Underwater target line spectrum extraction method based on double-input Dense U-net model

Abstract

The invention discloses an underwater target line spectrum extraction method based on a dual-input Dense U-net model, and belongs to the technical field of underwater acoustic signal processing. According to the method, the problems of poor performance and high calculation complexity of an existing target line spectrum extraction method are solved. A convolutional layer in a common U-net is replaced by DenseBlock to obtain a Dense U-net model, the Dense U-net model performs dimension reduction on a sample through the DenseBlock and a pooling layer, then performs dimension raising on the sample through an up-sampling layer and the DenseBlock, the Dense U-net model can be used for extracting aliasing time-frequency characteristics and interference time-frequency characteristics in a received signal, a signal power spectrum is estimated based on conventional beam forming and a Welch method, and the power spectrum of the received signal is calculated. According to the Welch method, due to segmented averaging and windowing processing, spectrum diffusion of strong interference and other random interference can be effectively restrained. The trained network can effectively cope with insufficient annotation data in the field of underwater acoustic detection and strong dependence of supervised learning on the annotation data, and the performance of target line spectrum extraction is improved. The method can be applied to underwater target line spectrum extraction.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater acoustic signal processing, and in particular relates to a method for extracting underwater target line spectra based on a dual-input Dense U-net model. Background Art

[0002] Line spectrum purification is a core technology for underwater acoustic target feature extraction. It has extensive applications in underwater acoustic target detection and array signal processing, and is of great significance in underwater detection, identification, and positioning. Its core goal is to remove contaminating noise and interference to obtain the target's line spectrum features. In the actual use of hydrophone arrays for underwater acoustic target detection, the desired target is often affected by strong interference. This results in the interference's characteristics being mixed into the extracted target frequency domain features. To obtain a pure target line spectrum, a line spectrum purification method that can suppress the influence of interference is required. Traditional algorithms rely on an ideal array model. However, in actual use, the array state is often suboptimal due to factors such as array installation errors and inconsistent amplitude and phase responses of array element channels. When the actual array has defects, the actual array model does not match the ideal array model, and the algorithm's interference suppression capability is reduced, significantly affecting the performance of target line spectrum feature extraction. For example, literature 1 (Shenyang University. A noise suppression method in line spectrum feature extraction based on double singular value decomposition: 202411593307.7[P]. 2025-02-28.) and literature 2 (National University of Defense Technology of China. Ship noise modulation line spectrum extraction and shaft frequency estimation method based on line segment detection: 202310673112.2[P]. 2023-08-18.) mainly focus on purifying and extracting target line spectrum features under noise background. Under interference background, the performance of target line spectrum feature extraction is reduced.

[0003] With the development of machine learning, some scholars have begun to use neural networks to solve the DOA estimation problem in recent years. Machine learning methods are data-driven and do not rely on pre-designed array models. Therefore, such methods are more robust to array defects in practical applications. For example, Reference 3 (Cui X, He Z, Xue Y, Tang K, Zhu P, Han J.Cross-Domain Contrastive Learning-Based Few-Shot Underwater Acoustic Target Recognition[J]. Journal of Marine Science and Engineering. 2024; 12(2):264.) and Reference 4 (Irfan M, Jiangbin Z, Ali S, et al. DeepShip: An Underwater AcousticBenchmark Dataset and a Separable Convolution Based Autoencoder for Classification[J]. Expert Systems with Applications, 2021, 183(5):115270.) used the supervised learning paradigm to brute force the mapping of data to physical features. The underlying logic of supervised learning is to forcibly establish statistical correlations between signal aliasing patterns and target features using massive amounts of labeled data. Essentially, it is a data-driven approximation of the target-interference distribution boundary in high-dimensional time-frequency space. The core assumption of supervised learning is that the spectrum of the target ship's radiated noise exhibits some implicit separable pattern in the time-frequency domain, which can be automatically extracted through nonlinear transformations in machine learning. Supervised learning is highly dependent on labeled data, and labeling errors significantly impact the system's performance in extracting target line spectrum features.

[0004] References 5 (Martino JCD, Colnet B, Martino M D. The use of non-supervised neural networks to detect lines in lofargram [J]. IEEE International Conference on Acoustics. IEEE, 1994.) and 6 (Horzyk A. Unsupervised Clustering using Self-Optimizing Neural Networks [J]. IEEE, 2005. DOI: 10.1109 / ISDA.2005.95.) employ the unsupervised learning paradigm to find order in chaotic data. Unsupervised learning attempts to circumvent the limitations of labeled data by forcing the model to exploit the underlying separation patterns between target and interference from mixed signals through self-consistent optimization objectives (such as generative adversarial loss and latent variable orthogonality constraints). The core assumption of unsupervised learning is that the target and interference have a separability boundary in the latent space (such as statistical independence or distributional difference), which can be captured through machine learning. While unsupervised learning breaks free from the constraints of labeled data, its dissociation assumption may not be physically applicable. In real-world scenarios, ship targets and interference noise are not strictly independent. For example, when the interference and target spectral lines overlap, the target line spectrum feature extraction performance will be significantly degraded. Furthermore, unsupervised models often require iterative optimization, which leads to high computational complexity in such algorithms. Summary of the Invention

[0005] The purpose of the present invention is to solve the problems of poor performance and high computational complexity of existing target line spectrum extraction methods, and to propose an underwater target line spectrum extraction method based on a dual-input Dense U-net model.

