Multi-dimensional angular flicker characteristic prediction method and system based on transfer learning

Abstract

The invention provides a multi-dimensional angular flicker characteristic prediction method and system based on transfer learning. The method comprises the following steps: step 1, generating source data of a target multi-dimensional angular flicker characteristic according to a known target type and a high-frequency electromagnetic solver; 2, merging the target domain data and the generated source domain data to obtain a total sample data set, and setting weights, prediction error thresholds and maximum iterations of the target domain data and the source domain data; 3, constructing a multi-dimensional angular flicker characteristic prediction neural network structure; 4, training the prediction neural network by using the total sample data set and the weights of the target domain data and the source domain data, and calculating the prediction error of the prediction neural network; 5, adjusting the weights of the target domain data and the source domain data according to the prediction error; and 6, judging whether the prediction error is smaller than a prediction error threshold value or whether the number of iterations reaches the maximum number of iterations, if so, ending the process, and otherwise, repeatedly executing the step 4 and the step 5.

Description

Technical Field

[0001] The present invention relates to the technical field of target characteristic modeling and simulation, and in particular to a multi-dimensional angular glint characteristic prediction method and system based on transfer learning. Background Art

[0002] Angular scintillation characteristics refer to the phenomenon that the direction of the reflected wave of an extended target deviates after being illuminated by the radar, which is usually caused by the distortion of the wavefront of the electromagnetic wave. The angular scintillation characteristics of the extended target will cause the radar observation angle to deviate from the true direction of the target, which will have a serious impact on the radar tracking performance. At the same time, the angular scintillation characteristics of the extended target are related to multi-dimensional variables such as observation angle, frequency, observation distance, and polarization mode. Therefore, in the design and verification process of the radar system, the multi-dimensional angular scintillation characteristics of the extended target need to be accurately reconstructed in order to fully verify the performance of the radar system.

[0003] With the improvement of radar's multi-dimensional perception capability and the increasing diversity of radar target material structures, the requirements for the accuracy and computational efficiency of angular glint characteristics modeling are also higher. The traditional modeling method based on scattering centers requires the radar target to be converted into a set of equivalent scattering centers in advance. This method requires sufficient target structure, material and scattering characteristics information to ensure the accuracy of modeling. In practical applications, only partial information of the target can be obtained. Therefore, it is difficult for this method to accurately model the target angular glint characteristics with only a small amount of scattering characteristic data.

[0004] Patent document CN105182301A discloses a method for calibrating the near-field angular glint of a target under maneuvering rendezvous. It uses the statistical root mean square to calibrate the fluctuation characteristics of the target angular glint in the distance dimension under near-field conditions, and gives a simplified model of the near-field angular glint characteristics of the target by modeling the angular glint fluctuation as a random noise. However, this method does not give an accurate correspondence between the angular glint characteristics and the distance dimension, and does not consider factors such as frequency and observation angle, making it difficult to solve the problem of predicting angular glint characteristics under different frequencies, distances, and angles.

[0005] Patent document CN111581886A discloses a method for rapid electromagnetic field simulation solution based on parallel acceleration of convolutional neural networks. The convolutional neural network is used to accelerate the solution of the matrix equation in the method of moments (MoM), which greatly improves the parallel computing efficiency and shortens the calculation time. However, this method cannot use a small amount of existing high-reliability data (such as field measured data) to improve the calculation accuracy.

[0006] In 2023, Sun Shengkai, He Zi and others published a non-patent article in the Journal of Radio Science titled "Research on Intelligent Generation Network of Target Electromagnetic Characteristics Based on Scattering Center Model", which introduced a far-field electromagnetic prediction network for targets at all angles and wide bandwidths. This method uses information such as the position, frequency, and amplitude of the target scattering center to achieve rapid prediction of the real and imaginary parts of the far-field electric field. This method requires obtaining the structure and material information of the target in advance. The accuracy of the model depends on the extraction results of the scattering center, and there is a certain degree of uncertainty. At the same time, this method cannot improve the prediction accuracy using a small amount of high-credibility data. Summary of the invention

[0007] In view of the defects in the prior art, the object of the present invention is to provide a multi-dimensional angular glint characteristic prediction method and system based on transfer learning.

