Satellite communication malicious interference identification method based on multi-kernel convolutional neural network
Through the identification method based on multi-core convolutional neural network, multi-dimensional transformation processing and supervised learning training are carried out on malicious interference in satellite communication links, which solves the problem that the existing technology is difficult to identify malicious interference under weak interference and high noise conditions. , realize accurate identification of satellite communication transmission links and improve their reliability.
Patent Information
- Application Number
- CN202411592172.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-08
- Publication Date
- 2025-02-18
AI Technical Summary
The prior art is difficult to accurately identify malicious interference in satellite communication transmission links under weak interference and high noise conditions, affecting the reliability of the transmission links.
Using the recognition method based on multi-core convolutional neural network, multi-dimensional transformation processing is performed on the received signals of satellite communication links, a multi-core convolutional neural network model is constructed, and a supervised learning training model is trained to identify and classify different types of malicious interference. .
It realizes accurate identification of malicious interference under complex channel conditions, improves the reliability and anti-interference capability of satellite communication transmission links, and is suitable for satellite communication systems with different transmission systems.
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Figure CN119483712A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of satellite communication technology, and in particular relates to a method for identifying malicious interference in satellite communications based on a multi-core convolutional neural network, which can be used for space-based electromagnetic situation awareness and satellite communication physical layer transmission link interference cognition and suppression. Background Art
[0002] Compared with other wireless communication methods such as ultra-short waves and microwaves, satellite communications have many advantages such as long communication distance and relatively stable transmission links. They have become an indispensable means of information transmission in both civil and military applications. However, the determinism of satellite orbits and the openness of satellite-to-ground transmission links inevitably introduce electromagnetic interference to satellite communication systems. Various forms of malicious interference will seriously affect the transmission performance of satellite communications. Therefore, in order to further improve the reliable transmission capability of satellite communication systems, it is urgent to analyze the channel conditions of the transmission links, accurately identify the malicious interference faced, and provide support for subsequent effective interference suppression.
[0003] The malicious interference faced by the satellite communication physical layer transmission link is artificially implemented and highly targeted, and its purpose is to destroy the reliable transmission of the link. For satellite communication links with fixed working frequencies, artificial implementation is mainly based on suppression interference with diverse signal types. Common interference styles include single tone, multi-tone, frequency modulation, partial band noise, phase modulation and full-band noise. Different types of interference have their own characteristics, and different processing methods need to be adopted when suppressing interference. Therefore, it is necessary to accurately identify interference first, which is the basis for suppressing interference and improving the reliability of transmission links. Taking the time domain and frequency domain feature parameters of the received signal as input, using decision trees and support vector machines to construct classifiers, common interference can be identified. For details, please refer to the literature: Liang Jindi, Cheng Yufan, Du Yue, Wang Pengyu "Research on Interference Identification Technology Based on Joint Multidimensional Features", Signal Processing, 2017, Vol. 33, No. 12, Pages: 1609-1615. The six characteristic parameters of the interference signal, namely the energy limit factor, normalized spectrum 3dB bandwidth, normalized spectrum kurtosis coefficient, normalized spectrum impulse part standard deviation, time domain peak-to-average ratio and fractional Fourier transform energy concentration, are used as attribute values to construct a knowledge graph corresponding to the interference pattern. The SoftMax regression algorithm can then be used to classify the received signal and achieve the purpose of interference identification. For details, please refer to the literature: Chen Xuan, Li Yihao, and Chen Jinli, "Interference Signal Identification Method Based on Knowledge Graph and SoftMax Regression", Journal of China Academy of Electronics Science, 2021, Vol. 16, No. 9, Pages: 856-861. For transient interference faced by over-the-horizon radar, the texture features of the range-Doppler map can be combined with the machine learning classifier to distinguish between strong interference, weak interference and no interference. For details, please refer to the literature: Luo Zhongtao, Xia Hang, Lu Kun, He Zishu "Automatic recognition method of transient interference in range-Doppler map of over-the-horizon radar", Journal of Electronics, 2021, Vol. 49, No. 7, Pages: 1279-1285. By fusing multiple features in the time domain and frequency domain, and then using classification methods such as support vector machine, KNN (K nearest neighbor), decision tree, etc., communication interference can be identified to a certain extent. For details, please refer to the literature: Mingrui Xin, Zhuoran Cai "A feature fusion-based communication jamming recognition method", Wireless Network, 2023, Vol. 29, Pages: 2993-3004.
