CN112733811A - Underwater sound signal modulation mode inter-class identification method based on improved dense neural network - Google Patents

Underwater sound signal modulation mode inter-class identification method based on improved dense neural network Download PDF

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CN112733811A
CN112733811A CN202110214167.8A CN202110214167A CN112733811A CN 112733811 A CN112733811 A CN 112733811A CN 202110214167 A CN202110214167 A CN 202110214167A CN 112733811 A CN112733811 A CN 112733811A
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王景景
黄子豪
张威龙
闫正强
杨星海
施威
刘世萱
李海涛
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Abstract

The invention discloses an underwater sound signal modulation mode inter-class identification method based on an improved dense neural network, which comprises the steps of firstly receiving an underwater sound modulation signal to be identified and extracting characteristics of the underwater sound modulation signal; carrying out dimension reduction and denoising on the characteristics of the underwater sound modulation signal by using a principal component analysis method; then normalization and dimension change are carried out; based on the dense neural network, removing the pooling layer to obtain an improved dense neural network, and training the neural network; and inputting the processed characteristics of the underwater sound modulation signal into the trained improved dense neural network, and finally finishing the inter-class identification of the modulation modes. The method finally realizes the identification between the underwater acoustic signal modulation modes with low delay and high accuracy, and the identification method has strong anti-interference capability, low calculation cost and high identification accuracy.

Description

Underwater sound signal modulation mode inter-class identification method based on improved dense neural network
Technical Field
The invention belongs to the technical field of underwater acoustic communication, and particularly relates to an underwater acoustic signal modulation mode inter-class identification method based on an improved dense neural network.
Background
The underwater wireless data transmission technology is a key technology for building the ocean strong country. The underwater acoustic communication becomes the most widely applied underwater communication mode at present due to the advantages of small propagation loss, long transmission distance and the like. At present, an Adaptive Modulation Coding (AMC) technique capable of selecting a modulation mode according to a channel condition is widely used in an underwater acoustic communication system, the technique requires that two communication parties match the modulation mode by holding hands for many times, and a complex underwater channel environment may cause a handshake signal error, so that a receiving end adopts an unmatched demodulation mode, and further serious errors of demodulated data are caused.
The intelligent identification of the modulation mode can help the receiving end to automatically identify the modulation mode of the received signal, and the receiving end is ensured to demodulate data by adopting a correct demodulation mode. The current modulation mode intelligent identification method mainly comprises modulation mode identification based on maximum likelihood ratio hypothesis test, modulation mode identification based on feature extraction and modulation mode identification based on different neural network models. The modulation mode identification method based on the maximum likelihood ratio hypothesis test needs prior information of signals and is complex in calculation and not suitable for practical application; the traditional modulation mode identification method based on feature extraction is extremely dependent on the quality of extracted features, although the technical thought is simple and clear and the engineering application is easy. However, in a complicated and variable underwater channel, signal characteristics are seriously interfered by noise and are difficult to be used for identifying a modulation mode; in the modulation mode identification method based on the neural network model, models with good identification performance mainly comprise a convolutional neural network and the like, however, most of the adopted neural networks are existing network models, the research on the model for pertinence improvement is relatively less, in addition, a large number of training samples are needed for training a deep neural network, the existing underwater acoustic communication data in China is scarce and the acquisition cost is high, and the existing underwater acoustic data amount is not enough to support the training of the neural network.
Disclosure of Invention
Aiming at the technical problems of poor anti-interference capability, high calculation cost, low identification accuracy and the like of the existing underwater sound signal modulation mode inter-class identification method, the invention aims to provide an underwater sound signal modulation mode inter-class identification method based on an improved dense neural network to solve the problems.
In order to realize the purpose of the invention, the invention is realized by adopting the following technical scheme:
an underwater sound signal modulation mode inter-class identification method based on an improved dense neural network comprises the following steps:
s1, receiving the underwater sound modulation signal to be identified and extracting the characteristics of the underwater sound modulation signal;
s2: carrying out dimensionality reduction and denoising on the underwater sound modulation signal characteristics extracted by S1 by using a Principal Component Analysis (PCA);
s3: normalizing and changing the dimension of the characteristics of the underwater sound modulation signal processed by the S2;
s4: based on the dense neural network, removing the pooling layer to obtain an improved dense neural network, and training the neural network;
s5: and inputting the characteristics of the underwater sound modulation signal processed in the step S3 into the improved dense neural network trained in the step S4, and finally finishing the identification among the modulation modes.