[0006] The technical solution adopted by the present invention to solve the above technical problems is: a method for extracting underwater target line spectra based on a dual-input Dense U-net model, the method specifically comprising the following steps:

[0007] Step 1: obtain the received signals of the hydrophone array under different environmental parameters through simulation, and then preprocess the received signals of the hydrophone array under each set of environmental parameters to extract the interference time-frequency characteristics and the target and interference aliasing time-frequency characteristics of the received signals of the hydrophone array under each set of environmental parameters;

[0008] Step 2: Divide the hydrophone array received signals under each set of environmental parameters into a training set and a test set, and use the target line spectrum corresponding to the received signal as a label;

[0009] Step 3: Build a Dense U-net model and train it using the interference time-frequency characteristics corresponding to the received signal in the training set and the target and interference aliasing time-frequency characteristics. Stop training when the extraction accuracy of the Dense U-net model on the test set no longer improves, and obtain a trained Dense U-net model.

[0010] Step 4: Process the actual received signal of the hydrophone array using the method of step 1 to obtain the interference time-frequency characteristics of the actual received signal and the time-frequency characteristics of the target and interference aliasing;

[0011] The interference time-frequency characteristics of the actual received signal and the aliased time-frequency characteristics of the target and interference are used as the input of the trained Dense U-net model, and the underwater target line spectrum is output through the trained Dense U-net model.

[0012] Furthermore, the hydrophone array is a uniform linear array consisting of M non-directional hydrophones.

[0013] Furthermore, when the received signals of the hydrophone array under different environmental parameters are obtained through simulation, an interference signal and a target signal are incident on the hydrophone array in a plane.

[0014] Furthermore, the pre-processing of the hydrophone array received signals under each set of environmental parameters is specifically as follows: For the hydrophone array receiving signal under any set of environmental parameters, the interference and target aliased signal parts and the interference-only signal part in the hydrophone array receiving signal are obtained respectively; Then the interference and target aliasing signal parts are divided into segments, dividing the signal part with only interference into fragments; Similarly, the received signals of the hydrophone array under each set of environmental parameters are preprocessed respectively.

[0015] Furthermore, the specific process of extracting the interference time-frequency characteristics and the target and interference aliasing time-frequency characteristics of the hydrophone array received signal under each set of environmental parameters is as follows: Step 1: Mix the interference and target aliasing signals. The fragment is recorded as : in, The first aliased signal of the interference and target The received signal of the first element in the segment; The first aliased signal of the interference and target In the fragment, The received signal of each array element; right 、 、…、 Perform DFT transform of L points separately: in, Indicates the frequency domain subbands;

[0016] express Middle The value of a point;

[0017] represents an imaginary unit;

[0018] Indicates the DFT transform results of frequency domain subbands;

[0019] The first Frequency domain data of segments for:

[0020]

[0021] Among them, the superscript represents transpose;

[0022] Step 2: Calculate the The output of the beam of frequency domain sub-bands :

[0023]

[0024] in, For the The beamforming weight vector for frequency domain subbands;

[0025] The superscript H indicates conjugate transpose;

[0026] Step 3: Perform IDFT transformation to obtain the time domain output of the beam, then the first value for:

[0027]

[0028] Step 4: Split the time domain output of the beam into sub-segments and there are overlaps between adjacent sub-segments, the first Sub-fragments are recorded as , ;

[0029] according to Calculate the Power spectrum of sub-segments :

[0030]

[0031] in, is the normalization factor;

[0032] For the The length of each sub-segment;

[0033] For the The first sub-fragment values;

[0034] is the window function;

[0035] is the frequency;

[0036] Rule No. The power spectrum of the fragment for:

[0037]

[0038] Similarly, the power spectrum of each fragment of the interference and target aliasing signals is obtained respectively, and then the interference and target aliasing time-frequency characteristics are obtained according to the power spectrum of each fragment of the interference and target aliasing signals. :

[0039]

[0040] Step 5: Using the methods of Step 1 to Step 4, process each segment containing only the interference signal separately to obtain the interference time-frequency characteristics.

[0041] Furthermore, the The beamforming weight vector for frequency domain subbands is for:

[0042]

[0043] in, is the array manifold vector of the hydrophone array;

[0044] is the pointing direction of the beam, , is the incident angle of the target;

[0045]

[0046] Among them, the vector ;

[0047] Indicates the The frequency corresponding to the frequency domain sub-band;

[0048] represents the spacing between adjacent elements in the hydrophone array;

[0049] Indicates the speed of sound.

[0050] Furthermore, the The frequency domain subband corresponds to the frequency for:

[0051]

[0052] in, Indicates the sampling frequency.

