CN115047423A - Comparison learning unsupervised pre-training-fine tuning type radar target identification method - Google Patents
Comparison learning unsupervised pre-training-fine tuning type radar target identification method Download PDFInfo
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Abstract
The invention discloses a radar target identification method based on comparison learning unsupervised pre-training-fine tuning, which comprises the steps of firstly preprocessing an original sample and carrying out data expansion; then, increasing the structural diversity of the HRRP sample by adopting a reshape and data enhancement mode; inputting the data into a SimDual module; finely adjusting the output of the SimSimSimMode encoder network on a downstream classification module, inputting the output into the downstream classification module after shape operation, and finally realizing HRRP identification classification; in the invention, a data enhancement mode is adopted, so that the model learns more effective characteristic information, and the identification performance of the task migrated to the downstream classification task is improved. Various different universal robust models applied to HRRP target recognition can be obtained by defining different downstream classification modules, and a new thought and a new method are provided for the field of radar HRRP target recognition.
Description
Technical Field
The invention belongs to the field of radar target identification, and particularly relates to a radar target identification method based on comparison learning unsupervised pre-training-fine tuning.
Background
The range resolution of a high-resolution broadband radar is much smaller than the target size, and its echo is also called one-dimensional high-resolution range profile (HRRP) of the target. The HRRP contains structure information which is extremely valuable for classification and identification, such as the radial size of a target, the distribution of scattering points and the like, and has wide engineering application prospect. Therefore, the HRRP-based radar automatic target identification method gradually becomes a hot spot of research in the field of radar automatic target identification.
With the continuous maturation of radar technology, most of traditional HRRP identification methods based on statistical models, popular learning and kernel methods in the early stage can acquire the distribution of target strong scattering points and perform identification and classification, but most of the traditional methods perform framing modeling based on full-connection structures, omit inter-frame correlation information, cannot capture structural information reflecting HRRP characteristics, and have high requirements on the completeness of target data. In recent years, the profound learning algorithm changes the traditional full-connection structure, and can automatically acquire the deep-level features contained in the HRRP data.
The traditional HRRP characteristic extraction method mainly comprises two parts: (1) transform (Transformer) based feature extraction methods, such as spectrograms and the like. The method projects the HRRP signal to the frequency domain, and then models and identifies the frequency domain characteristics of the HRRP signal. (2) And (4) performing feature extraction based on the data subjected to dimension reduction. Although the traditional feature extraction methods have good recognition performance, most of the methods are unsupervised and lossy, and the selection of the feature extraction methods is highly dependent on the knowledge and experience of scientific researchers on data, so that good effects are difficult to achieve in many cases. The learning and extraction of the HRRP target characteristics are a link which plays a significant role in the radar target identification process. Aiming at the defects of the traditional method and the characteristics of HRRP data, the improved deep learning network is used for identifying and classifying the target HRRP, the network with strong generalization capability is fused to fully capture the effective structural information in the HRRP, the parameters in the network are optimized while a complex model is constructed, and faster convergence and higher identification performance are realized.
Disclosure of Invention
In order to solve the problems, the invention provides a radar target identification method based on comparison learning unsupervised pre-training-fine tuning.
The invention provides a method for Learning the general characteristic representation of radar HRRP data by using a deep Learning model of a contrast Learning (contrast Learning) method and applying the model to a Downstream Task (Downstream Task), so that the unsupervised contrast Learning method realizes deeper training of a network, the unsupervised pre-trained model is used for Learning the effective characteristic representation in an HRRP sample, and then a large number of labeled HRRP training samples are not needed any more, so that the method can be applied to various Downstream tasks and Fine tuning (Fine-tune), thereby obtaining various high-performance robust models suitable for HRRP target identification, and providing a new method and a general method for radar HRRP identification. Compared with learning, the method has the greatest advantages that the method can better extract the similarity general characteristics contained between the HRRP samples in different angular domains, and can be used for identifying and classifying suitable downstream tasks, a certain identification capability can be still maintained under the harsh small sample target environment, and a new general idea and method are provided for radar target identification.
The radar target identification method based on the comparison learning unsupervised pre-training-fine tuning mode comprises the following steps:
s1: the original HRRP sample set is preprocessed.
By a 1 2 The intensity normalization method processes the original HRRP echo, thereby improving the intensity sensitivity problem of the HRRP. HRRP is intercepted from radar echo data through a range window, and the range recorded in the process of interception is like the rangeThe position in the gate is not fixed, resulting in translational sensitivity of the HRRP. In order to make training and testing have a unified standard, a center-of-gravity alignment method is adopted to eliminate the translational sensitivity.
S2: and performing translation processing on the processed HRRP sample to realize data expansion.
And S3, increasing the structural diversity of the HRRP sample by adopting a reshape and data enhancement mode, and enabling the model to learn more effective characteristic information.
And S4, inputting the HRRP samples obtained by different data enhancement methods into a SimSamSim module.
The SimDual module comprises four parts of a random data enhancement part, a backbone network, a projector and a predictor, wherein the backbone network and the projector form an encoder network. The expanded HRRP samples are sampled by different data enhancement methods, then the HRRP samples enter an encoder network for encoding, feature matching is carried out by maximizing consistency among feature vectors of different views from the same HRRP sample, and then high-quality main feature representation of the HRRP sample is extracted by a projector, which is beneficial to obtaining universal consistency representation by comparing a prediction task. And (4) inputting the output characteristics into a predictor, estimating the overall expectation of the SimSaim module, namely optimizing network parameters through back propagation, and filtering partial invalid characteristic information of high layers at the same time, so that the characteristic information in the HRRP sample is fully reserved for carrying out contrast prediction optimization.
S5, performing unsupervised pre-training on the SimSam module by adopting contrast learning on the extended radar HRRP sample, enabling the output of the encoder network and the output obtained by using the supervised training to have the same general characteristic information, then performing fine-tuning (fine-tune) on the output of the encoder network on a downstream classification module, inputting the output into the downstream classification module after shape operation, and finally realizing HRRP identification classification.
And S6, reconstructing target data of the correctly classified predicted capsule characteristics of the HRRP sample through a reconstruction module, restoring the target data into initial input, and participating in training.