[0004] However, for typical independent characteristic parameters such as energy limit factor, spectrum bandwidth, spectrum kurtosis coefficient, time domain peak-to-average ratio and spectrum impulse standard deviation, accurate calculation usually requires that the interference signal is significantly stronger than the communication signal. Under unfavorable conditions where the interference intensity is relatively weak and the channel noise is strong, it is still difficult to accurately identify the malicious interference of the satellite communication transmission link. Therefore, how to fully explore and extract the intrinsic characteristics of the received signal in different dimensions is the key to improving the accuracy of malicious interference identification under unfavorable channel conditions, and it is also the basis for further suppressing interference and improving the performance of satellite communication link transmission lines. Summary of the invention
[0005] The present invention aims at improving the reliability of space-based electromagnetic situational awareness and satellite communication link transmission, and provides a satellite communication malicious interference identification method based on a multi-core convolutional neural network to achieve accurate identification of artificial malicious interference and effectively support the final interference suppression.
[0006] To achieve the above object, the technical solution adopted by the present invention is:
[0007] A satellite communication malicious interference identification method based on a multi-core convolutional neural network is used to identify malicious interference faced by a satellite communication link, and includes the following steps:
[0008] Step 1, performing analog-to-digital conversion on the received signal of the satellite communication transmission link to obtain data to be processed; transforming and processing the data from different dimensions, and setting the processing dimension to L;
[0009] Step 2: Construct a multi-core convolutional neural network interference recognition model. The model uses different convolutional kernels to form multiple convolutional neural networks. Each network includes a corresponding convolution layer, pooling layer, fully connected layer and output layer. The final recognition result is obtained by weighting the output layers of multiple networks.
[0010] Step 3, adding known interference under different channel conditions, performing interference type identification processing on the data transformed in step 1, using it as learning training sample data for the multi-core convolutional neural network interference recognition model, and iteratively training the model in a supervised manner;
[0011] Step 4: Perform analog-to-digital conversion on the received signal of the satellite communication transmission link in the actual scenario to obtain L groups of transformed processed data, and input the L groups of transformed processed data into the trained multi-core convolutional neural network interference recognition model to identify malicious interference to the satellite communication link and obtain recognition results.
[0012] Further, step 1 includes the following steps:
[0013] Step 1-1, performing analog-to-digital conversion on a received signal of a satellite communication transmission link to convert it into a received signal in a digital domain;
[0014] Step 1-2, transforming the received signal in the digital domain, including short-time Fourier transform, correlation matrix distribution calculation and constellation diagram distribution; wherein the manner of performing short-time Fourier transform on the received signal r(n) is:
[0015]
[0016] Where N is the number of short-time Fourier transform points, i.e., the window length, D is the sliding length of the window each time, X(m,k) is the transform output, m is the time domain window number, k is the frequency domain identifier, and w(n) is the coefficient of the added window. When all are 1, it is a rectangular window.
[0017] Step 1-3, calculate the correlation matrix distribution of the received signal r(n) of length N:
[0018]
[0019] In the formula, R N×N represents an N×N-dimensional correlation matrix, the superscript H represents the conjugate transpose of a vector or matrix, and the superscript * represents the conjugate operation;
[0020] Step 1-4, decompose each symbol of the received signal r(n) into in-phase and quadrature components, and draw the constellation distribution corresponding to the signal as a dimension of the network model input;
[0021] Step 1-5, determine the parameter L according to the transformation processing dimension of the received signal r(n).
[0022] Further, in step 2, the multi-core convolutional neural network interference identification model includes L multi-core convolutional neural networks, each network consists of 1 input layer, J convolutional layers, J pooling layers, 1 fully connected layer and an output layer; the input layer corresponds to the L-dimensional transformation processing data of the received signal;
[0023] The jth convolutional layer uses c j Convolution kernels are used for convolution operation. As the number of layers j increases, the size of the corresponding convolution kernel decreases.
