A Finite-Sample Ballistic Target Recognition Method Based on Depthwise Separable Fusion Convolutional Neural Network

Abstract

The present invention belongs to the field of radar technology, and specifically relates to a method for identifying ballistic targets with limited samples based on a depthwise separable fusion convolutional neural network. The method includes: Step 1: Obtain HRRP samples of ballistic targets from a high-resolution radar, construct a training set and a test set, and the training period is Ω; Step 2: Construct a DSFCNN network; Step 3: Initialize the trainable parameters θ of the DSFCNN network in Step 2; Step 4: Construct a limited-sample learning loss function and calculate the loss function value of each batch of data; Step 5: Use the stochastic gradient descent algorithm to complete the update of the trainable parameters for 1 batch to obtain θ1; Step 6: Let θ0 = θ1, and repeat Steps 4 and 5 until the parameter θ is finally obtained. T , then predict the samples in the test dataset and perform statistics on the prediction results; Step 7: Let θ0 = θ T , repeat Step 6 until the training for Ω cycles is completed, and save the model parameters when the recognition accuracy rate of the test set is the highest. The method of the present invention has a high accuracy rate and high robustness.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar, and particularly relates to a method for identifying ballistic targets with finite samples by using a depthwise separable fusion convolutional neural network. Background Technique

[0002] Ballistic target recognition is to accurately identify warheads from a complex group of targets and is one of the important links in air defense and antimissile. The high-resolution range profile (HRRP) of a radar is the accumulation of the echoes of target scattering points along the radar line of sight, and has advantages such as easy acquisition and fast processing speed, and is one of the important bases for ballistic target recognition.

[0003] Automatic feature extraction and effective target recognition are key issues in Radar Automatic Target Recognition (RATR). In recent years, research on RATR problems based on HRRP by combining related machine learning technologies has become a hot topic. For example, in order to reduce the false alarm rate of radar automatic target recognition based on HRRP, the literature "DU L, LIU X, LI B, et al. HRRP Clutter Rejection Via One-Class Classifier With Hausdorff Distance [J]. Ieee TAero Elec Sys, 2020, 56(4): 2517-26." proposed a rejection algorithm for HRRP data using the joint features of the main scatterer intensity and position and the K-center one-class classifier based on the Hausdorff distance. This method can better eliminate the false alarm rate under different signal-to-noise ratios and parameter values; for the problem of group target recognition based on HRRP, the literature "GUO P C, LIU Z, WANG J J. Radar group target recognition based on HRRPs and weighted mean shift clustering [J]. J Syst Eng Electron, 2020, 31(6): 1152-9." proposed a group target recognition algorithm based on weighted mean shift and support vector machines. This method has advantages such as low computational complexity, automatic parameter setting, and anti-noise robustness; for the problem that traditional feature extraction methods ignore the different importance information in different regions of HRRP, the literature "DU C A, TIAN L, CHEN B, et al. Region-factorized recurrent attentional network with deep clustering for radar HRRP target recognition [J]. Signal Processing, 2021, 183." proposed a region-decomposed recurrent attention network that uses a recurrent neural network to represent the temporal dependence of HRRP samples and automatically finds important information regions in HRRP samples through a deep clustering mechanism. Experiments show that this algorithm has good recognition performance and interpretability; in order to explore the distinguishability between distance units in HRRP and extract distinguishable structural information, the literature "WAN J W, CHEN B, XU B, et al. Convolutional neural networks for radar HRRP target recognition and rejection [J].Eurasip Journal on Advances in Signal Processing, 2019. "Using Convolutional Neural Networks (CNNs) to process one-dimensional HRRP features and two-dimensional spectrogram features respectively, good results are obtained in HRRP target recognition tasks and outlier rejection tasks."

