HEMP double-exponential function parameter estimation method based on neural network

Abstract

The invention relates to an HEMP double-exponential function parameter estimation method based on a neural network, belongs to the technical field of electromagnetic compatibility, and solves the technical problem of low HEMP double-exponential function parameter estimation precision. The estimation method comprises the steps of establishing samples corresponding to HEMP physical parameters and mathematical parameters, setting input parameters of the neural network, setting output parameters of the neural network, training data of the neural network and estimating parameters of a double-exponential function. The method is used for HEMP numerical simulation and HEMP simulator design.

Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic compatibility, and particularly relates to a method for estimating the parameters of a HEMP double-exponential function based on a neural network. Background Art

[0002] High-altitude electromagnetic pulse (HEMP) has the characteristics of high field strength (up to dozens of kV / m), wide frequency spectrum (0 to hundreds of MHz), and wide action range (up to the order of thousands of kilometers). It can cause damage to electronic and electrical equipment over a large area, leading to large-scale failures of national critical infrastructures such as power and communication systems, which is directly related to the national economy and national security. Since 2004, the United States has listed the harm of HEMP to national critical infrastructures as one of the factors that can threaten the national security of the United States.

[0003] The standards and published works related to HEMP generally use a double-exponential function to describe the typical time-domain waveform of HEMP. In the numerical simulation of HEMP effects and the design of HEMP simulators, double-exponential functions with different parameters are used as reference objects. Physically, HEMP can be characterized by physical parameters (rise time t r , pulse width t w , and pulse peak E p ). The double-exponential function can be described by mathematical parameters α, β, and E p . For the HEMP time-domain waveform, the faster the rise time t r , the higher the high-frequency components contained in the electromagnetic pulse; the pulse width t w and the pulse peak E p determine the energy of the electromagnetic pulse. Therefore, the rise time t r , the pulse width t w , and the pulse peak E p are important physical characteristics of HEMP and are also the key physical parameters for studying the electromagnetic effects of HEMP. In addition, the rise time t r , the pulse width t w , and the pulse peak E p are the key indicators for designing HEMP simulators. Constructing a double-exponential time-domain waveform based on these physical parameters is an important aspect of simulator design. In practical engineering, especially in numerical simulations of problems such as the radiation, propagation, and coupling of HEMP, there are often situations where only physical parameters such as the pulse peak, rise time, and pulse width are given, and the mathematical parameters of the double-exponential function are not given. At this time, it is necessary to convert these physical parameters into the mathematical parameters of the double-exponential function. The accurate conversion between HEMP physical parameters and double-exponential function mathematical parameters is crucial for electromagnetic compatibility research and HEMP effect simulation.

[0004] At present, it is relatively easy to derive the physical parameters of the rise time \(t\) r and the pulse width \(t\) w from the mathematical parameters \(\alpha\) and \(\beta\) of the double-exponential function. In practical engineering applications, its inverse problem, converting from physical parameters to mathematical parameters, is very challenging. Calculating the mathematical parameters (\(\alpha\) and \(\beta\)) from the physical parameters (rise time \(t\) r and pulse width \(t\) w ) often requires piecing together by experience because the equation has no simple analytical solution, which is time-consuming and cannot guarantee the accuracy of the fitting curve. Due to the strong non-linear relationship between physical parameters and mathematical parameters, directly using artificial neural network methods to process these parameters will have certain limitations, facing problems of low accuracy and weak generalization ability. SUMMARY OF THE INVENTION

[0005] In order to overcome the deficiencies of time-consuming calculation and low accuracy when converting HEMP waveforms from physical parameters to mathematical parameters, the present invention proposes a method for estimating HEMP double-exponential function parameters based on a neural network.

[0006] The technical solution adopted by the present invention to solve its technical problems is as follows:

[0007] A method for estimating HEMP double-exponential function parameters based on a neural network, comprising the following steps:

[0008] Step 1, establishing samples corresponding to HEMP physical parameters and mathematical parameters

[0009] The HEMP physical parameters are the rise time \(t\) of the HEMP simulator r and the pulse width \(t\) w , and the mathematical parameters are the mathematical parameter \(\alpha\) and the mathematical parameter \(\beta\).

[0010] Taking the rise time \(t\) of the HEMP simulator r and the pulse width \(t\) w , the mathematical parameter \(\alpha\) and the mathematical parameter \(\beta\) as data, establishing samples corresponding to the rise time \(t\) r and the pulse width \(t\) w , the mathematical parameter \(\alpha\) and the mathematical parameter \(\beta\).

[0011] Step 2, setting the input parameters of the neural network

[0012] Setting the reciprocal of the rise time \(t\) of the HEMP simulator r and the reciprocal of the pulse width \(t\) w as the input parameters of the neural network.

[0013] Step 3, setting the output parameters of the neural network

[0014] Set the output parameters of the neural network as mathematical parameter α and mathematical parameter β, and the constraint condition is: 0 < 2α < β.

