Test method for equivalent lightning electrical parameters of materials or structures

Abstract

The present invention discloses a method for testing lightning equivalent electrical parameters of materials or structures: Step 1, establish an equivalent circuit model: establish an equivalent circuit model of the material or structure to be tested, and construct the transfer function of the equivalent circuit model; Step 2, test, data acquisition, and data preprocessing: inject a double-exponential lightning current waveform into the material or structure to be tested, record the output lightning current waveform, perform alignment processing on the input lightning current waveform data and the output lightning current waveform data, and fit to obtain the double-exponential waveform parameters; Step 3, parameter optimization and inversion: construct an optimization objective function, and solve for the optimal parameters R, L, and C through a non-linear optimization algorithm; Step 4, output the results. The method for testing lightning equivalent electrical parameters of materials or structures provided by the present invention solves the problem of parameter inversion under non-aligned time series and is applicable to the performance evaluation of transient pulse scenarios.

Description

Technical Field

[0001] The present invention belongs to the technical field of lightning equivalent electrical parameter testing, and relates to a method for testing the lightning equivalent electrical parameters of materials or structures. Background Art

[0002] The response characteristics of materials under lightning action are one of the important contents in the study of the lightning resistance characteristics of materials. Traditional methods are to solve the equivalent electrical parameters and test the transfer function of materials or structures. There are two methods specified in the Aerospace Recommended Practice (ARP) 5416B - 2013: the pulse injection method and the method using swept - frequency measurement. Among them, in the pulse injection method, lightning pulses are injected onto materials, structures, or wire bundles, and the open - circuit voltage and short - circuit current coupled to the materials, structures, or wires are measured, and then used to determine the transfer function; swept - frequency measurement is to inject several amperes of current into a shielded wire bundle through an amplifier using a network analyzer or other similar sources, and then measure the coupled response on the inner wire. The measurement result is the ratio of the response voltage or current to the driving current, which is a function of frequency.

[0003] Although the test results of traditional methods have great advantages, the application scope of traditional methods has the following limitations: (1) In the prior art, the measurement result is the transfer function of materials or structures, usually directly measured by an impedance analyzer or a network analyzer, which cannot directly reflect the dynamic response characteristics of materials under transient pulses (such as lightning strikes). The results of non - RLC equivalent circuit parameters are difficult to be directly used to evaluate material characteristics or match the cable terminal impedance, nor can they be directly used as material parameters in simulations. (2) Insufficient waveform matching: Most of the existing transient test methods use simple step or square - wave excitations, which are difficult to match the double - exponential waveform response of lightning waveforms. (3) Data misalignment problem: In actual tests, the time series of input and output waveforms are often misaligned due to sampling delay or equipment errors, resulting in a decrease in parameter fitting accuracy. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for testing the lightning equivalent electrical parameters of materials or structures, which solves the problem of parameter inversion under non - aligned time series and is applicable to the performance evaluation of transient pulse scenarios.

[0005] The technical solution adopted by the present invention is a method for testing the lightning equivalent electrical parameters of materials or structures, and the specific steps are as follows:

[0006] Step 1: Establish an equivalent circuit model: Establish an equivalent circuit model of the material or structure to be tested, and construct the transfer function of the equivalent circuit model;

[0007] Step 2, Testing, Data Acquisition, and Data Preprocessing: Inject a double-exponential lightning current waveform into the material or structure to be measured, record the output lightning current waveform, align the input lightning current waveform data and the output lightning current waveform data, and obtain the double-exponential waveform parameters by fitting;

[0008] Step 3, Parameter Optimization and Inversion: Construct an optimization objective function and solve for the optimal parameters R, L, and C through a non-linear optimization algorithm;

[0009] Step 4, Output the results.

[0010] The features of the present invention also lie in:

[0011] The specific method of Step 1 is:

[0012] Step 1.1, Establish equivalent circuit model 1

[0013] The circuit structure of equivalent circuit model 1 is: a resistor R is connected in series with an inductor L, and a capacitor C is connected in parallel to the series circuit of the resistor R and the inductor L; wherein, the input end of the circuit system is connected to the resistor R, and the output end of the circuit system is connected to the inductor L;

[0014] The method for measuring the current in equivalent circuit model 1 is: Inject the lightning current from the input end into the entire equivalent circuit and measure the output current from the output end, is the input current to the entire circuit, is the output current of the series branch of the resistor R and the inductor L;

[0015] Step 1.2, Construct the transfer function of equivalent circuit model 1:

[0016] (1);

[0017] is the transfer function of equivalent circuit model 1, is the Laplace transform of the input lightning current waveform function ; is the Laplace transform of the output lightning current waveform function ; S is the complex frequency variable, L is the equivalent inductance parameter of the circuit, C is the equivalent capacitance parameter of the circuit, R is the equivalent resistance parameter of the circuit. Construct an equivalent quadratic transfer function to match the transfer function of the double-exponential waveform:

[0018] (2);

[0019] In the formula, is the natural frequency, is the damping ratio, is the circuit amplification factor, is the complex frequency variable.

