Underwater acoustic target classification and orientation method based on array element correlation feature deep convolutional neural network

Abstract

The invention provides an underwater acoustic target classification and orientation method based on an array element correlation feature deep convolutional neural network, and the method comprises the steps: obtaining an underwater acoustic target radiation noise signal x (t), generating a data sample set X through the underwater acoustic target radiation noise signal x (t), and obtaining a frequency spectrum Yi of the underwater acoustic target radiation noise signal x (t) through Fourier transform; calculating covariance of the frequency spectrum Yi along the frequency dimension of the frequency spectrum to obtain a covariance matrix Rxi; performing complex component dimension expansion on the covariance matrix Rxi to obtain a covariance matrix Rxi'after dimension expansion; the covariance matrix Rxi'is input into a deep convolutional neural network model based on array element correlation characteristics, branches in the deep convolutional neural network model are associated with different target types, and the predicted orientation # imgabs0 # of the underwater acoustic target is output. Phase-frequency difference characteristics between underwater acoustic target radiation noise signals are extracted through a network model, a multi-branch network output structure is constructed, and classification and orientation tasks of underwater acoustic targets are achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater acoustic target information application, and in particular relates to an underwater acoustic target classification and orientation method based on a deep convolutional neural network with array element correlation characteristics. Background Art

[0002] By using the noise signals radiated by hydroacoustic targets to classify or orient targets, it is possible to obtain information about the type or orientation of hydroacoustic targets, which has important application value in the fields of ocean detection, underwater navigation, anti-submarine warfare, etc. However, due to the complexity of the marine environment, the sonar array system inevitably receives the noise signals radiated by multiple hydroacoustic targets during target detection. Existing methods can only resolve the orientation of hydroacoustic targets or identify the type of targets, but cannot simultaneously associate the orientation of each target with the type of hydroacoustic target, which is not conducive to the execution of subsequent hydroacoustic target detection tasks.

[0003] With the continuous development of deep learning technology, its adaptive ability enables the model to mine representative features from a large amount of data, and has been widely used in many fields such as target detection and recognition tasks. There is a phase delay between the underwater acoustic target radiation noise signals received by different array elements in the sonar array system, and the phase delay is jointly determined by the signal wave direction, array element position and signal center frequency. Therefore, by analyzing the phase delay information between the signals received by each array element, the classification and orientation tasks of underwater acoustic targets can be achieved. In addition, the correlation characteristics between the various array elements of the sonar array system describe the correlation between the responses of the underwater acoustic target radiation noise signals received by different array elements. This correlation feature is usually reflected by the covariance matrix of the target radiation noise signal. The physical quantity of the covariance matrix of the target radiation noise signal accurately captures the correlation characteristics between the signals received by each array element, and contains the power difference and phase difference of the signal. Therefore, the correlation characteristics between the various components in the spectrum covariance matrix of the underwater acoustic target radiation noise signal imply the phase-frequency characteristics of the radiation noise signals of different underwater acoustic targets, which provides a basis for the realization of underwater acoustic target classification and orientation tasks. Summary of the invention

[0004] The purpose of the present invention is to solve the shortcomings of the prior art that the two tasks cannot be correlated using the noise signals radiated by the underwater acoustic target, and to provide a method for classifying and orienting underwater acoustic targets based on a deep convolutional neural network with array element correlation characteristics. The covariance matrix of the spectrum of the noise signal radiated by the underwater acoustic target is used as the network input, and the phase-frequency difference characteristics between the noise signals radiated by the underwater acoustic target are extracted through the phase-frequency feature mining module, and a multi-branch network output structure is constructed to achieve the classification and orientation tasks of the underwater acoustic targets.

[0005] To achieve the above purpose, the technical solution provided by the present invention is:

[0006] A method for underwater acoustic target classification and orientation based on deep convolutional neural network with array element correlation features, comprising:

[0007] Step 1: Obtain the underwater acoustic target radiation noise signal x(t), the underwater acoustic target radiation noise signal x(t) generates a data sample set X, and the data sample set X is subjected to Fourier transformation to obtain the spectrum Y of the underwater acoustic target radiation noise signal x(t) i ;

[0008] Step 2: The spectrum Y i Calculate the covariance along the frequency dimension of the spectrum to obtain the spectrum Y i The covariance matrix Rx i ;

[0009] Step 3: The covariance matrix Rx i After the complex component dimension expansion, the covariance matrix Rx' after dimension expansion is obtained i ;

[0010] Step 4: The covariance matrix Rx' i Input a deep convolutional neural network model based on array element correlation features. Each branch in the deep convolutional neural network model is associated with different target types, and the predicted position of the underwater acoustic target is output.

[0011] As a further limitation of the present invention, the step 1 comprises:

[0012] Step (11) obtains the underwater acoustic target radiation noise signal x(t) received by the sonar array system, which is expressed as:

[0013] x(t)=x1(t)+x2(t)+…+x n (t)+noise(t) Formula (1)

[0014] In formula (1), x1(t) represents the radiation noise signal of hydroacoustic target 1, x2(t) represents the radiation noise signal of hydroacoustic target 2, and x n (t) represents the radiation noise signal of the underwater acoustic target n, noise(t) represents the ocean noise signal; x1(t), x2(t), x n The expression of (t) is:

[0015]

[0016] In formula (2), f1 represents the center frequency of the noise signal radiated by the hydroacoustic target 1, s1(t) represents the noise source signal of the hydroacoustic target 1, a1(f1,θ1) represents the direction vector of the noise signal radiated by the hydroacoustic target 1, f2 represents the center frequency of the noise signal radiated by the hydroacoustic target 2, s2(t) represents the noise source signal of the hydroacoustic target 2, a2(f2,θ2) represents the direction vector of the noise signal radiated by the hydroacoustic target 2, and f n represents the center frequency of the noise signal radiated by the underwater acoustic target n, s n (t) represents the noise source signal of the underwater acoustic target n, a n (f n ,θ n ) represents the direction vector of the noise signal radiated by the hydroacoustic target n, d represents the array element spacing, c represents the underwater sound speed, M represents the number of array elements, θ1 represents the azimuth of the noise signal radiated by the hydroacoustic target 1 relative to the sonar array system, θ2 represents the azimuth of the noise signal radiated by the hydroacoustic target 2 relative to the sonar array system, and θ n Indicates the direction of the noise signal radiated by the hydroacoustic target n relative to the sonar array system;