[0053] Furthermore, the normalization factor is:

[0054]

[0055] Furthermore, the Dense U-net model includes a contraction path and an expansion path, the contraction path includes a first convolutional layer, a second convolutional layer, a first ReLU activation function layer, a second ReLU activation function layer, a first DenseBlock, a first maximum pooling layer, a second DenseBlock, a second maximum pooling layer, a third DenseBlock and a third maximum pooling layer; the expansion path includes a first upsampling layer, a fifth DenseBlock, a second upsampling layer, a sixth DenseBlock, a third upsampling layer, a seventh DenseBlock, a third convolutional layer and a SoftMax activation function layer, and the contraction path and the expansion path are connected through a fourth DenseBlock;

[0056] The working process of the Dense U-net model is:

[0057] The interference time-frequency features and the target and interference aliasing time-frequency features are used as the input of the Dense U-net model. In the Dense U-net model, the interference time-frequency features are sequentially passed through the first convolution layer and the first ReLU activation function layer, and the target and interference aliasing time-frequency features are passed through the second convolution layer and the second ReLU activation function layer.

[0058] Then, the output of the first ReLU activation function layer is connected in series with the output of the second ReLU activation function layer to obtain the connection result s1;

[0059] Use s1 as the input of the first DenseBlock, and then use the output of the first DenseBlock as the input of the first maximum pooling layer;

[0060] Use the output of the first maximum pooling layer as the input of the second DenseBlock, and use the output of the second DenseBlock as the input of the second maximum pooling layer;

[0061] The output of the second maximum pooling layer is used as the input of the third DenseBlock, and the output of the third DenseBlock is used as the input of the third maximum pooling layer;

[0062] Use the output of the third maximum pooling layer as the input of the fourth DenseBlock, and use the output of the fourth DenseBlock as the input of the first upsampling layer;

[0063] The output of the first upsampling layer is concatenated with the output of the third DenseBlock to obtain a concatenation result S2;

[0064] Use S2 as the input of the fifth DenseBlock, use the output of the fifth DenseBlock as the input of the second upsampling layer, and then concatenate the output of the second upsampling layer with the output of the second DenseBlock to obtain the concatenation result S3;

[0065] Use S3 as the input of the sixth DenseBlock, use the output of the sixth DenseBlock as the input of the third upsampling layer, and then concatenate the output of the third upsampling layer with the output of the first DenseBlock to obtain the concatenation result S4;

[0066] S4 is used as the input of the seventh DenseBlock, the output of the seventh DenseBlock is used as the input of the third convolutional layer, and the output of the third convolutional layer is used as the output of the SoftMax activation function layer, and the target line spectrum is output through the SoftMax activation function layer.

[0067] Furthermore, the first DenseBlock includes a first composite function and a second composite function, each composite function includes a BN layer, an activation function layer and a convolution layer with a convolution kernel size of 3*3;

[0068] The working process of the first DenseBlock is:

[0069] The input of the first DenseBlock is recorded as , enter After the first composite function, the output of the first composite function is recorded as , and then and The concatenation is performed to obtain a concatenation result S5, and the concatenation result S5 is used as the input of the second composite function to obtain the output of the second composite function;

[0070] Then concatenate the output of the second composite function with S5 to obtain the concatenation result S6, and use the concatenation result S6 as the output of the first DenseBlock .

[0071] The beneficial effects of the present invention are:

[0072] The present invention extracts aliasing time-frequency features and interference time-frequency features from the received signal, and then uses the extracted features as input to the Dense U-net model. The Dense U-net model reduces the dimensionality of the samples through DenseBlock and pooling layers, and then increases the dimensionality of the samples through upsampling layers and DenseBlock, ultimately obtaining a two-dimensional matrix. In the present invention, the convolutional layers in the conventional U-net are replaced with DenseBlock, an efficient convolutional structure composed of several convolutional layers. This special structure enables DenseBlock to effectively improve information flow and more efficiently utilize parameters, thereby alleviating the vanishing gradient problem and significantly reducing the number of parameters, thereby reducing computational complexity.

[0073] The method of the present invention estimates the signal power spectrum based on conventional beamforming and the Welch method. In spectrum estimation scenarios with strong interference, the Welch method can effectively suppress the spectrum diffusion of strong interference and other random interference due to segmented averaging and windowing processing, making the robustness and generalization performance of the method of the present invention significantly higher than traditional methods. Applying the trained network of the present invention to actual data can effectively address the shortage of labeled data in the field of underwater acoustic detection and the strong dependence of supervised learning on labeled data, thereby improving the performance of the target line spectrum extraction method. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 This is a flow chart of a method for extracting underwater target line spectrum based on a dual-input Dense U-net model of the present invention;

[0075] Figure 2 This is the structural diagram of DenseBlock;

[0076] Figure 3 This is the structural diagram of the Dense U-net model;

[0077] Figure 4The output signal-to-interference-noise ratio of the method of the present invention and the second-order cone nulling method under different input signal-to-interference-noise ratios;

[0078] Wherein, SOCP represents the second-order cone nulling method;

[0079] Figure 5 is the normalized Hamming distance between the proposed method and the second-order cone nulling method under different input signal-to-interference-noise ratios;

[0080] Figure 6 It is the output signal-to-interference-noise ratio of the method of the present invention and the second-order cone nulling method under different array element position errors;

[0081] Figure 7 is the normalized Hamming distance between the method of the present invention and the second-order cone nulling method under different array element position errors;

[0082] Figure 8 It is the output signal-to-noise ratio of the method of the present invention and the second-order cone nulling method under different target input signal-to-noise ratios;