[0015] Step 4, Neural network training data

[0016] Take the reciprocal of the rise time t of the HEMP simulator r of pulse width t w of and the sample data of mathematical parameter α and mathematical parameter β are provided to the neural network for neural network training. After the training is completed, the trained neural network is obtained.

[0017] Step 5, Double-exponential function parameter estimation

[0018] For a given HEMP simulator, input its rise time t r and pulse width t w to the trained neural network. The trained neural network outputs mathematical parameters, and the mathematical parameters are double-exponential function parameters, thereby obtaining the double-exponential function parameters of the given HEMP simulator.

[0019] In the above HEMP double-exponential function parameter estimation method, the selection range of the mathematical parameter α is [10 6 , 5×10 7 , and the selection range of the mathematical parameter β is [10 8 , 10 9 .

[0020] In the above HEMP double-exponential function parameter estimation method, the sampling points of the mathematical parameter α of the HEMP simulator are 1001, the sampling points of the mathematical parameter β are 1001, the number of training set samples is 801600, and the number of test set samples is 200401.

[0021] The HEMP physical parameter is a double-exponential waveform, the rise time t r = 2.054383×10 -9 s, and the pulse width t w = 5.721758×10 -8 s.

[0022] The obtained double-exponential function parameters of the HEMP simulator are: mathematical parameter α = 1.330227×10 7 , mathematical parameter β = 9.143485×10 8 .

[0023] The beneficial effects of the present invention are:

[0024] A method for estimating the parameters of the HEMP double-exponential function based on a neural network improves the accuracy of mathematical parameter estimation with high precision by means of the neural network; it reduces the processing time of the traditional method and improves the efficiency of mathematical parameter estimation, featuring high efficiency.

[0025] A method for estimating the parameters of the HEMP double-exponential function based on a neural network can adapt to the numerical fitting of the HEMP double-exponential waveform with various rise times t r and pulse widths t w .

[0026] A method for estimating the parameters of the HEMP double-exponential function based on a neural network provides practical value for the basic research in aspects such as HEMP numerical simulation and simulator design. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is the definition of the double-exponential function waveform and its related physical parameters;

[0028] Figure 2 is the distribution of t r and t w when α and β are uniformly sampled. There are 100 samples in total, and t r and t w are densely distributed in the lower left corner;

[0029] Figure 3 is the distribution of the reciprocal space of t r and t w when α and β are uniformly sampled. There are 100 samples in total, and are relatively evenly distributed;

[0030] Figure 4 is the comparison result of the predicted waveform and the actual waveform in the second embodiment of the present invention;

[0031] Figure 5 is the flowchart of the double-exponential function parameter estimation method in the first embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0032] The present invention will be further described in detail below with reference to the drawings and specific embodiments.

[0033] Embodiment 1

[0034] The mathematical properties of the HEMP double-exponential function involved in the present invention are analyzed as follows:

[0035] The expression of the HEMP double-exponential function in the time domain waveform is

[0036] E(t = kE p (e -αt -e-βt ) (1)

[0037] Among them, E(t) is the time-domain pulse, t is the time, and E p is the pulse peak value, k is the amplitude correction coefficient, such that the peak value of the HEMP double-exponential time-domain waveform is E p , and α and β are mathematical parameters that affect the pulse peak value, rise time, and pulse width. The expression for k can be derived as follows:

[0038]

[0039] For the physical parameters involved in HEMP (rise time t r , pulse width t w , and pulse peak value E p ), as Figure 1 shown, k can be solved through α and β. Therefore, the conversion from physical parameters to mathematical parameters only requires converting the rise time t r and pulse width t w into α and β.

[0040] For formula (2), it can be further derived that

[0041] E(t) = kE p [1 - e -(β-α)t e -αt (3) Among them, 1 - e -(β-α)t increases with the increase of time, and e -αt decreases with the increase of time. The mathematical parameters α and β have distinct physical meanings, represents the rise time constant, which determines the rising speed of 1 - e -(β-α)t . A smaller value means a faster rising edge, that is, the time for the pulse to increase from zero to the peak value is shorter. represents the decay time constant of e -αt , which determines the decay speed of the pulse and also determines the overall width of the pulse. A smaller value means the pulse decays faster and the pulse width is shorter.

[0042] Since the rise time is much smaller than the fall time, it can be approximated that the rise time is determined by 1 - e -(β-α)t , and the fall time is determined by e -αt .

[0043] For the rise time, if only considering the contribution of 1 - e -(β-α)t (refer to Figure 1 )

[0044]

[0045] In the above formula, t1 is the time when the HEMP waveform first reaches 0.1Ep The time corresponding to the value, and t3 is the time when the HEMP waveform reaches 0.1E for the second time p The time corresponding to the value.

[0046] It is deduced that

[0047]

[0048] For the pulse width, only the contribution of e is considered (refer to -αt ) Figure 1 )

[0049]

[0050] In the above formula, t5 is the time when the HEMP waveform reaches 0.5E for the second time p The time corresponding to the value.