Further, the detailed step of S1 is:
s1.1: and (4) intensity normalization. Denote the original HRRP as
Wherein L is 1 Representing the total number of range cells contained within the HRRP, the HRRP after intensity normalization can be represented as:
s1.2: the samples are aligned. Translating HRRP to make its gravity center g 1 Move to
Nearby, such that those distance cells in the HRRP that contain information will be distributed near the center. Wherein HRRP center of gravity g 1 The calculation method of (2) is as follows:
further, the detailed step of S2 is:
in order to avoid overfitting in the pre-training process and obtain important semantic information in HRRP data, the gravity center of each HRRP sample subjected to sensitivity processing is respectively translated to the left and the right by 1 to 4 distance units for data expansion, so that the data volume of unsupervised pre-trained samples can be increased by 8 times on the basis of an original training set, and further the generalization capability of a network to new samples is improved to a certain extent.
Further, the detailed step of S3 is:
s3.1, firstly, the radar HRRP sample after the data sensitivity preprocessing is still 1 x 256 one-dimensional vector data, in order to match the data dimension, the dimension of the data is increased by using an unscqueeze () function, and the shape of the HRRP sample is converted into a four-dimensional tensor
Then, reshape operation is carried out on the HRRP sample, and the mode of entering the encoder network in the SimSam module at the moment is
Second, data enhancement operations including random clipping, random gaussian blurring, horizontal flipping, and scaling are performed on the HRRP samples in 16 × 16 format to increase the structural diversity of the HRRP. And finally, carrying out normalization operation on the HRRP sample subjected to data enhancement.
Further, the detailed step of S4 is:
s4.1 random data enhancement:
the random data enhancement operation is to generate two different sets of views of each HRRP sample for the self-supervised contrast learning task, i.e. the views x' and x "for the contrast learning task are obtained by the HRRP samples respectively through two random data enhancements.
S4.2, backbone network part:
selecting Resnet-50 as a backbone network, wherein the Resnet-50 consists of 1 convolution input layer, 4 residual convolution blocks and 1 fully-connected output layer, the residual convolution blocks comprise 16 convolution blocks, and each convolution block consists of the same number of convolution layers. The convolution input layer is arranged to reserve semantic information and global feature information of the enhanced HRRP view adjacent features, and construct a reasonable spatial relationship, which is beneficial to extracting the effective features of the HRRP. The residual block, as a main component of the network, first uses the dimension (ascending or descending) of the convolution layer transform feature of the 1 × 1 convolution kernel. And extracting effective characteristics by using the convolution layer of the 3 multiplied by 3 convolution kernel, introducing identity mapping to accelerate the flow of the associated information between the deep network layers and fully utilizing the characteristics of each layer, and finally extracting effective and meaningful HRRP characteristic representation to improve the identification performance. Each residual volume block uses a ReLU activation function and a batch normalization unit, so that the generalization capability of the model is improved.
S4.3, projector part:
the core role of the projector is to filter redundant information or irrelevant semantic information in HRRP view feature representation, retain the most dominant nonlinear feature and carry out l on the feature vector 2 Regularization and then mapping it to a unit hypersphere spaceAnd performing comparison matching prediction, and maximizing similarity structure information between two HRRP view representations, namely constraining the consistency degree between vectors in the hypersphere space and the training process of a network, so as to obtain a universal HRRP sample similarity characteristic representation. The deep-layer projector can improve the quality of HRRP feature expression and the performance of contrast learning, so that three linear fully-connected layers (FC) are constructed for the projector, each layer is connected with a BN layer, and the output dimension of each fully-connected layer is 2048. The feature output via the backbone network is denoted as y i Output characteristic z of the encoder network i The calculation expression of (a) is as follows:
z i ＝g(y i )＝W (3) σ(W (2) σ(W (1) y i ))
where σ denotes the ReLU activation function, g denotes the projection function, and W denotes the weight matrix for each fully-connected layer. The effect of the bias term on the network is ignored for ease of analysis. The existence of BN layer in the projector enables the spatial distribution of each layer output to be readjusted, partial features shared among HRRP samples in each batch are removed, and features with difference are reserved and used for the task of comparative prediction.
S4.4 predictor part:
the predictor comprises three parts of two full connection layers, a BN layer and an activation layer. Where the first fully-connected layer has an input dimension and an output dimension of 2048 and the second fully-connected layer has an output dimension of 512. Feature vector p output by predictor i The calculation expression is as follows:
p i ＝h(z i )＝W (2) σ(W (1) z i )
where h denotes the prediction function, σ denotes the ReLU activation function, W (1) 、W (2) The weight matrices of the first fully-connected layer and the second fully-connected layer are represented, respectively.
S4.5, the SimSam working mechanism:
the loss of simsim is defined using the EM algorithm, as follows:
wherein
Representing the encoder network for feature extraction, theta is a learnable parameter, x is the HRRP sample,
representing random data enhancement function before HRPP data input, expectation
Representing methods for HRRP sample x and random data enhancement
The distribution of (a), in other words,
equivalent to the sum of loss expectation for all HRRP samples and random data enhancement. Eta x Is a feature expression of HRRP samples x, i.e. a feature vector z of the encoder network output i . The similarity is calculated using Mean Squared Error (MSE). At the moment, the working mode of the SimSaim is similar to that of a K-means clustering algorithm, one variable is fixed, and the other variable is solved, namely the EM iterative algorithm. This translates into the following two subproblems:
where ← represents the assignment operation, and r represents the number of iterative updates of the algorithm. Computing θ in the first sub-problem using a Stochastic Gradient Descender (SGD) algorithm r By publicEquation (4-5-2), stopping the back propagation of the gradient to eta r-1 Eta is then r-1 It is a constant in the formula (4-5-2), and if the back propagation of the gradient is not stopped, two variables exist in the formula, so that the solution cannot be realized.
Determining theta r After solving, it is substituted into the second sub-problem, where only one variable η exists in equation (4-5-3), the expectation of each HRRP sample x needs to be minimized
Substituting equation (4-5-1) into equation (4-5-3), the solution of the second sub-problem is converted into:
transformed according to the desired formula to yield:
in this case, the characteristic representation of a certain HRRP sample x at the time of the r-th iteration update is expected to be obtained from the sample x through random data enhancement.
Performing random data enhancement on the transformed second sub-problem according to formula (4-5-5)
The formula is as follows:
then substituting into the formula (4-5-2) to obtain:
wherein theta is r Is a solution of the equation of equation (4-5-2),
and
representing two different data enhancement methods acting on a certain HRRP sample, the equation can be regarded as a twin double tower architecture.
Adding a predictor on one side of the branch of the SimDiam module, and defining the predictor as h 1 ，z 1 For the characterization of the HRRP sample, equation (4-5-4) is converted to:
h 1 (z 1 )＝E z [z 1 ]＝E T [f(T(x))] (4-5-8)
random enhancement due to direct computation
Expected value of (2)
It is difficult to equate the enhanced expectations to their own for ease of analysis.