[0083] Figure 9 is the normalized Hamming distance between the proposed method and the second-order cone nulling method under different target input signal-to-noise ratios;

[0084] Figure 10 is the interference time-frequency characteristic of the actual experimental data;

[0085] Figure 11 It is the time-frequency characteristics of interference and target aliasing of actual experimental data;

[0086] Figure 12 is the purification result of the second-order cone nulling method;

[0087] Figure 13 It is the purification result of the method of the present invention. DETAILED DESCRIPTION

[0088] Specific implementation method 1: Combination Figure 1 This embodiment describes a method for extracting underwater target line spectra based on a dual-input Dense U-net model, which specifically includes the following steps:

[0089] Step 1: The received signals of the hydrophone array under different environmental parameters are obtained through simulation. The received signals of the hydrophone array under each set of environmental parameters are then preprocessed to extract the interference time-frequency characteristics (containing only interference and noise) and the aliased time-frequency characteristics of the target and interference (the aliased time-frequency characteristics contain interference, target, and noise) of the received signals under each set of environmental parameters.

[0090] Step 2: Divide the hydrophone array received signals under each set of environmental parameters into a training set and a test set, and use the target line spectrum corresponding to the received signal as a label;

[0091] Step 3: Build a Dense U-net model and train it using the interference time-frequency features and target and interference aliasing time-frequency features corresponding to the received signal in the training set (before training, data enhancement can be performed on the interference time-frequency features and target and interference aliasing time-frequency features corresponding to the received signal to increase the number of training samples. The enhanced feature samples and the original feature samples have the same label). Stop training when the extraction accuracy of the Dense U-net model on the test set no longer improves, and obtain a trained Dense U-net model.

[0092] Step 4: Process the actual received signal of the hydrophone array using the method of step 1 to obtain the interference time-frequency characteristics of the actual received signal and the time-frequency characteristics of the target and interference aliasing;

[0093] The interference time-frequency characteristics of the actual received signal and the aliased time-frequency characteristics of the target and interference are used as the input of the trained Dense U-net model, and the underwater target line spectrum is output through the trained Dense U-net model.

[0094] Specific embodiment 2: This embodiment further limits specific embodiment 1, and the hydrophone array is a uniform linear array composed of M non-directional hydrophones.

[0095] Other steps and parameters are the same as those in the first embodiment.

[0096] Specific embodiment three: This embodiment further limits specific embodiment two. When the received signals of the hydrophone array under different environmental parameters are obtained through simulation, an interference signal and a target signal are incident on the hydrophone array in a plane.

[0097] Other steps and parameters are the same as those in the second embodiment.

[0098] Specific embodiment 4: This embodiment is a further limitation of specific embodiment 3. The pre-processing of the hydrophone array received signal under each set of environmental parameters is as follows:

[0099] For the hydrophone array receiving signal under any set of environmental parameters, the interference and target aliased signal parts and the interference-only signal part in the hydrophone array receiving signal are obtained respectively;

[0100] Then the interference and target aliasing signal parts are divided into segments, dividing the signal part with only interference into fragments;

[0101] Similarly, the received signals of the hydrophone array under each set of environmental parameters are preprocessed respectively.

[0102] Other steps and parameters are the same as those in the third embodiment.

[0103] Specific embodiment 5: This embodiment is a further limitation of specific embodiment 4. The specific process of extracting the interference time-frequency characteristics and the target and interference aliasing time-frequency characteristics of the hydrophone array receiving signal under each set of environmental parameters is as follows:

[0104] Step 1: Mix the interference and target aliasing signals. The fragment is recorded as :

[0105]

[0106] in, The first aliased signal of the interference and target The received signal of the first element in the segment;

[0107] The first aliased signal of the interference and target In the fragment, The received signal of each array element;

[0108] right 、 、…、 Perform DFT transform (discrete Fourier transform) of point L respectively:

[0109]

[0110] in, Indicates the frequency domain subbands;

[0111] express Middle The value of a point;

[0112] represents an imaginary unit;

[0113] Indicates the DFT transform results of frequency domain subbands;

[0114] The first Frequency domain data of segments for:

[0115]

[0116] Among them, the superscript represents transpose;

[0117] Step 2: Calculate the The output of the beam of frequency domain sub-bands :

[0118]

[0119] in, For the The beamforming weight vector for frequency domain subbands;

[0120] The superscript H indicates conjugate transpose;

[0121] Step 3: Perform IDFT transformation (Inverse Discrete Fourier Transform) to obtain the time domain output of the beam. The first value for:

[0122]

[0123] Step 4: Split the time domain output of the beam into sub-segments and there are overlaps between adjacent sub-segments, the first Sub-fragments are recorded as , ;

[0124] According to the Welch method and Calculate the Power spectrum of sub-segments :

[0125]

[0126] in, is the normalization factor;

[0127] For the The length of each sub-segment;

[0128] For the The first sub-fragment values;

[0129] is the window function;

[0130] is the frequency;

[0131] Rule No. The power spectrum of the fragment for:

[0132]

[0133] Similarly, the power spectrum of each fragment of the interference and target aliasing signals is obtained respectively, and then the interference and target aliasing time-frequency characteristics are obtained according to the power spectrum of each fragment of the interference and target aliasing signals. :

[0134]

[0135] Step 5: Using the methods of Step 1 to Step 4, process each segment containing only the interference signal separately to obtain the interference time-frequency characteristics.