[0020] Replace the equivalent circuit model 1 established in step 1.1 with the equivalent circuit replacement model 2:

[0021] The circuit structure of the equivalent circuit replacement model 2 is:

[0022] A resistor R is in series with an inductor L, and a capacitor C is in parallel with the series circuit of the resistor R and the inductor L; wherein, the input end of the circuit system is connected to the resistor R, and the output end of the circuit system is connected to the inductor L;

[0023] The method for testing the current in the equivalent circuit replacement model 2 is:

[0024] The lightning current is injected into the entire equivalent circuit from the input end, and the output current is measured from the output end, is the input current on the entire circuit, is the output current on the capacitor C branch.

[0025] Replace the equivalent circuit model 1 established in step 1.1 with the equivalent circuit replacement model 3 or the equivalent circuit replacement model 4:

[0026] The circuit structure of the equivalent circuit replacement model 3 is: a resistor R is in series with a capacitor C, and an inductor L is in parallel with the series circuit of the resistor R and the capacitor C; wherein, the input end of the circuit system is connected to the resistor R, and the output end of the circuit system is connected to the capacitor C;

[0027] The method for testing the current in the equivalent circuit replacement model 3 is:

[0028] The lightning current is injected into the entire equivalent circuit from the input end, and the output current is measured from the output end, is the input current on the entire circuit, is the output current on the series branch of the resistor R and the capacitor C;

[0029] The circuit structure of the equivalent circuit replacement model 4 is: a resistor R is in series with a capacitor C, and an inductor L is in parallel with the series circuit of the resistor R and the capacitor C; wherein, the input end of the circuit system is connected to the resistor R, and the output end of the circuit system is connected to the capacitor C;

[0030] The method for testing the current in the equivalent circuit replacement model 4 is: The lightning current is injected into the entire equivalent circuit from the input end, and the output current is measured from the output end, is the input current on the entire circuit, is the output current on the inductor L branch.

[0031] Replace the equivalent circuit model 1 established in step 1.1 with the equivalent circuit replacement model 5 or the equivalent circuit replacement model 6:

[0032] The circuit structure of the equivalent circuit replacement model 5 is as follows: an inductor L is connected in series with a capacitor C, and a resistor R is connected in parallel to the series circuit of the inductor L and the capacitor C; among them, the input end of the circuit system is connected to the inductor L, and the output end of the circuit system is connected to the capacitor C;

[0033] The method for testing the current in the equivalent circuit replacement model 5 is as follows: the lightning current is injected from the input end into the entire equivalent circuit, and the output current is measured from the output end, is the input current to the entire circuit, is the output current on the series branch of the inductor L and the capacitor C;

[0034] The circuit structure of the equivalent circuit replacement model 6 is as follows: an inductor L is connected in series with a capacitor C, and a resistor R is connected in parallel to the series circuit of the inductor L and the capacitor C; among them, the input end of the circuit system is connected to the inductor L, and the output end of the circuit system is connected to the capacitor C;

[0035] The method for testing the current in the equivalent circuit replacement model 6 is as follows: the lightning current is injected from the input end into the entire equivalent circuit, and the output current is measured from the output end, is the input current to the entire circuit, is the output current on the branch of the resistor R.

[0036] The specific method of step 2 is as follows:

[0037] Step 2.1, Testing and data acquisition: Test and collect the input lightning current waveform data and the output lightning current waveform data ;

[0038] Step 2.2, Alignment processing of the input lightning current waveform data and the output lightning current waveform data collected during the test: Map the misaligned input lightning current waveform data and the output lightning current waveform data to a unified time base t common ;

[0039] Step 2.3, Fitting processing of input and output data: The input lightning current waveform function and the output lightning current waveform function are both double-exponential waveforms, specifically as follows:

[0040] The input lightning current waveform function :

[0041] (3);

[0042] Where: A is the peak amplitude of the input lightning current, and are the input lightning current test waveform parameters, t is the time, and the input lightning current waveform function is calculated according to the measured input lightning current waveform Parameter rise time and the input lightning current waveform function Parameter peak time ;

[0043] Output lightning current waveform function :

[0044] (4);

[0045] Where: B is the peak amplitude of the output lightning current, and B < A, and are the output lightning current test waveform parameters, t is the time, and the output lightning current waveform function is calculated according to the measured output lightning current waveform Parameter rise time and the output lightning current waveform function Parameter peak time .

[0046] In step 2.3, the calculation methods of the parameter rise time of the input lightning current waveform function , the parameter peak time of the input lightning current waveform function are as follows:

[0047] The parameter rise time of the input lightning current waveform function is the time when the lightning current amplitude rises from 10% of the peak to 90% of the peak, and the calculation formula is:

[0048] (5),

[0049] The parameter peak time of the input lightning current waveform function is the time when the lightning current amplitude rises from 0 to the peak, and the calculation formula is:

[0050] (6);

[0051] Among them, the parameter rise time of the output lightning current waveform function , the parameter peak time of the output lightning current waveform function The calculation method is as follows:

[0052] Output lightning current waveform function Parameter rise time Is the time when the lightning current amplitude rises from 10% of the peak value to 90% of the peak value, and the calculation formula is:

[0053] (7),

[0054] Output lightning current waveform function Parameter peak time Is the time when the lightning current amplitude rises from 0 to the peak value, and the calculation formula is:

[0055] (8);

[0056] The above values are restricted to satisfy A > B > 0, and , ;

[0057] By giving , , , , A, B to construct a non - linear equation about α and β and solve it using numerical methods.