[0017] Step (12) sets the number of array elements of the sonar array system to M, the sampling frequency of the underwater acoustic target radiation noise signal x(t) to fs, the signal duration to T, and the dimension of the underwater acoustic target radiation noise signal received by each array element of the sonar array system to 1×N (N=T·fs), then the dimension of the underwater acoustic target radiation noise signal x(t) is M×N;

[0018] Step (13) sets the value range of the incident azimuth θ of the underwater acoustic target radiation noise signal x(t) to The signal-to-noise ratio SNR of the underwater acoustic target radiation noise signal x(t) is in the range of [S sta ,S end ], a data sample set X is generated within the range of the incident azimuth θ and the signal-to-noise ratio SNR, and the expression is:

[0019] X={X1,X2,…X K} Formula (3)

[0020] In formula (3), X1 represents the noise signal x(t) radiated by the sonar array system under condition 1, X2 represents the noise signal x(t) radiated by the sonar array system under condition 2, and X K represents the underwater acoustic target radiation noise signal x(t) received by the sonar array system under condition K; wherein the incident azimuth θ and the signal-to-noise ratio SNR of conditions 1, 2 and K have different values;

[0021] Each data sample X in the data sample set X in step (14)i is a data matrix with M rows and N columns. The data sample set X is Fourier transformed along the dimension where the array element channel in the sonar array system is located to obtain M frequency spectrum vectors with a dimension size of 1×F (F=N / 2+1), where F represents the number of frequency points δ in the frequency dimension, and the data sample X i The expression is:

[0022] X i ,(i=1,2,…,K) Formula (4)

[0023] In formula (4), the data sample X i The dimensions are all M×N, K represents the data sample X i The number of

[0024] As a further limitation of the present invention, the step 2 comprises:

[0025] Step (21) stacks M frequency spectrum vectors with a dimension size of 1×F to obtain each data sample X in the data sample set X. i The spectrum of Y i , the spectrum Y i The dimension size is M×F;

[0026] Step (22) along the spectrum Y i The dimension of each frequency point δ is used to calculate the corresponding spectrum data Y i The covariance matrix Rx of (δ) i (δ), where the covariance matrix Rx i The calculation formula of (δ) is:

[0027] Rx i (δ) = E{Y i (δ)·Y i H (δ)} Formula (5)

[0028] In formula (5), E{·} represents the mathematical expectation, Y i H (δ) represents the spectrum data Y i The conjugate transpose of (δ), the covariance matrix Rx i The dimension of (δ) is M×M, and a total of F M×M covariance matrices Rx are obtained i (δ), and the covariance matrix Rx i (δ) is a Hermitian matrix, which is a complex matrix;

[0029] Step (23) converts F M×M covariance matrices Rx i (δ) are stacked to obtain the spectrum Yi The covariance matrix Rx i , the covariance matrix Rx i The dimensions are M×M×F.

[0030] As a further limitation of the present invention, the step three comprises:

[0031] Step (31) is to calculate the covariance matrix Rx in step 2 i Perform complex component dimension expansion and extract the covariance matrix Rx i The real part of and the imaginary component The real part and the imaginary component Stacking forms a new dimension and obtains the expanded covariance matrix Rx' i , where the covariance matrix Rx' i The dimension size is M×M×2×F;

[0032] Step (32) is to calculate the covariance matrix Rx' i After normalization, the expression is:

[0033] Rx' i =Rx' i / max(|Rx' i |).

[0034] As a further limitation of the present invention, the step 4 comprises:

[0035] Step (41) constructs and trains a deep convolutional neural network model based on array element correlation features to obtain the trained deep convolutional neural network model;

[0036] Step (42) converts the covariance matrix Rx' obtained in step 3 into i After inputting the deep convolutional neural network model, the deep convolutional neural network model deeply mines the covariance matrix Rx' i The underwater acoustic target category features and azimuth features contained in the multi-branch output structure of the deep convolutional neural network model are associated with different target types, and the predicted azimuth of each underwater acoustic target is output simultaneously.

[0037] As a further limitation of the present invention, step (41) comprises:

[0038] Step (411) sets the azimuth label L of the underwater acoustic target radiation noise signal i,p ;

[0039] Step (412) obtains a data set X for underwater acoustic target classification and orientation tasks data , the data set X data According to the ratio of a:b, it is divided into training set X train and validation set X val ;

[0040] Step (413) constructs a Correlation Feature Deep Convolutional Neural Network (CFDCNN) model based on the element correlation feature, constructs a PFFM module, sets an activation function, constructs a multi-branch network output structure, and sets a loss function corresponding to each branch; specifically, the CFDCNN model uses the PFFM module to calculate the covariance matrix Rx' i Perform feature extraction and mining, and then use the activation function to perform nonlinear transformation on the extracted features to highlight key features and suppress invalid features, thereby enhancing the nonlinear expression ability of the CFDCNN model; then, the CFDCNN model calculates the difference between the prediction result and the true label through the loss function, and optimizes the network performance by minimizing the loss, and finally realizes the orientation prediction of different targets through the multi-branch network output structure;

[0041] Step (414) converts the training set X train Divided into I train Contains N train A batch dataset B of samples train , select a mini-batch of the training dataset As the input of the CFDCNN network model, under the action of the network training parameters, the output of each branch of the CFDCNN network model is calculated, and the loss obtained is calculated according to each branch Update the parameter Ω1 of the CFDCNN network model; where J represents the Jth batch of data, J = 1, 2, ..., I train ;y p Indicates the labels corresponding to each branch. Indicates the predicted position of each branch output of the CFDCNN network model;

[0042] Step (415) converts the validation set X val Through the parameter Ω1 of the CFDCNN network model, the verification set X is output under the action of the parameter Ω1 val The accuracy rate is the ratio of the number of correctly predicted samples to the total number of predicted samples;

[0043] Step (416) repeats step (414) and step (415). When the accuracy of the output calculated by the CFDCNN network model no longer improves after S consecutive iterations, or when the number of iterations e satisfies e=E, the iteration is stopped to obtain the trained CFDCNN network model.