[0136] Other steps and parameters are the same as those in the fourth embodiment.

[0137] The only difference between step 5 and the previous one is , Indicates the incident angle of interference, using Get array manifold vector And the corresponding weights Under the far-field plane wave assumption, the angles of incidence of the same target on the M array elements are equal, the angles of incidence of the interference on the M array elements are also equal, and within each signal segment, the orientation of the interference and the target can be considered to be unchanged.

[0138] Specific implementation method 6: This implementation method is a further limitation of the specific implementation method 5. The beamforming weight vector for frequency domain subbands is for:

[0139]

[0140] in, is the array manifold vector of the hydrophone array;

[0141] is the pointing direction of the beam, , is the incident angle of the target;

[0142]

[0143] Among them, the vector ;

[0144] Indicates the The frequency corresponding to the frequency domain sub-band;

[0145] represents the spacing between adjacent elements in the hydrophone array;

[0146] Indicates the speed of sound.

[0147] Other steps and parameters are the same as those in the fifth embodiment.

[0148] Specific implementation method seven: This implementation method is a further limitation of specific implementation method six. The frequency domain subband corresponds to the frequency for:

[0149]

[0150] in, Indicates the sampling frequency.

[0151] Other steps and parameters are the same as those in the sixth embodiment.

[0152] Specific embodiment eight: This embodiment further limits specific embodiment seven, and the normalization factor is:

[0153]

[0154] Other steps and parameters are the same as those in the seventh embodiment.

[0155] Specific implementation method nine: Combination Figure 3 This embodiment further limits the specific embodiment eight, wherein the Dense U-net model includes a contraction path and an expansion path, wherein the contraction path includes a first convolutional layer, a second convolutional layer, a first ReLU activation function layer, a second ReLU activation function layer, a first DenseBlock, a first maximum pooling layer, a second DenseBlock, a second maximum pooling layer, a third DenseBlock, and a third maximum pooling layer; the expansion path includes a first upsampling layer, a fifth DenseBlock, a second upsampling layer, a sixth DenseBlock, a third upsampling layer, a seventh DenseBlock, a third convolutional layer, and a SoftMax activation function layer, and the contraction path and the expansion path are connected via a fourth DenseBlock;

[0156] The working process of the Dense U-net model is:

[0157] The interference time-frequency features and the target and interference aliasing time-frequency features are used as the input of the Dense U-net model. In the Dense U-net model, the interference time-frequency features are sequentially passed through the first convolution layer and the first ReLU activation function layer, and the target and interference aliasing time-frequency features are passed through the second convolution layer and the second ReLU activation function layer.

[0158] Then, the output of the first ReLU activation function layer is concatenated with the output of the second ReLU activation function layer (concatenation refers to concatenating two two-dimensional matrices in the third dimension, so a three-dimensional matrix can be obtained by concatenation), and the concatenation result s1 is obtained;

[0159] Use s1 as the input of the first DenseBlock, and then use the output of the first DenseBlock as the input of the first maximum pooling layer;

[0160] Use the output of the first maximum pooling layer as the input of the second DenseBlock, and use the output of the second DenseBlock as the input of the second maximum pooling layer;

[0161] The output of the second maximum pooling layer is used as the input of the third DenseBlock, and the output of the third DenseBlock is used as the input of the third maximum pooling layer;

[0162] Use the output of the third maximum pooling layer as the input of the fourth DenseBlock, and use the output of the fourth DenseBlock as the input of the first upsampling layer;

[0163] The output of the first upsampling layer is concatenated with the output of the third DenseBlock to obtain a concatenation result S2;

[0164] Use S2 as the input of the fifth DenseBlock, use the output of the fifth DenseBlock as the input of the second upsampling layer, and then concatenate the output of the second upsampling layer with the output of the second DenseBlock to obtain the concatenation result S3;

[0165] Use S3 as the input of the sixth DenseBlock, use the output of the sixth DenseBlock as the input of the third upsampling layer, and then concatenate the output of the third upsampling layer with the output of the first DenseBlock to obtain the concatenation result S4;

[0166] S4 is used as the input of the seventh DenseBlock, the output of the seventh DenseBlock is used as the input of the third convolutional layer, and the output of the third convolutional layer is used as the output of the SoftMax activation function layer, and the target line spectrum is output through the SoftMax activation function layer.

[0167] Other steps and parameters are the same as those in the eighth embodiment.

[0168] The contraction path is used to reduce the size of the feature map and obtain feature information. The input matrix first passes through a convolution layer with a convolution kernel size of 1×1 to increase the number of feature channels, thereby increasing the amount of information input to DenseBlock, and then DenseBlock is used to extract the features of the input samples. The pooling layer is used to reduce the dimension of the feature map, which can prevent overfitting and improve the stability of the network. The expansion path is used to increase the size of the feature map and restore the features of the original image. Before the feature matrix is ​​input to DenseBlock, it is first connected in series with the corresponding feature matrix in the contraction path through a direct connection to directly connect the features in the contraction path to the expansion path, which enables the network to learn the original input features more effectively. However, these operations will double the feature channels in the expansion path, and DenseBlock will further increase the number of channels. Therefore, the upsampling layer has two functions:

[0169] a) Adjust the number of feature channels;

[0170] b) Increase the size of the feature map.