[0058] The specific method of step 3 is as follows:

[0059] Step 3.1, construct the optimization objective function

[0060] Input signal:

[0061] (9);

[0062] Output signal:

[0063] (10);

[0064] Where is the Laplace transform operator;

[0065] Use the mean square error MSE as an index of waveform consistency to construct the optimization objective function :

[0066] (11);

[0067] Step 3.2, calculate the initial R 0, initial L 0 and initial C 0, specifically as follows:

[0068] (12),

[0069] (13),

[0070] (14),

[0071] (15),

[0072] (16);

[0073] Wherein, is the natural frequency, is the damping ratio, is the circuit amplification factor;

[0074] Step 3.3, starting from the initial R 0, initial L 0 and initial C 0, optimize the objective function through the non - linear least - squares fitting method to obtain the optimal parameters R, L, C.

[0075] The beneficial effects of the present invention are:

[0076] (1) The method for testing the lightning equivalent electrical parameters of the material or structure of the present invention proposes an equivalent electrical parameter testing method. The lightning input and output time - domain waveforms are obtained by a testing method that complies with the standard regulations. The non - aligned time - domain waveform sequences are constructed into aligned data sequences by using the interpolation algorithm to obtain the transfer function; a structured equivalent RLC parameter is constructed; an optimization algorithm is applied to fit the RLC second - order transfer function to make it have the maximum similarity with the tested transfer function; the equivalent electrical parameters of the material or structure are obtained, solving the problem of parameter inversion under non - aligned time series and being applicable to the performance evaluation of transient pulse scenarios;

[0077] (2) The method for testing the lightning equivalent electrical parameters of the material or structure of the present invention extracts the key parameters of the lightning wave characteristics, is more in line with the actual application scenario, and realizes the high - precision parameter extraction of the double - exponential waveform; by combining the interpolation and optimization algorithms, the time - shift error is eliminated to complete the adaptation of non - aligned data; the measured parameters of the material or structure are embedded as constraint conditions in the objective function to ensure the physical authenticity and usability of the parameters. The method for obtaining the equivalent electrical parameters of the present invention has the characteristics of strong intuitiveness, wide application range, and can be directly used as simulation input parameters, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 is the calculation flow chart of the method for testing the lightning equivalent electrical parameters of the material or structure of the present invention;

[0079] Figure 2It is the test layout diagram of the current component for the test method of the lightning equivalent electrical parameters of the material or structure of the present invention;

[0080] Figure 3 It is the circuit schematic diagram of equivalent circuit model 1 for the test method of the lightning equivalent electrical parameters of the material or structure of the present invention;

[0081] Figure 4 It is the circuit schematic diagram of equivalent circuit replacement model 2 for the test method of the lightning equivalent electrical parameters of the present invention;

[0082] Figure 5 It is the circuit schematic diagram of equivalent circuit replacement model 3 for the test method of the lightning equivalent electrical parameters of the present invention;

[0083] Figure 6 It is the circuit schematic diagram of equivalent circuit replacement model 4 for the test method of the lightning equivalent electrical parameters of the present invention;

[0084] Figure 7 It is the circuit schematic diagram of equivalent circuit replacement model 5 for the test method of the lightning equivalent electrical parameters of the present invention;

[0085] Figure 8 It is the circuit schematic diagram of equivalent circuit replacement model 6 for the test method of the lightning equivalent electrical parameters of the present invention;

[0086] Figure 9 It is the test layout diagram of the voltage component for the test method of the lightning equivalent electrical parameters of the material or structure of the present invention. Detailed implementation manners

[0087] The present invention will be described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0088] The test method for the lightning equivalent electrical parameters of the material or structure of the present invention is as Figure 1 shown, and the specific steps are as follows:

[0089] Step 1. Establish an equivalent circuit model: As Figure 2 shown, establish an equivalent circuit model of the material or structure to be tested, and construct the transfer function of the equivalent circuit model. The specific method is:

[0090] Step 1.1. Establish equivalent circuit model 1

[0091] The circuit structure of equivalent circuit model 1 is: As Figure 3 shown, a resistor R is connected in series with an inductor L, and a capacitor C is connected in parallel to the series circuit of the resistor R and the inductor L; among them, the input end of the circuit system is connected to the resistor R, and the output end of the circuit system is connected to the inductor L;

[0092] The test method for the current in equivalent circuit model 1 is: The lightning current is injected from the input end into the entire equivalent circuit, and the output current is measured from the output end. is the input current across the entire circuit, is the output current across the series branch of resistor R and inductor L;

[0093] Step 1.2, construct the transfer function of equivalent circuit model 1:

[0094] (1);

[0095] In the formula, is the transfer function of equivalent circuit model 1, is the Laplace transform of the input lightning current waveform function ; is the Laplace transform of the output lightning current waveform function ; S is the complex frequency variable, L is the equivalent inductance parameter of the circuit, C is the equivalent capacitance parameter of the circuit, R is the equivalent resistance parameter of the circuit. Construct an equivalent quadratic transfer function to match the transfer function of the double exponential waveform:

[0096] (2);

[0097] In the formula, is the natural frequency, is the damping ratio, is the circuit amplification factor, is the complex frequency variable.