[0044] As a further limitation of the present invention, the position label L in step (411) i,p , where i represents the i-th input sample (i=1,2,…,K), p represents the p-th hydroacoustic target (p=1,2,…,n), and each hydroacoustic target radiation signal has a corresponding azimuth label;

[0045] The position label L in step (411) i,p , whose dimension depends on the angular range of spatial scanning [Φ sta °,Φ end °] and spatial scanning angle resolution ΔΦ; azimuth label L i,p The dimension size is 1×Z(Z=(Φ end °-Φ sta °) / ΔΦ+1);

[0046] The position label L in step (411) i,p , defined in the form of one-hot encoding, specifically, L i,p =[01,02,13,…,0 Z ,0 Z+1 ], (h=1,2,…,Z,Z+1), position label L i,p is a sparse vector with only one position being 1 and the rest being 0, and the position label L i,p The first Z index positions of represent the direction information of the underwater acoustic target radiation noise signal, and the last index position (h=Z+1) represents the situation of the underwater acoustic target radiation noise signal in the sonar array system receiving signal, which is 1 if there is a underwater acoustic target radiation noise signal, and 0 if there is no such signal;

[0047] The position label L in step (411) i,p , whose dimension size is 1×Z' (Z'=Z+1).

[0048] As a further limitation of the present invention, in step (412), the data set X data The expression is:

[0049]

[0050] In formula (6), K represents the dataset X data Sample data, n represents the number of categories of underwater acoustic targets, Rx' irepresents the expanded covariance matrix, i represents the i-th data set sample pair, L i,1 represents the azimuth label of the noise signal radiated by the underwater acoustic target 1 in the i-th sample, L i,2 represents the azimuth label of the noise signal radiated by the underwater acoustic target 2 in the i-th sample, L i,n Represents the azimuth label of the noise signal radiated by the acoustic target n in the i-th sample.

[0051] As a further limitation of the present invention, the constructing of the CFDCNN model comprises:

[0052] The constructed CFDCNN model consists of B phase-frequency feature mining modules, P three-dimensional convolutional layers, P global average pooling layers, P fully connected layers, and P output layers. The dimension of the three-dimensional convolutional layer is g×g×1, and P=n.

[0053] The construction of the PFFM module includes:

[0054] The constructed PFFM module consists of one 3D convolutional layer and one normalization layer, where the dimension of the 3D convolutional layer is m×m×1;

[0055] The setting of the activation function comprises:

[0056] The tanh function is used as the activation function in the three-dimensional convolutional layer. The expression of the activation function is:

[0057]

[0058] In formula (7), χ represents the output of the previous layer;

[0059] The ReLU function is used as the activation function in the fully connected layer. The expression of the activation function is:

[0060] ReLU(γ)=max(0,γ) Formula (8)

[0061] In formula (8), γ represents the output of the global average pooling layer;

[0062] use As the activation function of the output layer, z represents the output of the last fully connected layer, and h represents the hth neuron in the output layer, where h = 1, 2, ..., Z';

[0063] The constructing of a multi-branch network output structure includes:

[0064] The first branch outputs the azimuth label L corresponding to the noise signal radiated by the underwater acoustic target 1 i,1 , the second branch outputs the azimuth label L corresponding to the noise signal radiated by the underwater acoustic target 2 i,2, the nth branch outputs the azimuth label L corresponding to the noise signal radiated by the underwater acoustic target n i,n , there are n output branches in total, i represents the i-th input sample; each branch corresponds to a different type of underwater acoustic target and outputs the predicted direction of the underwater acoustic target at the same time;

[0065] The setting of the loss function corresponding to each branch includes:

[0066] Set the loss function loss-f corresponding to each branch p ,(p=1,2,…,n), set the weight of each branch loss function p ;

[0067] Get the loss function of the CFDCNN model Loss = weight p ⊙loss-f p , each branch is labeled according to the corresponding label L i,p And their respective loss functions loss-f p Calculate the corresponding loss and update and optimize the parameters Ω of the CFDCNN model.

[0068] As a further limitation of the present invention, in the step (414), under the action of the network training parameters, the network training parameters include:

[0069] Set the network training parameters of the CFDCNN model, where the network training parameters include: initial learning rate lr0, batch size N of the training set train , validation set batch size N val , number of iterations Epoch, number of early stopping steps S, optimizer type, and initialized network model parameters Ω0.

[0070] The advantages of the present invention are:

[0071] 1. The present invention uses the covariance matrix of the spectrum of the underwater acoustic target radiation noise signal as the network input, extracts the phase-frequency difference characteristics between the underwater acoustic target radiation noise signals through the phase-frequency feature mining module, constructs a multi-branch network output structure, and realizes the classification and orientation tasks of the underwater acoustic target;

[0072] 2. The present invention provides a method for classifying and orienting underwater acoustic targets based on a deep convolutional neural network model with array element correlation characteristics. The covariance matrix of the spectrum of the noise signal radiated by the underwater acoustic target is used as the input of the deep convolutional neural network model. Through a phase-frequency feature mining module and a constructed multi-branch network output structure, each branch is associated with a different type of underwater acoustic target, and the azimuth of the underwater acoustic target is output simultaneously, thereby realizing the association and correspondence between the target azimuth and the target type.

[0073] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0075] Figure 1 : A flow chart of a method for underwater acoustic target classification and orientation based on a deep convolutional neural network with array element correlation characteristics provided by the present invention;

[0076] Figure 2 : A flowchart of an example of a method for underwater acoustic target classification and orientation based on a deep convolutional neural network with array element correlation characteristics provided by the present invention;

[0077] Figure 3 : Schematic diagram of the expansion of the complex component dimension provided by the present invention;

[0078] Figure 4 : A structural diagram of the CFDCNN model based on array element correlation features provided by the present invention;

[0079] Figure 5 : When the hydroacoustic target radiation noise signal provided by the present invention only includes the hydroacoustic target 1 radiation noise signal, the mean absolute error result distribution diagram of the output prediction result of the first branch;

[0080] Figure 6 : MAE result distribution diagram of the output prediction result of the second branch when the hydroacoustic target radiation noise signal provided by the present invention only includes the hydroacoustic target 2 radiation noise signal;

[0081] Figure 7 : When the hydroacoustic target radiation noise signal provided by the present invention includes the hydroacoustic target 1 and the hydroacoustic target 2 radiation noise signals at the same time, the MAE result distribution diagram of the two branch output prediction results. DETAILED DESCRIPTION

[0082] Embodiments of the present invention are described in detail below. The embodiments are exemplary and intended to be used to explain the present invention, but should not be construed as limiting the present invention.