Further, the detailed step of S5 is:
selecting a capsule network as a downstream classification module, only finely adjusting and updating parameters in the capsule network during training, obtaining and fixing weight parameters of an encoder in the SimSam by unsupervised pre-training learning, and extracting meaningful key features from an HRRP sample by using the encoder as a feature extraction network. The characteristic dimension extracted by the encoder network is 2048, namely the vector feature of 1 × 2048, then dimension reduction is carried out through a full connection layer of 2048 × 256 to obtain the feature with the dimension of 256, and the feature is input into the capsule network after shape operation, so that HRRP identification and classification are finally realized.
Further, the detailed step of S6 is:
s6.1, the reconstruction module can be regarded as a decoder and used for restoring the predicted capsule characteristics of the HRRP sample correctly classified into initial input, namely a vector with 256 output dimensions, and participating in the training of the whole model for assisting in contrasting the result of the HRRP classification. Specifically, a high-level capsule with the maximum unit length in a capsule network prediction capsule layer is taken as a reconstruction target, and reconstructed target data are output through three full-connection layers with activation functions.
S6.2, the radar target identification method based on comparison learning unsupervised pre-training-fine tuning comprises a data preprocessing module, a SimSam module, a downstream classification module and a reconstruction module. Initializing all weights and biases to be trained in the SimSaim module and the downstream classification module, setting training parameters including learning rate, batch _ size and training batch, and training the SimSaim module and the capsule network.
Further, the total loss of the network constructed by the comparison learning unsupervised pre-training-fine tuning type radar target identification method is represented by the capsule classification loss L d And reconstruction loss L rec Two-part construction, and loss L d The expression plays a dominant role as follows:
Loss general (1) ＝L d +L rec
The capsule form enables multiple classes to exist simultaneously, so the training process of the capsule network is performed by MarginLoss as a loss function L d The sum of the losses of each predicted capsule is expressed as:
L d ＝Y d max(0,m + -||v d ||) 2 +λ(1-Y d )max(0,||v d ||-m - ) 2
wherein d represents the HRRP target class, Y d Is to represent a class label in training, m + 、m - The fixed hyper-parameters are respectively set to 0.9 and 0.1, and lambda is a coefficient for preventing the network from solving local optimum and is set to 0.5. When the predicted capsule matches the correct HRRP sample d during the training process, Y d When the predicted probability of the predicted capsule exceeds 0.9, the loss is set to zero, and when the probability is lower than 0.9, the corresponding loss value is calculated to be optimized; similarly, when a capsule is predicted to match the wrong HRRP sample, i.e., there is no class d in the sample, then Y d ＝0. The above process actually performs the operation of two classifications on each prediction capsule, and simultaneously introduces the parameter lambda to ensure the stability of the network training process.
Reconstruction loss L of decoding process in reconstruction module rec The difference between the input HRRP sample and the reconstruction data is expressed, the Euclidean distance between the input HRRP sample and the reconstruction data is used as reconstruction loss, the loss of the whole capsule network is added to train the parameters of the network, and the expression is as follows:
wherein h is ic Denotes the initial HRRP sample, h ir Representing the reconstruction data, α is a scaling factor and is set to 0.0005, making the capsule classification penalty dominant in the total penalty.
Thus, the capsule network total loss function can be defined by:
the invention has the beneficial effects that:
the invention is inspired by the great progress of a large-scale unsupervised pre-training model in the aspect of learning representation, and provides a method for acquiring consistency general characteristics contained in HRRP samples under different angular domains based on a comparison learning SimSaim module, and the characteristics are applied to different downstream tasks for classification to form a set of general HRRP identification method standards. Meanwhile, data are additionally preprocessed in a pre-training stage to increase the diversity of HRRP samples, the preprocessed model is not limited by a large number of training samples any more, and the model has better recognition performance on a small-scale sample amount through fine adjustment, so that the small sample sensitivity of the HRRP is overcome to a certain extent, and the method has practical significance in practical application.
1. In the invention, the structural diversity of the HRRP sample is increased by adopting a data enhancement mode, and a large number of training samples with rich diversity are provided for comparison learning unsupervised pre-training, so that a better pre-training effect can be obtained on a large Resnet-50, a model learns more effective characteristic information, and the identification performance of migrating to a downstream classification task is improved.
2. The invention adopts an automatic supervision learning method, utilizes the label-free samples to carry out automatic supervision representation learning, fully excavates abstract semantic information in a data set by a contrast learning method, helps a model to learn the label-free data to obtain an encoder, extracts effective general characteristics and applies the effective general characteristics to different downstream tasks. The performance of contrast learning also depends on the depth of the network, the deeper the depth, the stronger the characteristic learning ability, and in addition, the longer the training time of the contrast learning, the performance is also enhanced. By applying a suitable deep network, training mode and optimization method to the contrast learning method, the performance may not be weaker than that of end-to-end supervised learning. Compared with learning as a relatively novel research direction at present, the development of the method in practical engineering application in different fields has immeasurable potential in the future. In terms of the goal of scientific and technological means, unsupervised learning is the trend of artificial intelligence development in the future, compared with supervised learning applied in a large scale, the comparison learning method reduces the investment of time, human resources and other costs, and the performance is not lost in the supervised learning on the premise of improving the efficiency, so that the radar HRRP target identification based on the comparison learning method has higher research prospect and value.
3. The invention applies SimSaim to characterize a learning network, wherein the SimSaim is a characterization learning network with an asymmetric twin structure of a stop-grad mechanism, a predictor is introduced into one branch of a simple twin network, a stop-gard mechanism is introduced into the other branch of the simple twin network, and two asymmetric branch networks are constructed to avoid mode collapse. The module furthest retains meaningful feature information in an original HRRP sample, obtains a feature extractor for extracting HRRP effective consistency information through pre-training learning, and then accesses a downstream classifier to finely adjust parameters of the classifier part, so that the method is beneficial to better learning similarity structure information among different HRRP samples, fully extracts and utilizes the similarity structure information, and achieves a good identification effect.
4. The invention applies a downstream classification module, and after unsupervised pre-training by contrast learning on an extended radar HRRP data set, the output from an encoder and the output obtained by using supervised training have the same general characteristic information, and then fine-tuning (fine-tune) is carried out on the downstream classification module by using the characteristics. By defining different downstream classification modules, various different universal robust models applied to HRRP target recognition can be obtained, and a new thought and a new method are provided for the field of radar HRRP target recognition.