[0008] The multi-dimensional angular glint characteristic prediction method based on transfer learning provided by the present invention includes:

[0009] Step 1: Generate source data of target multi-dimensional angular scintillation characteristics based on known target types and high-frequency electromagnetic solver;

[0010] Step 2: Merge the target domain data and the generated source domain data to obtain the total sample data set, and set the weights of the target domain data and the source domain data, the prediction error threshold and the maximum number of iterations;

[0011] Step 3: Construct a multi-dimensional angular glint characteristic prediction neural network structure;

[0012] Step 4: Use the total sample data set and the weights of the target domain data and the source domain data to train the prediction neural network, and calculate the prediction error of the prediction neural network;

[0013] Step 5: Adjust the weights of the target domain data and the source domain data according to the prediction error;

[0014] Step 6: Determine whether the prediction error is less than the prediction error threshold or whether the number of iterations reaches the maximum number of iterations. If so, end the process; otherwise, repeat steps 4 and 5.

[0015] Preferably, the step 1 comprises:

[0016] According to the known target type and size information, the target three-dimensional model is constructed, and the frequency, pitch angle, yaw angle, observation distance range and sampling interval information are set. The Poynting vector under different setting conditions is calculated using a high-frequency electromagnetic approximate solver. Let the distance r, pitch angle θ, yaw angle The lower average Poynting vector is S, and the three components of vector S in the spherical coordinate system are S r , S θ , The pitch angle deviation Δθ is calculated by the following formula:

[0017] Δθ=arctan(e θ / r)

[0018]

[0019] Among them, e θ is the pitch angle direction line deviation;

[0020] Similarly, the yaw angle deviation is obtained as follows:

[0021]

[0022]

[0023] in, is the pitch angle direction line deviation.

[0024] Preferably, step 2 comprises:

[0025] Assuming the number of generated source data is m, and the number of target domain data is n, the total sample data set input vector set is in represents the input vector, m+n represents the number of data vectors, the first m input vector samples are source domain dataset samples, the next n input vector samples are target domain dataset samples, Represent the observed distance, observed pitch angle, and observed yaw angle respectively. Each output vector corresponds to a corresponding angular glint characteristic vector. Γ is used to represent the set of output vectors. Then in represents the output vector, Represents the pitch angle error and yaw angle error, then there is the formula:

[0026] f(·):Α→Γ

[0027] Where, f(·) represents the mapping from the input vector set A to the output vector set Γ; let f(x i )=y i , then the input vector is x i When , the output vector is y i , then let Λ={Θ1,Θ2,...,Θ m ,Θ m+1 ,...,Θ m+n} is the training data set, where Θ i ={x i ,y i}, i=1,2,...,m+n is the i-th sample in the training data set. The weight of the training data set in Λ is initialized, and the weight of the i-th sample is calculated by the following formula:

[0028]

[0029] Among them, ω k,i is the weight of the i-th sample in the total sample set at the k-th iteration, and currently k=0.

[0030] Preferably, the step 3 comprises:

[0031] For a given training data set, design a neural network F w , so that it can map the input vector space Α in the data set Λ to the output vector space Γ. The neural network consists of d+1 layers of cascaded fully connected neural networks, and the number of nodes in each layer is m i , i=0,1,...,d, the activation function of each node in the middle layer is σ, σ(·) is the sigmoid activation function, and the connection matrix between the i-th layer and the i+1-th layer is Assuming x is the input vector, the output of the neural network is expressed as: F w (x) = W (d-1)d σ(W (d-2)(d-1) ...σ(W 01 x)).

[0032] Preferably, step 4 comprises:

[0033] The neural network parameters are pre-trained using the data set generated by the electromagnetic solver. First, a loss function is defined. The training process is to find F w The connection matrix W of , makes the loss function minimum, that is:

[0034]

[0035] Where MSE(·) represents the prediction error of the computational model for the i-th sample, subscript k represents the k-th iteration, and subscript i represents the i-th sample in the total sample set;

[0036] Represents the neural network at the kth iteration When the input is the i-th sample x i The output value when W k Represents the value of the neural network connection matrix at the kth iteration;

[0037] According to the above loss function, the connection matrix W is optimized and trained using the Levenberg-Marquardt back-propagation algorithm;

[0038] The step 5 comprises:

[0039] The prediction error of the target domain data set is estimated using the following calculation formula:

[0040]

[0041] Among them, ε k is the prediction error of the prediction model in the target domain in the kth iteration. The weight change coefficient is defined according to the prediction error. The expression is:

[0042]

[0043] According to the weight change coefficient, the sample weight is updated, and the update formula is as follows:

[0044]

[0045] For the weight coefficient ω k+1,i Normalize it so that it satisfies the following formula:

[0046]

[0047] The multi-dimensional angular glint characteristic prediction system based on transfer learning provided by the present invention includes:

[0048] Module M1: Generates source data of target multi-dimensional angular scintillation characteristics based on known target types and high-frequency electromagnetic solver;

[0049] Module M2: Merge the target domain data and the generated source domain data to obtain the total sample data set, and set the weights of the target domain data and the source domain data, the prediction error threshold and the maximum number of iterations;

[0050] Module M3: Constructing a multi-dimensional angular glint characteristic prediction neural network structure;

[0051] Module M4: train the prediction neural network using the total sample data set and the weights of the target domain data and the source domain data, and calculate the prediction error of the prediction neural network;

[0052] Module M5: adjust the weights of target domain data and source domain data according to the prediction error;

[0053] Module M6: Determine whether the prediction error is less than the prediction error threshold or whether the number of iterations reaches the maximum number of iterations. If so, end the process; otherwise, repeatedly trigger module M4 and module M5.

[0054] Preferably, the module M1 comprises:

[0055] According to the known target type and size information, the target three-dimensional model is constructed, and the frequency, pitch angle, yaw angle, observation distance range and sampling interval information are set. The Poynting vector under different setting conditions is calculated using a high-frequency electromagnetic approximate solver. Let the distance r, pitch angle θ, yaw angle The lower average Poynting vector is S, and the three components of vector S in the spherical coordinate system are S r , S θ , The pitch angle deviation Δθ is calculated by the following formula:

[0056] Δθ=arctan(e θ / r)

[0057]

[0058] Among them, e θ is the pitch angle direction line deviation;

[0059] Similarly, the yaw angle deviation is obtained as follows:

[0060]

[0061] in, is the pitch angle direction line deviation.

[0062] Preferably, the module M2 comprises:

[0063] Assuming the number of generated source data is m, and the number of target domain data is n, the total sample data set input vector set is in represents the input vector, m+n represents the number of data vectors, the first m input vector samples are source domain dataset samples, the next n input vector samples are target domain dataset samples, Represent the observed distance, observed pitch angle, and observed yaw angle respectively. Each output vector corresponds to a corresponding angular glint characteristic vector. Γ is used to represent the set of output vectors. Then in represents the output vector, Represents the pitch angle error and yaw angle error, then there is the formula:

[0064] f(·):Α→Γ

[0065] Where, f(·) represents the mapping from the input vector set A to the output vector set Γ; let f(x i )=y i , then the input vector is x i When , the output vector is y i , then let Λ={Θ1,Θ2,...,Θ m ,Θ m+1 ,...,Θ m+n} is the training data set, where Θ i ={x i ,y i}, i=1,2,...,m+n is the i-th sample in the training data set. The weight of the training data set in Λ is initialized, and the weight of the i-th sample is calculated by the following formula:

[0066]

[0067] Among them, ω k,i is the weight of the i-th sample in the total sample set at the k-th iteration, and currently k=0.

[0068] Preferably, the module M3 comprises:

[0069] For a given training data set, design a neural network F w , so that it can map the input vector space Α in the data set Λ to the output vector space Γ. The neural network consists of d+1 layers of cascaded fully connected neural networks, and the number of nodes in each layer is m i , i=0,1,...,d, the activation function of each node in the middle layer is σ, σ(·) is the sigmoid activation function, and the connection matrix between the i-th layer and the i+1-th layer is Assuming x is the input vector, the output of the neural network is expressed as: F w (x) = W (d-1)d σ(W (d-2)(d-1) ...σ(W 01 x)).