[0098] Transfer function: It refers to the ratio of the Laplace transform (z-transform when it is a non-continuous function) of the response (i.e., output) quantity of a linear system under zero initial conditions to the Laplace transform of the excitation (i.e., input) quantity.

[0099] Step 2, testing, data acquisition, and data preprocessing: Inject a double exponential lightning current waveform into the material or structure to be measured, record the output lightning current waveform, align the input lightning current waveform data and the output lightning current waveform data, and obtain the double exponential waveform parameters by fitting. The specific method is as follows:

[0100] Step 2.1, testing and data acquisition: Conduct tests and acquire the input lightning current waveform data according to the SAE ARP 5416A-2013 Aircraft Lightning TestMethods standard and the output lightning current waveform data ;

[0101] Step 2.2, for the input lightning current waveform data collected during the test and the output lightning current waveform data Perform alignment processing: Map the unaligned input lightning current waveform data and the output lightning current waveform data to a unified time reference t common ;

[0102] Step 2.3, Input-output data fitting processing: The input lightning current waveform function and the output lightning current waveform function are both double-exponential waveforms, specifically as follows:

[0103] Input lightning current waveform function :

[0104] (3);

[0105] Where: A is the peak amplitude of the input lightning current, and are the input lightning current test waveform parameters, t is the time, and the input lightning current waveform function parameter rise time and the input lightning current waveform function parameter peak time ;

[0106] Output lightning current waveform function :

[0107] (4);

[0108] Where: B is the peak amplitude of the output lightning current, and B < A, and are the output lightning current test waveform parameters, t is the time, and the output lightning current waveform function parameter rise time and the output lightning current waveform function parameter peak time ;

[0109] Furthermore, the calculation methods for the input lightning current waveform function parameter rise time and the input lightning current waveform function parameter peak time are as follows:

[0110] Input lightning current waveform function parameter rise time is the time for the lightning current amplitude to rise from 10% of the peak value to 90% of the peak value, and the calculation formula is:

[0111] (5),

[0112] Input lightning current waveform function Parameter peak time is the time for the lightning current amplitude to rise from 0 to the peak value, and the calculation formula is:

[0113] (6);

[0114] Among them, the output lightning current waveform function Parameter rise time and the output lightning current waveform function Parameter peak time The calculation method is as follows:

[0115] Output lightning current waveform function Parameter rise time is the time for the lightning current amplitude to rise from 10% of the peak value to 90% of the peak value, and the calculation formula is:

[0116] (7),

[0117] Output lightning current waveform function Parameter peak time is the time for the lightning current amplitude to rise from 0 to the peak value, and the calculation formula is:

[0118] (8);

[0119] The above value constraints satisfy A > B > 0, and , ;

[0120] By giving , , , , A, B to construct a non - linear equation about α and β and solve it by numerical method.

[0121] Step 3. Parameter optimization inversion: Construct an optimization objective function and solve the optimal parameters R, L, C through a non - linear optimization algorithm. The specific method is:

[0122] Step 3.1. Construct an optimization objective function

[0123] Input signal:

[0124] (9);

[0125] Output signal:

[0126] (10);

[0127] Where is the Laplace transform operator;

[0128] Use the mean square error MSE as an index of waveform consistency to construct an optimization objective function :

[0129] (11);

[0130] Step 3.2, calculate the initial R 0, initial L 0 and initial C 0, specifically as follows:

[0131] (12),

[0132] (13),

[0133] (14),

[0134] (15),

[0135] (16);

[0136] In the formula, is the natural frequency, is the damping ratio, is the circuit amplification factor;

[0137] Step 3.3, starting from the initial R 0, initial L 0 and initial C 0, through the nonlinear least squares fitting method to optimize the objective function to obtain the optimal parameters R, L, C.

[0138] Step 4, output the result.

[0139] Least Squares Method for Nonlinear Curve Fitting: A special least squares fitting method that originates from nonlinear regression and is usually used to fit complex curve data. This method consists of two parts: data solution and parameter fitting. In the parameter fitting part, the least squares method is used to fit and obtain the optimal parameters, thereby completing the fitting of the nonlinear curve. The least squares method for nonlinear curve fitting is widely used in mathematical calculations, signal processing, machine learning, and theoretical calculations and experimental research in many fields such as physics and chemistry. In this invention, the optimization algorithm is not limited to the least squares optimization algorithm, and algorithms such as neural networks / genetic algorithms can also be used for optimization, which will not be elaborated here.