Drawings
FIG. 1: the steps of the radar target identification method based on the comparison learning unsupervised pre-training-fine tuning paradigm are in a flow chart.
FIG. 2 is a schematic diagram of a SimSam module workflow.
Detailed Description
Referring to fig. 1, it is a flowchart of a radar high-resolution range profile recognition technique based on an unsupervised pre-training-fine tuning paradigm of contrast learning, and the specific implementation steps are as follows:
s1: the original HRRP sample set is preprocessed.
Because the intensity of the HRRP is determined by the factors of radar transmitting power, target distance, radar antenna gain, radar receiver gain and the like, before target identification is carried out by using the HRRP, the HRRP is used for identifying the target 2 The intensity normalization method processes the original HRRP echo, thereby improving the intensity sensitivity problem of the HRRP. HRRP is intercepted from the radar echo data through a range window, and the position of the intercepted range image in the range gate is not fixed during the interception process, thereby causing the translational sensitivity of the HRRP. In order to make training and testing have a unified standard, a center-of-gravity alignment method is adopted to eliminate the translational sensitivity.
S1.1: and (6) intensity normalization. Denote the original HRRP as
Wherein L is 1 Representing the total number of range cells contained within the HRRP, the HRRP after intensity normalization can be represented as:
s1.2: the samples are aligned. Translating HRRP to make its gravity center g 1 Move to
Nearby, such that those distance cells in the HRRP that contain information will be distributed near the center. Wherein HRRP center of gravity g 1 The calculation method of (2) is as follows:
after the original HRRP sample is processed by the intensity normalization and gravity center alignment method, the amplitude value is limited between 0 and 1, so that the scale is unified, and the value between 0 and 1 is very favorable for subsequent neural network processing; HRRP echo signals with right or left distribution are adjusted to be near the center point.
S2: the processed HRRP sample is subjected to translation processing to realize data expansion, a large number of training samples with rich diversity are provided for comparison learning unsupervised pre-training, and the generalization capability of the network to new samples is further improved to a certain extent.
In order to avoid overfitting in the pre-training process and obtain important semantic information in HRRP data, the gravity center of each HRRP sample subjected to sensitivity processing is respectively translated to the left and the right by 1 to 4 distance units for data expansion, so that the data volume of unsupervised pre-trained samples can be increased by 8 times on the basis of an original training set, and further the generalization capability of a network to new samples is improved to a certain extent.
And S3, increasing the structural diversity of the HRRP sample by adopting a reshape and data enhancement mode, so that the model learns more effective characteristic information and is beneficial to improving the identification performance of the downstream classification task.
S3.1 first, the radar HRRP sample after data sensitivity preprocessing is still a 1 x 256 one-dimensional vectorData, in order to match the data dimension, increasing the data dimension by using an unscueze () function, and converting the shape of the HRRP sample into a four-dimensional tensor
Then, reshape operation is carried out on the HRRP sample, and the mode of entering the encoder network in the SimSam module at the moment is
Second, data enhancement operations including random clipping, random gaussian blurring, horizontal flipping and scaling are performed on the HRRP samples in 16 × 16 format to increase the structural diversity of the HRRP. And finally, performing normalization operation on the HRRP samples after data enhancement, removing a part of common features by subtracting the mean value from each HRRP sample, highlighting the difference of the features among different samples, facilitating model learning and identification of main features in the HRRP samples, reducing the gradient during reverse propagation, accelerating the convergence of comparison learning pre-training and the learning speed of a network, and increasing the generalization capability.
And S4, inputting the HRRP samples obtained by different data enhancement methods into a SimSamiam module.
The SimDiam module comprises four parts of a random data enhancement module, a backbone network, a projector and a predictor, wherein the backbone network and the projector form an encoder network. The expanded HRRP samples are sampled by different data enhancement methods, then the samples enter an encoder network for encoding, feature matching is carried out by maximizing the consistency among feature vectors from different views of the same HRRP sample, and then the high-quality main feature representation of the HRRP sample is extracted by a projector, which is beneficial to obtaining general consistency representation by a contrast prediction task. And (4) inputting the output characteristics into a predictor, estimating the overall expectation of the SimSaim module, namely optimizing network parameters through back propagation, and filtering partial invalid characteristic information of high layers at the same time, so that the characteristic information in the HRRP sample is fully reserved for carrying out contrast prediction optimization.
S4.1 random data enhancement:
the random data enhancement operation is to generate two different sets of views of each HRRP sample for the self-supervised contrast learning task, that is, the views x' and x ″ for the contrast learning task are obtained by the HRRP samples through two random data enhancements respectively. Different from the output obtained by the input with a label of supervised learning, the self-supervised learning carries out self-supervision in a reasonable mode under the condition that data has no label, a training sample x is divided into an x 'part and an x' part, the x 'is input into a model to obtain an output y, then the y and the x' are compared, the smaller the distance between the x 'and the x' in a certain characteristic space is, the better the y is, one part of the x 'of the data is used as the input, the other part of the x' is used as a supervision signal, and the self-supervised learning is realized.
S4.2, backbone network part:
according to the method, by comparing the influences of the parameters, the calculated amount and the network structure in the networks with different depths on the HRRP data characteristic representation quality and the identification performance, Resnet-50 with strong representation capability, high cost performance and a three-dimensional network structure is finally selected as a backbone network, and the network not only shows good identification performance on an HRRP sample, but also has strong real-time performance, and is very suitable for an identification task of an HRRP target in an actual radar detection environment. ResNet-50 consists of 1 convolutional input layer, 4 residual convolutional blocks, and 1 fully-connected output layer, where the residual convolutional blocks include 16 convolutional blocks, each of which consists of the same number of convolutional layers. The convolution input layer is arranged to reserve semantic information and global feature information of the enhanced HRRP view adjacent features, construct a reasonable spatial relationship and facilitate extraction of the effective features of the HRRP. The residual block is used as a main component of the network, firstly, the dimensionality (ascending or descending) of the convolution layer conversion characteristic of the 1 x 1 convolution kernel is utilized, the number of the convolution kernels influences the output dimensionality of each layer, meanwhile, the number of output parameters is reduced, and the effect of reducing the overall network parameter number is achieved. And extracting effective characteristics by using the convolution layer of the 3 multiplied by 3 convolution kernel, introducing identity mapping to accelerate the flow of the associated information between the deep network layers and fully utilizing the characteristics of each layer, and finally extracting effective and meaningful HRRP characteristic representation to improve the identification performance. Each residual volume block uses a ReLU activation function and a batch normalization unit, so that the generalization capability of the model is improved.
