High-altitude electromagnetic pulse waveform parameter solving method, system, equipment and medium

Abstract

The invention discloses a high-altitude electromagnetic pulse waveform parameter solving method, system and device and a medium. The method comprises the steps that the rapid rise time tr and the pulse width tw of a high-altitude electromagnetic pulse waveform are acquired; the fast rising time tr and the pulse width tw of the high-altitude electromagnetic pulse waveform are input into the trained PINN network, alpha, beta, t1 and t2 are obtained, alpha and beta are parameters representing rising time and falling time, t1 and t2 represent time needed by pulse intensity change, the PINN network is trained by using a sample set obtained through dual-scale probability sampling, and the pulse width tw of the high-altitude electromagnetic pulse waveform is obtained. According to the method, the system, the equipment and the medium, the number of used samples is small, and the solving error is low.

Description

Technical Field

[0001] The invention belongs to the technical field of high-altitude electromagnetic pulse waveforms, and relates to a method, system, equipment and medium for solving high-altitude electromagnetic pulse waveform parameters. Background Art

[0002] Since integrated circuits are widely used in modern electronic systems, the anti-interference ability of electronic systems is severely challenged when facing high-altitude electromagnetic pulses (HEMP). The physical characteristics of HEMP are reflected by the fast rise time t r , pulse width t w and the maximum electric field strength E max The HEMP waveform is usually characterized by the key parameters α, β and E p In the electromagnetic compatibility research and HEMP effect simulation, the accurate mapping between physical quantities and mathematical parameters is crucial to study the stability and reliability of electronic systems in HEMP environment.

[0003] When the mathematical parameters are determined, accurate physical characteristic quantities can be directly obtained by solving nonlinear equations, but actual engineering is the inverse operation of nonlinear equations, such as reconstructing pulse waveforms for numerical calculations, coupling simulations, and effect evaluation. To solve this problem, several numerical methods have been proposed. For example, Mao established t w / t r , βt w and β / α and four auxiliary variables A, B, C and D. However, when the ratio of β / α is different, the four auxiliary variables change significantly, and when β / α, the error increases significantly; Magdowski introduced an approximate closed-form formula. With the help of the least squares method and the Nelder-Mead algorithm, the estimation error of α and β is less than 3.8%. However, these fitting methods rely heavily on the statistical analysis of the data. Wei proposed to use t r and t wThe physical meaning of the equation is converted into four nonlinear equations, and then α and β are solved numerically. However, when the initial solution is not chosen properly, solving these nonlinear equations is prone to fall into local optimality, and it is not easy to implement batch analysis. Artificial neural networks (ANN) have become an important tool for solving challenging nonlinear problems due to their excellent nonlinear characterization capabilities and batch processing capabilities. In the field of HEMP waveform parameter estimation, Zhu was the first to apply neural networks to create a mapping between physical and mathematical parameters, achieving impressive results in both accuracy and efficiency. However, this method requires tens of thousands of training samples, and the estimation error for test samples beyond the range of training samples will increase dramatically, that is, the generalization performance is insufficient. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art and provide a method, system, device and medium for solving high-altitude electromagnetic pulse waveform parameters. The method, system, device and medium use a small number of samples and have a low solution error.

[0005] In order to achieve the above object, the present invention adopts the following technical scheme:

[0006] In one aspect, the present invention provides a method for solving high-altitude electromagnetic pulse waveform parameters, comprising:

[0007] Obtain the rapid rise time t of the high-altitude electromagnetic pulse waveform r and pulse width t w ;

[0008] The rapid rise time t of the high-altitude electromagnetic pulse waveform r and pulse width t w The input is input into the trained PINN network to obtain α, β, t1 and t2, wherein α and β are parameters characterizing the rise time and fall time, t1 and t2 characterize the time required for the pulse intensity change, and the PINN network is trained using a sample set obtained by dual-scale probability sampling.

