abstract

The application discloses a ship radiation noise line spectrum estimation method based on multi-snapshot sparse Bayesian learning, and belongs to the field of underwater acoustic signal processing; the method utilizes the sparse characteristics of the ship radiation noise line spectrum, that is, the line spectrum is not uniformly distributed in the whole frequency range, but is discrete and sparse, converts the line spectrum estimation problem into a sparse signal recovery problem, so as to solve the problems in the background technology, under the condition that the data sample length is limited and the sparsity is unknown, the Bayesian framework utilizes probability modeling to adaptively adjust the hyperparameters from the global optimization angle, can effectively reduce the sidelobe, realizes high resolution, reduces the background noise fluctuation variance through multiple observation snapshots statistical average, enhances the signal-to-noise ratio of the line spectrum output, and improves the line spectrum feature detection performance.

Description

Technical Field

[0001] This application belongs to the field of underwater acoustic signal processing, specifically involving a method for estimating the line spectrum of ship radiated noise based on multi-snapshot sparse Bayesian learning. Background Technology

[0002] Line spectra are a crucial component of ship radiated noise. Due to their high energy and stability, they are key features for passive detection of weak targets and ship target classification and identification. LOFAR (Low Frequency Analysis and Recording) spectral analysis is the most classic and widely used line spectrum analysis method. By performing low-frequency power spectrum analysis on the target's radiated noise, it obtains low-frequency discrete line spectra and continuous spectrum characteristics. The low-frequency discrete line spectra are caused by the periodic vibrations of the target's mechanical components and can directly reflect the target's operational characteristics. LOFAR spectral analysis is a time-frequency analysis method based on the Short Time Fourier Transform (STFT) theoretical framework. When performing line spectrum analysis on finite-length data samples, time and frequency resolution are mutually constrained.

[0003] Due to the influence of ocean channels and the movement of ship targets, the radiated noise received by sonar systems typically exhibits non-stationary characteristics, meaning it experiences frequency and energy fluctuations. When performing time-frequency analysis on ship radiated noise, it is usually assumed to be a stationary signal over a short period, leading to piecewise line spectrum estimation. However, the length of each piece is affected by the signal fluctuations, limiting the frequency resolution of the line spectrum estimation results. Therefore, high-resolution spectrum estimation methods are needed to improve the frequency resolution of time-frequency analysis results. Simultaneously, it is necessary to suppress spectral leakage and reduce inter-spectral interference to better estimate and extract line spectrum features under conditions of close frequencies or strong interference.

[0004] The Wigner-Ville distribution (WVD) is a representative high-resolution time-frequency analysis method. However, when processing broadband ship radiated noise data, it introduces cross-term interference, which is typically highly oscillating and severely affects the accuracy and resolution of the time-frequency distribution. Although algorithms have been proposed to eliminate cross-terms by solving the time-frequency distribution of the wavelet components and then reconstructing the full data time-frequency analysis, the decomposition of the noise data requires manual parameter control, which can easily introduce human error. Furthermore, high-resolution spatial spectrum estimation methods can also be used for ship line spectrum estimation. For example, the Minimum Variance Distortionless Response (MVDR) can significantly improve frequency resolution and suppress sidelobes; however, the number of snapshots, signal-to-noise ratio, and statistical characteristics of the received signal have a significant impact on its algorithm performance, easily leading to model mismatch problems. Compared to the MVDR algorithm, subspace methods such as Multiple Signal Classification (MUSIC) and Estimating Signal Parameters via Rotational Invariance Techniques (ESPRIT), while having high frequency resolution and noise robustness, require pre-setting the number of line spectrum signals. However, in real-world scenarios, the number of line spectrum signals is generally unknown or changes over time, and incorrect estimation can lead to performance degradation.

[0005] In cutting-edge signal processing technologies, sparse signal processing is an important area of ​​high-resolution signal processing, mainly involving how to reconstruct or recover the original signal from a small amount of observation data. Compressed sensing (CS) and sparse Bayesian learning (SBL) algorithms have achieved significant research results in high-resolution azimuth estimation of sonar array signals and also show great promise for estimating the line spectrum of ship radiated noise. Therefore, this invention combines the characteristics of ship radiated noise and marine environmental noise, and based on the theoretical framework of sparse Bayesian learning, achieves high-resolution line spectrum estimation with limited data samples. Summary of the Invention

[0006] The purpose of this invention is to provide a method for estimating the line spectrum of ship radiated noise based on multi-snapshot sparse Bayesian learning. This method utilizes the sparsity of the ship radiated noise line spectrum—that is, the line spectrum is not uniformly distributed across the entire frequency range but exists discretely and sparsely—to transform the line spectrum estimation problem into a sparse signal recovery problem, thus addressing the issues in the background techniques. When the data sample length is finite and the sparsity is unknown, the Bayesian framework uses probabilistic modeling to adaptively adjust hyperparameters from a global optimization perspective, effectively reducing sidelobes to achieve high resolution. Furthermore, by statistically averaging multiple observation snapshots, the variance of background noise fluctuations is reduced, enhancing the signal-to-noise ratio of the line spectrum output and improving the performance of line spectrum feature detection.