[0083] See also Figure 1The embodiment of the present invention provides a method for classifying and orienting underwater acoustic targets based on deep convolutional neural networks with array element correlation features. First, a phase-frequency feature mining module based on the spectrum covariance matrix of underwater acoustic target radiation noise signals is constructed to extract the difference characteristics between the spectra of different underwater acoustic targets. Then, a multi-branch network output structure is designed, in which each branch corresponds to a different type of underwater acoustic target and outputs the direction of the underwater acoustic target at the same time. Finally, the classification and orientation tasks of underwater acoustic targets are achieved according to the type and direction of the underwater acoustic target. Please refer to Figure 1 and Figure 2 The underwater acoustic target classification and orientation method of the embodiment of the present invention specifically includes the following steps:

[0084] Step 1: Obtain the noise signal radiated by the underwater acoustic target. The noise signal radiated by the underwater acoustic target generates a data sample set X. The data sample set X is transformed by Fourier transform to obtain the spectrum Y of the noise signal radiated by the underwater acoustic target i .

[0085] Step 1 of the embodiment of the present invention includes the following steps (11) to (14):

[0086] Step (11) obtains the underwater acoustic target radiation noise signal x(t) received by the sonar array system, which is expressed as:

[0087] x(t)=x1(t)+x2(t)+…+x n (t)+noise(t) Formula (1)

[0088] In formula (1), x1(t) represents the radiation noise signal of hydroacoustic target 1, x2(t) represents the radiation noise signal of hydroacoustic target 2, and x n (t) represents the radiation noise signal of the hydroacoustic target n, and noise(t) represents the ocean noise signal; where:

[0089]

[0090] In formula (2), f1 represents the center frequency of the noise signal radiated by the hydroacoustic target 1, s1(t) represents the noise source signal of the hydroacoustic target 1, a1(f1,θ1) represents the direction vector of the noise signal radiated by the hydroacoustic target 1, f2 represents the center frequency of the noise signal radiated by the hydroacoustic target 2, s2(t) represents the noise source signal of the hydroacoustic target 2, a2(f2,θ2) represents the direction vector of the noise signal radiated by the hydroacoustic target 2, and f n represents the center frequency of the noise signal radiated by the underwater acoustic target n, s n (t) represents the noise source signal of the underwater acoustic target n, a n (f n ,θ n) represents the direction vector of the noise signal radiated by the hydroacoustic target n, d represents the array element spacing, c represents the underwater sound speed, M represents the number of array elements, θ1 represents the azimuth of the noise signal radiated by the hydroacoustic target 1 relative to the sonar array system, θ2 represents the azimuth of the noise signal radiated by the hydroacoustic target 2 relative to the sonar array system, and θ n Indicates the direction of the noise signal radiated by the hydroacoustic target n relative to the sonar array system; preferably f1 = 88 Hz, f2 = 121 Hz, d = 3.75 m, c = 1500 m / s.

[0091] In step (12), the number of array elements of the sonar array system is set to M, the sampling frequency of the underwater acoustic target radiation noise signal x(t) is set to fs, the signal duration is set to T, and the dimension of the underwater acoustic target radiation noise signal received by each array element is set to 1×N (N=T·fs=1×512=512). Then, the dimension of the underwater acoustic target radiation noise signal x(t) is set to M×N=12×512.

[0092] Considering the complexity of the real ocean environment, the signal x(t) received by the sonar array system may not always contain the target radiation noise signal, while the ocean noise signal always exists. Therefore, there are four cases of the underwater acoustic target radiation noise signal x(t): (1) only contains the ocean noise signal x(t) = n(t); (2) contains the radiation noise signal of underwater acoustic target 1 x(t) = x1(t) + n(t); (3) contains the radiation noise signal of underwater acoustic target 2 x(t) = x2(t) + n(t); (4) contains the radiation noise signals of underwater acoustic target 1 and underwater acoustic target 2 x(t) = x1(t) + x2(t) + n(t).

[0093] Step (13) sets the value range of the incident azimuth θ of the underwater acoustic target radiation noise signal x(t) to [30°, 150°], and the value range of the signal-to-noise ratio SNR of the underwater acoustic target radiation noise signal x(t) to [-10dB, 5dB]. The data sample set X is generated within the range of the incident azimuth θ and the signal-to-noise ratio SNR. The expression is:

[0094] X={X1,X2,…X K} Formula (3)

[0095] In formula (3), X1 represents the noise signal x(t) radiated by the sonar array system under condition 1, X2 represents the noise signal x(t) radiated by the sonar array system under condition 2, and X K represents the underwater acoustic target radiation noise signal x(t) received by the sonar array system under condition K; the incident azimuth θ and signal-to-noise ratio SNR values ​​of conditions 1, 2 and K are different; preferably K = 73,600, K represents the number of data samples.

[0096] Step (14) Each data sample X in the data sample set X i , (i=1,2,…,K) is a data matrix with M rows and N columns. The data sample set X is Fourier transformed along the dimension where the array element channel is located to obtain 12 frequency spectrum vectors with a dimension size of 1×257, where 257 represents the number of frequency points in the frequency dimension (δ=1,2,…,257). The data sample X i The expression is:

[0097] X i ,(i=1,2,…,K) Formula (4)

[0098] In formula (4), 12 spectral vectors of size 1×257 are stacked along the “row” dimension, and K represents the data sample X i Get the number of data samples X i The spectrum of Y i , whose dimension size is 12×257.

[0099] In practical applications, in step 1 of the embodiment of the present invention, the underwater acoustic target radiation noise signal x(t) is a water acoustic target radiation noise signal simulated by python, the sonar array system is a uniform linear array of M=12 elements, the sampling frequency fs=512 Hz, the signal duration T=1s, and the number of target categories n=2.

[0100] Step 2: Spectrum Y of the noise signal radiated by the underwater acoustic target i Calculate the covariance along the frequency dimension and get the signal spectrum Y i The covariance matrix Rx i .