[0004] In the above method, due to the strong automatic feature extraction ability of CNN, the research on the improvement of CNN and its application in radar target recognition based on HRRP has gradually become a key direction in the field of RATR. For example, the literature "ZHANG L, LI Y, WANG Y H, et al. Polarimetric HRRP Recognition Based on ConvLSTM With Self-Attention[J]. Ieee Sens J, 2021, 21(6): 7884-98." first uses an attention module to focus on discriminative range cells, and then combines CNN with the Long Short-Term Memory (LSTM) model to extract the scattering information and polarization information of each range cell, effectively improving the recognition effect of HRRP.The literature "PAN M, LIU AL, YU Y Z, et al. Radar HRRP Target Recognition Model Based on a Stacked CNNBi-RNN With Attention Mechanism[J]. Ieee Transactions on Geoscience and RemoteSensing, 2022, 60." proposed a nested neural network based on a convolutional module, an attention module, and a Bidirectional Recurrent Neural Network (Bi-RNN) module. Among them, the attention module is used to enhance the ability of the convolutional module to extract HRRP envelope features and local features, while the Bi-RNN can effectively extract the rich physical features contained in HRRP. The literature "LIN C L, CHEN T P, FAN K C, et al. Radar High-ResolutionRange Profile Ship Recognition Using Two-Channel Convolutional NeuralNetworks Concatenated with Bidirectional Long Short-Term Memory[J]. RemoteSensing, 2021, 13(7)." proposed an HRRP recognition network based on a two-channel convolutional neural network and bidirectional LSTM, which effectively improved the recognition effect of ship HRRP. To enhance the feature extraction ability of each channel in the CNN, the literature "XIANG Q, WANGX, SONGY, et al. One-dimensional convolutional neural networks for high-resolution range profile recognition via adaptively feature recalibrating andautomatically channel pruning[J]. International Journal of IntelligentSystems, 2021, 36(1): 332-61." used an efficient APR attention module to adaptively enhance the channels beneficial to the recognition task in the CNN, weaken the harmful or redundant channels, and used an improved Artificial Bee Colony (ABC) algorithm to achieve pruning of the redundant channels. A cost-sensitive pruning CNN was further proposed for the cost-sensitive problem. [9]To reduce the overall misrecognition cost of ballistic targets.

[0005] Although the above CNN-based HRRP recognition method solves the HRRP recognition problem under specific conditions, there are still two deficiencies:

[0006] The above methods all use standard CNN as the main module for feature extraction, but standard CNN has a high computational complexity. As Figure 1 shown, in the standard convolutional layer, the input feature map and the convolutional kernel are calculated in a fully connected form with high density, and there are a large number of parameter redundancies and computational complexities. Although the literature "Xiang Qian, Wang Xiaodan, Song Yafei, et al. Ballistic Target Recognition Based on Cost-Sensitive Pruning Convolutional Neural Network [J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(11): 2387-98." and the literature "XIANG Q, WANG X, SONG Y, et al. One-dimensional Convolutional Neural Networks for High-Resolution Range Profile Recognition via Adaptively Feature Recalibrating and Automatically Channel Pruning [J]. International Journal of Intelligent Systems, 2021, 36(1): 332-61." combine pruning methods to reduce the computational complexity of CNN, but the model is still a standard CNN in essence. Therefore, it is necessary to further study the method of using convolutional kernels with fewer parameters to replace the standard convolutional kernel.

[0007] The above CNN-based HRRP recognition method lacks research on the HRRP recognition problem under the condition of limited samples. For example, in the actual scenario, ballistic target recognition is a non-cooperative target recognition problem. One of the core difficulties of this problem is that the number of available ballistic target samples is small. However, the above CNN-based HRRP recognition methods all use complete data sets, and the proposed methods lack verification under the condition of limited samples. Summary of the Invention

[0008] Aiming at the above existing problems, the present invention uses depthwise separable fusion convolution to replace the standard convolution to reduce the model complexity of the deep neural network. At the same time, the cross-entropy loss function is improved to reduce the similarity of samples of the same category and increase the difference degree of samples of different categories, thereby improving the ballistic target recognition problem under the condition of limited samples. The effectiveness of the algorithm of the present invention is proved by simulation experiments.

[0009] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0010] A method for identifying ballistic targets with limited samples based on a depthwise separable fusion convolutional neural network, comprising:

[0011] Step 1: Obtain HRRP samples of Q types of ballistic targets from a high-resolution radar, randomly select 80% of the total samples to form a training set, and use the remaining samples as a test set. Set the total number of training cycles to Ω;

[0012] Step 2: Construct a DSFCNN network including an input layer, L convolutional modules, a flatten layer, and a Softmax classifier. Each convolutional module sequentially includes a one-dimensional depthwise separable fusion convolutional layer, a batch normalization layer, a non-linear activation layer, and a pooling layer. Let the number of channels of each convolutional module be C (1) , C (2) , …, C (L) , and use a one-dimensional array C = [C (1) , C (2) ,..., C (L) to represent the model structure of the network;

[0013] Step 3: Initialize the trainable parameters θ of the DSFCNN network in Step 2 using the Kaiming initialization method, that is, initialize θ to θ0 close to 0, such that where U represents a uniform distribution, and n in is the number of input channels of the convolutional layer where the parameter is located;

[0014] Step 4: Construct a limited-sample learning loss function. After the initialization in Step 3, input the HRRP samples of ballistic targets in the training set in Step 1 into the DSFCNN network, and bring the output of the Softmax classifier of each batch of training samples and the true labels into the limited-sample learning loss function to calculate the loss function value of each batch of data;