[0009] The method for solving the high-altitude electromagnetic pulse waveform parameters of the present invention is further improved in that:

[0010] Furthermore, the rapid rise time t of the high-altitude electromagnetic pulse waveform is r and pulse width t w Before inputting into the trained PINN network, it also includes:

[0011] Build PINN network;

[0012] Get a sample set;

[0013] The PINN network is trained and verified using the sample set to obtain a trained PINN network.

[0014] Furthermore, the loss function in the process of training and verifying the PINN network using the sample set is:

[0015] L(θ)=L data (θ)+L physics (θ)

[0016] Among them, θ represents the weight and bias of the network, L data (θ) represents the data-driven loss function, L physics (θ) represents the physics-driven loss function.

[0017] Furthermore, the data-driven loss function is expressed as:

[0018]

[0019] Where N is the total number of training samples, ||·|| represents the Euclidean norm, is the true value of the auxiliary variable of the i-th training sample, and is the corresponding predicted value.

[0020] Furthermore, the physical driven loss function is expressed as:

[0021]

[0022] in,

[0023] t r,i and t w,i is the physical parameter of the input data in the i-th training sample, α i ,β i ,t 1,i ,t 2,i is the network prediction result of the mathematical parameters (α, β) and physical parameters (t1, t2) of the i-th training sample.

[0024] Furthermore, the process of obtaining the sample set is:

[0025] Get the original space (α, β);

[0026] Perform double-scale probability sampling on the original space (α, β) to obtain several samples (α i , β i );

[0027] Each sample (α i , β i) are respectively brought into the nonlinear relationship, and the samples (α i , β i ) corresponds to the physical parameter t 1,i ,t 2,i ,t r,i and t w,i , according to each sample (α i , β i ) and its corresponding physical parameter t 1,i ,t 2,i ,t r,i and t w,i Build a sample set.

[0028] Furthermore, a method combining grid search and five-fold cross validation is adopted to train and verify the PINN network using the sample set.

[0029] In a second aspect of the present invention, the present invention provides a high-altitude electromagnetic pulse waveform parameter solution system, comprising:

[0030] Acquisition module, used to obtain the rapid rise time t of the high-altitude electromagnetic pulse waveform r and pulse width t w ;

[0031] A solution module is used to calculate the rapid rise time t of the high-altitude electromagnetic pulse waveform r and pulse width t w The input is input into the trained PINN network to obtain α, β, t1 and t2, wherein α and β are parameters characterizing the rise time and fall time, t1 and t2 characterize the time required for the pulse intensity change, and the PINN network is trained using a sample set obtained by dual-scale probability sampling.

[0032] In a third aspect of the present invention, a computer device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method for solving the high-altitude electromagnetic pulse waveform parameters when executing the computer program.

[0033] In a fourth aspect of the present invention, the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method for solving the high-altitude electromagnetic pulse waveform parameters are implemented.

[0034] The present invention has the following beneficial effects:

[0035] In the specific operation of the method, system, device and medium for solving the high-altitude electromagnetic pulse waveform parameters described in the present invention, the PINN network is trained using the sample set obtained by dual-scale probability sampling, and the problem of uneven sampling distribution is solved by dual-scale probability sampling. More representative samples are obtained under the condition of limited data volume to reduce the number of training samples. At the same time, the present invention uses the rapid rise time t of the high-altitude electromagnetic pulse waveform r and pulse width t w Input into the trained PINN network to obtain α, β, t1 and t2, and solve based on the PINN network. According to the physical constraints followed by the mathematical parameters, the input layer of the artificial neural network is designed to reduce the error of the solution, which is extremely practical. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The accompanying drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the accompanying drawings:

[0037] Figure 1 It is a schematic diagram of the double exponential pulse waveform and physical characterization quantity;

[0038] Figure 2 This is a diagram of the PINN network structure proposed by the present invention;

[0039] Figure 3 Scatter plot of 100 samples obtained using double-scale probability sampling within the range of α and β: (a) represents (b) indicates