[0101] The above step 2 of the embodiment of the present invention includes step (21) to step (23):

[0102] Step (21) stacks M frequency spectrum vectors with a dimension size of 1×F to obtain data sample X i The spectrum of Y i , spectrum Y i The dimension size is M×F;

[0103] Step (22) along the spectrum Y i The dimension of each frequency point δ is used to calculate the corresponding spectrum data Y i The covariance matrix Rx of (δ) i (δ), where the covariance matrix Rx i The calculation formula of (δ) is:

[0104] Rx i (δ) = E{Y i (δ)·Y iH (δ)} Formula (5)

[0105] In formula (5), E{·} represents the mathematical expectation, which is also called the mean, and Y i H (δ) represents the spectrum data Y i The conjugate transpose of (δ), the covariance matrix Rx i The dimension size of (δ) is 12×12, and a total of 257 12×12 covariance matrices Rx are obtained i (δ), and the covariance matrix Rx i (δ) is a Hermitian matrix, which is a complex matrix;

[0106] Step (23) converts 257 12×12 covariance matrices Rx i (δ) is stacked to obtain the spectrum Y i The covariance matrix Rx i , the covariance matrix Rx i The dimension size is 12×12×257.

[0107] Step 3: The covariance matrix Rx of the spectrum of the underwater acoustic target radiation noise signal i After the complex component dimension expansion, the covariance matrix Rx' after dimension expansion is obtained i The specific diagram of complex component dimension expansion is as follows Figure 3 shown.

[0108] Step 3 of the embodiment of the present invention includes steps (31) to (32):

[0109] Step (31) is to calculate the spectrum Y of the underwater acoustic target radiation noise signal x(t) i The covariance matrix Rx i Expand the complex component dimensions and extract the covariance matrix Rx i The real part of and the imaginary component The real part and the imaginary component Stack to form a new dimension and obtain the expanded covariance matrix Rx' i , covariance matrix Rx' i The dimensions are 12×12×2×257.

[0110] Step (32) is to calculate the expanded covariance matrix Rx' i After normalization, the expression is:

[0111] Rx' i =Rx' i / max(|Rx' i |), where Rx'i represents the input sample of the deep convolutional neural network model.

[0112] Step 4: Input the covariance matrix Rx'i into the deep convolutional neural network model of the array element correlation feature. Each branch of the deep convolutional neural network model is associated with different target types to achieve the classification of underwater acoustic targets, and each branch outputs the predicted direction of the corresponding underwater acoustic target.

[0113] Step 4 of the embodiment of the present invention includes steps (41) to (42):

[0114] Step (41) constructs and trains a deep convolutional neural network model based on array element correlation features to obtain a trained deep convolutional neural network model.

[0115] The above step (41) of the embodiment of the present invention includes:

[0116] Step (411) sets the azimuth label L of the underwater acoustic target radiation noise signal i,p ; The location label L in the above step (411) of the embodiment of the present invention i,p , i represents the i-th input sample (i=1,2,…,73600), p represents the p-th acoustic target (p=1,2), and each acoustic target radiation signal has a corresponding azimuth label. The azimuth label L in the above step (411) of the present invention is i,p , whose dimension depends on the spatial scanning angle range [0°, 180°] and the spatial scanning angle resolution ΔΦ=1°; the orientation label L i,p The dimension size is 1×Z (Z=180 / 1+1=181); the orientation label L in the above step (411) of the embodiment of the present invention i,p , defined in the form of one-hot encoding, specifically, L i,p =[01,02,13,…,0 Z ,0 Z+1 ], (h=1,2,…,Z,Z+1), position label L i,p is a sparse vector with only one position being 1 and the rest being 0, and the position label L i,p The first Z index positions of represent the direction information of the underwater acoustic target radiation noise signal, and the last index position (h=Z+1) represents the situation of the underwater acoustic target radiation noise signal in the sonar array system receiving signal, which is 1 if there is a underwater acoustic target radiation noise signal, and 0 if there is no such signal; the azimuth label L in the above step (411) of the embodiment of the present invention i,p , whose dimension size is 1×Z'=1×182, (Z'=Z+1=182).

[0117] Step (412) obtains a data set X for underwater acoustic target classification and orientation tasks data , the data set X data Divide it into training set X according to the ratio of 4:1 train and validation set X val ; Dataset X data The number of samples K = 73,600, the training set X train The number of samples is 58,880, and the validation set X val The number of samples is 14,720.

[0118] Specifically, in step (412) of the embodiment of the present invention, the data set X data The expression is:

[0119]

[0120] In formula (6), K represents the dataset X data Sample data, K = 73600, n represents the number of categories of underwater acoustic targets, Rx' i represents the expanded covariance matrix, i represents the i-th data set sample pair, L i,1 represents the azimuth label of the noise signal radiated by the underwater acoustic target 1 in the i-th sample, L i,2 represents the azimuth label of the noise signal radiated by the underwater acoustic target 2 in the i-th sample, L i,n Represents the azimuth label of the noise signal radiated by the acoustic target n in the i-th sample.

[0121] Step (413) constructs a Correlation Feature Deep Convolutional Neural Network (CFDCNN) model based on the element correlation feature, constructs a PFFM module, sets an activation function, constructs a multi-branch network output structure, and sets a loss function corresponding to each branch. Specifically, the CFDCNN model uses the PFFM module to calculate the covariance matrix Rx' i Perform feature extraction and mining, and then use the activation function to perform nonlinear transformation on the extracted features to highlight key features and suppress invalid features, thereby enhancing the nonlinear expression ability of the CFDCNN model; then, the CFDCNN model calculates the difference between the predicted result and the true label through the loss function, and optimizes the network performance by minimizing the loss, and finally realizes the orientation prediction of different targets through the multi-branch network output structure. The specific structure of the CFDCNN model of the embodiment of the present invention is as follows Figure 4 shown.

[0122] Further: Step (413) of the embodiment of the present invention includes:

[0123] (413-1) The above-mentioned construction of the CFDCNN model in the embodiment of the present invention includes: the constructed CFDCNN model is composed of B phase-frequency feature mining modules, P three-dimensional convolutional layers, P global average pooling layers, P fully connected layers, and P output layers, wherein the dimension size of the three-dimensional convolutional layer is 3×3×1, and P=n.

[0124] (413-2) The above-mentioned construction of the PFFM module in the embodiment of the present invention includes: the constructed PFFM module is composed of 1 three-dimensional convolution layer and 1 normalization layer, wherein the dimension size of the three-dimensional convolution layer is m×m×1.