[0070] Preferably, the module M4 comprises:

[0071] The neural network parameters are pre-trained using the data set generated by the electromagnetic solver. First, a loss function is defined. The training process is to find F w The connection matrix W of , makes the loss function minimum, that is:

[0072]

[0073] Where MSE(·) represents the prediction error of the computational model for the i-th sample, subscript k represents the k-th iteration, and subscript i represents the i-th sample in the total sample set;

[0074] Represents the neural network at the kth iteration When the input is the i-th sample x i The output value when W k Represents the value of the neural network connection matrix at the kth iteration;

[0075] According to the above loss function, the connection matrix W is optimized and trained using the Levenberg-Marquardt back-propagation algorithm;

[0076] The module M5 comprises:

[0077] The prediction error of the target domain data set is estimated using the following calculation formula:

[0078]

[0079] Among them, ε k is the prediction error of the prediction model in the target domain in the kth iteration. The weight change coefficient is defined according to the prediction error. The expression is:

[0080]

[0081] According to the weight change coefficient, the sample weight is updated, and the update formula is as follows:

[0082]

[0083] For the weight coefficient ω k+1,i Normalize it so that it satisfies the following formula:

[0084]

[0085] Compared with the prior art, the present invention has the following beneficial effects:

[0086] The present invention provides a multi-dimensional angular scintillation characteristic prediction method based on transfer learning. The prediction model is pre-trained by using data generated by an electromagnetic solver, and the model parameters are fine-tuned using a small amount of high-confidence data. This allows the method to accurately predict the changing trend of the angular scintillation characteristics of radar targets at different distances, observation angles, and frequencies when only a small amount of high-confidence measured data is available. This solves the problem of insufficient prediction accuracy of existing angular scintillation modeling methods under multi-dimensional conditions such as distance, frequency, and angle, especially the problem of being unable to construct a multi-dimensional observation model when only a small amount of high-confidence measured data is available. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0088] Figure 1 It is a flow chart for constructing multi-dimensional angular glint characteristics based on transfer learning;

[0089] Figure 2 It is a flow chart for constructing source domain data;

[0090] Figure 3 Multi-dimensional angular glint characteristics prediction neural network structure. DETAILED DESCRIPTION

[0091] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0092] Example 1

[0093] The present invention proposes a multi-dimensional angular glint characteristic prediction method based on transfer learning. The principle and process of the method are as follows: Figure 1 As shown:

[0094] Step 1: Figure 2 As shown, a large amount of target multi-dimensional angular glint characteristic data is generated based on known target type and other information and a high-frequency electromagnetic solver;

[0095] First, a three-dimensional model of the target is constructed based on known target type, size and other information, and the frequency, pitch angle, yaw angle, observation distance range and sampling interval are set. The Poynting vector under different setting conditions is calculated using a high-frequency electromagnetic approximate solver. The lower average Poynting vector is S, and its three components in the spherical coordinate system are S r , S θ , The pitch angle deviation Δθ can be calculated by the following formula:

[0096] Δθ=arctan(e θ / r)

[0097] In the above formula, e θ is the pitch angle direction line deviation, which can be defined as:

[0098]

[0099] Similarly, the yaw angle deviation formula can be obtained as:

[0100]

[0101] In the above formula, is the pitch angle direction line deviation, which can be defined as:

[0102]

[0103] According to the above method, the angular flicker characteristic data at a given distance, pitch angle, yaw angle and frequency can be calculated.

[0104] Step 2: Combine the source domain data generated in step 1 and a small amount of high-confidence target domain data to obtain the total sample data set, and set the initial target domain data weight and source domain data weight, as well as the maximum number of iterations k. max .

[0105] Assume that the number of samples in the source domain dataset generated in step 1 is m, and the number of samples in the high-confidence target domain dataset is n. Then the total dataset input vector set after the source domain dataset and the target domain dataset are merged is: in represents the input vector, m+n represents the number of data vectors, the first m input vector samples are source domain dataset samples, the next n input vector samples are target domain dataset samples, Represent the observed distance, observed pitch angle, and observed yaw angle respectively. Each output vector corresponds to a corresponding angular glint characteristic vector. Using Γ to represent the set of output vectors, then in represents the output vector, represents the pitch angle error and the yaw angle error, then the angular glint characteristic prediction model can be expressed as:

[0106] f(·):Α→Γ

[0107] Where f(·) represents the mapping of the input vector set A to the output vector set Γ. Let f(x i )=y i , then the input vector is x i When , the output vector is y i , then let Λ={Θ1,Θ2,...,Θ m ,Θ m+1 ,...,Θ m+n} is the training data set, where Θ i ={x i ,y i}, i=1,2,...,m+n is the i-th sample in the training data set. The weight of the training data set in Λ is initialized, and the weight of the i-th sample can be calculated as follows:

[0108]

[0109] In the above formula, ω k,i is the weight of the i-th sample in the total sample set at the k-th iteration, and currently k=0.