[0040] Figure 4 Scatter plot of 10,000 samples obtained using double-scale probability sampling within the range of α and β: (a) represents (b) indicates

[0041] Figure 5 The scatter plot of 100 samples obtained by uniform sampling within the range of α and β: (a) represents (b) indicates

[0042] Figure 6 The scatter plot of 1,000,000 samples obtained using uniform sampling within the range of α and β: (a) represents (b) indicates

[0043] Figure 7 Relative error diagram of PINN network and traditional ANN network;

[0044] Figure 8 This is a graph verifying the generalization performance of the PINN network. DETAILED DESCRIPTION

[0045] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is only an embodiment of a part of the present invention, not all embodiments, and is not intended to limit the scope of the present invention. In addition, in the following description, the description of well-known structures and technologies is omitted to avoid unnecessary confusion of the concepts disclosed in the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work should fall within the scope of protection of the present invention.

[0046] The accompanying drawings show schematic diagrams of structures according to the disclosed embodiments of the present invention. These figures are not drawn to scale, and some details are magnified and some details may be omitted for the purpose of clear expression. The shapes of various regions and layers shown in the figures and the relative sizes and positional relationships therebetween are only exemplary, and may deviate in practice due to manufacturing tolerances or technical limitations, and those skilled in the art may additionally design regions / layers with different shapes, sizes, and relative positions according to actual needs.

[0047] Embodiment 1

[0048] refer to Figure 1 The method for solving the high-altitude electromagnetic pulse waveform parameters of the present invention comprises the following steps:

[0049] 1) Based on the mathematical expression of high altitude electromagnetic pulse (HEMP) and the meaning of the physical parameters of the pulse waveform, a model including the physical parameters t is established. r ,t w And the nonlinear relationship between mathematical parameters α and β.

[0050] The mathematical expression of the high altitude electromagnetic pulse (HEMP) is:

[0051] E(t)=kE p (e -αt -e -βt )

[0052] Among them, α and β are parameters that characterize the rise time and fall time, and k is to ensure E max =E p The relationship between the correction factor k and the parameters α and β is:

[0053]

[0054] Among them, E pis the peak value of the pulse. In practical applications, E p Determined by direct measurement or based on simulated requirements.

[0055] Figure 1 is a typical pulse waveform, t p Indicates the time when the pulse intensity reaches its peak value, the pulse rise time t r Indicates pulse intensity from 0.1E p (t1) increases to 0.9E p (t3) The time required. Pulse width t w The instantaneous value before and after the pulse is 0.5E p The time interval between (t2 and t5). r and t w The physical meaning of is expressed by mathematical expression, and the physical parameter t r ,t w And the nonlinear equations of mathematical parameters α, β:

[0056]

[0057] 2) Design the network structure.

[0058] Based on the basic structure of the ANN network, the network structure is optimized in combination with physical priors, the input layer and output layer are improved, and the loss function is designed to obtain the neural network PINN combined with physical priors.

[0059] The PINN neural network is a neural network composed of three hidden layers, and the neuron counts of each hidden layer are 32, 32 and 4 respectively. The activation function used in the first two hidden layers is the scaled exponential linear unit, which is used to induce self-normalization characteristics to avoid gradient vanishing and explosion. The input information of the PINN network is the fast rise time t r and pulse width t w , the output information is α, β, t1 and t2, the input information and output information of the PINN network satisfy:

[0060]

[0061] In addition, in order to avoid the problem of gradient imbalance, the input layer and output layer of the PINN network are improved. Specifically, for the input layer, not only the input fast rise time t r and pulse width t w interface, and for fast rise times t r and pulse width t w Perform logarithmic operations, namely:

[0062]

[0063] For the output layer, a nonlinear transformation is introduced, namely:

[0064]

[0065] in, and are the intermediate scalars corresponding to α, β, t1 and t2 respectively.

[0066] The loss function of the PINN network consists of two parts: data-driven loss function and physical-driven loss function, namely:

[0067] L(θ)=L data (θ)+L physics (θ)

[0068] Among them, θ represents the weight and bias of the network.