[0015] Step 5: Take the derivative of the limited-sample learning loss function when the trainable parameter is θ0 in Step 4, bring the derivative of the limited-sample learning loss function into the formula of the stochastic gradient descent algorithm, and use the stochastic gradient descent algorithm to complete the update of the trainable parameter for 1 batch to obtain θ1;

[0016] Step 6: Let θ0 = θ1, repeat Step 4 and Step 5, and successively train the data of T batches to complete one cycle of training, and finally obtain the parameter θ T , then predict the samples in the test dataset and count the prediction results;

[0017] Step 7: Let θ0 = θ T, Repeat step 6 until the training of Ω cycles is completed, and save the model parameters when the recognition accuracy rate of the test set is the highest.

[0018] Preferably, the operation of the input layer in step 2 is:

[0019] Normalize the signal intensity of each range cell of the input ballistic target HRRP to the range of [0, 1].

[0020] Preferably, the one-dimensional depthwise separable fusion convolutional layer in step 2 is successively composed of three ordered modules: a pointwise convolutional kernel for channel transformation, a depthwise convolutional kernel activated by the Mish function, and a pointwise convolutional kernel for feature fusion. The specific operation is:

[0021] Step 1.1: The first pointwise convolutional kernel performs channel transformation on the input feature map passing through the input layer;

[0022] Step 1.2: Further process the feature map obtained by channel transformation in step 2.1 using depthwise convolution, perform zero-padding on the feature map, and activate the depthwise convolution using the Mish function;

[0023] Step 2.3: The second pointwise convolution performs fusion transformation on the feature map obtained by depthwise convolution in step 2.2.

[0024] Preferably, the operation of the non-linear activation layer is: Use a non-linear activation function to activate the output of the one-dimensional depthwise separable fusion convolutional layer, and all non-linear activation functions in the DSFCNN model structure adopt the Mish function.

[0025] Preferably, the operation of the pooling layer is:

[0026] Perform max-pooling operation on the k-th output feature map of the l-th one-dimensional depthwise separable fusion convolutional layer in step 2.3, and the number of feature maps after max-pooling remains unchanged.

[0027] Preferably, the operations of the flatten layer and the classifier are:

[0028] The output of the last convolutional module passes through the flattening operation of the flatten layer, and all feature maps are arranged as a one-dimensional vector as the input of the Softmax classifier. The number of neurons in the Softmax classifier is equal to the total number of categories of the targets to be classified. For each ballistic target HRRP sample (x (k) , y (k) ), x (k) and y (k) represent the ballistic target HRRP sample data and the corresponding true label respectively. The output of the q-th neuron in the Softmax classifier represents the probability of judging the sample x (k) as the q-th category.

[0029] Preferably, step 4 is specifically as follows:

[0030] Step 4.1: In each small batch of sample data sets M t , establish a loss function formula;

[0031] Step 4.2: For the small batch data set M in step 3.1 t , randomly sample an anchor sample and its corresponding positive and negative samples, and establish a Triplet loss function on the small batch data set M t ;

[0032] Step 4.3: In the problem of finite sample recognition, combine step 4.1 and step 4.2 to establish a final finite sample learning loss function.

[0033] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0034] 1. Aiming at the problem of high computational complexity of one-dimensional standard convolution, a depthwise separable fusion convolution with fewer parameters is used to replace the standard convolution, and a depthwise separable fusion convolutional neural network (DSFCNN) is proposed. The convolutional layer of DSFCNN includes a pointwise convolution - depth convolution - pointwise convolution structure. Among them, the first pointwise convolution performs feature map channel transformation, the second pointwise convolution realizes feature fusion of each channel, and the depth convolution breaks the "fully connected" structure of the standard convolution, with a smaller total number of parameters and computational complexity. Experimental results show that the proposed DSFCNN improves the recognition effect and reduces the number of parameters under most conditions, and the larger the convolution kernel, the more obvious the proportion of parameter reduction under other unchanged conditions.

[0035] 2. Aiming at the problem of ballistic target HRRP recognition in the finite sample scenario, a method for extracting more distinguishable features is studied, and a new loss function is proposed for the training of a depthwise separable convolutional neural network under finite sample conditions. In this paper, a penalty term that can represent the intra-class distance and inter-class distance is introduced into the standard cross-entropy function, so that the network not only considers the fitting degree of the overall samples during the training process, but also considers the discrimination between various types of targets. This loss function combines traditional supervised learning and metric learning, and improves the recognition effect of the model under finite sample conditions

[0036] 3. Experiments on the HRRP data set of five types of ballistic targets show that compared with the standard CNN, DSFCNN has fewer model parameters and higher recognition accuracy. The training results on different degrees of finite sample data sets show that the model is significantly higher than the standard convolutional neural network under finite sample conditions. Therefore, the method of this paper simultaneously achieves three goals: reducing the computational complexity of the model, improving the recognition accuracy, and having a high finite sample learning ability. Brief Description of the Drawings

[0037] The drawings are used to provide a further understanding of the present invention, and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention, and do not constitute a limitation to the present invention.