[0140] Based on the test principle of the above equivalent circuit model 1, in step 1.2 of the present invention, the equivalent circuit model 1 can also be replaced by the following two-branch equivalent circuit model:

[0141] As Figure 4 shown, an equivalent circuit replacement model 2 is established. The circuit structure of the equivalent circuit replacement model 2 is: a resistor R is connected in series with an inductor L, and a capacitor C is connected in parallel to the series circuit of the resistor R and the inductor L; among them, the input end of the circuit system is connected to the resistor R, and the output end of the circuit system is connected to the inductor L;

[0142] The test method for the current in the equivalent circuit replacement model 2 is: the lightning current is injected from the input end into the entire equivalent circuit, and the output current is measured from the output end, is the input current to the entire circuit, is the output current on the capacitor C branch.

[0143] The transfer function is:

[0144] (17).

[0145] As Figure 5 shown, an equivalent circuit replacement model 3 is established. The circuit structure of the equivalent circuit replacement model 3 is: a resistor R is connected in series with a capacitor C, and an inductor L is connected in parallel to the series circuit of the resistor R and the capacitor C; among them, the input end of the circuit system is connected to the resistor R, and the output end of the circuit system is connected to the capacitor C;

[0146] The test method for the current in the equivalent circuit replacement model 3 is: the lightning current is injected from the input end into the entire equivalent circuit, and the output current is measured from the output end, is the input current to the entire circuit, is the output current on the series branch of the resistor R and the capacitor C;

[0147] The transfer function is:

[0148] (18).

[0149] As Figure 6As shown in the figure, an equivalent circuit replacement model 4 is established. The circuit structure of the equivalent circuit replacement model 4 is as follows: a resistor R is connected in series with a capacitor C, and an inductor L is connected in parallel to the series circuit of the resistor R and the capacitor C; among them, the input end of the circuit system is connected to the resistor R, and the output end of the circuit system is connected to the capacitor C;

[0150] The test method for the current in the equivalent circuit replacement model 4 is as follows: the lightning current is injected into the entire equivalent circuit from the input end, and the output current is measured from the output end, is the input current to the entire circuit, is the output current on the inductor L branch.

[0151] The transfer function is:

[0152] (19).

[0153] As Figure 7 shown in the figure, an equivalent circuit replacement model 5 is established. The circuit structure of the equivalent circuit replacement model 5 is as follows: an inductor L is connected in series with a capacitor C, and a resistor R is connected in parallel to the series circuit of the inductor L and the capacitor C; among them, the input end of the circuit system is connected to the inductor L, and the output end of the circuit system is connected to the capacitor C;

[0154] The test method for the current in the equivalent circuit replacement model 5 is as follows: the lightning current is injected into the entire equivalent circuit from the input end, and the output current is measured from the output end, is the input current to the entire circuit, is the output current on the series branch of the inductor L and the capacitor C;

[0155] The transfer function is:

[0156] (20).

[0157] As Figure 8 shown in the figure, an equivalent circuit replacement model 6 is established. The circuit structure of the equivalent circuit replacement model 6 is as follows: an inductor L is connected in series with a capacitor C, and a resistor R is connected in parallel to the series circuit of the inductor L and the capacitor C; among them, the input end of the circuit system is connected to the inductor L, and the output end of the circuit system is connected to the capacitor C;

[0158] The test method for the current in the equivalent circuit replacement model 6 is as follows: the lightning current is injected into the entire equivalent circuit from the input end, and the output current is measured from the output end, is the input current to the entire circuit, is the output current on the resistor R branch.

[0159] The transfer function is:

[0160] (21).

[0161] Based on the test principle of the above equivalent circuit model 1, in the present invention, the measurement or application object can also be achieved by means of voltage, such as Figure 9 as shown

[0162] Voltage model: RLC in series, and the output is the voltage division on R. Its circuit structure is: a voltage source is applied across the RLC series circuit, and the output is the voltage across R .

[0163] The transfer function is:

[0164] (22).

[0165] The above model principle is the same as that of the equivalent circuit model 1, and will not be elaborated here

[0166] Example 1

[0167] The test method for the lightning equivalent electrical parameters of the material or structure in this example is as follows:

[0168] Step 1. Establish an equivalent circuit model: Establish an equivalent circuit model of the material or structure to be measured, and construct the transfer function of the equivalent circuit model

[0169] Step 2. Test, data acquisition, and data preprocessing: Inject a double-exponential lightning current waveform into the material or structure to be measured, record the output lightning current waveform, align the input lightning current waveform data and the output lightning current waveform data, and fit to obtain the double-exponential waveform parameters

[0170] Step 3. Parameter optimization and inversion: Construct an optimization objective function, and solve for the optimal parameters R, L, and C through a nonlinear optimization algorithm

[0171] Step 4. Output the results

[0172] Example 2

[0173] The test method for the lightning equivalent electrical parameters of the material or structure in this example is as follows:

[0174] Step 1. Establish an equivalent circuit model: Establish an equivalent circuit model of the material or structure to be measured, and construct the transfer function of the equivalent circuit model. The specific method is:

[0175] Step 1.1. Establish equivalent circuit model 1

[0176] The circuit structure of equivalent circuit model 1 is: as Figure 3 shown, a resistor R is in series with an inductor L, and a capacitor C is further connected in parallel to the series circuit of the resistor R and the inductor L; among them, the input end of the circuit system is connected to the resistor R, and the output end of the circuit system is connected to the inductor L

[0177] The test method for the current in the equivalent circuit model 1 is as follows: The lightning current is injected into the entire equivalent circuit from the input end, and the output current is measured from the output end. is the input current to the entire circuit. is the output current of the series branch of resistor R and inductor L.