[0069] The present invention adopts the mean square error (MSE) loss function as the data-driven loss, namely:

[0070]

[0071] Where N is the total number of training samples, ||·|| represents the Euclidean norm, is the true value of the auxiliary variable of the i-th training sample, and is the corresponding predicted value.

[0072] The physics-driven loss quantifies the difference between the model predictions and the residuals of known physical equations, ensuring that the model predictions follow the laws of physics, namely:

[0073]

[0074] in, t r,i and t w,i is the physical parameter of the i-th training sample (input), α i ,β i ,t 1,i ,t 2,i is the network prediction result of the mathematical parameters (α, β) and physical parameters (t1, t2) of the i-th training sample (output).

[0075] 3) Construct a sample set. Specifically, a dual-scale probability sampling is proposed. In α∈[1.0×10 6 ,5.0×10 7 ] and β∈[6.0×10 7 ,3.0×10 9 ] range to obtain data.

[0076] The specific steps of the dual-scale probability sampling are:

[0077] 31) Convert the original space (α, β) to the natural logarithmic space Right now and and will The enclosed area is divided into 1,000,000 sub-areas. For the sake of distinction, the corresponding sub-areas in the original space are called original sub-areas.

[0078] 32) According to Calculate the probability that the sample falls into each sub-region, where is the center of the i-th original sub-region, and the probability interval corresponding to each sub-region is obtained, that is,

[0079] 33) Generate N random numbers in the range [0,1], and determine the sub-region where the N samples are located according to the probability interval of the N random numbers.

[0080] 34) Take samples within the determined sub-areas.

[0081] Assume that the i-th sample (α i , β i ) falls in the jth sub-region, then in, is the center of the jth subregion, ξ and η are independent random variables uniformly distributed in the interval (0,1), and The sub-regions are and Length.

[0082] 35) Solve the nonlinear relationship in step 1) and obtain the physical parameter t 1,i ,t 2,i ,t r,i and t w,i , and then get the final sample set {(t r,i ,t w,i ,α i ,β i ,t 1,i ,t 2,i )|i=1,...,N}.

[0083] 4) Using the sample set obtained in step 3), the PINN network obtained in step 2) is trained and verified to obtain a trained PINN network.

[0084] The process of training the PINN network obtained in step 2) using the sample set obtained in step 3) is as follows:

[0085] First, the He method is used for initialization, and then the Adam optimizer is used to optimize under the supervision of the training samples to minimize the loss function. Considering that the setting of hyperparameters (including learning rate and training time) has a great influence on the learning effect of the network, especially when the training data is sparsely sampled, a combination of grid search and five-fold cross validation is used to find the optimal hyperparameters. It should be noted that during the hyperparameter optimization process, the maximum number of training rounds of the network is set to 20,000, but in order to prevent overfitting and obtain the optimal number of training rounds, the early stopping method is also used.

[0086] After training, a trained PINN network is finally obtained. The trained PINN network can convert (t r ,t w ) is converted to (α, β). The solution process includes: p (θ) is supervised by the network parameter θ until it is less than a given threshold. The threshold is set to 3e-12. It should be noted that the learning rate used during fine-tuning is one tenth of the learning rate used during training.

[0087] Simulation experiment

[0088] The present invention designs the input layer of the artificial neural network according to the physical constraints followed by the mathematical parameters, and sets the rapid rise time t r and pulse width t w The explicit interpretation of is incorporated into the loss function as a physical constraint, thereby strictly supervising the optimization process of the ANN. The proposed dual-scale probability sampling solves the problem of uneven sampling distribution and obtains more representative samples when the amount of data is limited. By utilizing the interdisciplinary advantages of ANN and physical priors, the present invention enables physical parameters to be converted into mathematical parameters of the double exponential function with high precision when the sample size is small, and the generalization performance of the model is higher than that of traditional neural networks. The following analysis is conducted from three aspects: sampling method comparison, accuracy comparison, and generalization performance comparison:

[0089] The dual-scale probability sampling is in α∈[1.0×10 6 ,5.0×10 7 ] and β∈[6.0×10 7 ,3.0×10 9 The results of sampling 100 samples within the range are as follows Figure 3 As shown, the results of sampling 10,000 samples are as follows Figure 4 Compared with the case where 100 samples and 100,000 samples are obtained by uniform sampling, as shown in Figure 5 and Figure 6. It can be seen that the uniformly sampled samples are mainly concentrated in the lower left corner area, and only a small number of samples are sparsely distributed in the upper right corner area. When the number of samples is relatively small, a large blank area will appear in the upper right corner, that is, there are no samples. Such data distribution is not conducive to the training and verification of neural networks. The distribution of samples obtained by the dual-scale probability sampling described in the present invention in the input variable space shows significantly improved uniformity, and therefore has higher representativeness when the amount of data is equivalent.

[0090] The performance of the proposed PINN network and the traditional ANN network in solving HEMP is compared on the training set, such as Figure 7 As shown in Figure 2, it can be clearly seen that the relative error distribution of the PINN network is closely concentrated around 0, while the relative error distribution width of the ANN network is wider. Quantitatively compare the differences between the two, among which, represents the predicted values ​​of α and β, and y represents the true values ​​of α and β. The mean relative errors of α and β obtained by the PINN network are only -0.00071 and 0.00087, and the variances are 0.00008 and 0.00012, respectively. The mean relative errors of α and β obtained by the ANN network are 0.02205 and 0.04434, and the variances are 0.02199 and 0.06672, respectively.

[0091] In order to verify the generalization performance, in addition to verifying the electromagnetic pulse waves within the two training sample ranges of the IEC61000-2-9 standard and the Bell Laboratory standard, we also selected samples outside the other two training ranges for verification. The estimation results are shown in Table 1. It can be seen that the relative error of the PINN network is very small, while the relative error of the ANN network is large. The corresponding pulse waveform is as follows Figure 8 As shown, it can be seen that the results of the PINN network match the standard waveform well, while the results estimated by the ANN network have obvious deviations, which fully demonstrates that the PINN network has good generalization performance.

[0092] Table 1

[0093]

[0094] Embodiment 2

[0095] The high-altitude electromagnetic pulse waveform parameter solving system of the present invention comprises:

[0096] Acquisition module, used to obtain the rapid rise time t of the high-altitude electromagnetic pulse waveform r and pulse width t w ;

[0097] A solution module is used to calculate the rapid rise time t of the high-altitude electromagnetic pulse waveformr and pulse width t w The input is input into the trained PINN network to obtain α, β, t1 and t2, wherein α and β are parameters characterizing the rise time and fall time, t1 and t2 characterize the time required for the pulse intensity change, and the PINN network is trained using a sample set obtained by dual-scale probability sampling.

[0098] As an embodiment of the present invention, the rapid rise time t of the high-altitude electromagnetic pulse waveform is r and pulse width t w Before inputting into the trained PINN network, it also includes:

[0099] Build PINN network;

[0100] Get a sample set;

[0101] The PINN network is trained and verified using the sample set to obtain a trained PINN network.

[0102] As an implementation manner of the present invention, the loss function in the process of training and verifying the PINN network using the sample set is:

[0103] L(θ)=L data (θ)+L physics (θ)

[0104] Among them, θ represents the weight and bias of the network, L data (θ) represents the data-driven loss function, L physics (θ) represents the physics-driven loss function.

[0105] As an implementation mode of the present invention, the data-driven loss function is expressed as:

[0106]

[0107] Where N is the total number of training samples, ||·|| represents the Euclidean norm, is the true value of the auxiliary variable of the i-th training sample, and is the corresponding predicted value.

[0108] As an embodiment of the present invention, the physical driven loss function is expressed as:

[0109]

[0110] in,

[0111] t r,i and tw,i is the physical parameter of the input data in the i-th training sample, α i ,β i ,t 1,i ,t 2,i is the network prediction result of the mathematical parameters (α, β) and physical parameters (t1, t2) of the i-th training sample.