S4.3, projector part:
the core function of the projector is to filter redundant information or irrelevant semantic information in HRRP view feature representation, retain the most dominant nonlinear feature and carry out l on the feature vector 2 Regularization, mapping the regularization to a unit hypersphere space for comparison matching prediction, and maximizing similarity structure information between two HRRP view representations, namely, constraining the consistency degree between vectors in the hypersphere space and the training process of a network, thereby obtaining universal HRRP sample similarity characteristic representation. The deep-layer projector can improve the quality of HRRP feature expression and also can improve the performance of contrast learning, so three linear fully-connected layers (FC) are constructed for the projector, each layer is followed by a BN layer, and the output dimension of the fully-connected layer is 2048. The features output via the backbone network are denoted as y i Output characteristic z of the encoder network i The calculation expression of (a) is as follows:
z i ＝g(y i )＝W (3) σ(W (2) σ(W (1) y i ))
where σ denotes the ReLU activation function, g denotes the projection function, and W denotes the weight matrix for each fully connected layer. The effect of the bias term on the network is ignored for ease of analysis. The existence of BN layer in the projector enables the spatial distribution of each layer output to be readjusted, partial features shared among HRRP samples in each batch are removed, and features with difference are reserved and used for the task of contrast prediction, so that the implicit contrast is performed to a certain extent.
S4.4 predictor part:
the predictor comprises three parts of two full connection layers, a BN layer and an activation layer. Where the input and output dimensions of the first fully-connected layer are 2048 and the output dimension of the second fully-connected layer is 512. Feature vector p output by predictor i The calculation expression is as follows:
p i ＝h(z i )＝W (2) σ(W (1) z i )
where h denotes the prediction function, σ denotes the ReLU activation function, W (1) 、W (2) The weight matrices of the first fully-connected layer and the second fully-connected layer are represented, respectively.
S4.5, the SimSam working mechanism:
the loss of simsim is defined using the EM algorithm, as follows:
wherein
Representing the encoder network for feature extraction, theta is a learnable parameter, x is the HRRP sample,
representing random data enhancement function before HRPP data input, expectation
Representing methods for HRRP sample x and random data enhancement
The distribution of (a), in other words,
equivalent to the sum of loss expectation for all HRRP samples and random data enhancement. Eta x Is a feature expression of HRRP samples x, i.e. a feature vector z of the encoder network output i . The similarity is calculated by Mean Squared Error (MSE), which is very similar to the EM algorithm or K-means algorithm, and the variable θ is a parameter that can be learned in the encoder and can be regarded as a cluster center. Variable eta x Then similar to the corresponding vector of the HRRP sample x (e.g., the one-hot vector of K-means), it is the characterization of the HRRP sample. At the moment, the working mode of the SimSaim is similar to that of a K-means clustering algorithm, one variable is fixed to solve the other variableQuantity, this is the EM iterative algorithm. This translates into the following two subproblems:
where ← represents the assignment operation, and r represents the number of iterative updates of the algorithm. Computing θ in the first sub-problem using a Stochastic Gradient Descent (SGD) algorithm r By equation (4-5-2), stopping the back propagation of the gradient to η r-1 Eta is then r-1 It is a constant in the formula (4-5-2), and if the back propagation of the gradient is not stopped, two variables exist in the formula, so that the solution cannot be realized. The stop-grad operation in simsim is therefore reasonably well interpreted.
Determining theta r After solving, it is substituted into the second sub-problem, where only one variable η exists in equation (4-5-3), the expectation of each HRRP sample x needs to be minimized
Substituting the formula (4-5-1) into the formula (4-5-3), the solution of the second sub-problem is converted into:
transformed according to the desired formula to yield:
in this case, the characteristic representation of a certain HRRP sample x at the time of the r-th iteration update is expected to be obtained from the sample x through random data enhancement.
To do one for these two sub-problemsThe process of sub-SGD optimization solution may be similar to the simsim process. Performing random data enhancement on the transformed second subproblem according to formula (4-5-5)
The formula is as follows:
then substituting into the formula (4-5-2) to obtain:
wherein theta is r Is a solution of the equation of equation (4-5-2),
and
representing two different data enhancement methods acting on a certain HRRP sample, the equation can be regarded as a twin double tower architecture.
We use one SGD optimization in one iteration to reduce the loss, and such a calculation process is similar to the SimSaim optimization process of twin tower architecture with the introduction of stop-grad mechanism. In addition, by increasing the number of SGDs in iterative optimization, the generalization capability and performance of the SimSaim can be improved to a certain extent, and only one-time SGD is used in the method.
Adding a predictor on one side of the branch of the SimDiam module, and defining the predictor as h 1 ，z 1 For the characterization of the HRRP sample, equation (4-5-4) is converted to the desired equation:
h 1 (z 1 )＝E z [z 1 ]＝E T [f(T(x))] (4-5-8)
random enhancement due to direct computation
Expected value of
It is difficult to equate the enhanced expectation to its own expectation for ease of analysis, when the presence of the predictor can compensate for the signature z 1 The gap that is difficult to directly correlate with expectations because sampling using random enhancement methods in several different epochs conforms to a stable uniform distribution that is relatively easy to remember by network learning to characterize z 1 To predict the expected value.
S5, after unsupervised pre-training is carried out on the SimSa-Miam module on the extended radar HRRP sample by adopting contrast learning, the output of the encoder network and the output obtained by utilizing the supervised training have the same general characteristic information, then fine-tuning (fine-tune) is carried out on the output of the encoder network on a downstream classification module, and the output is input into the downstream classification module after shape operation, thus realizing HRRP recognition classification finally.
Selecting a capsule network as a downstream classification module, only finely adjusting and updating parameters in the capsule network during training, obtaining and fixing weight parameters of an encoder network in SimSam through unsupervised pre-training learning, using the encoder network as a feature extraction network, extracting meaningful key features from an HRRP sample, and well transferring the general feature expression to different downstream tasks with extremely strong performance. The characteristic dimension extracted by the encoder network is 2048, namely the vector feature of 1 × 2048, then dimension reduction is carried out through a full connection layer of 2048 × 256 to obtain the feature with the dimension of 256, and the feature is input into the capsule network after shape operation, so that HRRP identification and classification are finally realized.
And S6, reconstructing target data of the correctly classified predicted capsule characteristics of the HRRP sample through a reconstruction module, restoring the target data into initial input, and participating in training.