[0024] Each convolutional layer is cascaded with a pooling layer, and the calculation of the jth pooling layer is determined by the corresponding weight w j and bias b j decision; order represents the output of the jth pooling layer, represents the feature set output by the jth convolutional layer, For feature set The (m,n)th subset of Represents the resulting pooling set The element in the mth row and nth column of , then:
[0025]
[0026] The jth pooling layer and the j+1th convolutional layer are connected by an activation function;
[0027] The last pooling layer is connected to the fully connected layer, which is then connected to the output layer. Each neuron in the fully connected layer uses Sigmoid nonlinear function mapping calculation, and the output layer uses normalized exponential function SoftMax for logistic regression classification;
[0028] The output layers of L multi-core convolutional neural networks are weighted to obtain the final interference recognition result of the recognition model.
[0029] Further, step 3 includes the following steps:
[0030] Step 3-1, obtaining received signal data with various interferences under different channel conditions by actual device generation or computer simulation;
[0031] Step 3-2, performing multi-dimensional transformation processing on the received signal in the manner of step 1, and adding an interference type label to the transformation processing result to obtain learning training data for the multi-core convolutional neural network recognition model;
[0032] Step 3-3, use the acquired sample data to perform supervised training on the model, and the training adopts a variable step size method. When the network parameters of the model reach a convergence state, the learning and training are completed.
[0033] The beneficial effects of the present invention are:
[0034] 1. The present invention can accurately identify malicious interference in the satellite communication physical layer transmission link and determine the specific signal pattern of the received interference.
[0035] 2. The present invention has no special requirements for the satellite communication system transmission system and the specific hardware architecture of the receiving end. Under the premise that the recognition model completes offline learning and training, the computational processing complexity of the received signal is low, and it can be applied to satellite communication transmission links with different transmission systems, and has strong adaptability.
[0036] 3. The present invention utilizes the advantage of convolutional neural network in extracting potential local features of data by convolution kernels, and utilizes multiple flexibly set convolution kernels to extract different intrinsic features of received signal data, which can effectively identify interference with similar conventional feature parameters.
[0037] 4. Compared with interference identification methods such as support vector machines and high-order cumulants, the present invention can significantly improve the interference identification performance under complex conditions such as low interference-to-signal ratio and interference-to-noise ratio.
[0038] In summary, the present invention aims to solve the problems of interference recognition using conventional characteristic parameters, designs and constructs a multi-core convolutional neural network recognition model, takes multi-dimensional transformed data as input, and can autonomously extract the intrinsic characteristics of different interferences through learning and training, thereby minimizing the impact of communication signals and channel noise, and thereby effectively improving the ability to recognize malicious interference faced by satellite communication transmission links. BRIEF DESCRIPTION OF THE DRAWINGS
[0039] Figure 1 is a processing flow chart of a method according to an embodiment of the present invention;
[0040] Figure 2 This is a schematic diagram of a multi-core convolutional neural network recognition model in an embodiment of the present invention;
[0041] Figure 3 1 is a diagram of interference identification performance under different interference-to-signal ratio conditions in an embodiment of the present invention. DETAILED DESCRIPTION
[0042] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and specific implementation methods.
[0043] A method for identifying malicious interference in satellite communications based on a multi-core convolutional neural network is proposed. The method is based on the digital domain processing of the received signal after ADC sampling, and performs different dimensional transformation processing on the received signal as the data to be identified, including time-frequency analysis, correlation matrix distribution and constellation diagram mapping. Combined with the multi-dimensional processing of satellite communication signals, a corresponding multi-core convolutional neural network is designed and constructed. The network model uses data processed in different dimensions as input, and the specific parameters are set according to the processing capacity. The results of different convolution kernels are weighted in the output layer as the final interference identification result. The constructed multi-core convolutional neural network needs to use signal data containing various types of interference under different channel conditions for learning and training. The learning and training is used to obtain the optimal parameter settings of the network model. After the network model learning and training is completed, malicious interference identification of satellite communications can be realized.
[0044] like Figure 1 As shown, the method includes:
[0045] (1) Perform analog-to-digital conversion on the received signal of the satellite communication transmission link to obtain the data to be processed, transform the data from different dimensions, and use the transformation results as the input of the multi-core convolutional neural network model;
[0046] (2) Construct a multi-core convolutional neural network interference recognition model. The key to the model is to use different convolutional kernels to form multiple convolutional neural networks. Each network includes a corresponding convolution layer, pooling layer, fully connected layer and output layer. The final recognition result is obtained by weighting the output layers of multiple networks.