[0125] (413-3) The above-mentioned setting of the activation function in the embodiment of the present invention includes: using the tanh function as the activation function in the three-dimensional convolution layer, and the expression of the activation function is:

[0126]

[0127] In formula (7), χ represents the output of the previous layer.

[0128] (413-4) In the above embodiment of the present invention, the ReLU function is used as the activation function in the fully connected layer, and the expression of the activation function is:

[0129] ReLU(γ)=max(0,γ) Formula (8)

[0130] In formula (8), a represents the output of the global average pooling layer.

[0131] (413-5) The above-mentioned embodiments of the present invention adopt As the activation function of the output layer, z represents the output of the last fully connected layer, and h represents the hth neuron in the output layer, where h = 1, 2, … 182.

[0132] (413-6) The above-mentioned multi-branch network output structure constructed in the embodiment of the present invention includes: the first branch outputs the azimuth label L corresponding to the noise signal radiated by the underwater acoustic target 1 i,1 (i represents the i-th input sample), the second branch outputs the azimuth label L corresponding to the noise signal radiated by the underwater acoustic target 2 i,2 , the output result of the first branch is the azimuth prediction result of the noise signal radiated by the underwater acoustic target 1 The output of the second branch is the azimuth prediction result of the noise signal radiated by the underwater acoustic target 2.

[0133] (413-7) The above-mentioned setting of the loss function (Cross Entropy-function, CE-f) corresponding to each branch of the embodiment of the present invention includes: setting the loss function loss-f corresponding to each branchp =[loss-f1,loss-f2]=[CE-f,CE-f](p=1,2), set the weight of each branch loss function p ; Get the loss function of the network model Loss = weight p ⊙loss-f p , each branch is labeled according to the corresponding label L i,p And their respective loss functions loss-f p Calculate the corresponding loss and update and optimize the parameters Ω of the CFDCNN model.

[0134] Step (414) converts the training set X train Divided into I train =460 including N train =Batch dataset B of 128 samples train , select a mini-batch training dataset As the input of the CFDCNN network model, under the action of the network training parameters, the output of each branch of the CFDCNN network model is calculated, and the loss obtained is calculated based on each branch Update the parameters Ω1 of the CFDCNN network model; where J represents the Jth batch of data, J = 1, 2, ..., 460; y p Indicates the labels corresponding to each branch. Indicates the predicted position of each branch output of the CFDCNN network model.

[0135] In the above step (414) of the embodiment of the present invention, under the action of the network training parameters, the network training parameters include: setting the network training parameters of the CFDCNN model, wherein the network training parameters include: initial learning rate lr0 = 0.001, batch size N of the training set train =128, validation set batch size N val =50, number of iterations Epoch, number of early stopping steps Step = 40, optimizer type Adam, initialize network model parameters Ω0.

[0136] Step (415) sets the validation set X val Through the parameter Ω1 of the CFDCNN network model, the accuracy of the validation set is output under the action of the parameter Ω1, where: the accuracy is the ratio of the number of correctly predicted samples to the total number of predicted samples.

[0137] Step (416) repeats step (414) and step (415). When the accuracy of the output calculated by the CFDCNN network model no longer improves after S consecutive iterations, or when the number of iterations e satisfies e=50, the iteration is stopped to obtain a trained CFDCNN network model.

[0138] Step (42) converts the spectrum Y of the underwater acoustic target radiation noise signal x(t) into i The covariance matrix Rx' i After input into the CFDCNN model, each branch of the CFDCNN model is associated with different types of underwater acoustic targets, and each branch outputs the predicted position of each underwater acoustic target. The classification and orientation tasks of underwater acoustic targets are realized. In the range of SNR = -10dB ~ 5dB, the incident azimuth θ∈[30°,150°], a data set for CFDCNN model testing is generated. The test data set contains 121 angle conditions, each angle corresponds to 50 samples, which are used to evaluate the performance of the underwater acoustic target classification and orientation method of the embodiment of the present invention. Specifically, when the underwater acoustic target radiation noise signal only contains the radiation noise of underwater acoustic target 1, the predicted azimuth output of the first branch is focused on. In the range of SNR = -10dB ~ 5dB, The average absolute error results are concentrated in the range of 0° to 1°. For detailed experimental results, see Figure 5 When the acoustic target radiation noise signal only contains the radiation noise of acoustic target 2, the predicted direction output by the second branch is considered. In the range of SNR = -10dB ~ 5dB, The average absolute error results are concentrated in the range of 0° to 0.75°. For detailed experimental results, see Figure 6 When the radiation noise signal of the underwater acoustic target contains the radiation noise of both the underwater acoustic target 1 and the underwater acoustic target 2, the first branch outputs the predicted direction of the radiation noise signal of the underwater acoustic target 1. The second branch outputs the predicted direction of the noise signal radiated by the underwater acoustic target 2 The average absolute error of the predicted azimuth is concentrated between 0° and 2.5°. For detailed experimental results, see Figure 7 shown.

[0139] The embodiment of the present invention uses the covariance matrix of the spectrum of the noise signal radiated by the underwater acoustic target as the network input, extracts the phase-frequency difference characteristics between the noise signals radiated by the underwater acoustic target through the phase-frequency feature mining module, constructs a multi-branch network output structure, and realizes the classification and orientation tasks of the underwater acoustic target. The embodiment of the present invention is based on the underwater acoustic target classification and orientation method of the deep convolutional neural network model with array element correlation characteristics, uses the covariance matrix of the spectrum of the noise signal radiated by the underwater acoustic target as the input of the deep convolutional neural network model, associates each branch with different types of underwater acoustic targets through the phase-frequency feature mining module and the constructed multi-branch network output structure, and simultaneously outputs the azimuth of the underwater acoustic target, realizing the association and correspondence between the target azimuth and the target type.

[0140] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should be included in the protection scope of the present invention.