[0171] After three DenseBlocks and three upsampling layers, the size of the feature map is consistent with the input image. Finally, a convolution layer with a convolution kernel size of 1×1 is used to combine the features of each channel to obtain a unique output. The SoftMax function is selected as the activation function and is defined as:

[0172]

[0173] Specific implementation method ten: Combination Figure 2 This embodiment is a further limitation of the ninth embodiment. The first DenseBlock includes a first composite function and a second composite function. Each composite function includes a BN (Batch Normalization) layer, an activation function layer, and a convolution kernel size of Convolutional layers;

[0174] The working process of the first DenseBlock is:

[0175] The input of the first DenseBlock is recorded as , enter After the first composite function, the output of the first composite function is recorded as , and then and The concatenation is performed to obtain a concatenation result S5, and the concatenation result S5 is used as the input of the second composite function to obtain the output of the second composite function;

[0176] Then concatenate the output of the second composite function with S5 to obtain the concatenation result S6, and use the concatenation result S6 as the output of the first DenseBlock .

[0177] Other steps and parameters are the same as those in the ninth embodiment.

[0178] It should be noted that the concatenation of A and B described in the present invention refers to splicing A and B in the third dimension, and in the splicing result, B is located after A. The two adjacent layers in DenseBlock are propagated through a nonlinear composite function. Each feature layer is copied to the subsequent layer through a direct path, and after being concatenated with the features of the layer, it is input to the composite function of the next level. The role of the BN layer is to adjust the distribution of all feature maps in a batch during batch training, so that the network can converge faster and effectively prevent gradient explosion and gradient disappearance. After the BN layer, an activation function and a convolution kernel size of The convolutional layer.

[0179] The activation function in the present invention adopts the ReLU function, and the formula of ReLU is:

[0180]

[0181] Before convolution, the input feature matrix is ​​padded to ensure that the input and output sizes are the same. If each convolution layer generates k feature channels, k is called the growth rate of DenseBlock. Then for a DenseBlock with L layers and an input of k0 feature channels, the number of feature channels of its output is k0+k×(L-1). The feature channels of the DenseBlock used in the present invention are k=16 and L=3. Moreover, in the present invention, the working processes of the first to seventh DenseBlocks are the same.

[0182] Simulation part

[0183] 1. The performance of the proposed method is analyzed using simulated test data and compared with the second-order conical null beam design method (SOCP).

[0184] Consider a 20-element ULA with 2m element spacing. Two signals, one interference signal and one target signal, are incident on the array from the far field. Both signals contain line spectra and continuous spectra. The line spectra of the interference signal and the target signal are distinguishable in frequency, but the continuous spectra overlap. The signal processing bandwidth is 0–960 Hz. The simulated noise is Gaussian white noise. A U-net network (with data augmentation) is trained using 200 samples. Each sample consists of 500 time segments, each containing 1920 snapshots. The sample signals in the training set cover different incidence angles and signal-to-noise ratios, and the line spectra of the signals have different numbers of spectral lines and different frequencies.

[0185] Algorithm performance is evaluated using the signal-to-interference-plus-noise ratio (SINR) and Hamming distance. The signal-to-interference-plus-noise ratio (SINR) measures the purification capability of a method from an energy perspective. A higher output SINR indicates better purification results. The Hamming distance measures the similarity between two matrices. The more similar the purified features are to the ideal features, the better the purification results. The Hamming distance is calculated and normalized using the mean hashing algorithm. The closer the normalized Hamming distance is to 1, the more similar the output features are to the reference features. A normalized zero indicates the similarity between the output features and the ideal features when the target signal is completely absent.

[0186] Simulation 1: The incident angles of the interference and target are -60.9° and -44.6° respectively. For the second-order cone nulling method, the beam is set to form a -30dB null at -56° to -66° to eliminate the influence of the interference. The input samples are extracted according to the U-net method of the present invention and input into the trained network. The in-band signal-to-noise ratio of the target is about 15dB. The energy of the interference is changed to make the input signal-to-noise ratio between -20dB and 10dB. The output signal-to-noise ratio of the method of the present invention and the second-order cone nulling method is 15dB. Figure 4 As shown, the normalized Hamming distance between the method of the present invention and the second-order cone nulling method is as follows: Figure 5 shown.

[0187] from Figure 4 and Figure 5 It can be seen that the U-net method of the present invention has a higher output signal-to-interference-noise ratio and higher estimation accuracy. Therefore, the U-net method of the present invention has a higher anti-interference ability than the second-order cone nulling method.

[0188] Simulation 2: Assume that there is a position error in the array. For each array element, add a uniformly distributed perturbation from -δ to +δ to its array element position. The array manifold vector with perturbation is expressed as:

[0189]

[0190] Depend on The interference time-frequency characteristics with array error can be calculated and recorded as , the time-frequency characteristics of the interference superposition target with array error are recorded as In the test set, and Input the trained Dense U-net model.