[0007] To achieve the above objectives, this invention provides a method for estimating the line spectrum of ship radiated noise based on multi-snapshot sparse Bayesian learning, comprising:

[0008] S1: Collect ship radiated noise data;

[0009] S2: The collected ship radiated noise data will be processed according to frequency resolution. Calculate the frame length M (sliding window length) and divide the ship radiated noise data into overlapping frames; specifically as follows:

[0010] Calculate the frame length M, select the inter-frame overlap length O, and then transfer the collected ship radiated noise data. Evenly divided into overlapping sections Frame, in which The first part representing the ship's radiated noise data The value of each sampling point, index Indicates the sampling point number. , This represents the total number of sampling points. Indicates rounding down; i-th frame The starting position is The end position is ,in Each frame is processed by mean removal and normalization to obtain... ,in This represents the value of the i-th frame after mean removal and normalization. For frames The mean, Represents the 2-norm, frequency resolution , Sampling rate;

[0011] S3: Starting from frame 0, extract consecutive P frames with a preset frame number s as the step size, and construct a multi-snapshot matrix; as detailed below:

[0012] Set the number of snapshots P, starting from frame 0 and ending at frame IP. Extract adjacent P frames with a preset frame count s as the step size to construct a multi-snapshot matrix. Where b represents the sequence number of the multiple snapshot matrix, , Indicates the first Frame, where p represents the frame number in the multiple snapshot matrix. ;

[0013] S4: Divide the time-frequency grid, combine the Gaussian window with the complex exponential basis function, and construct the dictionary matrix at the time-frequency grid points; the details are as follows:

[0014] Set the frequency range of the line spectrum Construct an equally spaced discrete grid in a time-frequency two-dimensional coordinate system and generate grid point coordinates. ,in This represents the nth discrete frequency value on the frequency axis, corresponding to the vertical coordinate in the coordinate system. n represents the index number of the frequency point, used to identify the discrete position on the frequency axis, and its value is... N represents the total number of discrete frequency points on the frequency axis. , This represents the m-th discrete time point on the time axis, where m represents the time index, corresponding to a discrete sampling point on the time axis, and its value is... M represents the total number of discrete time points on the time axis. Indicates the minimum frequency. Indicates the maximum frequency;

[0015] Generate complex exponential basis functions on grid point coordinates. and Gaussian window function ,in, It is an extended parameter of the window function. c is an empirical coefficient used to adjust the expansion of the window function, with a value ranging from 2 to 6; a Gaussian window function is used to weight the complex exponential basis functions to form localized basis functions. ,in, Indicates taking the real part;

[0016] Construct a dictionary matrix using all generated localization basis functions. ,in , Represents the nth column of the dictionary matrix. This represents the matrix transpose; normalizing all columns of the dictionary matrix yields... , Represents a dictionary matrix. Represents the nth column of the dictionary matrix. ;

[0017] S5: Set the hyperparameters and iteration parameters, import the multiple snapshot matrix and dictionary matrix into the sparse Bayesian learning algorithm, and obtain the time-frequency diagram of the ship's radiated noise;

[0018] From the first multi-snapshot matrix From the beginning to the last multi-snapshot matrix Finally, the sparse Bayesian learning algorithm is used sequentially to calculate the multiple snapshot matrix. Corresponding spectral power The details are as follows:

[0019] S5.1. Initialize hyperparameters and iteration parameters: (1) Hyperparameter initialization: The sparse parameter vector is initialized as follows: ,in express A 1-dimensional matrix; noise parameters initialized to... ,in (2) Iteration parameter initialization: regularization parameter , Typically, the value is between 1e-3 and 1e-6; the maximum number of iterations K, which is usually between 30 and 200, and the convergence threshold. , Typically, the value is 1e-6 to 1e-8;

[0020] S5.2. Calculate the covariance matrix and mean of the k-th iteration:

[0021] The formula for calculating the covariance matrix is: ,in, This indicates that a diagonal matrix is ​​generated from vectors. This represents the sparse parameter vector for the k-th iteration. , This represents the noise parameter in the k-th iteration. express An identity matrix of order 1;

[0022] The formula for calculating the mean is: ,in, , The nth row represents the mean. This represents the estimated spectral amplitude of the signal at the nth frequency component in the p-th frame during the k-th iteration.