[0178] Step 1.2: Construct the transfer function of the equivalent circuit model 1:

[0179] (1);

[0180] In the formula, is the transfer function of the equivalent circuit model 1. is the Laplace transform of the input lightning current waveform function ; is the Laplace transform of the output lightning current waveform function ; S is the complex frequency variable. L is the equivalent inductance parameter of the circuit. C is the equivalent capacitance parameter of the circuit. R is the equivalent resistance parameter of the circuit. Construct an equivalent quadratic transfer function to match the transfer function of the double-exponential waveform:

[0181] (2);

[0182] In the formula, is the natural frequency. is the damping ratio. is the circuit amplification factor. is the complex frequency variable.

[0183] Step 2: Test, data acquisition, and data preprocessing: Inject a double-exponential lightning current waveform into the material or structure to be measured, record the output lightning current waveform, align the input lightning current waveform data and the output lightning current waveform data, and fit to obtain the double-exponential waveform parameters.

[0184] Step 3: Parameter optimization and inversion: Construct an optimization objective function and solve for the optimal parameters R, L, and C through a non-linear optimization algorithm.

[0185] Step 4: Output the results.

[0186] Example 3

[0187] For the test method of the lightning equivalent electrical parameters of the material or structure in this example, on the basis of Example 2, the specific method for Step 2 is as follows:

[0188] Step 2.1, Testing and Data Acquisition: Conduct tests and collect input lightning current waveform data in accordance with the SAE ARP 5416A-2013 Aircraft Lightning Test Methods standard and output lightning current waveform data ;

[0189] Step 2.2, Alignment Processing of the Input and Output Lightning Current Waveform Data Collected during Testing and output lightning current waveform data : Map the misaligned input and output lightning current waveform data and output lightning current waveform data to a unified time reference t common ;

[0190] Step 2.3, Fitting Processing of Input and Output Data: The input lightning current waveform function and the output lightning current waveform function are both double-exponential waveforms, specifically as follows:

[0191] Input lightning current waveform function :

[0192] (3);

[0193] where: A is the peak amplitude of the input lightning current, and are the input lightning current test waveform parameters, t is the time, and calculate the input lightning current waveform function parameter rise time and the input lightning current waveform function parameter peak time ;

[0194] Output lightning current waveform function :

[0195] (4);

[0196] where: B is the peak amplitude of the output lightning current, and B < A, and are the output lightning current test waveform parameters, t is the time, and calculate the output lightning current waveform function parameter rise time and the output lightning current waveform function parameter peak time ;

[0197] Further, in step 2.3, input the lightning current waveform function Parameter rise time and input the lightning current waveform function Parameter peak time The calculation methods are as follows:

[0198] Input the lightning current waveform function Parameter rise time is the time when the lightning current amplitude rises from 10% of the peak to 90% of the peak, and the calculation formula is:

[0199] (5),

[0200] Input the lightning current waveform function Parameter peak time is the time when the lightning current amplitude rises from 0 to the peak, and the calculation formula is:

[0201] (6);

[0202] Among them, for the output lightning current waveform function Parameter rise time and the output lightning current waveform function Parameter peak time The calculation methods are as follows:

[0203] Output the lightning current waveform function Parameter rise time is the time when the lightning current amplitude rises from 10% of the peak to 90% of the peak, and the calculation formula is:

[0204] (7),

[0205] Output the lightning current waveform function Parameter peak time is the time when the lightning current amplitude rises from 0 to the rising peak, and the calculation formula is:

[0206] (8);

[0207] The above values are constrained to satisfy A > B > 0, and , ;

[0208] By giving , , , , A, B, construct a non - linear equation about α and β and solve it using numerical methods.

[0209] Example 4

[0210] For the method for testing the lightning equivalent electrical parameters of the materials or structures in this example, on the basis of Example 3, the specific method in Step 3 is as follows:

[0211] Step 3.1: Construct the optimization objective function

[0212] Input signal:

[0213] (9);

[0214] Output signal:

[0215] (10);

[0216] Where is the Laplace transform operator;

[0217] Use the mean square error MSE as an index of waveform consistency to construct the optimization objective function :

[0218] (11);

[0219] Step 3.2: Calculate the initial R 0, the initial L 0 and the initial C 0, specifically as follows:

[0220] (12),

[0221] (13),

[0222] (14),

[0223] (15),

[0224] (16);

[0225] In the formula, is the natural frequency, is the damping ratio, is the circuit amplification factor;

[0226] Step 3.3: Starting from the initial R 0, the initial L 0 and the initial C 0, optimize the objective function through the nonlinear least squares fitting method to obtain the optimal parameters R, L, C.