Further, the extracting of the characteristics of the underwater acoustic modulation signal in S1 specifically includes:
s1-1: firstly, solving a power spectrum, a singular spectrum, an envelope spectrum, a frequency spectrum and a phase spectrum of the underwater sound modulation signal;
s1-2: then calculating spectral features and entropy features;
the spectral characteristics are: maximum value gamma of Q parameter, peak number of power spectrum, R parameter and zero-center normalized instantaneous amplitude spectrum densitymax；
The entropy characteristics are as follows: the entropy of the power spectrum Shannon entropy, the entropy of the power spectrum index, the entropy of the singular spectrum Shannon entropy, the entropy of the singular spectrum index, the entropy of the frequency spectrum amplitude Shannon entropy, the entropy of the frequency spectrum amplitude index, the entropy of the phase spectrum Shannon entropy and the entropy of the phase spectrum index.
The physical meaning and the specific formula of the Q parameter are as follows:
Q＝V/μ
where V and μ represent the variance and mean of the signal, respectively.
The physical meaning of the peak number of the power spectrum is the peak number of the power spectrum of the signal.
Wherein, the physical meaning and the calculation formula of the R parameter are as follows:
R＝σ2/μ2
in the formula sigma2And μ represents the variance and mean of the signal envelope squared, and the R parameter can reflect the degree of variation of the envelope spectrum.
Wherein the maximum value gamma of the zero-center normalized instantaneous amplitude spectral densitymaxThe concrete formula of (1) is as follows: gamma raymax＝max{DFTαcn(n)}2/N
Wherein N is the number of sampling points, acn(n) is the zero-centered normalized instantaneous amplitude, which is formulated as follows:
acn(n)＝an(n)-1
in the formula, acn(n)＝a(n)/ma，maIs the average of the instantaneous amplitudes a (n).
The calculation formula of the Shannon entropy and the power spectrum index entropy of the power spectrum is as follows:
power spectrum shannon entropy:
Figure BDA0002953321270000021
power spectrum exponential entropy:
Figure BDA0002953321270000022
in the formula piThe weight of each point in the signal power spectrum is K, and the number of points in the power spectrum is K.
The method for calculating the singular spectrum Shannon entropy and the singular spectrum index entropy comprises the following steps:
embedding the discrete underwater sound sampling signal into the dimension m and the delay time n to obtain a reconstructed phase space matrix:
Figure BDA0002953321270000023
performing singular value decomposition on the matrix to obtain:
Figure BDA0002953321270000031
the matrix Q is a diagonal matrix, and singular values σ on the diagonal form a singular value spectrum σ ═ σ { (σ)1，σ2，...，σjAnd | j is less than or equal to K }. Defining normalized singular values as σiHas a weight of piThen, the singular spectrum shannon entropy and the index entropy can be respectively obtained as follows:
singular spectrum shannon entropy:
Figure BDA0002953321270000032
singular spectral exponential entropy:
Figure BDA0002953321270000033
the calculation formula of the spectrum amplitude Shannon entropy and the spectrum amplitude exponential entropy is as follows:
spectrum amplitude shannonEntropy:
Figure BDA0002953321270000034
spectral amplitude exponential entropy:
Figure BDA0002953321270000035
in the formula piThe weight value of each point in the signal amplitude-frequency response curve is shown, and K is the point number of the amplitude-frequency response curve.
The calculation formula of the Shannon entropy and the exponential entropy of the phase spectrum is as follows:
entropy of the phase spectrum shannon:
Figure BDA0002953321270000036
phase spectrum exponential entropy:
Figure BDA0002953321270000037
in the formula piThe weight value of each point in the signal phase-frequency response curve is K, and the point number of the phase-frequency response curve is K.