[0191] When δ increases from 0m to 1m, the output signal-to-noise ratio and normalized Hamming distance of different methods are as follows: Figure 6 and Figure 7 As shown in . The samples with array errors are not trained. Figure 6 and Figure 7 It can be seen that the robustness of the U-net method of the present invention is higher than that of other algorithms. When there is a large array error, the U-net method of the present invention can still maintain a high purification level.

[0192] Simulation 3: When the target input SNR is from -20dB to 10dB, the output SNR and normalized Hamming distance of different methods are as follows: Figure 8 and Figure 9 As shown in Figure 2, under low signal-to-noise ratio conditions, the U-net method of the present invention still maintains a high estimation accuracy. Therefore, the U-net method of the present invention is more robust to noise.

[0193] 2. The performance of the proposed method was verified using actual experimental data and compared with a second-order cone nulling algorithm. The experiment employed a 20-element uniform linear array with an element spacing of 2 meters. Multiple ships were present in the waters, and a strong signal was selected from among them as interference. An independent weak signal was also extracted as a target and superimposed on the signals of each element, with the target angle close to the strong interference. Both the interference and target radiated signals consisted of ship noise consisting of several line spectra and a continuous spectrum. The signal processing bandwidth was 0–960 Hz.

[0194] The interference and target signals in the training set both consist of line spectra and continuous spectra, with their line spectra non-overlapping in frequency. The training set contains 400 samples (with data augmentation). The sample signals in the training set cover a variety of incident angles and signal-to-noise ratios. The simulated signals contain 8 to 12 spectral lines with varying numbers, distributed at random frequencies between 0 and 960 Hz. The interference and target signals in the test set are both actual ship-radiated noise, with incident angles of -63.4° and -45.7° between the interference and target, respectively, resulting in a signal-to-interference ratio of approximately -15 dB. The second-order cone nulling method produces a -30 dB null between -59° and -69°.

[0195] Figure 10 is the interference time-frequency characteristic of the actual data, Figure 11is the interference and target aliasing time-frequency characteristics of the actual data, Figure 12 and Figure 13 The target line spectrum purification results for the second-order cone nulling method and the method of the present invention are shown, respectively. The results demonstrate that the U-net method of the present invention achieves a higher output signal-to-interference-noise ratio and high accuracy, thus possessing enhanced line spectrum purification capabilities. For other practical application scenarios, the same data processing approach can be applied to obtain the desired line spectrum purification results. Experimental results demonstrate that the method of the present invention can achieve good results in practical applications.

[0196] The above examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.

Claims

1. An underwater target line spectrum extraction method based on a dual-input Dense U-net model is characterized by: The method specifically comprises the following steps: Step 1: obtain the received signals of the hydrophone array under different environmental parameters through simulation, and then preprocess the received signals of the hydrophone array under each set of environmental parameters to extract the interference time-frequency characteristics and the target and interference aliasing time-frequency characteristics of the received signals of the hydrophone array under each set of environmental parameters; Step 2: Divide the hydrophone array received signals under each set of environmental parameters into a training set and a test set, and use the target line spectrum corresponding to the received signal as a label; Step 3: Build a Dense U-net model and train it using the interference time-frequency characteristics corresponding to the received signal in the training set and the target and interference aliasing time-frequency characteristics. Stop training when the extraction accuracy of the Dense U-net model on the test set no longer improves, and obtain a trained Dense U-net model. Step 4: Process the actual received signal of the hydrophone array using the method of step 1 to obtain the interference time-frequency characteristics of the actual received signal and the time-frequency characteristics of the target and interference aliasing; The interference time-frequency characteristics of the actual received signal and the aliased time-frequency characteristics of the target and interference are used as the input of the trained Dense U-net model, and the trained Dense U-net model outputs the underwater target line spectrum.

2. The underwater target line spectrum extraction method based on the dual-input Dense U-net model according to claim 1 is characterized in that: The hydrophone array is a uniform linear array consisting of M non-directional hydrophones.

3. The underwater target line spectrum extraction method based on the dual-input Dense U-net model according to claim 2 is characterized in that: When the received signals of the hydrophone array under different environmental parameters are obtained through simulation, an interference signal and a target signal are incident on the hydrophone array in a plane.

4. The underwater target line spectrum extraction method based on the dual-input Dense U-net model according to claim 3 is characterized in that: The pre-processing of the hydrophone array received signals under each set of environmental parameters is specifically as follows: For the hydrophone array receiving signal under any set of environmental parameters, the interference and target aliased signal parts and the interference-only signal part in the hydrophone array receiving signal are obtained respectively; Then the interference and target aliasing signal parts are divided into segments, dividing the signal part with only interference into fragments; Similarly, the received signals of the hydrophone array under each set of environmental parameters are preprocessed respectively.