[0023] S5.3. Updating Hyperparameters: Sparse Parameter Vector The nth element is updated to Noise parameters updated to ,in Denotes the F-norm;

[0024] S5.4. Determine if the iteration termination condition is met: Calculate the relative update amount of the sparse parameter vector. ,like or If the condition is met, stop iterating; otherwise, continue iterating.

[0025] S5.5. Calculate the multiple snapshot matrix. Corresponding spectral power ,in This represents the starting time of the b-th multiple snapshot matrix. ;

[0026] S5.6. Repeat S5.2-S5.5 to obtain the spectral power corresponding to all multiple snapshot matrices. Normalization is performed: , This is a time-frequency diagram of the ship's radiated noise line spectrum at all times.

[0027] Compared with existing technologies, the advantages of this application are:

[0028] 1. Spectrum estimation methods based on classical Fourier theory are often limited by the sample length, which causes spectral leakage and leads to the generation of side lobes.

[0029] This invention utilizes the sparse characteristics of the ship radiated noise line spectrum to transform the line spectrum estimation problem into a sparse signal recovery problem, which can effectively reduce side lobes and thus avoid the problem of the target line spectrum being overwhelmed by the side lobe interference of the strong line spectrum in the frequency domain.

[0030] 2. High-resolution spectrum estimation methods such as MUSIC require prior information, and whether the parameter settings match has a significant impact on the algorithm performance. However, this invention achieves high resolution without prior information, thus solving the problem of the difficulty in obtaining prior information.

[0031] 3. This invention can effectively suppress background noise, enhance the signal-to-noise ratio of line spectrum output, and improve the performance of line spectrum feature detection. Attached Figure Description

[0032] Figure 1 This is a flowchart of the ship radiated noise line spectrum estimation method based on multi-snapshot sparse Bayesian learning according to the present invention;

[0033] Figure 2 This is a comparison of the time-frequency plot of the line spectrum estimation obtained by processing the simulation data in this invention with the classical STFT method (frequency range 82Hz-472Hz).

[0034] Figure 3 This is a comparison of the line spectrum estimation curve obtained by processing the simulated data in this invention with the classical STFT method (frequency range 82Hz-472Hz).

[0035] Figure 4 This is a comparison of the time-frequency plot of the line spectrum estimation obtained by processing the simulated data in this invention with the classical STFT method (frequency range 260Hz-275Hz).

[0036] Figure 5 This is a comparison of the line spectrum estimation curve obtained by processing the simulated data in this invention with the classical STFT method (frequency range 260Hz-275Hz).

[0037] Figure 6 This invention compares the time-frequency plot of the line spectrum estimation obtained by processing SWellEx-96 experimental data with the classical STFT method.

[0038] Figure 7 This invention provides a comparison of the line spectrum estimation curves obtained from processing SWellEx-96 experimental data with the classic STFT method. Detailed Implementation

[0039] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, illustrates a method for estimating the line spectrum of ship radiated noise based on multi-snapshot sparse Bayesian learning, provided by the present invention.

[0040] Figure 1 A flowchart of a method for estimating the line spectrum of ship radiated noise based on multi-snapshot sparse Bayesian learning provided by the present invention;

[0041] like Figure 1 As shown, the present invention provides a method for estimating the line spectrum of ship radiated noise based on multi-snapshot sparse Bayesian learning, which includes the following steps performed in sequence:

[0042] S1: Collect ship radiated noise data;

[0043] S2: The collected noise data is processed according to the required frequency resolution. Calculate the required frame length M (sliding window length) and divide it evenly into several overlapping frames.

[0044] S3: Starting from frame 0, extract consecutive P frames with a preset frame number s as the step size, and construct a multi-snapshot matrix;

[0045] S4: Divide the time-frequency grid, combine the Gaussian window with the complex exponential basis function, and construct the dictionary matrix at the time-frequency grid points;

[0046] S5: Set the hyperparameters and iteration parameters, import the multiple snapshot matrices and dictionary matrices into the sparse Bayesian learning algorithm, and obtain the time-frequency diagram of ship radiated noise.

[0047] Furthermore, the effectiveness of the method of the present invention was verified through simulation test results in this embodiment.