[0051] It is deduced that

[0052]

[0053] Through the above formula, it can be found that there is an approximate reciprocal relationship between the physical parameters and the mathematical parameters, which can better understand the theoretical basis and implementation manner of the present invention.

[0054] A method for estimating the parameters of the HEMP double-exponential function based on a neural network, as Figure 5 shown, includes the following steps:

[0055] The first step: Data preparation.

[0056] Through the double-exponential equation, calculate the physical parameters (rise time t r and pulse width t w ) corresponding to different mathematical parameters (α, β), where the selection range of α is [10 6 , 5×10 7 , and the selection range of β is [10 8 , 10 9 . Samples corresponding to the HEMP physical parameters (rise time t r and pulse width t w ) and the mathematical parameters (α, β) can be established.

[0057] The second step: Design the input parameters of the neural network.

[0058] Since the HEMP physical parameters and the mathematical parameters of the double-exponential function are approximately in a reciprocal relationship. Perform a reciprocal mapping on the physical parameters (rise time t r and pulse width t w ) so that there is an approximate linear relationship between the physical parameters and the mathematical parameters, which is used as the input of the neural network.

[0059]

[0060] Take and as the output of the neural network.

[0061] If t r and t w are used as the inputs of the neural network, they are mainly distributed in the lower left corner of the sample space (as shown in Figure 2 ), and the quality of the samples used as the neural network inputs is poor. If and are used as the inputs of the neural network, their distribution in the sample space is relatively uniform (as shown in Figure 3 ), and the quality of the samples used as the neural network inputs is good.

[0062] Step 3: Design the output parameters of the neural network.

[0063] The output parameters are mathematical parameters (α and β). Since the rise time of HEMP is less than the fall time, make it satisfy the constraint condition 0 < 2α < β during the neural network training.

[0064] Step 4: Neural network training data.

[0065] Take and the sample data of α and β and provide them to the neural network for training.

[0066] Step 5: Mathematical parameter estimation.

[0067] After the training is completed, for the given physical parameter rise time t r and pulse width t w , input them into the trained neural network, and then calculate the mathematical parameters.

[0068] Example 2

[0069] The selection range of α is [10 6 , 5×10 7 , and the selection range of β is [10 8 , 10 9 . Among them, the sampling points of α are 1001, the sampling points of β are 1001, and the total number of samples is 1002001, including 801600 training set samples and 200401 test set samples. For t r = 2.054383×10 -9 s, t w = 5.721758×10 -8 s of the double-exponential waveform, the actual mathematical parameter α = 1.3299×10 7 , β = 9.144999×108 , the mathematical parameters predicted by the present invention are α = 1.330227×10 7 , β = 9.143485×10 8 . Figure 4 The waveforms actually required to be designed by the simulator and the waveforms predicted by the present invention are shown, verifying the accuracy of the present invention.

Claims

1. A method for estimating parameters of HEMP double exponential function based on neural network, characterized in that: The following steps are involved: Step 1: Establish samples corresponding to HEMP physical parameters and mathematical parameters: The HEMP physical parameter is the rising edge time t of the HEMP simulator r and pulse width t w , the mathematical parameters are mathematical parameter α and mathematical parameter β; The rising edge time t of the HEMP simulator is r and pulse width t w , mathematical parameters α and β as data to establish the rising edge time t r and pulse width t w , the samples corresponding to the mathematical parameters α and β; Step 2, set the input parameters of the neural network: Set the rising edge time t of the HEMP simulator r The reciprocal of Pulse width t w The reciprocal of is the input parameter of the neural network; Step 3, set the output parameters of the neural network: The output parameters of the neural network are set to mathematical parameters α and β, and the constraints are: 0<2a<β; Step 4, neural network training data: The rising edge time t of the HEMP simulator r The reciprocal of Pulse width t w The reciprocal of The sample data with mathematical parameters α and β are provided to the neural network for neural network training. After the training is completed, the trained neural network is obtained. Step 5, double exponential function parameter estimation: For a given HEMP simulator, its rising edge time t r and pulse width t w The input is given to the trained neural network, and the trained neural network outputs mathematical parameters, the mathematical parameters are double exponential function parameters, and the double exponential function parameters of a given HEMP simulator are obtained.

2. The method for estimating parameters of HEMP double exponential function based on neural network according to claim 1, characterized in that: The mathematical parameter α is selected in the range of [10 6 , 5×10 7 ], the range of mathematical parameter β is [10 8 , 10 9 ].

3. The method for estimating parameters of HEMP double exponential function based on neural network according to claim 1, characterized in that: The number of sampling points of the mathematical parameter α and the mathematical parameter β of the HEMP simulator is 1001, the number of samples in the training set is 801600, and the number of samples in the test set is 200401; HEMP physical parameters are double exponential waveforms, with rising edge time t r =2.054383×10 -9 s, pulse width t w =5.721758×10 -8 s; The double exponential function parameters of the HEMP simulator are: mathematical parameter α = 1.330227 × 10 7 , mathematical parameter β = 9.143485 × 10 8 .

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