[0038] In the drawings:

[0039] Figure 1 is the flowchart of the method of the present invention;

[0040] Figure 2 is the schematic diagram of the DSFCNN model structure of the present invention;

[0041] Figure 3 is the physical feature map of the simulation target of the present invention;

[0042] Figure 4 are the recognition results of DSFCNN and standard CNN under the condition of limited samples. Detailed Embodiments

[0043] The following describes the preferred embodiments of the present invention with reference to the drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0044] Embodiment:

[0045] Referring to the attached Figures 1-4 As shown, a method for recognizing ballistic targets with limited samples by a depth separable fusion convolutional neural network includes:

[0046] Step 1: Obtain Q types of ballistic target HRRP samples from a high-resolution radar, randomly select 80% of the total samples to form a training set, and use the remaining samples as a test set. Let the training set x (k) and y (k) respectively represent the k-th ballistic target HRRP sample and its label. The number of samples in each small batch is B, and the total number of samples is N. Then the training set is randomly divided into T = ceil(N / B) small batches, where ceil(·) represents rounding up to an integer, that is Denote the number of range cells of the ballistic target HRRP as E, and set the total number of training epochs as Ω;

[0047] Step 2: Construct a DSFCNN network including an input layer, L convolutional modules, a flatten layer, and a Softmax classifier. Each convolutional module sequentially includes: a one-dimensional depth separable fusion convolutional layer, a batch normalization layer, a non-linear activation layer, and a pooling layer. Let the number of channels of each convolutional module be C (1) , C (2) , …, C (L), the model structure of the network is represented by a one-dimensional array C = [C (1) , C (2) ,..., C (L) .

[0048] Furthermore, the operation of the input layer in step 2 is as follows:

[0049] Normalize the signal strength of each range cell of the ballistic target HRRP to the range of [0, 1] using the formula:

[0050]

[0051] where represents the signal strength of the j-th range cell of the k-th ballistic target HRRP sample, and E is the number of range cells.

[0052] The one-dimensional convolutional layer performs a convolution operation on the input data and a convolutional kernel with a fixed window size to automatically extract features. Generally, the scale of the convolutional kernel is much smaller than the size of the input data. Therefore, the convolutional kernel moves on the input data with a certain stride, and the same convolutional kernel is used at each step to achieve weight sharing.

[0053] Furthermore, the one-dimensional depthwise separable fusion convolutional layer in step 2 consists of three ordered modules in sequence: a pointwise convolutional kernel for channel transformation, a depthwise convolutional kernel activated by the Mish function, and a pointwise convolutional kernel for feature fusion. Let represent the multi-channel input of the l-th (l ∈ {1, 2,..., L}) one-dimensional depthwise separable fusion convolutional layer, represent the real positive integer space, D (l) and C (l) represent the length and number of channels of the feature map respectively. The one-dimensional depthwise separable fusion convolutional layer converts the multi-channel input X (l) into a multi-channel output where D (l+1) and C (l+1) represent the length and number of channels of the feature map X (l+1) after convolution respectively. Since the input of the first one-dimensional depthwise separable fusion convolutional layer is the original data of the ballistic target HRRP, which has only one channel, i.e., C (1) = 1, the feature map input to the input layer of the one-dimensional depthwise separable fusion convolutional layer is denoted as where D (1) = E, then Since DSFCNN performs the same operation on all HRRP samples, the sample sequence number k is not used in the feature map symbol X (l) (l ∈ {1, 2,..., L}).

[0054] The specific operation of the one-dimensional depthwise separable fusion convolutional layer is as follows:

[0055] Step 2.1: The first pointwise convolution kernel transforms the input feature map X (l) by performing a channel transformation. Using the formula, X with C channels (l) is (l) transformed into X' with C channels (l+1) , that is (l) . Here, represents the space of real positive integers, and the tensors and represent the weight parameter and bias parameter of the first pointwise convolution kernel respectively. Among them, the window size H' (l) = 1, the zero-padding number P' (l) = 0, and the stride S' (l) = 1.

[0056]

[0057] where i ∈ {1, 2,..., D (l)}}, k ∈ {1, 2,..., C (l+1)}}.