[0227] Example 5

[0228] The method for testing the lightning equivalent electrical parameters of the materials or structures in this embodiment is the same as that in Embodiment 1. The difference from Embodiment 1 is that the equivalent circuit model established in Step 1.2 is replaced by the following equivalent circuit model:

[0229] Equivalent circuit replacement model 3. The circuit structure of equivalent circuit replacement model 3 is: a resistor R is connected in series with a capacitor C, and an inductor L is connected in parallel to the series circuit of the resistor R and the capacitor C; wherein, the input end of the circuit system is connected to the resistor R, and the output end of the circuit system is connected to the capacitor C;

[0230] The method for testing the current in equivalent circuit replacement model 3 is: the lightning current is injected from the input end into the entire equivalent circuit, and the output current is measured from the output end, is the input current to the entire circuit, is the output current of the series branch of the resistor R and the capacitor C;

[0231] The transfer function is:

[0232] (18).

[0233] Embodiment 6

[0234] The method for testing the lightning equivalent electrical parameters of the materials or structures in this embodiment is the same as that in Embodiment 1. The difference from Embodiment 1 is that the equivalent circuit model established in Step 1.2 is replaced by the following equivalent circuit model:

[0235] Equivalent circuit replacement model 5. The circuit structure of equivalent circuit replacement model 5 is: an inductor L is connected in series with a capacitor C, and a resistor R is connected in parallel to the series circuit of the inductor L and the capacitor C; wherein, the input end of the circuit system is connected to the inductor L, and the output end of the circuit system is connected to the capacitor C;

[0236] The method for testing the current in equivalent circuit replacement model 5 is: the lightning current is injected from the input end into the entire equivalent circuit, and the output current is measured from the output end, is the input current to the entire circuit, is the output current of the series branch of the inductor L and the capacitor C;

[0237] The transfer function is:

[0238] (20).

[0239] Embodiment 7

[0240] The method for testing the lightning equivalent electrical parameters of the materials or structures in this embodiment is the same as that in Embodiment 1. The difference from Embodiment 1 is that the measurement or application object is realized by means of voltage, such as Figure 9 as shown, voltage model: RLC in series, and the output is the voltage division on R. Its circuit structure is: voltage sourceV in Applied across the RLC series circuit, the output is the voltage across R V R 。

[0241] The transfer function is: (22)。

Claims

1. Test method for equivalent electrical parameters of lightning on materials, characterized in that The specific steps are as follows: Step 1. Establish an equivalent circuit model: Establish an equivalent circuit model of the material under test and construct the transfer function of the equivalent circuit model ; Step 2: Testing, data acquisition, and data preprocessing: Inject a double-exponential lightning current waveform into the material under test, record the output lightning current waveform, align the input lightning current waveform data and the output lightning current waveform data, and obtain the double-exponential waveform parameters by fitting; Step 3: Parameter optimization inversion: Construct an optimization objective function and solve for the optimal parameters R, L, and C through a nonlinear optimization algorithm; Step 4: Output the results; The specific method of the said Step 2 is as follows: Step 2.1, Testing and data acquisition: Acquire the input lightning current waveform data and the output lightning current waveform data ; Step 2.2: Align the input lightning current waveform data and the output lightning current waveform data collected during the test; Step 2.

3. Fitting process of input and output data: Input the lightning current waveform function and the output lightning current waveform function are both double-exponential waveforms, specifically as follows: Input lightning current waveform function : （3）； where: A is the peak amplitude of the input lightning current, and are the input lightning current test waveform parameters, t is time, and the input lightning current waveform function is calculated according to the measured input lightning current waveform Parameter rise time and the input lightning current waveform function Parameter peak time ; Output lightning current waveform function :[[]]END]] （4）； Where: B is the peak amplitude of the output lightning current, and B < A, and are the test waveform parameters of the output lightning current, t is the time. Calculate the output lightning current waveform function based on the measured output lightning current waveform Parameter rise time and the output lightning current waveform function Parameter peak time ; By given , , , , A and B construct a nonlinear equation about α and β and solve it by numerical method; The specific method for Step 3 is as follows: Step 3.1: Construct an optimization objective function Input signal: （9）； Output signal: （10）； where is the Laplace transform operator; Construct an optimization objective function using the mean square error (MSE) as an indicator of waveform consistency : （11）； Step 3.2: Calculate the initial R0, initial L0, and initial C0, specifically as follows: （12）， （13）， （14）， （15）， （16）； wherein, is the natural frequency; is the damping ratio; is the circuit amplification factor; Step 3.3: Starting from the initial R0, initial L0, and initial C0, optimize the objective function by means of the nonlinear least squares fitting method to obtain the optimal parameters R, L, and C.

2. The method for testing the lightning equivalent electrical parameters of the material according to claim 1, wherein The specific method for Step 1 is as follows: Step 1.1: Establish equivalent circuit model 1 The circuit structure of equivalent circuit model 1 is: a resistor R is in series with an inductor L, and a capacitor C is connected in parallel to the series circuit of the resistor R and the inductor L; among them, the input end of the circuit system is connected to the resistor R, and the output end of the circuit system is connected to the inductor L; The test method for the current in the equivalent circuit model 1 is as follows: The lightning current is injected from the input end into the entire equivalent circuit, and the output current is measured from the output end. is the input current on the entire circuit. is the output current on the series branch of the resistor R and the inductor L. Step 1.2: Construct the transfer function of equivalent circuit model 1: （1）； Wherein, is the transfer function of the equivalent circuit model 1, is the input lightning current waveform function of the Laplace transform; is the output lightning current waveform function of the Laplace transform, S is the complex frequency variable, L is the equivalent inductance parameter of the circuit, C is the equivalent capacitance parameter of the circuit, R is the equivalent resistance parameter of the circuit, and an equivalent quadratic transfer function is constructed to match the transfer function of the double-exponential waveform: （2）； wherein, is the natural frequency, is the damping ratio, is the circuit amplification factor, is the complex frequency variable.