Further, the principal component analysis method in S2 includes the specific steps of:
s2-1 assumes that the kth feature of the hydroacoustic signal is Xk＝(x1，x2，...，xb)TThen the covariance matrix of the K features is
Figure BDA0002953321270000038
K is the total number of features,
Figure BDA0002953321270000039
the average value of all characteristic parameters is obtained;
s2-2 calculating the eigenvalue lambda of the S matrix1，λ1，λ2，λ3，...，λnAnd the feature vector alpha1，α2，α3，...，αnAnd is characterized bySorting the values in descending order;
s2-3, calculating the cumulative variance contribution rate of the first m characteristic components:
Figure BDA00029533212700000310
s2-4 selection of XkAnd (3) performing linear transformation on the first m characteristic components with the middle accumulated variance contribution rate reaching 90 percent: y isk＝ATXkWherein A is a feature vector corresponding to the first m feature values, YkIs the final feature vector after PCA processing.
Further, in S3, normalization and dimension modification are performed on the extracted features;
the characteristic normalization formula is as follows:
Figure BDA00029533212700000311
x is original characteristic data, X' is normalized data, and Max and Min are respectively the maximum value and the minimum value of the characteristic data;
the dimension change is specifically as follows:
the original feature data of n x m dimensions is converted into feature data of n x m x 1 dimensions suitable for the dense neural network, the feature quantity of the feature data does not change, but logically changes from two dimensions to three dimensions.
Further, in S4, the dense neural network training step includes:
s4-1: the dense neural network is improved, and a pooling layer for simplifying features is omitted on the basis of the original dense neural network, so that the problem of losing important features caused by pooling action is avoided;
s4-2: pre-training the neural network by using the existing sea trial real data and simulation data and utilizing a greedy algorithm;
s4-3: and carrying out transfer learning on the pre-trained neural network in the target sea area to obtain a neural network model suitable for the target sea area.
Further, the greedy algorithm may obtain a global optimal solution through a series of local optimal solutions, and the steps of training the network with the greedy algorithm are as follows:
(1) training the first layer of neural network independently until reaching a given precision;
(2) keeping the first layer network data, and training the second layer network independently until reaching the given precision;
(3) and repeating the processes until the whole neural network training is completed.
Further, the transfer learning method comprises:
and keeping the weight of the pre-trained improved dense neural network convolution layer unchanged, putting the pre-trained improved dense neural network convolution layer into a target sea area, and modulating the full-connection layer part of the neural network according to the actual underwater sound signal.
Compared with the prior art, the invention has the advantages and positive effects that:
according to the method for identifying the modulation modes of the underwater acoustic signals, firstly, the spectral characteristics and the entropy characteristics which are insensitive to noise are selected and extracted, so that the robustness of the characteristics is improved; secondly, the feature is subjected to dimension reduction optimization by using a principal component analysis method, so that certain signal-noise separation is realized while the calculation cost is reduced; finally, migration learning is used, the problem that underwater acoustic signal training samples are insufficient is solved to a great extent, the accuracy of the neural network classifier is guaranteed, and the underwater acoustic signal modulation mode inter-class recognition with low delay and high accuracy is finally achieved.
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FIG. 1 is a flow chart of an embodiment of the present invention.
FIG. 2 is a model diagram of an improved dense neural network in an embodiment of the present invention.
FIG. 3 is a flow chart of pre-training a network using a greedy algorithm in an embodiment of the invention.
FIG. 4 is a flow chart of training a network using transfer learning in an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings and examples.
Example 1
In an underwater sound adaptive modulation and coding communication system, a signal transmitting end and a signal receiving end generally agree with a modulation mode through a handshake signal, but an underwater sound channel is complex and changeable, the handshake signal is easy to generate errors, and the signal receiving end can automatically identify the modulation mode of a received signal through an intelligent identification method of the modulation mode, so that correct data demodulation is guaranteed.
The embodiment is a method for identifying modulation modes between classes of a fast and accurate underwater sound signal based on an improved dense neural network, and after receiving an underwater sound modulation signal, the method comprises the following parts, as shown in fig. 1:
s1 modulated signal feature extraction and processing steps, including:
s11, solving a power spectrum, a singular spectrum, an envelope spectrum, a frequency spectrum and a phase spectrum of the modulation signal;
s12, calculating the spectral characteristic and the entropy characteristic of the signal;
in the embodiment, the spectral characteristic and the entropy characteristic with strong anti-noise capability are selected as the characteristics for identifying the modulation modes; the spectral feature and the entropy feature of the signal specifically include:
the spectral characteristics are: maximum value gamma of Q parameter, peak number of power spectrum, R parameter and zero-center normalized instantaneous amplitude spectrum densitymax；
The entropy characteristics are as follows: the entropy of the power spectrum Shannon entropy, the entropy of the power spectrum index, the entropy of the singular spectrum Shannon entropy, the entropy of the singular spectrum index, the entropy of the frequency spectrum amplitude Shannon entropy, the entropy of the frequency spectrum amplitude index, the entropy of the phase spectrum Shannon entropy and the entropy of the phase spectrum index.