[0047] (3) Add known interference under different channel conditions, identify the interference type of the multi-dimensional change processing data, and use it as the learning and training sample data of the multi-core convolutional neural network recognition model to iteratively train the model in a supervised manner;
[0048] (4) The parameters of the trained network model remain unchanged and can be used to identify malicious interference in satellite communication links.
[0049] Furthermore, step (1) includes the following steps:
[0050] (1-1) The received satellite communication signal is converted into a digital signal for subsequent processing. The analog-to-digital conversion is the same as the setting of the conventional satellite communication receiving end.
[0051] (1-2) The received signal in the digital domain is transformed, including short-time Fourier transform, correlation matrix distribution calculation and constellation diagram distribution. The transformation processing can be expanded on the basis of the above three. The received signal r(n) is transformed by short-time Fourier transform, which can be expressed as:
[0052]
[0053] Where N is the number of short-time Fourier transform points, i.e., the window length, D is the sliding length of the window each time, X(m,k) is the transform output, m is the time domain window number, k is the frequency domain identifier, and w(n) is the coefficient of the added window. When all are 1, it is a rectangular window.
[0054] (1-3) The correlation matrix distribution calculation of the received signal r(n) with a length of N can be expressed as:
[0055]
[0056] In the formula, R N×N represents an N×N dimensional correlation matrix. The superscript H represents the conjugate transpose of a vector or matrix. The superscript * represents the conjugate operation.
[0057] (1-4) Considering the fact that satellite communication transmission links mostly use orthogonal modulation, each symbol of the received signal r(n) is decomposed into in-phase and orthogonal components, and the constellation distribution S corresponding to the signal is drawn N×N , as a dimension of the network model input, where N is the number of symbols corresponding to the received signal r(n), which is the sequence length when the sampling rate is the same as the symbol rate.
[0058] (1-5) Determine the parameter L based on the transformation processing dimension of the received signal r(n).
[0059] like Figure 2As shown in FIG, the multi-core convolutional neural network interference recognition model includes L multi-core convolutional neural networks, each of which consists of 1 input layer, J convolutional layers, J pooling layers, 1 fully connected layer and an output layer.
[0060] The input layer corresponds to the L-dimensional transformation processing data of the received signal, and the size of the data matrix of the L multi-core convolutional neural network inputs can be flexibly set.
[0061] The jth convolutional layer uses c j Convolution kernels are used for convolution operation, c j The convolution kernels can be set to different values. As the number of layers j increases, the corresponding convolution kernel size can be flexibly reduced to facilitate the retention of data features during calculation.
[0062] Each convolutional layer is cascaded with a pooling layer, and the calculation of the jth pooling layer is determined by the corresponding weight w j and bias b j Decide.
[0063] The jth pooling layer and the j+1th convolutional layer are connected by an activation function.
[0064] The last pooling layer is connected to the fully connected layer, and the fully connected layer is connected to the output layer. Each neuron in the fully connected layer is connected to the output layer using nonlinear functions such as Sigmoid. The output layer can use the normalized exponential function SoftMax for logistic regression classification.
[0065] The output layers of L multi-core convolutional neural networks are weighted to obtain the final interference recognition result of the recognition model.
[0066] Step (3) comprises the following steps:
[0067] (3-1) Obtain sufficient received signal data under different channel conditions and with various types of interference in various forms such as actual device generation or computer simulation.
[0068] (3-2) According to step (1), the received signal is subjected to multi-dimensional transformation processing, and an interference type label is added to the transformation processing result to obtain learning training data for the multi-core convolutional neural network recognition model.
[0069] (3-3) The obtained sample data is used to perform supervised training on the recognition model. The training can adopt flexible and efficient methods such as variable step size. When the network parameters of the recognition model reach a convergence state, the learning and training is completed.
[0070] The specific method of step (4) is:
[0071] The solidified recognition model completes the state of learning and training, keeps the network parameters unchanged, takes L groups of transformed and processed data of the actual received signal as input, and the model output is the final interference recognition result.