S6.1 the reconstruction module can be regarded as a decoder, and is used for restoring the prediction capsule characteristics of the HRRP sample correct classification into initial input, namely a vector with 256 output dimensions, and participating in the training of the whole model for assisting in contrasting the result of the HRRP classification. Specifically, a high-grade capsule representation with the maximum unit length in a capsule network prediction capsule layer is taken as a reconstruction target, and reconstructed target data are output through three full-connection layers with activation functions.
S6.2, the radar target identification method based on comparison learning unsupervised pre-training-fine tuning comprises a data preprocessing module, a SimSam module, a downstream classification module and a reconstruction module. Initializing all weights and biases to be trained in the SimSaim module and the downstream classification module, setting training parameters including learning rate, batch _ size and training batch, and training the SimSaim module and the capsule network.
Examples
A training stage:
and S1, collecting a data set, merging HRRP samples collected by the radar according to the types of targets, selecting training samples and testing samples from different data sections for each type of sample, and ensuring that the postures formed by the selected training set samples and the radar cover the postures formed by the testing set samples and the radar in the selection process of the training set and the testing set. The ratio of the number of samples in each target training set to the number of samples in the test set was 7: 3.
S2, preprocessing the sample in the data set extracted by the S1, and the concrete operation steps are as follows:
s2.1: and (6) intensity normalization. Denote the original HRRP as
Wherein L is 1 Representing the total number of range cells contained within the HRRP, the HRRP after intensity normalization can be represented as:
s2.2: the samples are aligned. Translating HRRP to make its gravity center g 1 Move to
Nearby, so that the HRRP includes the messageDistance cells of information are distributed near the center. The calculation method of the HRRP gravity center is as follows:
s3: carrying out reshape and data enhancement processing on the sample, and specifically comprising the following steps:
S3.1-Radar HRRP sample after data sensitivity preprocessing is still 1 x 256 one-dimensional vector data, and in order to match the data dimensions, we increase the data dimensions by using an unscueze () function at the beginning of the experiment, and the shape of the HRRP data is converted into a four-dimensional tensor
Then carrying out reshape operation on the HRRP sample, wherein the form of the encoder network entering the comparison learning module at the moment is
S3.2, secondly, performing data enhancement operation on the HRRP training sample in a 16 × 16 form, wherein the data enhancement operation comprises random clipping, random Gaussian blur, horizontal inversion and scaling to increase the structural diversity of the HRRP. Finally, the clipped and scaled HRRP samples are normalized, and a part of common features are removed by subtracting the mean value from each HRRP sample, so that the feature difference among different samples is highlighted.
S4: and (3) introducing the processed sample into a SimSaim module, and specifically comprising the following steps:
s4.1, inputting the HRRP samples obtained by different data enhancement methods into a SimSamSim module consisting of random data enhancement, a backbone network, a projector and a predictor, entering an encoder for encoding after random data enhancement, performing feature matching by maximizing the consistency of feature vectors from different views of the same HRRP sample, and then entering the projector to extract high-quality main feature representation of the HRRP sample. And transmitting the output characteristics into a predictor to carry out back propagation to optimize network parameters.
S5: and transmitting the output characteristics to a downstream classification module after shape operation, and specifically comprising the following steps:
after unsupervised pre-training is performed on an extended radar HRRP sample by contrast learning, the output from an encoder and the output obtained by using supervised training have the same general characteristic information, fine-tune (fine-tune) is performed on a downstream classification module by using the characteristics, and the HRRP is input into a capsule network after shape operation, so that HRRP identification and classification are finally realized.
S6, constructing a reconstruction module, designing a loss function, and starting training, wherein the method comprises the following specific steps:
s6.1, taking the high-grade capsule with the maximum unit length in the capsule network prediction capsule layer as a reconstruction target, and outputting through three full-connection layers with activation functions to obtain reconstructed target data.
S6.2, designing a loss function. The total loss of the network constructed by the radar target identification method based on the comparison learning unsupervised pre-training-fine tuning is the capsule classification loss L d And reconstruction loss L rec Two-part construction, and loss L d The expression plays a dominant role as follows:
Loss general assembly ＝L d +L rec
The capsule form enables multiple classes to exist simultaneously, so the training process of the capsule network is performed by MarginLoss as a loss function L d The sum of the losses of each predicted capsule is expressed as:
L d ＝Y d max(0,m + -||v d ||) 2 +λ(1-Y d )max(0,||v d ||-m - ) 2
wherein d represents the HRRP target class, Y d Is to represent a class label in training, m + 、m - The fixed hyper-parameters are set to 0.9 and 0.1 respectively, and the lambda is a coefficient for preventing the network from solving local optimum and is set to 0.5. When the predicted capsule matches the correct HRRP sample d during the training process, Y d 1 and the loss is zeroed when the predicted probability of this predicted capsule exceeds 0.9, when the probability is lowCalculating corresponding loss value at 0.9 to optimize; similarly, when a capsule is predicted to match the wrong HRRP sample, i.e., there is no class d in the sample, then Y d 0. The above process actually performs the operation of two classifications on each prediction capsule, and simultaneously introduces the parameter lambda to ensure the stability of the network training process.
Reconstruction loss L of decoding process in reconstruction module rec The difference between the input HRRP sample and the reconstruction data is expressed, the Euclidean distance between the input HRRP sample and the reconstruction data is used as reconstruction loss, the loss of the whole capsule network is added to train the parameters of the network, and the expression is as follows:
wherein h is ic Denotes the initial HRRP sample, h ir Representing the reconstruction data, α is a scaling factor and is set to 0.0005, making the capsule classification penalty dominant in the total penalty.
Thus, the capsule network total loss function can be defined by:
s6.3: initializing a SimSaim module and all weights and biases to be trained in a capsule network, setting training parameters including learning rate, batch _ size and training batch, and starting model training.
And (3) a testing stage:
s7, carrying out preprocessing operations of steps S2 and S3 in a training phase on the test data acquired in S1;
and S8, sending the sample processed by the S7 into a trained SimSaim module and a capsule network for testing to obtain a result, namely, finally classifying the output of the SimSaim through a downstream classification module. HRRP test sample x test The probability corresponding to a kth class radar target in the target set may be calculated as:
where exp (·) denotes an index operation, and c denotes the number of categories.
Testing HRRP sample x by maximum posterior probability test K to maximum target probability 0 The method comprises the following steps:
through the 8 steps, the radar target identification method based on comparison learning unsupervised pre-training-fine tuning provided by the invention can be obtained.