Claims

1. A method for underwater acoustic target classification and orientation based on deep convolutional neural network with array element correlation features, characterized in that: include: Step 1: Obtain the underwater acoustic target radiation noise signal x(t), the underwater acoustic target radiation noise signal x(t) generates a data sample set X, and the data sample set X is subjected to Fourier transformation to obtain the spectrum Y of the underwater acoustic target radiation noise signal x(t) i ; Step 2: The spectrum Y i Calculate the covariance along the frequency dimension of the spectrum to obtain the spectrum Y i The covariance matrix Rx i ; Step 3: The covariance matrix Rx i After the complex component dimension expansion, the covariance matrix Rx' is obtained i ; Step 4: Substitute the covariance matrix Rx i 'Input a deep convolutional neural network model based on the array element correlation characteristics, each branch in the deep convolutional neural network model is associated with different target types, and the predicted position of the underwater acoustic target is output 2. The underwater acoustic target classification and orientation method based on the deep convolutional neural network with array element correlation characteristics according to claim 1 is characterized in that: The step one comprises: Step (11) obtains the underwater acoustic target radiation noise signal x(t) received by the sonar array system, which is expressed as: x(t)=x1(t)+x2(t)+…+x n (t)+noise(t) Formula (1) In formula (1), x1(t) represents the radiation noise signal of hydroacoustic target 1, x2(t) represents the radiation noise signal of hydroacoustic target 2, and x n (t) represents the radiation noise signal of the underwater acoustic target n, noise(t) represents the ocean noise signal; x1(t), x2(t), x n The expression of (t) is: In formula (2), f1 represents the center frequency of the noise signal radiated by the hydroacoustic target 1, s1(t) represents the noise source signal of the hydroacoustic target 1, a1(f1,θ1) represents the direction vector of the noise signal radiated by the hydroacoustic target 1, f2 represents the center frequency of the noise signal radiated by the hydroacoustic target 2, s2(t) represents the noise source signal of the hydroacoustic target 2, a2(f2,θ2) represents the direction vector of the noise signal radiated by the hydroacoustic target 2, and f n represents the center frequency of the noise signal radiated by the underwater acoustic target n, s n (t) represents the noise source signal of the underwater acoustic target n, a n (f n ,θ n ) represents the direction vector of the noise signal radiated by the hydroacoustic target n, d represents the array element spacing, c represents the underwater sound speed, M represents the number of array elements, θ1 represents the azimuth of the noise signal radiated by the hydroacoustic target 1 relative to the sonar array system, θ2 represents the azimuth of the noise signal radiated by the hydroacoustic target 2 relative to the sonar array system, and θ n Indicates the direction of the noise signal radiated by the hydroacoustic target n relative to the sonar array system; Step (12) sets the number of array elements of the sonar array system to M, the sampling frequency of the underwater acoustic target radiation noise signal x(t) to fs, the signal duration to T, and the dimension of the underwater acoustic target radiation noise signal received by each array element of the sonar array system to be 1×N (N=T·fs), then the dimension of the underwater acoustic target radiation noise signal x(t) is M×N; Step (13) sets the value range of the incident azimuth θ of the underwater acoustic target radiation noise signal x(t) to The signal-to-noise ratio SNR of the underwater acoustic target radiation noise signal x(t) ranges from [S sta ,S end ], a data sample set X is generated within the range of the incident azimuth θ and the signal-to-noise ratio SNR, and the expression is: X={X1,X2,…X K } Formula (3) In formula (3), X1 represents the noise signal x(t) radiated by the sonar array system under condition 1, X2 represents the noise signal x(t) radiated by the sonar array system under condition 2, and X K represents the underwater acoustic target radiation noise signal x(t) received by the sonar array system under condition K; wherein the incident azimuth θ and the signal-to-noise ratio SNR of conditions 1, 2 and K have different values; Each data sample X in the data sample set X in step (14) i is a data matrix with M rows and N columns. The data sample set X is Fourier transformed along the dimension where the array element channel in the sonar array system is located to obtain M frequency spectrum vectors with a dimension size of 1×F (F=N / 2+1), where F represents the number of frequency points δ in the frequency dimension, and the data sample X i The expression is: X i ,(i=1,2,…,K) Formula (4) In formula (4), the data sample X i The dimensions are all M×N, K represents the data sample X i The number of 3. The underwater acoustic target classification and orientation method based on the deep convolutional neural network with element correlation characteristics according to claim 1 is characterized in that: The second step comprises: Step (21) stacks M frequency spectrum vectors with a dimension size of 1×F to obtain each data sample X in the data sample set X. i The spectrum of Y i , the spectrum Y i The dimension size is M×F; Step (22) along the spectrum Y i The dimension of each frequency point δ is used to calculate the corresponding spectrum data Y i The covariance matrix Rx of (δ) i (δ), where the covariance matrix Rx i The calculation formula of (δ) is: Rx i (δ) = E{Y i (δ)·Y i H (δ)} Equation (5) In formula (5), E{·} represents the mathematical expectation, Y i H (δ) represents the spectrum data Y i The conjugate transpose of (δ), the covariance matrix Rx i The dimension of (δ) is M×M, and a total of F M×M covariance matrices Rx are obtained i (δ), and the covariance matrix Rx i (δ) is a Hermitian matrix, which is a complex matrix; Step (23) converts F M×M covariance matrices Rx i (δ) are stacked to obtain the spectrum Y i The covariance matrix Rx i , the covariance matrix Rx i The dimensions are M×M×F.