[0048] Simulation parameters: The sonar array has 128 elements, an element spacing of 1.5 meters, a sampling rate of 2500Hz, and an operating frequency band of 10Hz~500Hz. The target sound source emits multiple line spectra of different intensities, with line spectrum frequencies of 88Hz, 94Hz, 198Hz, 267Hz, 268Hz, and 468Hz; and line spectrum signal-to-noise ratios of 10.8dB, 22dB, 18.7dB, 9.5dB, 26dB, and 17.7dB, respectively. Beam data for the target's azimuth over a period of 3 minutes is extracted and processed. The parameter settings for this invention are shown in Table 1.

[0049]

[0050] Simulation results: Figure 2 , Figure 4 The following is a comparison of the time-frequency plot of the line spectrum estimation obtained by processing the above-mentioned simulation data with the classical STFT method. Figure 3 , Figure 5 The results show a comparison between the line spectrum estimation curve obtained by processing the above-mentioned simulation data in this invention and the classical STFT method.

[0051] from Figure 2 , Figure 3 It can be seen that the method of this invention has more concentrated energy and higher frequency resolution at the online spectrum frequencies. The classical STFT method suffers from spectral leakage due to the use of window functions, leading to sidelobes, while the method of this invention can effectively reduce sidelobes. Figure 4 , Figure 5 As shown, in the classical STFT method, due to interspectral interference caused by side lobes, the weak 267Hz line spectrum is submerged by the side lobes of the strong 268Hz line spectrum. However, the method of this invention can distinguish between these two line spectra. Figures 2-5 As can be seen, compared with the classic STFT method, the method of this invention can effectively suppress background noise and enhance the signal-to-noise ratio of line spectrum output, laying a good foundation for line spectrum feature detection.

[0052] Furthermore, in this embodiment, the effectiveness of the method of the present invention was verified by processing SWellEx-96 experimental data (data download URL: Welcome to the SWellEx-96 Experiment (ucsd.edu)).

[0053] The HLA North array was selected as the data source, with a sampling rate of 3276.8 Hz, an array depth of 213 m, and 32 array elements, of which 27 were functioning normally. The deep-drafted source emitted line spectra of varying intensities between 49 and 400 Hz. The first group of line spectra was emitted at a source level of 158 dB, with the following frequency ranges: 49 Hz, 64 Hz, 79 Hz, 94 Hz, 112 Hz, 130 Hz, 148 Hz, 166 Hz, 201 Hz, 235 Hz, 283 Hz, 338 Hz, and 388 Hz. The shallow-drafted source emitted line spectra between 109 and 385 Hz, with the following frequency ranges: 109 Hz, 127 Hz, 145 Hz, 163 Hz, 198 Hz, 232 Hz, 280 Hz, 335 Hz, and 385 Hz. The beam data of the target azimuth for 2 minutes is extracted and processed. The parameter settings of the method of the present invention are shown in Table 2.

[0054]

[0055] Simulation results: Figure 6 This is a comparison of the time-frequency plot of the line spectrum estimation obtained by processing SWellEx-96 experimental data in this invention with the classical STFT method. Figure 7 The image shows a comparison between the line spectrum estimation curve obtained from processing SWellEx-96 experimental data according to this invention and the classical STFT method. It can be seen that the method of this invention has more concentrated energy at the line spectrum frequencies, higher frequency resolution, and can effectively suppress background noise, enhancing the signal-to-noise ratio of the line spectrum output, thus laying a good foundation for line spectrum feature detection.