[0072] This method does not need to directly calculate independent feature parameters such as time domain, frequency domain and energy domain. It can autonomously extract the intrinsic characteristics of interference data through learning and training of the recognition model. It has a high recognition accuracy and can be applied to the identification of malicious interference in satellite communications under complex conditions such as weak interference intensity and strong channel noise.
[0073] The principle of the interference identification method is as follows:
[0074] (1) Based on the digital domain processing after analog-to-digital conversion, the malicious interference patterns faced by satellite communication links are identified;
[0075] (2) Performing multi-dimensional transformation processing on the received signal to obtain a data matrix corresponding to each dimension as the input of the interference recognition model;
[0076] (3) Construct a convolutional neural network that is consistent with the transformation processing dimension. Each network uses multiple convolution kernels that are flexibly set, and then weight the outputs of multiple convolution networks as the final interference recognition result;
[0077] (4) The constructed recognition model is iteratively trained in a supervised manner. Once the model reaches a convergence state, it can be used to identify interference in satellite communication transmission links.
[0078] Here is a specific example:
[0079] First, a large number of satellite communication signals are generated as learning training sample data through actual acquisition and simulation, including different types of interference and different channel conditions. The signal data r(n) is subjected to short-time Fourier transform, correlation matrix calculation and constellation diagram distribution processing to obtain the corresponding processing data matrix set and The size of the processed data matrix in each dimension is N×N, and k indicates that the data matrix is the kth group of the sample data set.
[0080] The data matrix for the transformation and Add interference style labels to obtain the final learning training sample data I train .
[0081] The recognition model is set to consist of 3 multi-core convolutional neural networks (i.e., L=3). The convolutional neural network has a total of J layers, including an input layer, a fully connected layer, an output layer, (J-3) / 2 convolutional layers, and (J-3) / 2 pooling layers. The number of convolutional kernels used in different convolutional layers is set to 2, and the size of the convolutional kernel gradually decreases from the first layer to the last layer.
[0082] The activation function corresponding to each pooling layer uses the common linear rectification function ReLU(·). The fully connected layer is connected to the output layer through the Sigmoid function, and the output layer uses the SoftMax function for logistic regression classification.
[0083] Using sample dataset I train The recognition model is trained and the network parameters of the trained recognition model are saved.
[0084] The received signal to be identified is subjected to multi-dimensional transformation processing, and the processed data matrix is input into the multi-core convolutional neural network recognition model to obtain the interference identification result.
[0085] This method can use the advantages of multi-core convolutional neural networks to autonomously extract the intrinsic characteristics of different types of interference signals, thereby significantly improving the accuracy of identifying malicious interference in satellite communication transmission links under complex conditions.
[0086] Assume that a satellite communication system adopts QPSK modulation with a symbol rate of 1.2Msps. Six kinds of artificial malicious interference are added to the transmission link, including single tone, multi-tone, frequency modulation, partial band noise, partial band modulation and full band noise. The power ratio of the interference at the receiving end to the communication signal ranges from -15dB to 10dB, the communication signal strength remains unchanged, the power ratio of the communication signal to the channel noise is 10dB, and the channel noise is Gaussian white noise.
[0087] Under the above example parameter conditions, the interference identification method of the present invention is simulated for performance, and the Monte Carlo simulation results are averaged for 1000 times. Figure 3 The figure in the figure shows the curve of the accuracy of the six malicious interferences in this method under different interference-to-signal ratios. It can be seen that when the interference-to-signal ratio is not less than -2dB, that is, when the interference intensity is less than the signal intensity, the accuracy of the six interferences can still reach more than 90%, which can realize the accurate identification of malicious interference in satellite communications under complex conditions.
[0088] In summary, the method of the present invention targets the malicious interference faced by satellite communication transmission links, fully utilizes the advantages of multi-core convolutional neural networks in autonomously extracting potential features of data, and realizes accurate identification of different types of interference under complex conditions. Compared with recognition methods such as support vector machines and high-order cumulants, it has more superior performance and can be applied to complex scenarios such as low interference-to-signal ratio and interference-to-noise ratio. The method of the present invention can obtain a relatively high interference identification accuracy when the interference-to-signal ratio and interference-to-noise ratio of the satellite communication link are low. It is applicable to satellite communication systems with different transmission systems, can accurately identify different styles of malicious interference, and provide strong support for space-based electromagnetic situational awareness and interference suppression of satellite communication transmission links.