[0110] Step 3: Design Figure 3 The multi-dimensional angular glint characteristic prediction neural network structure is shown;

[0111] For a given training data set, we need to design a neural network F w, so that it can map the input vector space Α in the data set Λ to the output vector space Γ. Assume that the neural network consists of d+1 layers of cascaded fully connected neural networks, and the number of nodes in each layer is m i , i=0,1,...,d, the activation function of each node in the middle layer is σ, σ(·) is the sigmoid activation function, assuming that the connection matrix between the i-th layer and the i+1-th layer is Assuming x is the input vector, the output of the neural network can be expressed as:

[0112] F w (x) = W (d-1)d σ(W (d-2)(d-1) ...σ(W 01 x))

[0113] Step 4: Use the total sample data and sample weights to train the prediction model designed in step 3, and calculate the prediction error of the prediction model;

[0114] The neural network parameters are pre-trained using the data set generated by the electromagnetic solver. First, a loss function is defined. The training process is to find F w The connection matrix W of , makes the loss function minimum, that is:

[0115]

[0116] In the above formula, MSE(·) represents the prediction error of the computational model for the i-th sample, subscript k represents the k-th iteration, and subscript i represents the i-th sample in the total sample set. According to the above loss function, the connection matrix W is optimized and trained using the Levenberg-Marquardt (LM) backpropagation algorithm. The LM algorithm is an algorithm based on Newton optimization, so there is no need to specify the training rate.

[0117] Step 5: Adjust the target domain data weight and source domain data weight according to the prediction error in step 4;

[0118] According to the prediction model obtained in step 4, the prediction error of the target domain data set can be estimated. The calculation formula is as follows:

[0119]

[0120] In the above formula, ε k is the prediction error of the prediction model in the target domain in the kth iteration. According to the prediction error, the weight change coefficient can be defined according to the following formula:

[0121]

[0122] According to the weight change coefficient, the sample weight can be updated, and the update formula is as follows:

[0123]

[0124] Finally, the weight coefficient ω k+1,i Normalize it so that it satisfies the following formula:

[0125]

[0126] Step 6: Determine whether the number of iterations reaches k max If not, repeat steps 4 and 5.

[0127] Example 2

[0128] The present invention also provides a multi-dimensional angular flicker characteristic prediction system based on transfer learning. The multi-dimensional angular flicker characteristic prediction system based on transfer learning can be realized by executing the process steps of the multi-dimensional angular flicker characteristic prediction method based on transfer learning, that is, technical personnel in this field can understand the multi-dimensional angular flicker characteristic prediction method based on transfer learning as a preferred implementation of the multi-dimensional angular flicker characteristic prediction system based on transfer learning.

[0129] The multi-dimensional angular glint characteristic prediction system based on transfer learning provided by the present invention includes:

[0130] Module M1: Generates source data of target multi-dimensional angular scintillation characteristics based on known target types and high-frequency electromagnetic solver;

[0131] Module M2: Merge the target domain data and the generated source domain data to obtain the total sample data set, and set the weights of the target domain data and the source domain data, the prediction error threshold and the maximum number of iterations;

[0132] Module M3: Constructing a multi-dimensional angular glint characteristic prediction neural network structure;

[0133] Module M4: train the prediction neural network using the total sample data set and the weights of the target domain data and the source domain data, and calculate the prediction error of the prediction neural network;

[0134] Module M5: adjust the weights of target domain data and source domain data according to the prediction error;

[0135] Module M6: Determine whether the prediction error is less than the prediction error threshold or whether the number of iterations reaches the maximum number of iterations. If so, end the process; otherwise, repeatedly trigger module M4 and module M5.

[0136] The module M1 comprises:

[0137] According to the known target type and size information, the target three-dimensional model is constructed, and the frequency, pitch angle, yaw angle, observation distance range and sampling interval information are set. The Poynting vector under different setting conditions is calculated using a high-frequency electromagnetic approximate solver. Let the distance r, pitch angle θ, yaw angle The lower average Poynting vector is S, and the three components of vector S in the spherical coordinate system are S r , S θ , The pitch angle deviation Δθ is calculated by the following formula:

[0138] Δθ=arctan(e θ / r)

[0139]

[0140] Among them, e θ is the pitch angle direction line deviation;

[0141] Similarly, the yaw angle deviation is obtained as follows:

[0142]

[0143] in, is the pitch angle direction line deviation.