[0112] As an implementation manner of the present invention, the process of obtaining the sample set is:

[0113] Get the original space (α, β);

[0114] Perform double-scale probability sampling on the original space (α, β) to obtain several samples (α i , β i );

[0115] Each sample (α i , β i ) are respectively brought into the nonlinear relationship, and the samples (α i , β i ) corresponds to the physical parameter t 1,i ,t 2,i ,t r,i and t w,i , according to each sample (α i , β i ) and its corresponding physical parameter t 1,i ,t 2,i ,t r,i and t w,i Build a sample set.

[0116] As an implementation mode of the present invention, a method combining grid search and five-fold cross validation is adopted to train and validate the PINN network using the sample set.

[0117] The division of modules in the embodiments of the present application is schematic and is only a logical function division. There may be other division methods in actual implementation. In addition, each functional module in each embodiment of the present application may be integrated into a processor, or may exist physically separately, or two or more modules may be integrated into one module. The above-mentioned integrated modules may be implemented in the form of hardware or in the form of software functional modules.

[0118] Embodiment 3

[0119] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the method for solving the high-altitude electromagnetic pulse waveform parameters are implemented, for example, including: constructing a PINN network; obtaining a sample set; using the sample set to train and verify the PINN network to obtain a trained PINN network; obtaining a fast rise time t of the high-altitude electromagnetic pulse waveform r and pulse width t w ; The rapid rise time t of the high-altitude electromagnetic pulse waveform r and pulse width t w The input is input into the trained PINN network to obtain α, β, t1 and t2, wherein α and β are parameters representing the rise time and the fall time, and t1 and t2 represent the time required for the pulse intensity change. The PINN network is trained using a sample set obtained by double-scale probability sampling. The process of obtaining the sample set is: obtaining the original space (α, β); performing double-scale probability sampling on the original space (α, β) to obtain a number of samples (α i , β i ); each sample (α i , β i ) are respectively brought into the nonlinear relationship, and the samples (α i , β i ) corresponds to the physical parameter t 1,i ,t 2,i ,t r,i and t w,i , according to each sample (α i , β i ) and its corresponding physical parameter t 1,i ,t 2,i ,t r,i and t w,i Construct a sample set. The memory may include a memory, such as a high-speed random access memory, and may also include a non-volatile memory, such as at least one disk memory, etc. The processor, the network interface, and the memory are interconnected through an internal bus, and the internal bus may be an industrial standard architecture bus, a peripheral component interconnection standard bus, an extended industrial standard structure bus, etc. The bus may be divided into an address bus, a data bus, a control bus, etc. The memory is used to store programs. Specifically, the program may include a program code, and the program code includes computer operation instructions. The memory may include a memory and a non-volatile memory, and provide instructions and data to the processor.

[0120] Embodiment 4

[0121] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the steps of the method for solving the high-altitude electromagnetic pulse waveform parameters are implemented, for example, including: constructing a PINN network; obtaining a sample set; using the sample set to train and verify the PINN network to obtain a trained PINN network; obtaining a fast rise time t of the high-altitude electromagnetic pulse waveform r and pulse width t w ; The rapid rise time t of the high-altitude electromagnetic pulse waveform r and pulse width t w The input is input into the trained PINN network to obtain α, β, t1 and t2, wherein α and β are parameters representing the rise time and the fall time, and t1 and t2 represent the time required for the pulse intensity change. The PINN network is trained using a sample set obtained by double-scale probability sampling. The process of obtaining the sample set is: obtaining the original space (α, β); performing double-scale probability sampling on the original space (α, β) to obtain a number of samples (α i , β i ); each sample (α i , β i ) are respectively brought into the nonlinear relationship, and the samples (α i , β i ) corresponds to the physical parameter t 1,i ,t 2,i ,t r,i and t w,i , according to each sample (α i , β i ) and its corresponding physical parameter t 1,i ,t 2,i ,t r,i and t w,i Construct a sample set. Specifically, the computer-readable storage medium includes, but is not limited to, for example, a volatile memory and / or a non-volatile memory. The volatile memory may include a random access memory (RAM) and / or a cache memory (cache), etc. The non-volatile memory may include a read-only memory (ROM), a hard disk, a flash memory, an optical disk, a magnetic disk, etc.