Claims
1. A method for identifying malicious interference in satellite communications based on a multi-core convolutional neural network, characterized in that: The method is used to identify malicious interference faced by a satellite communication link, including the following steps: Step 1, performing analog-to-digital conversion on the received signal of the satellite communication transmission link to obtain data to be processed; transforming and processing the data from different dimensions, and setting the processing dimension to L; Step 2: Construct a multi-core convolutional neural network interference recognition model. The model uses different convolutional kernels to form multiple convolutional neural networks. Each network includes a corresponding convolution layer, pooling layer, fully connected layer and output layer. The final recognition result is obtained by weighting the output layers of multiple networks. Step 3, adding known interference under different channel conditions, performing interference type identification processing on the data transformed in step 1, using it as learning training sample data for the multi-core convolutional neural network interference recognition model, and iteratively training the model in a supervised manner; Step 4: Perform analog-to-digital conversion on the received signal of the satellite communication transmission link in the actual scenario to obtain L groups of transformed processed data, and input the L groups of transformed processed data into the trained multi-core convolutional neural network interference recognition model to identify malicious interference to the satellite communication link and obtain recognition results.
2. The method for identifying malicious interference in satellite communications based on a multi-core convolutional neural network according to claim 1, characterized in that: Step 1 includes the following steps: Step 1-1, performing analog-to-digital conversion on a received signal of a satellite communication transmission link to convert it into a received signal in a digital domain; Step 1-2, transforming the received signal in the digital domain, including short-time Fourier transform, correlation matrix distribution calculation and constellation diagram distribution; wherein the manner of performing short-time Fourier transform on the received signal r(n) is: Where N is the number of short-time Fourier transform points, i.e., the window length, D is the sliding length of the window each time, X(m,k) is the transform output, m is the time domain window number, k is the frequency domain identifier, and w(n) is the coefficient of the added window. When all are 1, it is a rectangular window. Step 1-3, calculate the correlation matrix distribution of the received signal r(n) of length N: In the formula, R N×N represents an N×N-dimensional correlation matrix, the superscript H represents the conjugate transpose of a vector or matrix, and the superscript * represents the conjugate operation; Step 1-4, decompose each symbol of the received signal r(n) into in-phase and quadrature components, and draw the constellation distribution corresponding to the signal as a dimension of the network model input; Step 1-5, determine the parameter L according to the transformation processing dimension of the received signal r(n).
3. The method for identifying malicious interference in satellite communications based on a multi-core convolutional neural network according to claim 1, characterized in that: In step 2, the multi-core convolutional neural network interference recognition model includes L multi-core convolutional neural networks, each of which consists of 1 input layer, J convolutional layers, J pooling layers, 1 fully connected layer and an output layer; the input layer corresponds to the L-dimensional transformation processing data of the received signal; The jth convolutional layer uses c j Convolution kernels are used for convolution operation. As the number of layers j increases, the size of the corresponding convolution kernel decreases. Each convolutional layer is cascaded with a pooling layer, and the calculation of the jth pooling layer is determined by the corresponding weight w j and bias b j decision; order represents the output of the jth pooling layer, represents the feature set output by the jth convolutional layer, For feature set The (m,n)th subset of Represents the resulting pooling set The element in the mth row and nth column of , then: The jth pooling layer and the j+1th convolutional layer are connected by an activation function; The last pooling layer is connected to the fully connected layer, which is then connected to the output layer. Each neuron in the fully connected layer uses Sigmoid nonlinear function mapping calculation, and the output layer uses normalized exponential function SoftMax for logistic regression classification; The output layers of L multi-core convolutional neural networks are weighted to obtain the final interference recognition result of the recognition model.
4. The method for identifying malicious interference in satellite communications based on a multi-core convolutional neural network according to claim 3 is characterized in that: Step 3 includes the following steps: Step 3-1, obtaining received signal data with various interferences under different channel conditions by actual device generation or computer simulation; Step 3-2, performing multi-dimensional transformation processing on the received signal in the manner of step 1, and adding an interference type label to the transformation processing result to obtain learning training data for the multi-core convolutional neural network recognition model; Step 3-3, use the acquired sample data to perform supervised training on the model, and the training adopts a variable step size method. When the network parameters of the model reach a convergence state, the learning and training are completed.