[0144] The module M2 comprises:

[0145] Assuming the number of generated source data is m, and the number of target domain data is n, the total sample data set input vector set is in represents the input vector, m+n represents the number of data vectors, the first m input vector samples are source domain dataset samples, the next n input vector samples are target domain dataset samples, Represent the observed distance, observed pitch angle, and observed yaw angle respectively. Each output vector corresponds to a corresponding angular glint characteristic vector. Γ is used to represent the set of output vectors. Then in represents the output vector, Represents the pitch angle error and yaw angle error, then there is the formula:

[0146] f(·):Α→Γ

[0147] Where, f(·) represents the mapping from the input vector set A to the output vector set Γ; let f(x i )=y i , then the input vector is x i When , the output vector is y i , then let Λ={Θ1,Θ2,...,Θ m ,Θ m+1,...,Θ m+n} is the training data set, where Θ i ={x i ,y i}, i=1,2,...,m+n is the i-th sample in the training data set. The weight of the training data set in Λ is initialized, and the weight of the i-th sample is calculated by the following formula:

[0148]

[0149] Among them, ω k,i is the weight of the i-th sample in the total sample set at the k-th iteration, and currently k=0.

[0150] The module M3 comprises:

[0151] For a given training data set, design a neural network F w , so that it can map the input vector space Α in the data set Λ to the output vector space Γ. The neural network consists of d+1 layers of cascaded fully connected neural networks, and the number of nodes in each layer is m i , i=0,1,...,d, the activation function of each node in the middle layer is σ, σ(·) is the sigmoid activation function, and the connection matrix between the i-th layer and the i+1-th layer is Assuming x is the input vector, the output of the neural network is expressed as: F w (x) = W (d-1)d σ(W (d-2)(d-1) ...σ(W 01 x)).

[0152] The module M4 comprises:

[0153] The neural network parameters are pre-trained using the data set generated by the electromagnetic solver. First, a loss function is defined. The training process is to find F w The connection matrix W of , makes the loss function minimum, that is:

[0154]

[0155] Where MSE(·) represents the prediction error of the computational model for the i-th sample, subscript k represents the k-th iteration, and subscript i represents the i-th sample in the total sample set;

[0156] Represents the neural network at the kth iteration When the input is the i-th sample x i The output value when W k Represents the value of the neural network connection matrix at the kth iteration;

[0157] According to the above loss function, the connection matrix W is optimized and trained using the Levenberg-Marquardt back-propagation algorithm;

[0158] The module M5 comprises:

[0159] The prediction error of the target domain data set is estimated using the following calculation formula:

[0160]

[0161] Among them, ε k is the prediction error of the prediction model in the target domain in the kth iteration. The weight change coefficient is defined according to the prediction error. The expression is:

[0162]

[0163] According to the weight change coefficient, the sample weight is updated, and the update formula is as follows:

[0164]

[0165] For the weight coefficient ω k+1,i Normalize it so that it satisfies the following formula:

[0166]

[0167] Those skilled in the art know that, in addition to implementing the system, device and its various modules provided by the present invention in a purely computer-readable program code, it is entirely possible to implement the same program in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers and embedded microcontrollers by logically programming the method steps. Therefore, the system, device and its various modules provided by the present invention can be considered as a hardware component, and the modules included therein for implementing various programs can also be considered as structures within the hardware component; the modules for implementing various functions can also be considered as both software programs for implementing the method and structures within the hardware component.

[0168] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A multi-dimensional angular glint characteristic prediction method based on transfer learning, characterized in that: include: Step 1: Generate source data of target multi-dimensional angular scintillation characteristics based on known target types and high-frequency electromagnetic solver; Step 2: Merge the target domain data and the generated source domain data to obtain the total sample data set, and set the weights of the target domain data and the source domain data, the prediction error threshold and the maximum number of iterations; Step 3: Construct a multi-dimensional angular glint characteristic prediction neural network structure; Step 4: Use the total sample data set and the weights of the target domain data and the source domain data to train the prediction neural network, and calculate the prediction error of the prediction neural network; Step 5: Adjust the weights of the target domain data and the source domain data according to the prediction error; Step 6: Determine whether the prediction error is less than the prediction error threshold or whether the number of iterations reaches the maximum number of iterations. If so, end the process; otherwise, repeat steps 4 and 5.