[0058] Step 2.2: Further process the feature map X' obtained from the channel transformation in Step 2.1 using depthwise convolution. Let the weight and bias parameters of the depthwise convolution kernel be (l) and respectively. The generated feature map is . Perform zero-padding on the feature map X' . Then (l) the depthwise convolution uses the Mish function for activation, and the depthwise convolution operation process is

[0059]

[0060] where S (l) is the stride of the depthwise convolution, i ∈ {1, 2,..., D (l+1)}}, k ∈ {1, 2,..., C (l+1)}};

[0061] Step 2.3: The second pointwise convolution performs a fusion transformation on the feature map obtained from the depthwise convolution in Step 2.2. Use the tensors and to represent the weight parameter and bias parameter of the second pointwise convolution kernel respectively. Its window size H″ (l) = 1, the zero-padding number P″ (l) = 0, and the stride S″ (l) = 1. Then the fusion transformation process is represented by the following formula:

[0062]

[0063] Furthermore, the operation of the non-linear activation layer in step 2 is as follows: use a non-linear activation function to activate the output of the one-dimensional depthwise separable fusion convolutional layer. All non-linear activation functions in the DSFCNN model structure adopt the Mish function, and the expression is:

[0064] δ(x) = x · tanh(ln(1 + e x )) (5)

[0065] where tanh(·) is the hyperbolic tangent function, ln(·) is the natural logarithm, e is the natural constant, and x is the input of the Mish function. For specific reference, see formula (3).

[0066] Furthermore, due to the limitation of computer processing power, generally not all data are sent into the network for training at the same time, but all data are input in batches. Using batch normalization to normalize the output of each batch of the convolutional layer to a distribution with a mean of 0 and a standard deviation of 1 can accelerate the training generalization ability of the DSFCNN model. Therefore, in the present invention, a batch normalization layer is connected after all convolutional layers.

[0067] Furthermore, in order to reduce the dimension of the output of the one-dimensional convolutional layer and remove adjacent feature redundancy, the pooling layer downsamples the output of the one-dimensional convolutional layer. The operation of the pooling layer in step 2 is max pooling, and the specific process is as follows:

[0068] For the k-th output feature map X of the l-th one-dimensional depthwise separable fusion convolutional layer in step 2.3 k (l+1) , the result after max pooling at position i is:

[0069]

[0070] where H *(l) and S *(l) respectively represent the window size and stride of max pooling. Therefore, the number of feature maps remains unchanged after max pooling, and the length of the feature map becomes:

[0071]

[0072] where floor(·) represents rounding down.

[0073] Furthermore, the operations of the flattening layer and the classifier in step 2 are as follows:

[0074] The output X of the last convolutional module (L) after passing through the flattening operation of the flattening layer, X (L)All the feature maps are arranged as a one-dimensional vector \(u\) as the input of the Softmax classifier. Then, the input of the \(k\)-th sample after the flattening operation to the Softmax classifier is denoted as \(u\). (k) The number of neurons in the Softmax classifier is equal to the total number \(Q\) of categories of the objects to be classified. The weight and bias parameters of the Softmax classifier are denoted as \(\theta\). sm \(=\{W\) sm , b sm \}\). Then, the weight and bias parameters of the \(j\)-th neuron of the Softmax classifier are respectively denoted as and For each HRRP sample \((x\) (k) , y (k) ) of a ballistic target, \(x\) (k) and \(y\) (k) respectively represent the data of the \(k\)-th HRRP sample of the ballistic target and the corresponding true label. The output of the \(q\)-th neuron of the Softmax classifier represents the probability of classifying the sample \(x\) (k) as the \(q\)-th category, that is

[0075]

[0076]

[0077] where represents the multi-dimensional features extracted by all the previous layers of the classifier, \(\theta^*\) is the parameters of all the feature extraction layers except the classifier, Flatten(\(\cdot\)) represents the flattening operation, \(\theta = \{\theta^*, \theta\) sm \} represents all the trainable parameters of the DSFCNN network. The prediction process of the sample \(x\) (k) is the process of maximizing the posterior probability, that is

[0078]

[0079] Therefore, the entire DSFCNN network realizes a mapping \(f\) with parameter \(\theta\) from the sample space to the feature space , that is: θ Namely:

[0080]

[0081] where the vector represents the output after the sample \(x\) (k) is mapped by the DSFCNN network, that is, the embedded feature. The true label \(y\) of the sample \(x\) (k) is represented by its unique coding vector (k) , where:

[0082] ​

[0083] Step 3: Initialize the trainable parameters θ of the DSFCNN network in Step 2 using the Kaiming initialization method, that is, initialize θ to θ0 which is close to 0, such that where U represents a uniform distribution, and n in is the number of input channels of the convolutional layer where the parameter is located;