Claims (8)
1. The radar target identification method based on the comparison learning unsupervised pre-training-fine tuning mode is characterized by comprising the following steps of:
s1: preprocessing an original HRRP sample set;
by a 1 2 The intensity normalization method processes the original HRRP echo, thereby improving the intensity sensitivity problem of the HRRP; HRRP is intercepted from radar echo data through a range window, and the position of an intercepted range image in a range gate is not fixed in the intercepting process, so that the translation sensitivity of the HRRP is caused; in order to enable training and testing to have a unified standard, a gravity center alignment method is adopted to eliminate translational sensitivity;
s2: performing translation processing on the processed HRRP sample to realize data expansion;
s3, increasing the structural diversity of the HRRP sample by adopting reshape and data enhancement modes, and enabling the model to learn more effective characteristic information;
s4, inputting HRRP samples obtained by different data enhancement methods into a SimSaim module;
the system comprises a SimSaim module, a coder module and a data processing module, wherein the SimSaim module comprises four parts of a random data enhancement module, a backbone network, a projector and a predictor, wherein the backbone network and the projector form a coder network; the expanded HRRP samples are sampled by different data enhancement methods, then the HRRP samples enter an encoder network for encoding, feature matching is carried out by maximizing the consistency among feature vectors from different views of the same HRRP sample, and then the high-quality main feature representation of the HRRP sample is extracted by a projector, which is beneficial to obtaining general consistency representation by comparing a prediction task; inputting the output characteristics into a predictor, estimating the overall expectation of the SimSam module, namely optimizing network parameters through back propagation, and filtering partial high-level invalid characteristic information to fully reserve the characteristic information in the HRRP sample for comparison prediction optimization;
s5, performing unsupervised pre-training on the SimSam module by adopting contrast learning on an extended radar HRRP sample, enabling the output of the encoder network and the output obtained by using supervised training to have the same general characteristic information, then performing fine adjustment on the output of the encoder network on a downstream classification module, inputting the output into the downstream classification module after shape operation, and finally realizing HRRP identification and classification;
and S6, reconstructing target data of the correctly classified predicted capsule characteristics of the HRRP sample through a reconstruction module, restoring the target data into initial input, and participating in training.
2. The radar target identification method based on the comparative learning unsupervised pre-training-fine tuning formula as claimed in claim 1, wherein the step S1 is detailed as follows:
s1.1: intensity normalization; denote the original HRRP as
Wherein L is 1 Representing the total number of range cells contained within the HRRP, the HRRP after intensity normalization can be expressed as:
s1.2: aligning the samples; translating HRRP to make its gravity center g 1 Move to
Nearby, such that those distance elements in the HRRP that contain information will be distributed near the center; wherein HRRP center of gravity g 1 The calculation method of (2) is as follows:
3. the radar target identification method based on the comparative learning unsupervised pre-training-fine tuning formula as claimed in claim 2, wherein the step S2 is detailed as follows:
in order to avoid overfitting in the pre-training process and obtain important semantic information in HRRP data, the gravity center of each HRRP sample subjected to sensitivity processing is respectively translated to the left and the right by 1 to 4 distance units for data expansion, so that the data volume of unsupervised pre-trained samples can be increased by 8 times on the basis of an original training set, and further the generalization capability of a network to new samples is improved to a certain extent.
4. The radar target identification method based on the comparative learning unsupervised pre-training-fine tuning formula as claimed in claim 3, wherein the step S3 is detailed as follows:
s3.1, firstly, the radar HRRP sample after the data sensitivity preprocessing is still 1 x 256 one-dimensional vector data, in order to match the data dimension, the dimension of the data is increased by using an unscqueeze () function, and the shape of the HRRP sample is converted into a four-dimensional tensor
Then, reshape operation is carried out on the HRRP sample, and the mode of entering the encoder network in the SimSam module at the moment is
Secondly, performing data enhancement operations including random clipping and random Gaussian blur on the HRRP sample in the form of 16 × 16Horizontal flipping and scaling to increase the structural diversity of HRRP; and finally, carrying out normalization operation on the HRRP sample subjected to data enhancement.
5. The radar target identification method based on the comparative learning unsupervised pre-training-fine tuning formula as claimed in claim 4, wherein the step S4 is detailed as follows:
s4.1 random data enhancement:
the random data enhancement operation is to generate two groups of different views of each HRRP sample for the self-supervision contrast learning task, namely the views x 'and x' for the contrast learning task are obtained by the HRRP samples through two random data enhancement respectively;
s4.2, backbone network part:
selecting Resnet-50 as a backbone network, wherein the Resnet-50 is composed of 1 convolution input layer, 4 residual convolution blocks and 1 full-connection output layer, the residual convolution blocks comprise 16 convolution blocks, and each convolution block is composed of convolution layers with the same number; the convolution input layer is arranged for reserving semantic information and global feature information of the enhanced HRRP view adjacent features, constructing a reasonable spatial relationship and being beneficial to extracting the effective features of the HRRP; the residual block is used as the main component of the network, and the dimensionality of the convolution layer conversion characteristic of the 1 multiplied by 1 convolution kernel is firstly utilized; extracting effective characteristics by using convolution layers of a 3 multiplied by 3 convolution kernel, introducing identity mapping to accelerate the flow of the associated information between deep network layers and fully utilizing the characteristics of each layer, and extracting effective and meaningful HRRP characteristics to express so as to improve the identification performance; each residual volume block uses a ReLU activation function and a batch normalization unit, so that the generalization capability of the model is improved;
s4.3, projector part:
the core function of the projector is to filter redundant information or irrelevant semantic information in HRRP view feature representation, retain the most dominant nonlinear feature and carry out l on the feature vector 2 Regularization, and mapping the regularization to a unit hypersphere space for comparison matching prediction to maximize similarity structure information between two HRRP view representations, namely constraintThe consistency degree between vectors in the hypersphere space and the training process of the network are carried out, so that universal HRRP sample similarity characteristic representation is obtained; the deep-layer projector can improve the quality of HRRP characteristic expression and the performance of contrast learning, so that three linear full-connection layers are constructed for the projector, a BN layer is connected behind each layer, and the output dimensionality of each full-connection layer is 2048; the feature output via the backbone network is denoted as y i Output characteristic z of the encoder network i The calculation expression of (a) is as follows:
z i ＝g(y i )＝W (3) σ(W (2) σ(W (1) y i ))
wherein σ denotes a ReLU activation function, g denotes a projection function, and W denotes a weight matrix for each fully-connected layer; the influence of the bias term on the network is ignored for the convenience of analysis; the existence of BN layer in the projector enables the spatial distribution of each layer output to be readjusted, common partial features among HRRP samples in each batch are removed, and the features with difference are reserved and used for the task of comparison and prediction;
s4.4 predictor part:
the predictor comprises three parts, namely a full connection layer, a BN layer and an activation layer; wherein the input dimension and the output dimension of the first fully-connected layer are both 2048 and the output dimension of the second fully-connected layer is 512; feature vector p output by predictor i The calculation expression is as follows:
p i ＝h(z i )＝W (2) σ(W (1) z i )
where h denotes the prediction function, σ denotes the ReLU activation function, W (1) 、W (2) Weight matrices representing a first fully connected layer and a second fully connected layer, respectively;
s4.5, the SimSam working mechanism:
the loss of simsim is defined using the EM algorithm, as follows:
wherein
Representing the encoder network for feature extraction, theta is a learnable parameter, x is the HRRP sample,
representing random data enhancement function before HRPP data input, expectation
Representing methods for HRRP sample x and random data enhancement
The distribution of (a), in other words,
loss expectation sum equivalent to all HRRP samples and random data enhancement; eta x Is a feature expression of HRRP samples x, i.e. a feature vector z of the encoder network output i (ii) a Calculating a similarity using a Mean Square Error (MSE); at the moment, the working mode of the SimSaim is similar to that of a K-means clustering algorithm, one variable is fixed to solve the other variable, and the fixed variable is an EM iterative algorithm; this translates into the following two subproblems:
wherein ← represents the assignment operation, and r represents the number of times of iterative updating of the algorithm; computing theta in the first sub-problem using a stochastic gradient descent SGD algorithm r By equation (4-5-2), stopping the back propagation of the gradient to η r-1 Eta is then r-1 The equation (4-5-2) is a constant, and if the back propagation of the gradient is not stopped, two variables exist in the equation, so that the solution cannot be carried out;
determining theta r After solving, it is substituted into the second sub-problem, where only one variable η exists in equation (4-5-3), the expectation of each HRRP sample x needs to be minimized
Substituting the formula (4-5-1) into the formula (4-5-3), the solution of the second sub-problem is converted into:
transformed according to the desired formula to yield:
the characteristic representation of a certain HRRP sample x at the time of the r-th iteration updating is obtained by the sample x through random data enhancement expectation;
performing random data enhancement on the transformed second subproblem according to formula (4-5-5)
The formula is as follows:
then substituting into the formula (4-5-2) to obtain:
wherein theta is r Is a solution of the equation of equation (4-5-2),
and
representing two different data enhancement methods acting on a certain HRRP sample, the formula can be regarded as a twin double-tower structure;
adding a predictor on one side of the branch of the SimDiam module, and defining the predictor as h 1 ，z 1 For the characterization of the HRRP sample, equation (4-5-4) is converted to the desired equation:
h 1 (z 1 )＝E z [z 1 ]＝E T [f(T(x))] (4-5-8)
random enhancement due to direct computation
Expected value of
It is difficult to equate the enhanced expectation to its own expectation for ease of analysis.
6. The unsupervised pre-training-tuning radar target recognition method based on contrast learning according to claim 5, wherein the step S5 comprises the following detailed steps:
selecting a capsule network as a downstream classification module, only finely adjusting and updating parameters in the capsule network during training, obtaining and fixing weight parameters of an encoder in the SimDual by unsupervised pre-training learning, and extracting meaningful key features from an HRRP sample by using the encoder as a feature extraction network; the characteristic dimension extracted by the encoder network is 2048, namely the vector feature of 1 × 2048, then dimension reduction is carried out through a full connection layer of 2048 × 256 to obtain the feature with the dimension of 256, and the feature is input into the capsule network after shape operation, so that HRRP identification and classification are finally realized.
7. The radar target identification method based on the comparative learning unsupervised pre-training-fine tuning formula as claimed in claim 6, wherein the step S6 is detailed as follows:
s6.1, the reconstruction module can be regarded as a decoder and is used for restoring the prediction capsule characteristics of the HRRP sample correctly classified into initial input, namely, outputting a vector with the dimensionality of 256, participating in the training of the whole model and assisting in contrasting the result of HRRP classification; specifically, a high-grade capsule with the maximum unit length in a capsule network prediction capsule layer is taken as a reconstruction target, and reconstructed target data are output through three full-connection layers with activation functions;
s6.2, the radar target identification method based on comparison learning unsupervised pre-training-fine tuning comprises a data preprocessing module, a SimSam module, a downstream classification module and a reconstruction module; initializing all weights and biases to be trained in the SimSaim module and the downstream classification module, setting training parameters including learning rate, batch _ size and training batch, and training the SimSaim module and the capsule network.
8. The method of claim 7, wherein the total loss of the network constructed by the method is represented by the capsule classification loss L d And reconstruction loss L rec Two-part construction, and loss L d The expression plays a dominant role as follows:
Loss general assembly ＝L d +L rec
The capsule form enables multiple classes to exist simultaneously, so the training process of the capsule network is performed by MarginLoss as a loss function L d The sum of the losses of each predicted capsule is expressed as:
L d ＝Y d max(0,m + -||v d ||) 2 +λ(1-Y d )max(0,||v d ||-m - ) 2
wherein d represents the HRRP target class, Y d Is to represent a class label in training, m + 、m - The fixed hyper-parameters are respectively set to be 0.9 and 0.1, and lambda is a coefficient for preventing the network from solving local optimum and is set to be 0.5; when the predicted capsule matches the correct HRRP sample d during the training process, Y d When the predicted probability of the predicted capsule exceeds 0.9, the loss is set to zero, and when the probability is lower than 0.9, the corresponding loss value is calculated to be optimized; similarly, when a capsule is predicted to match the wrong HRRP sample, i.e., there is no class d in the sample, then Y d 0; the above process actually performs two classification operations on each prediction capsule, and simultaneously introduces the parameter lambda to ensure the stability of the network training process;
reconstruction loss L of decoding process in reconstruction module rec The difference between the input HRRP sample and the reconstruction data is represented, the Euclidean distance between the input HRRP sample and the reconstruction data is taken as the reconstruction loss, the loss of the whole capsule network is added to train the parameters of the network, and the expression is as follows:
wherein h is ic Denotes the initial HRRP sample, h ir Representing the reconstruction data, α is a scaling factor and is set to 0.0005, making the capsule classification penalty dominant in the total penalty;
thus, the capsule network total loss function can be defined by:
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