4. The underwater acoustic target classification and orientation method based on the deep convolutional neural network with array element correlation characteristics according to claim 1 is characterized in that: The step three comprises: Step (31) is to calculate the covariance matrix Rx in step 2 i Perform complex component dimension expansion and extract the covariance matrix Rx i The real part of and the imaginary component The real part and the imaginary component Stacking forms a new dimension and obtains the expanded covariance matrix Rx' i , where the covariance matrix Rx' i The dimension size is M×M×2×F; Step (32) is to calculate the covariance matrix Rx' i After normalization, the expression is: Rx’ i =Rx’ i / max(|Rx’ i |)。 5. The underwater acoustic target classification and orientation method based on deep convolutional neural network with element correlation characteristics according to claim 1 is characterized in that: The fourth step comprises: Step (41) constructs and trains a deep convolutional neural network model based on array element correlation features to obtain the trained deep convolutional neural network model; Step (42) converts the covariance matrix Rx obtained in step 3 into i After inputting the deep convolutional neural network model, the deep convolutional neural network model deeply mines the covariance matrix Rx i The underwater acoustic target category features and azimuth features contained in the ', each branch in the multi-branch output structure of the deep convolutional neural network model is associated with a different target type, and simultaneously outputs the predicted azimuth of each underwater acoustic target 6. The underwater acoustic target classification and orientation method based on the deep convolutional neural network with array element correlation characteristics according to claim 5 is characterized in that: Step (41) comprises: Step (411) sets the azimuth label L of the underwater acoustic target radiation noise signal i,p ; Step (412) obtains a data set X for underwater acoustic target classification and orientation tasks data , the data set X data According to the ratio of a:b, it is divided into training set X train and validation set X val ; Step (413) constructs a CFDCNN model, constructs a PFFM module, sets an activation function, constructs a multi-branch network output structure, and sets a loss function corresponding to each branch; specifically, the CFDCNN model uses the PFFM module to calculate the covariance matrix Rx i 'Perform feature extraction and mining, and then use the activation function to perform nonlinear transformation on the extracted features to highlight key features and suppress invalid features, thereby enhancing the nonlinear expression ability of the CFDCNN model; then, the CFDCNN model calculates the difference between the prediction result and the true label through the loss function, and optimizes the network performance by minimizing the loss, and finally realizes the orientation prediction of different targets through the multi-branch network output structure; Step (414) converts the training set X train Divided into I train Contains N train A batch dataset B of samples train , select a mini-batch of the training dataset As the input of the CFDCNN network model, under the action of the network training parameters, the output of each branch of the CFDCNN network model is calculated, and the loss obtained is calculated according to each branch Update the parameter Ω1 of the CFDCNN network model; where J represents the Jth batch of data, J = 1, 2, ..., I train ;y p Indicates the labels corresponding to each branch. Indicates the predicted position of each branch output of the CFDCNN network model; Step (415) converts the validation set X val Through the parameter Ω1 of the CFDCNN network model, the verification set X is output under the action of the parameter Ω1 val The accuracy rate is the ratio of the number of correctly predicted samples to the total number of predicted samples; Step (416) repeats step (414) and step (415). When the accuracy of the output calculated by the CFDCNN network model no longer improves after S consecutive iterations, or when the number of iterations e satisfies e=E, the iteration is stopped to obtain the trained CFDCNN network model.

7. The underwater acoustic target classification and orientation method based on deep convolutional neural network with element correlation characteristics according to claim 6 is characterized in that: The position label L in step (411) i,p , where i represents the i-th input sample (i=1,2,…,K), p represents the p-th hydroacoustic target (p=1,2,…,n), and each hydroacoustic target radiation signal has a corresponding azimuth label; The position label L in step (411) i,p , whose dimension depends on the angular range of spatial scanning [Φ sta °,Φ end °] and spatial scanning angle resolution ΔΦ; azimuth label L i,p The dimension size is 1×Z(Z=(Φ end °-Φ sta °) / ΔΦ+1); The position label L in step (411) i,p , defined in the form of one-hot encoding, specifically, L i,p =[01,02,13,…,0 Z ,0 Z+1 ], (h=1,2,…,Z,Z+1), position label L i,p is a sparse vector with only one position being 1 and the rest being 0, and the position label L i,p The first Z index positions of represent the direction information of the underwater acoustic target radiation noise signal, and the last index position (h=Z+1) represents the situation of the underwater acoustic target radiation noise signal in the sonar array system receiving signal, which is 1 if there is a underwater acoustic target radiation noise signal, and 0 if there is no such signal; The position label L in step (411) i,p , whose dimension size is 1×Z' (Z'=Z+1).

8. The underwater acoustic target classification and orientation method based on deep convolutional neural network with element correlation characteristics according to claim 6 is characterized in that: In the step (412), the data set X data The expression is: In formula (6), K represents the dataset X data Sample data, n represents the number of categories of underwater acoustic targets, Rx' i represents the expanded covariance matrix, i represents the i-th data set sample pair, L i,1 represents the azimuth label of the noise signal radiated by the underwater acoustic target 1 in the i-th sample, L i,2 represents the azimuth label of the noise signal radiated by the underwater acoustic target 2 in the i-th sample, L i,n Represents the azimuth label of the noise signal radiated by the hydroacoustic target n in the i-th sample.

9. The underwater acoustic target classification and orientation method based on deep convolutional neural network with element correlation characteristics according to claim 6 is characterized in that: The construction of the CFDCNN model includes: The constructed CFDCNN model consists of B phase-frequency feature mining modules, P three-dimensional convolutional layers, P global average pooling layers, P fully connected layers, and P output layers. The dimension of the three-dimensional convolutional layer is g×g×1, and P=n. The construction of the PFFM module includes: The constructed PFFM module consists of one 3D convolutional layer and one normalization layer, where the dimension of the 3D convolutional layer is m×m×1; The setting of the activation function comprises: The tanh function is used as the activation function in the three-dimensional convolutional layer. The expression of the activation function is: In formula (7), χ represents the output of the previous layer; The ReLU function is used as the activation function in the fully connected layer. The expression of the activation function is: ReLU(γ)=max(0,γ) Formula (8) In formula (8), γ represents the output of the global average pooling layer; use As the activation function of the output layer, z represents the output of the last fully connected layer, and h represents the hth neuron in the output layer, where h = 1, 2, ..., Z'; The constructing of a multi-branch network output structure includes: The first branch outputs the azimuth label L corresponding to the noise signal radiated by the underwater acoustic target 1 i,1 , the second branch outputs the azimuth label L corresponding to the noise signal radiated by the underwater acoustic target 2 i,2 , the nth branch outputs the azimuth label L corresponding to the noise signal radiated by the underwater acoustic target n i,n , there are n output branches in total, i represents the i-th input sample; each branch corresponds to a different type of underwater acoustic target and outputs the predicted direction of the underwater acoustic target at the same time; The setting of the loss function corresponding to each branch includes: Set the loss function loss-f corresponding to each branch p ,(p=1,2,…,n), set the weight of each branch loss function p ; Get the loss function of the CFDCNN model Loss = weight p ⊙loss-f p , each branch is labeled according to the corresponding label L i,p And their respective loss functions loss-f p Calculate the corresponding loss and update and optimize the parameters Ω of the CFDCNN model.

10. The underwater acoustic target classification and orientation method based on deep convolutional neural network with element correlation characteristics according to claim 6 is characterized in that: In the step (414), under the effect of network training parameters, the network training parameters include: Set the network training parameters of the CFDCNN model, where the network training parameters include: initial learning rate lr0, batch size N of the training set train , validation set batch size N val , number of iterations Epoch, number of early stopping steps S, optimizer type, and initialized network model parameters Ω0.

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