[0084] Step 4: Construct a finite-sample learning loss function. After the initialization in Step 3, input the HRRP samples of the ballistic targets in the training set into the DSFCNN network, and bring the output of the Softmax classifier of each batch of training samples and the true labels into the finite-sample learning loss function to calculate the loss function value of each batch of data. Specifically:

[0085] Step 4.1: For each mini-batch sample dataset M i , the loss function is expressed by the formula

[0086]

[0087] where, ⊙ represents the dot product; E(x) represents taking the expectation of x; 1{·} is the indicator function, that is, 1{true} = 1, 1{false} = 0;

[0088] Step 4.2: For the mini-batch dataset M t in Step 4.1, randomly sample an anchor sample and its corresponding positive example sample and negative example sample where Then the Triplet loss function on the mini-batch dataset M t is:

[0089]

[0090]

[0091] where, α is a positive decimal close to 0;

[0092] Step 4.3: In the finite-sample recognition problem, combining Step 4.1 and Step 4.2, the final finite-sample learning loss function can be obtained as:

[0093] J LD (θ; M t ) = J CE (θ; M t ) + γJ Triplet (θ; M t ) (16)

[0094] Among them, γ ∈ [0, +∞] is used to adjust the overall sample fitting degree and the learning degree of the intra-class - inter-class distance.

[0095] Step 5: Take the derivative of the finite-sample learning loss function when the trainable parameter is θ0 in Step 4, substitute the derivative of the finite-sample learning loss function into the formula of the stochastic gradient descent algorithm, and use the stochastic gradient descent algorithm to complete the update of the trainable parameter for 1 batch, obtaining θ1.

[0096] Further, the update of the trainable parameter in Step 5 is specifically as follows:

[0097]

[0098] For the t-th (t ∈ {1, 2,..., T}) iteration, the update formula of the trainable parameter θ of the DSFCNN network by the stochastic gradient descent algorithm is:

[0099] θ t+1 =θ t -ηg t (18)

[0100] Among them, η is the learning rate, and g t is the gradient of the loss function with respect to θ t , that is:

[0101] g t =▽ θt J LD (θ t ;M t ) (19).

[0102] Step 6: Let θ0 = θ1, repeat Step 4 and Step 5, and train the data for T batches one by one to complete one cycle of training, finally obtaining the parameter θ T , substitute θ T into the formula to predict the samples in the test dataset, and count the prediction results;

[0103] Step 7: Let θ0 = θ T , repeat Step 6 until Ω cycles of training are completed, and save the model parameters when the recognition accuracy rate of the test set is the highest.

[0104] Complexity analysis:

[0105] In a neural network, the number of parameters is an important indicator to measure the computational complexity. In the same network architecture, the network with a larger number of parameters often has a higher computational complexity. To compare the computational complexity of the standard one-dimensional convolutional neural network and the one-dimensional depthwise separable convolutional neural network proposed by the present invention, the present invention uses the number of parameters for analysis and comparison. The present invention only considers the weight parameters for the analysis of the number of parameters here.

[0106] For a standard one-dimensional convolutional layer, the weights of its convolutional kernel The total number of parameter

[0107] Φ std = H (l) × C (l) × C (l+1) (20)

[0108] The improved depthwise separable one-dimensional convolutional layer of the present invention is respectively composed of a channel transformation convolution depth convolution and a fusion convolution and other three parts. Then the total number of weight parameters is

[0109] Φ sds = 1 × C (l) × C (l+1) + H (l) × C (l+1) + 1 × C (l+1) × C (l+1) (21)

[0110] From formulas (20) and (21), it can be obtained that

[0111]

[0112] Among them, H (l) Generally takes a positive odd number less than D (l) , C (1) and C (l+1) Take positive integers.

[0113] It can be seen from formula (22) that the larger the convolutional kernel window H (l) , the smaller the number of input channels and the larger the number of output channels. Then, compared with the one-dimensional standard convolution of the same layer, the number of parameters of the one-dimensional depthwise separable convolution decreases more significantly. Let C (l+1) = 2C (l) , for a very large C (l) , then

[0114] Φ sds / Φ std ≈ 3 / H (l) , since H (l) generally takes a positive odd number, so when H (l) > 3, the number of parameters of DSFCNN decreases significantly compared with that of the standard CNN.

[0115] Analysis of experimental results:

[0116] The experiment adopts the following idea: First, in order to verify the effectiveness of the DSFCNN proposed in this paper and its improvement effect relative to the standard CNN, the standard cross-entropy loss function JCE The DSFCNN and the standard CNN were trained respectively. Secondly, in order to compare the influence of the proposed limited-sample learning loss function J LD on the DSFCNN model, experiments were conducted with the hyperparameter γ of J LD taking 0.1, 0.01, and 0.001 respectively.