5. The underwater target line spectrum extraction method based on the dual-input Dense U-net model according to claim 4 is characterized in that: The specific process of extracting the interference time-frequency characteristics of the hydrophone array received signal under each set of environmental parameters and the target and interference aliasing time-frequency characteristics is as follows: Step 1: Mix the interference and target aliasing signals. The fragment is recorded as : in, The first aliased signal of the interference and target The received signal of the first element in the segment; The first aliased signal of the interference and target In the fragment, The received signal of each array element; right 、 、…、 Perform DFT transform of L points separately: in, Indicates the frequency domain subbands; express Middle The value of a point; represents an imaginary unit; Indicates the DFT transform results of frequency domain subbands; The first Frequency domain data of segments for: Among them, the superscript represents transpose; Step 2: Calculate the The output of the beam of frequency domain sub-bands : in, For the The beamforming weight vector for frequency domain subbands; The superscript H indicates conjugate transpose; Step 3: Perform IDFT transformation to obtain the time domain output of the beam, then the first value for: Step 4: Split the time domain output of the beam into sub-segments and there are overlaps between adjacent sub-segments, the first Sub-fragments are recorded as , ; according to Calculate the Power spectrum of sub-segments : in, is the normalization factor; For the The length of each sub-segment; For the The first sub-fragment values; is the window function; is the frequency; Rule No. The power spectrum of the fragment for: Similarly, the power spectrum of each fragment of the interference and target aliasing signals is obtained respectively, and then the interference and target aliasing time-frequency characteristics are obtained according to the power spectrum of each fragment of the interference and target aliasing signals. : Step 5: Using the methods of Step 1 to Step 4, process each segment containing only the interference signal separately to obtain the interference time-frequency characteristics.

6. The underwater target line spectrum extraction method based on the dual-input Dense U-net model according to claim 5 is characterized in that: The said The beamforming weight vector for frequency domain subbands is for: in, is the array manifold vector of the hydrophone array; is the pointing direction of the beam, , is the incident angle of the target; Among them, the vector ; Indicates the The frequency corresponding to the frequency domain sub-band; represents the spacing between adjacent elements in the hydrophone array; Indicates the speed of sound.

7. The underwater target line spectrum extraction method based on the dual-input Dense U-net model according to claim 6 is characterized in that: The said The frequency domain subband corresponds to the frequency for: in, Indicates the sampling frequency.

8. The underwater target line spectrum extraction method based on the dual-input Dense U-net model according to claim 7 is characterized in that: The normalization factor is: 。 9. The underwater target line spectrum extraction method based on the dual-input Dense U-net model according to claim 8 is characterized in that: The Dense U-net model includes a contraction path and an expansion path, the contraction path includes a first convolutional layer, a second convolutional layer, a first ReLU activation function layer, a second ReLU activation function layer, a first DenseBlock, a first maximum pooling layer, a second DenseBlock, a second maximum pooling layer, a third DenseBlock and a third maximum pooling layer; the expansion path includes a first upsampling layer, a fifth DenseBlock, a second upsampling layer, a sixth DenseBlock, a third upsampling layer, a seventh DenseBlock, a third convolutional layer and a SoftMax activation function layer, and the contraction path and the expansion path are connected through a fourth DenseBlock; The working process of the Dense U-net model is: The interference time-frequency features and the target and interference aliasing time-frequency features are used as the input of the Dense U-net model. In the Dense U-net model, the interference time-frequency features are sequentially passed through the first convolution layer and the first ReLU activation function layer, and the target and interference aliasing time-frequency features are passed through the second convolution layer and the second ReLU activation function layer; Then, the output of the first ReLU activation function layer is connected in series with the output of the second ReLU activation function layer to obtain the connection result s1; Use s1 as the input of the first DenseBlock, and then use the output of the first DenseBlock as the input of the first maximum pooling layer; Use the output of the first maximum pooling layer as the input of the second DenseBlock, and use the output of the second DenseBlock as the input of the second maximum pooling layer; The output of the second maximum pooling layer is used as the input of the third DenseBlock, and the output of the third DenseBlock is used as the input of the third maximum pooling layer; Use the output of the third maximum pooling layer as the input of the fourth DenseBlock, and use the output of the fourth DenseBlock as the input of the first upsampling layer; The output of the first upsampling layer is concatenated with the output of the third DenseBlock to obtain a concatenation result S2; Use S2 as the input of the fifth DenseBlock, use the output of the fifth DenseBlock as the input of the second upsampling layer, and then concatenate the output of the second upsampling layer with the output of the second DenseBlock to obtain the concatenation result S3; Use S3 as the input of the sixth DenseBlock, use the output of the sixth DenseBlock as the input of the third upsampling layer, and then concatenate the output of the third upsampling layer with the output of the first DenseBlock to obtain the concatenation result S4; S4 is used as the input of the seventh DenseBlock, the output of the seventh DenseBlock is used as the input of the third convolutional layer, and the output of the third convolutional layer is used as the output of the SoftMax activation function layer, and the target line spectrum is output through the SoftMax activation function layer.

10. The underwater target line spectrum extraction method based on the dual-input Dense U-net model according to claim 9 is characterized in that: The first DenseBlock includes a first composite function and a second composite function, each of which includes a BN layer, an activation function layer and a convolution kernel size of Convolutional layers; The working process of the first DenseBlock is: The input of the first DenseBlock is recorded as , enter After the first composite function, the output of the first composite function is recorded as , and then and The concatenation is performed to obtain a concatenation result S5, and the concatenation result S5 is used as the input of the second composite function to obtain the output of the second composite function; Then concatenate the output of the second composite function with S5 to obtain the concatenation result S6, and use the concatenation result S6 as the output of the first DenseBlock .

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