Claims

1. A method for estimating the line spectrum of ship radiated noise based on multi-snapshot sparse Bayesian learning, characterized in that, This method consists of the following steps: S1: Collect ship radiated noise data; S2: The collected ship radiated noise data will be processed according to frequency resolution. Calculate the frame length M and divide the ship radiated noise data into overlapping I frames. Each frame is processed by mean removal and normalization to obtain ,in This represents the value of the i-th frame after mean removal and normalization. For frames The mean, Represents the 2-norm, frequency resolution , Sampling rate; S3: Starting from frame 0, extract consecutive P frames with a preset frame number s as the step size, and construct a multi-snapshot matrix; as detailed below: Set the number of snapshots P, starting from frame 0 and ending at frame IP. Extract adjacent P frames with a preset frame count s as the step size to construct a multi-snapshot matrix. Where b represents the sequence number of the multiple snapshot matrix, , Indicates the first Frame, where p represents the frame number in the multiple snapshot matrix. ; S4: Divide the time-frequency grid, combine the Gaussian window with the complex exponential basis function, and construct the dictionary matrix at the time-frequency grid points; the details are as follows: Set the frequency range of the line spectrum Construct an equally spaced discrete grid in a time-frequency two-dimensional coordinate system and generate grid point coordinates. ,in This represents the nth discrete frequency value on the frequency axis, corresponding to the vertical coordinate in the coordinate system. n represents the index number of the frequency point, used to identify the discrete position on the frequency axis, and its value is... N represents the total number of discrete frequency points on the frequency axis. , This represents the m-th discrete time point on the time axis, where m represents the time index, corresponding to a discrete sampling point on the time axis, and its value is... M represents the total number of discrete time points on the time axis. Indicates the minimum frequency. Indicates the maximum frequency; Generate complex exponential basis functions on grid point coordinates. and Gaussian window function ,in, It is an extended parameter of the window function. c is an empirical coefficient used to adjust the extent of expansion of the window function; a Gaussian window function is used to weight the complex exponential basis functions to form localized basis functions: ,in, Indicates taking the real part; Construct a dictionary matrix using all generated localization basis functions. ,in , Represents the nth column of the dictionary matrix. This represents the matrix transpose; normalizing all columns of the dictionary matrix yields... , Represents a dictionary matrix. Represents the nth column of the dictionary matrix. ; S5: Set the hyperparameters and iteration parameters, import the multiple snapshot matrix and dictionary matrix into the sparse Bayesian learning algorithm, and obtain the time-frequency diagram of the ship's radiated noise; From the first multi-snapshot matrix From the beginning to the last multi-snapshot matrix Finally, the sparse Bayesian learning algorithm is used sequentially to calculate the multiple snapshot matrix. Corresponding spectral power The details are as follows: S5.

1. Initialize hyperparameters and iteration parameters; S5.

2. Calculate the covariance matrix and mean of the k-th iteration: The formula for calculating the covariance matrix is: ,in, This indicates that a diagonal matrix is ​​generated from vectors. This represents the sparse parameter vector for the k-th iteration. , This represents the noise parameter in the k-th iteration. For regularization parameters, express An identity matrix of order 1; The formula for calculating the mean is: ,in, , The nth row represents the mean. This represents the estimated spectral amplitude of the signal at the nth frequency component in the p-th frame during the k-th iteration. S5.

3. Updating Hyperparameters: Sparse Parameter Vector The nth element is updated to Noise parameters updated to ,in Denotes the F-norm; S5.

4. Determine if the iteration termination condition is met: Calculate the relative update amount of the sparse parameter vector. ,like or If the condition is met, stop iterating; otherwise, continue iterating. K is the convergence threshold, and K is the maximum number of iterations. S5.

5. Calculate the multiple snapshot matrix. Corresponding spectral power ,in This represents the starting time of the b-th multiple snapshot matrix. O represents the inter-frame overlap length; S5.

6. Repeat S5.2-S5.5 to obtain the spectral power corresponding to all multiple snapshot matrices. Normalization is performed: , This is a time-frequency diagram of the ship's radiated noise line spectrum at all times.

2. The method for estimating the line spectrum of ship radiated noise based on multi-snapshot sparse Bayesian learning according to claim 1, characterized in that: S2 is as follows: Calculate the frame length M, select the inter-frame overlap length O, and then transfer the collected ship radiated noise data. Evenly divided into overlapping sections Frame, in which The first part representing the ship's radiated noise data The value of each sampling point, index Indicates the sampling point number. , This represents the total number of sampling points. Indicates rounding down; i-th frame The starting position is The end position is ,in .

3. The method for estimating the line spectrum of ship radiated noise based on multi-snapshot sparse Bayesian learning according to claim 1, characterized in that: In S4, the empirical coefficient c ranges from 2 to 6.

4. The method for estimating the line spectrum of ship radiated noise based on multi-snapshot sparse Bayesian learning according to claim 3, characterized in that: In S4, the empirical coefficient c is set to 2.

5. The method for estimating the line spectrum of ship radiated noise based on multi-snapshot sparse Bayesian learning according to claim 1, characterized in that: In S5.1, (1) the hyperparameters are initialized as follows: the sparse parameter vector is initialized as follows: ,in express A 1-dimensional matrix; noise parameters initialized to... ,in (2) The iteration parameters are initialized as follows: regularization parameter , The range is from 1e-3 to 1e-6; the maximum number of iterations K is between 30 and 200; and the convergence threshold is... , Take 1e-6 to 1e-8.

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