The physical meaning and the specific formula of the Q parameter are as follows:
Q＝V/μ
where V and μ represent the variance and mean of the signal, respectively.
The physical meaning of the peak number of the power spectrum is the peak number of the power spectrum of the signal.
Wherein, the physical meaning and the calculation formula of the R parameter are as follows:
R＝σ2/μ2
in the formula sigma2And μ represents the variance and mean of the signal envelope squared, and the R parameter can reflect the degree of variation of the envelope spectrum.
Wherein the maximum value gamma of the zero-center normalized instantaneous amplitude spectral densitymaxThe concrete formula of (1) is as follows: gamma raymax＝max{DFTacn(n)}2/N
Wherein N is the number of sampling points, acn(n) is the zero-centered normalized instantaneous amplitude, which is formulated as follows:
acn(n)＝an(n)-1
in the formula, alphacn(n)＝a(n)/ma，maIs the average of the instantaneous amplitudes a (n).
The calculation formula of the Shannon entropy and the power spectrum index entropy of the power spectrum is as follows:
power spectrum shannon entropy:
Figure BDA0002953321270000051
power spectrum exponential entropy:
Figure BDA0002953321270000052
in the formula piThe weight of each point in the signal power spectrum is K, and the number of points in the power spectrum is K.
The singular spectrum entropy calculation method comprises the following steps:
embedding the discrete underwater sound sampling signal into the dimension m and the delay time n to obtain a reconstructed phase space matrix:
Figure BDA0002953321270000053
performing singular value decomposition on the matrix to obtain:
Figure BDA0002953321270000061
the matrix Q is a diagonal matrix, and singular values σ on the diagonal form a singular value spectrum σ ═ σ { (σ)1，σ2，...，σjAnd | j is less than or equal to K }. StatorSingular value after sense normalization is sigmaiHas a weight of piThen, the singular spectrum shannon entropy and the index entropy can be respectively obtained as follows:
singular spectrum shannon entropy:
Figure BDA0002953321270000062
singular spectral exponential entropy:
Figure BDA0002953321270000063
the calculation formula of the spectrum amplitude Shannon entropy and the spectrum amplitude exponential entropy is as follows:
spectrum amplitude shannon entropy:
Figure BDA0002953321270000064
spectral amplitude exponential entropy:
Figure BDA0002953321270000065
in the formula piThe weight value of each point in the signal amplitude-frequency response curve is shown, and K is the point number of the amplitude-frequency response curve.
The calculation formula of the Shannon entropy and the exponential entropy of the phase spectrum is as follows:
entropy of the phase spectrum shannon:
Figure BDA0002953321270000066
phase spectrum exponential entropy:
Figure BDA0002953321270000067
in the formula piThe weight of each point in the signal phase-frequency response curve is obtained. K is the number of points of the phase frequency response curve.
S13, performing dimensionality reduction and denoising on the extracted features by using a principal component analysis method;
the principal component analysis method comprises the following specific steps:
s131, supposing that the kth characteristic of the underwater acoustic signal is xk＝(x1，x2，...，xn)TThen the covariance matrix of the K features is
Figure BDA0002953321270000068
K is the total number of features,
Figure BDA0002953321270000069
the average value of all characteristic parameters is obtained;
s132, calculating the eigenvalue lambda of the S matrix1，λ1，λ2，λ3，...，λnAnd the feature vector alpha1，α2，α3，...，αnAnd sorting the characteristic values in a descending order;
s133, calculating the cumulative variance contribution rate of the first m characteristic components:
Figure BDA00029533212700000610
s134, selecting XkAnd (3) performing linear transformation on the first m characteristic components with the middle accumulated variance contribution rate reaching 90 percent: y isk＝ATXkWherein A is a feature vector corresponding to the first m feature values, YkIs the final feature vector after PCA processing.