2. The multi-dimensional angular glint characteristic prediction method based on transfer learning according to claim 1, characterized in that: The step 1 comprises: According to the known target type and size information, the target three-dimensional model is constructed, and the frequency, pitch angle, yaw angle, observation distance range and sampling interval information are set. The Poynting vector under different setting conditions is calculated using a high-frequency electromagnetic approximate solver. Let the distance r, pitch angle θ, yaw angle The lower average Poynting vector is S, and the three components of vector S in the spherical coordinate system are S r , S θ , The pitch angle deviation Δθ is calculated by the following formula: Δθ=arctan(e θ / r) Among them, e θ is the pitch angle direction line deviation; Similarly, the yaw angle deviation is obtained as follows: in, is the pitch angle direction line deviation.

3. The multi-dimensional angular glint characteristic prediction method based on transfer learning according to claim 2, characterized in that: The step 2 comprises: Assuming the number of generated source data is m, and the number of target domain data is n, the total sample data set input vector set is in i=1,2,...,m+n represents the input vector, m+n represents the number of data vectors, the first m input vector samples are source domain data set samples, the next n input vector samples are target domain data set samples, Represent the observed distance, observed pitch angle, and observed yaw angle respectively. Each output vector corresponds to a corresponding angular glint characteristic vector. Γ is used to represent the set of output vectors. Then in represents the output vector, Represents the pitch angle error and yaw angle error, then there is the formula: f(·):Α→Γ Where, f(·) represents the mapping from the input vector set A to the output vector set Γ; let f(x i )=y i , then the input vector is x i When , the output vector is y i , then let Λ={Θ1,Θ2,...,Θ m ,Θ m+1 ,...,Θ m+n } is the training data set, where Θ i ={x i ,y i }, i=1,2,...,m+n is the i-th sample in the training data set. The weight of the training data set in Λ is initialized, and the weight of the i-th sample is calculated by the following formula: Among them, ω k,i is the weight of the i-th sample in the total sample set at the k-th iteration, and currently k=0.

4. The multi-dimensional angular glint characteristic prediction method based on transfer learning according to claim 3 is characterized in that: The step 3 comprises: For a given training data set, design a neural network F w , so that it can map the input vector space Α in the data set Λ to the output vector space Γ. The neural network consists of d+1 layers of cascaded fully connected neural networks, and the number of nodes in each layer is m i , i=0,1,...,d, the activation function of each node in the middle layer is σ, σ(·) is the sigmoid activation function, and the connection matrix between the i-th layer and the i+1-th layer is Assuming x is the input vector, the output of the neural network is expressed as: F w (x) = W (d-1)d σ(W (d-2)(d-1) ...σ(W 01 x)).

5. The multi-dimensional angular glint characteristic prediction method based on transfer learning according to claim 4, characterized in that: The step 4 comprises: The neural network parameters are pre-trained using the data set generated by the electromagnetic solver. First, a loss function is defined. The training process is to find F w The connection matrix W of , makes the loss function minimum, that is: Where MSE(·) represents the prediction error of the computational model for the i-th sample, subscript k represents the k-th iteration, and subscript i represents the i-th sample in the total sample set; Represents the neural network at the kth iteration When the input is the i-th sample x i The output value when W k Represents the value of the neural network connection matrix at the kth iteration; According to the above loss function, the connection matrix W is optimized and trained using the Levenberg-Marquardt back-propagation algorithm; The step 5 comprises: The prediction error of the target domain data set is estimated using the following calculation formula: Among them, ε k is the prediction error of the prediction model in the target domain in the kth iteration. The weight change coefficient is defined according to the prediction error. The expression is: According to the weight change coefficient, the sample weight is updated, and the update formula is as follows: For the weight coefficient ω k+1,i Normalize it so that it satisfies the following formula:

6. A multi-dimensional angular glint characteristic prediction system based on transfer learning, characterized in that: include: Module M1: Generates source data of target multi-dimensional angular scintillation characteristics based on known target types and high-frequency electromagnetic solver; Module M2: Merge the target domain data and the generated source domain data to obtain the total sample data set, and set the weights of the target domain data and the source domain data, the prediction error threshold and the maximum number of iterations; Module M3: Constructing a multi-dimensional angular glint characteristic prediction neural network structure; Module M4: train the prediction neural network using the total sample data set and the weights of the target domain data and the source domain data, and calculate the prediction error of the prediction neural network; Module M5: adjust the weights of target domain data and source domain data according to the prediction error; Module M6: Determine whether the prediction error is less than the prediction error threshold or whether the number of iterations reaches the maximum number of iterations. If so, end the process; otherwise, repeatedly trigger module M4 and module M5.