[0117] Table 1 shows the mean and variance of the recognition accuracy rates of the test sets for the DSFCNN and the standard CNN under different hyperparameter settings.

[0118] Table 1 Recognition accuracy rates (%) of the test sets for the DSFCNN and the standard CNN under different hyperparameter settings

[0119]

[0120] The following conclusions can be drawn from Table 1:

[0121] (1) When other hyperparameters remain unchanged, as the number of output channels of each convolutional module and the convolutional kernel window gradually increase, the recognition accuracy rate of the test set generally shows an upward trend. The increase in the number of output channels of the convolutional module and the convolutional kernel window means an increase in the number of parameters, indicating that the increase in the number of parameters within the experimental range helps to improve the recognition accuracy rate of the model.

[0122] (2) When training the DSFCNN and the standard CNN using the cross-entropy loss function J CE the recognition accuracy rate of the DSFCNN is significantly higher under the same configuration of the number of channels and the convolutional kernel window, indicating that using the pointwise convolution-depth convolution-pointwise convolution structure to replace the standard convolution can effectively improve the recognition effect.

[0123] (3) When using the limited-sample learning loss function J LD to replace the cross-entropy loss function J CE to train the DSFCNN, under the same configuration of the number of channels and the convolutional kernel window, the recognition accuracy rate is significantly improved, and when the hyperparameter γ of J LD increases from 0.001 to 0.1, the recognition accuracy rate gradually increases, strongly proving the effectiveness of using the discrimination between categories to punish the standard loss function, and at the same time indicating that the features extracted by the DSFCNN trained using the limited-sample learning loss function are more distinguishable.

[0124] Table 2 shows the number of parameters of the DSFCNN and the standard CNN under different hyperparameter settings. It can be seen that the total number of parameters of the DSFCNN and the standard CNN always increases with the number of output channels of the convolutional module and the convolutional kernel window H (l)It increases with the increase of 4 from 207.56×10 4 to 482.87×10 (l) , an increase of (482.87 - 207.56) / 207.56≈132.64%, while DSFCNN only increases by (211.67 - 210.91) / 210.91≈0.36%. Under the condition of the same setting of the output channels of the convolutional module, only when H (l) = 3, the total number of parameters of DSFCNN is slightly larger than that of CNN, while when H

[0125] Table 2 Total number of model parameters of DSFCNN under different hyperparameter settings (×10 4 pieces)

[0126]

[0127] From the results of Table 1 and Table 2, for DSFCNN, when the output channels of the convolutional module are set to C5, the hyperparameter γ of J FS = 0.01, and H (l) = 7, the recognition accuracy rate of DSFCNN reaches the optimal value of 96.56±0.16%, and the total number of parameters is 211.67×10 4 , while the standard CNN also reaches the optimal value of the recognition accuracy rate when the output channels of the convolutional module are set to C5 and H (l) = 7, reaching 96.23±0.30%, and the total number of parameters is 482.87×10 4 . Therefore, under the optimal hyperparameter settings of DSFCNN and the standard CNN respectively, compared with the standard CNN, the average recognition accuracy rate of DSFCNN increases by 96.56% - 96.23% = 0.33%, and the total number of parameters decreases by (482.87 - 211.67) / 482.87≈56.16%.

[0128] To analyze the recognition effect of DSFCNN under finite sample conditions, part of the data is randomly sampled from the training dataset to train the model, while the test dataset remains unchanged. Figure 4 The sampling ratios for the training set are 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90% and 100% respectively, and J LDThe hyperparameter γ = 0.001. When the number of output channels of the convolutional module is set to C4, the recognition accuracy of the test set under different convolutional kernel window sizes H (l) The results are as follows, where 10 experiments are conducted for each hyperparameter configuration. From Figure 4 it can be seen that as the sampling ratio of the training set increases, the recognition accuracies of both DSFCNN and the standard CNN show an upward trend. However, under the same sampling ratio condition, the recognition accuracy of DSFCNN is better than that of the standard CNN. Additionally, under the condition of a relatively small sampling ratio, the variation range of the multiple experimental results of DSFCNN is relatively small, indicating that DSFCNN can extract more robust features to make the recognition results more stable.

[0129] The above shows and describes the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of the present invention claimed is defined by the appended claims and their equivalents.