S2: a neural network training step, comprising:
s21, pre-training the neural network by using the existing sea test data and simulation data and using a greedy algorithm;
the neural network used in this embodiment is an improved dense neural network, and as shown in fig. 2, on the basis of the original dense neural network, the neural network omits a pooling layer for simplifying features, so as to avoid the problem of losing important features due to pooling;
the greedy algorithm may obtain a global optimal solution through a series of local optimal solutions, as shown in fig. 3, the greedy algorithm trains the network by the following steps:
s211, training the first layer of neural network independently until reaching given precision;
s212, retaining the first layer network data, and training the second layer network independently until reaching a given precision;
s213, repeating the processes until the whole neural network training is finished;
and S3 inter-class identification step, which comprises the following steps:
s31, normalizing the extracted features and changing the dimensions;
further, the feature normalization formula is:
Figure BDA0002953321270000071
x is original characteristic data, X' is normalized data, and Max and Min are respectively the maximum value and the minimum value of the characteristic data.
The dimension change is specifically as follows:
the original feature data of n x m dimensions is converted into feature data of n x m x 1 dimensions suitable for the dense neural network, the feature quantity of the feature data does not change, but logically changes from two dimensions to three dimensions.
And S32, inputting the processed characteristics into the trained neural network to finish the identification among the modulation modes.
S4, in order to verify the method, Matlab software is used to simulate different types of modulation signals in the embodiment, and the modulation methods are as follows: BPSK, QPSK, BFSK, QFSK, 16QAM, 64QAM, OFDM; the signal-to-noise ratio ranges from minus 30dB to 30dB at an interval of 5 dB; each category of modulation signals has 100 groups of time domain waveform data under different signal-to-noise ratios; the data amount totals 5200 groups.
S41, analyzing the power spectrum, singular spectrum, envelope spectrum, frequency spectrum and phase spectrum of the signal time domain waveform data, and calculating to obtain the maximum value gamma of the Q parameter, the peak number of the power spectrum, the R parameter and the zero-center normalized instantaneous amplitude spectral densitymaxPower spectrum Shannon entropy, power spectrum index entropy, singular spectrum Shannon entropy, singular spectrum index entropy, frequency spectrum amplitude Shannon entropy, frequency spectrum amplitude index entropy, phase spectrum Shannon entropy and phase spectrum Shannon entropyThe bit spectrum index entropy totals a feature vector of 12 dimensions.
And S42, carrying out PCA processing on the extracted features to obtain 7-dimensional feature data after dimension reduction and denoising, and carrying out normalization and dimension change processing.
And S43, uniformly dividing the processed feature data under different signal-to-noise ratios into a training set and a testing set according to different modulation types and using the training set and the testing set for training the neural network, wherein 3900 groups of data in the training set and 1300 groups of data in the testing set are used.
S44, training and improving a dense neural network by using a greedy algorithm, and finally obtaining a modulation mode intelligent recognition model under a mixed signal-to-noise ratio, wherein the recognition performance is shown in Table 1:
TABLE 1 recognition accuracy results of neural network models at different signal-to-noise ratios
Figure BDA0002953321270000081
The results show that: the scheme can achieve 89.23% of overall identification accuracy on a test set with a signal-to-noise ratio of-30 dB to 30dB, can achieve nearly 100% of identification accuracy on signals with the signal-to-noise ratio of 0dB and above, and shows good identification performance and identification robustness on feature data under different signal-to-noise ratios.
The method has the advantages that the spectral features and entropy features insensitive to noise are selected and extracted, and the features are subjected to dimensionality reduction optimization by using a principal component analysis method, so that certain signal-noise separation is realized while the calculation cost is reduced, and the interference of underwater noise on modulation identification is removed; then, a dense neural network with higher convergence rate and higher accuracy is selected, a pooling layer is removed in a targeted manner aiming at the characteristic of lower characteristic redundancy after PCA processing in the invention so as to avoid the loss of important characteristics due to pooling action, a transfer learning deep neural network is introduced in the aspect of network training, the problem of insufficient underwater sound signal training samples is solved to a great extent, the accuracy of a neural network classifier is ensured, and finally the inter-class identification of the underwater sound signal modulation mode with low delay and high accuracy is realized.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions.