7. The multi-dimensional angular glint characteristic prediction system based on transfer learning according to claim 6, characterized in that: The module M1 comprises: According to the known target type and size information, the target three-dimensional model is constructed, and the frequency, pitch angle, yaw angle, observation distance range and sampling interval information are set. The Poynting vector under different setting conditions is calculated using a high-frequency electromagnetic approximate solver. Let the distance r, pitch angle θ, yaw angle The lower average Poynting vector is S, and the three components of vector S in the spherical coordinate system are S r , S θ , The pitch angle deviation Δθ is calculated by the following formula: Δθ=arctan(e θ / r) Among them, e θ is the pitch angle direction line deviation; Similarly, the yaw angle deviation is obtained as follows: in, is the pitch angle direction line deviation.

8. The multi-dimensional angular glint characteristic prediction system based on transfer learning according to claim 7, characterized in that: The module M2 comprises: Assuming the number of generated source data is m, and the number of target domain data is n, the total sample data set input vector set is in i=1,2,...,m+n represents the input vector, m+n represents the number of data vectors, the first m input vector samples are source domain data set samples, the next n input vector samples are target domain data set samples, Represent the observed distance, observed pitch angle, and observed yaw angle respectively. Each output vector corresponds to a corresponding angular glint characteristic vector. Γ is used to represent the set of output vectors. Then in represents the output vector, Represents the pitch angle error and yaw angle error, then there is the formula: f(·):Α→Γ Where, f(·) represents the mapping from the input vector set A to the output vector set Γ; let f(x i )=y i , then the input vector is x i When , the output vector is y i , then let Λ={Θ1,Θ2,...,Θ m ,Θ m+1 ,...,Θ m+n } is the training data set, where Θ i ={x i ,y i }, i=1,2,...,m+n is the i-th sample in the training data set. The weight of the training data set in Λ is initialized, and the weight of the i-th sample is calculated by the following formula: Among them, ω k,i is the weight of the i-th sample in the total sample set at the k-th iteration, and currently k=0.

9. The multi-dimensional angular glint characteristic prediction system based on transfer learning according to claim 8, characterized in that: The module M3 comprises: For a given training data set, design a neural network F w , so that it can map the input vector space Α in the data set Λ to the output vector space Γ. The neural network consists of d+1 layers of cascaded fully connected neural networks, and the number of nodes in each layer is m i , i=0,1,...,d, the activation function of each node in the middle layer is σ, σ(·) is the sigmoid activation function, and the connection matrix between the i-th layer and the i+1-th layer is Assuming x is the input vector, the output of the neural network is expressed as: F w (x) = W (d-1)d σ(W (d-2)(d-1) ...σ(W 01 x)).

10. The multi-dimensional angular glint characteristic prediction system based on transfer learning according to claim 9, characterized in that: The module M4 comprises: The neural network parameters are pre-trained using the data set generated by the electromagnetic solver. First, a loss function is defined. The training process is to find F w The connection matrix W of , makes the loss function minimum, that is: Where MSE(·) represents the prediction error of the computational model for the i-th sample, subscript k represents the k-th iteration, and subscript i represents the i-th sample in the total sample set; Represents the neural network at the kth iteration When the input is the i-th sample x i The output value when W k Represents the value of the neural network connection matrix at the kth iteration; According to the above loss function, the connection matrix W is optimized and trained using the Levenberg-Marquardt back-propagation algorithm; The module M5 comprises: The prediction error of the target domain data set is estimated using the following calculation formula: Among them, ε k is the prediction error of the prediction model in the target domain in the kth iteration. The weight change coefficient is defined according to the prediction error. The expression is: According to the weight change coefficient, the sample weight is updated, and the update formula is as follows: For the weight coefficient ω k+1,i Normalize it so that it satisfies the following formula:

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