[0122] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0123] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0124] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0125] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0126] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for solving high-altitude electromagnetic pulse waveform parameters, characterized in that: include: Obtain the rapid rise time t of the high-altitude electromagnetic pulse waveform r and pulse width t w ; The rapid rise time t of the high-altitude electromagnetic pulse waveform r and pulse width t w The input is input into the trained PINN network to obtain α, β, t1 and t2, wherein α and β are parameters characterizing the rise time and fall time, t1 and t2 characterize the time required for the pulse intensity change, and the PINN network is trained using a sample set obtained by dual-scale probability sampling.

2. The method for solving the high-altitude electromagnetic pulse waveform parameters according to claim 1 is characterized in that: The rapid rise time t of the high-altitude electromagnetic pulse waveform r and pulse width t w Before inputting into the trained PINN network, it also includes: Build PINN network; Get a sample set; The PINN network is trained and verified using the sample set to obtain a trained PINN network.

3. The method for solving the high-altitude electromagnetic pulse waveform parameters according to claim 2 is characterized in that: The loss function in the process of training and verifying the PINN network using the sample set is: L(θ)=L data (θ)+L physics (i) Among them, θ represents the weight and bias of the network, L data (θ) represents the data-driven loss function, L physics (θ) represents the physics-driven loss function.

4. The method for solving the high-altitude electromagnetic pulse waveform parameters according to claim 3 is characterized in that: The data-driven loss function is expressed as: Where N is the total number of training samples, ||·|| represents the Euclidean norm, is the true value of the auxiliary variable of the i-th training sample, and is the corresponding predicted value.

5. The method for solving the high-altitude electromagnetic pulse waveform parameters according to claim 3 is characterized in that: The physics-driven loss function is expressed as: in, t r，i and t w，i is the physical parameter of the input data in the i-th training sample, α i , β i , t 1，i , t 2，i is the network prediction result of the mathematical parameters (α, β) and physical parameters (t1, t2) of the i-th training sample.

6. The method for solving the high-altitude electromagnetic pulse waveform parameters according to claim 2 is characterized in that: The process of obtaining the sample set is as follows: Get the original space (α, β); Perform double-scale probability sampling on the original space (α, β) to obtain several samples (α i , β i ); Each sample (α i , β i ) are respectively brought into the nonlinear relationship, and the samples (α i , β i ) corresponds to the physical parameter t 1，i , t 2，i , t r，i and t w，i , according to each sample (α i , β i ) and its corresponding physical parameter t 1，i , t 2，i , t r，i and t w，i Build a sample set.

7. The method for solving the high-altitude electromagnetic pulse waveform parameters according to claim 2 is characterized in that: The PINN network is trained and validated using the sample set by combining grid search and five-fold cross validation.

8. A high-altitude electromagnetic pulse waveform parameter solution system, characterized in that: include: Acquisition module, used to obtain the rapid rise time t of the high-altitude electromagnetic pulse waveform r and pulse width t w ; A solution module is used to calculate the rapid rise time t of the high-altitude electromagnetic pulse waveform r and pulse width t w The input is input into the trained PINN network to obtain α, β, t1 and t2, wherein α and β are parameters characterizing the rise time and fall time, t1 and t2 characterize the time required for the pulse intensity change, and the PINN network is trained using a sample set obtained by dual-scale probability sampling.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method for solving the high-altitude electromagnetic pulse waveform parameters as described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method for solving the high-altitude electromagnetic pulse waveform parameters as described in any one of claims 1 to 7 are implemented.

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