Claims (7)

1. An underwater sound signal modulation mode inter-class identification method based on an improved dense neural network is characterized by comprising the following steps:
s1: receiving an underwater sound modulation signal to be identified, and extracting characteristics of the underwater sound modulation signal;
s2: carrying out dimension reduction and denoising on the characteristics of the underwater sound modulation signal extracted by the S1 by using a principal component analysis method;
s3: normalizing and changing the dimension of the characteristics of the underwater sound modulation signal processed by the S2;
s4: based on the dense neural network, removing the pooling layer to obtain an improved dense neural network, and training the neural network;
s5: and inputting the characteristics of the underwater sound modulation signal processed in the step S3 into the improved dense neural network trained in the step S4, and finally finishing the identification among the modulation modes.
2. The method for identifying between classes of underwater acoustic signal modulation schemes according to claim 1, wherein the extracting of the characteristics of the underwater acoustic modulation signal in S1 specifically includes:
s1-1: firstly, solving a power spectrum, a singular spectrum, an envelope spectrum, a frequency spectrum and a phase spectrum of the underwater sound modulation signal;
s1-2: then calculating spectral features and entropy features;
the spectral characteristics are: maximum value gamma of Q parameter, peak number of power spectrum, R parameter and zero-center normalized instantaneous amplitude spectrum densitymax；
The entropy characteristics are as follows: the entropy of the power spectrum Shannon entropy, the entropy of the power spectrum index, the entropy of the singular spectrum Shannon entropy, the entropy of the singular spectrum index, the entropy of the frequency spectrum amplitude Shannon entropy, the entropy of the frequency spectrum amplitude index, the entropy of the phase spectrum Shannon entropy and the entropy of the phase spectrum index.
3. The method for identifying between classes of underwater acoustic signal modulation modes according to claim 1, wherein the principal component analysis method in S2 comprises the following specific steps:
s2-1 assumes that the kth feature of the hydroacoustic signal is Xk＝(x1，x2，...，xn)TThen the covariance matrix of the K features is
Figure FDA0002953321260000011
K is the total number of features,
Figure FDA0002953321260000012
the average value of all characteristic parameters is obtained;
s2-2 calculating the eigenvalue lambda of the S matrix1,λ1，λ2，λ3，...，λnAnd the feature vector alpha1，α2，α3，...，αnAnd sorting the characteristic values in a descending order;
s2-3, calculating the cumulative variance contribution rate of the first m characteristic components:
Figure FDA0002953321260000013
s2-4 selection of XkAnd (3) performing linear transformation on the first m characteristic components with the middle accumulated variance contribution rate reaching 90 percent: y isk＝ATXkWherein A is a feature vector corresponding to the first m feature values, YkIs the final feature vector after PCA processing.
4. The method for identifying between classes of underwater acoustic signal modulation schemes according to claim 1, wherein in S3, normalization and dimension change are performed on the extracted features;
the characteristic normalization formula is as follows:
Figure FDA0002953321260000014
x is original characteristic data, X' is normalized data, and Max and Min are respectively the maximum value and the minimum value of the characteristic data;
the dimension change is specifically as follows:
the original feature data of n x m dimensions is converted into feature data of n x m x 1 dimensions suitable for the dense neural network, the feature quantity of the feature data does not change, but logically changes from two dimensions to three dimensions.
5. The method for identifying between classes of underwater acoustic signal modulation schemes of claim 1, wherein in S4, the dense neural network training step includes:
s4-1: the dense neural network is improved, and a pooling layer for simplifying features is omitted on the basis of the original dense neural network, so that the problem of losing important features caused by pooling action is avoided;
s4-2: pre-training the neural network by using the existing sea trial real data and simulation data and utilizing a greedy algorithm;
s4-3: and carrying out transfer learning on the pre-trained neural network in the target sea area to obtain a neural network model suitable for the target sea area.
6. The method for identifying between classes of underwater acoustic signal modulation modes according to claim 5, wherein said greedy algorithm can obtain a global optimal solution through a series of local optimal solutions, and the steps of training the network by the greedy algorithm are as follows:
(1) training the first layer of neural network independently until reaching a given precision;
(2) keeping the first layer network data, and training the second layer network independently until reaching the given precision;
(3) and repeating the processes until the whole neural network training is completed.
7. The method for identifying between classes of underwater acoustic signal modulation modes according to claim 5, wherein the method for transfer learning comprises: and keeping the weight of the pre-trained improved dense neural network convolution layer unchanged, putting the pre-trained improved dense neural network convolution layer into a target sea area, and modulating the full-connection layer part of the neural network according to the actual underwater sound signal.
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