Claims

1. A method for identifying ballistic targets with limited samples using a depthwise separable fusion convolutional neural network, characterized in that: Including: Step 1: Obtain HRRP samples of ballistic targets of types from a high-resolution radar. Randomly select 80% of the total samples to form a training set, and use the remaining samples as a test set. Set the total number of training cycles to Ω; Step 2: Construct a DSFCNN network including an input layer, convolution modules, a flattening layer, and a Softmax classifier, where each convolution module sequentially consists of a one-dimensional depthwise separable fusion convolutional layer, a batch normalization layer, a non-linear activation layer, and a pooling layer. Let the number of channels of each convolution module be Use a one-dimensional array to represent the model structure of the DSFCNN network; The one-dimensional depthwise separable fusion convolutional layer in step 2 consists of three ordered modules in sequence: a pointwise convolutional kernel for channel transformation, a depthwise convolutional kernel activated by the Mish function, and a pointwise convolutional kernel for feature fusion. The specific operations are as follows: Step 2.1: The first pointwise convolutional kernel performs channel transformation on the input feature map passing through the input layer. Step 2.2: The feature map obtained from the channel transformation in step 2.1 is further processed using depthwise convolution, and zero-padding is performed on the feature map. The depthwise convolution is activated by the Mish function. Step 2.3: The second pointwise convolution performs fusion transformation on the feature map obtained from the depthwise convolution in step 2.

2. Step 3: Initialize the trainable parameters θ of the DSFCNN network in Step 2 using the Kaiming initialization method, that is, initialize θ as θ0 close to 0, such that where U represents a uniform distribution, and n in is the number of input channels of the convolutional layer where the parameter is located; Step 4: Construct a finite-sample learning loss function. After the initialization in step 3, the ballistic target HRRP samples in the training set in step 1 are input into the DSFCNN network. The output of the Softmax classifier for each batch of training samples and the true labels are brought into the finite-sample learning loss function to calculate the loss function value for each batch of data. Step 5: Take the derivative of the finite-sample learning loss function when the trainable parameter is θ0 in step 4. Substitute the derivative of the finite-sample learning loss function into the formula of the stochastic gradient descent algorithm, and use the stochastic gradient descent algorithm to complete the update of the trainable parameter for 1 batch to obtain θ1. Step 6: Let θ0 = θ1, repeat Step 4 and Step 5, and successively train the data of batches to complete one cycle of training, and finally obtain the parameters Then, predict the samples in the test dataset and count the prediction results; Step 7: Let Repeat Step 6 until the training of Ω cycles is completed, and save the model parameters when the recognition accuracy rate of the test set is the highest.

2. The method for identifying ballistic targets with limited samples using a depthwise separable fusion convolutional neural network according to claim 1, characterized in that: The operation of the input layer in step 2 is as follows: Normalize the signal intensity of each range cell of the input ballistic target HRRP to the range of [0, 1].

3. The method for identifying ballistic targets with limited samples using a depthwise separable fusion convolutional neural network according to claim 2, characterized in that: The operation of the non-linear activation layer is as follows: Use a non-linear activation function to activate the output of the one-dimensional depthwise separable fusion convolutional layer. All non-linear activation functions in the DSFCNN model structure adopt the Mish function.

4. The method for identifying ballistic targets with limited samples using a depthwise separable fusion convolutional neural network according to claim 3, characterized in that: The operation of the pooling layer is as follows: Perform max pooling on the k-th output feature map of the l-th one-dimensional depthwise separable fusion convolutional layer in step 2.

3. The number of feature maps remains unchanged after max pooling.

5. The method for identifying ballistic targets with limited samples using a depthwise separable fusion convolutional neural network according to claim 4, characterized in that: The operations of the flatten layer and the classifier are as follows: The output of the last convolutional module is flattened by a flatten layer, and all feature maps are arranged as a one-dimensional vector as the input of the Softmax classifier. The number of neurons in the Softmax classifier is equal to the total number of categories of the targets to be classified. For each HRRP sample (x (k) , y (k) ) of a ballistic target, x (k) and y (k) respectively represent the HRRP sample data of the ballistic target and the corresponding true label. The output of the q-th neuron in the Softmax classifier represents the probability of classifying the sample x (k) as the q-th category.

6. The method for identifying ballistic targets with limited samples using a depthwise separable fusion convolutional neural network according to claim 5, characterized in that: Step 4 is specifically as follows: Step 4.1: In each mini-batch sample data set M t , establish the loss function formula; Step 4.2: For the small batch dataset M in Step 3.1 t , randomly sample an anchor sample and its corresponding positive and negative samples to establish a Triplet loss function on the small batch dataset M t ; Step 4.3: In the finite-sample recognition problem, combining step 4.1 and step 4.2, establish the final finite-sample learning loss function.

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