3. The method for testing the lightning equivalent electrical parameters of the material according to claim 1, wherein, In step 2.2, the input lightning current waveform data collected during the test and the output lightning current waveform data are aligned as follows: the misaligned input lightning current waveform data and the output lightning current waveform data are mapped to a unified time reference t common .

4. The method for testing the lightning equivalent electrical parameters of the material according to claim 1, characterized in that In step 2.3, input the lightning current waveform function Parameter rise time , input the lightning current waveform function Parameter peak time The calculation method is as follows: Input lightning current waveform function Parameter rise time It is the time when the lightning current amplitude rises from 10% of the peak value to 90% of the peak value, and the calculation formula is: （5）， Input lightning current waveform function Parameter peak time It is the time for the lightning current amplitude to rise from 0 to the peak value, and the calculation formula is: （6）； Among them, the output lightning current waveform function Parameter rise time and the output lightning current waveform function Parameter peak time are calculated as follows: Output lightning current waveform function Parameter rise time It is the time for the lightning current amplitude to rise from 10% of the peak value to 90% of the peak value, and the calculation formula is: （7）， Output lightning current waveform function Parameter peak time It is the time for the lightning current amplitude to rise from 0 to the peak value, and the calculation formula is: （8）； The above value constraints satisfy A > B > 0, and , .

5. The method for testing the lightning equivalent electrical parameters of the material according to claim 2, wherein Replace the equivalent circuit model 1 established in Step 1.1 with equivalent circuit replacement model 2: The circuit structure of equivalent circuit replacement model 2 is: a resistor R is in series with an inductor L, and a capacitor C is connected in parallel to the series circuit of the resistor R and the inductor L; among them, the input end of the circuit system is connected to the resistor R, and the output end of the circuit system is connected to the inductor L; The test method for the current in the equivalent circuit replacement model 2 is as follows: The lightning current is injected from the input end to the entire equivalent circuit, and the output current is measured from the output end. is the input current to the entire circuit. is the output current on the capacitor C branch.

6. The method for testing the lightning equivalent electrical parameters of the material according to claim 2, characterized in that Replace the equivalent circuit model 1 established in Step 1.1 with equivalent circuit replacement model 3 or equivalent circuit replacement model 4: The circuit structure of equivalent circuit replacement model 3 is: a resistor R is in series with a capacitor C, and an inductor L is connected in parallel to the series circuit of the resistor R and the capacitor C; among them, the input end of the circuit system is connected to the resistor R, and the output end of the circuit system is connected to the capacitor C; The test method for the current in the equivalent circuit replacement model 3 is as follows: The lightning current is injected into the entire equivalent circuit from the input end, and the output current is measured from the output end. is the input current on the entire circuit. is the output current on the series branch of the resistor R and the capacitor C. The circuit structure of equivalent circuit replacement model 4 is: a resistor R is in series with a capacitor C, and an inductor L is connected in parallel to the series circuit of the resistor R and the capacitor C; among them, the input end of the circuit system is connected to the resistor R, and the output end of the circuit system is connected to the capacitor C; The test method for the current in the equivalent circuit replacement model 4 is as follows: The lightning current is injected from the input end into the entire equivalent circuit, and the output current is measured from the output end. is the input current on the entire circuit. is the output current on the inductor L branch.

7. The method for testing the lightning equivalent electrical parameters of the material according to claim 2, wherein Replace the equivalent circuit model 1 established in Step 1.1 with equivalent circuit replacement model 5 or equivalent circuit replacement model 6: The circuit structure of equivalent circuit replacement model 5 is: an inductor L is in series with a capacitor C, and a resistor R is connected in parallel to the series circuit of the inductor L and the capacitor C; among them, the input end of the circuit system is connected to the inductor L, and the output end of the circuit system is connected to the capacitor C; The test method for the current in the equivalent circuit replacement model 5 is as follows: The lightning current is injected into the entire equivalent circuit from the input end, and the output current is measured from the output end. is the input current on the entire circuit. is the output current on the series branch of the inductor L and the capacitor C. The circuit structure of equivalent circuit replacement model 6 is: an inductor L is in series with a capacitor C, and a resistor R is connected in parallel to the series circuit of the inductor L and the capacitor C; among them, the input end of the circuit system is connected to the inductor L, and the output end of the circuit system is connected to the capacitor C; The test method for the current in the equivalent circuit replacement model 6 is as follows: The lightning current is injected into the entire equivalent circuit from the input end, and the output current is measured from the output end. is the input current on the entire circuit. is the output current on the resistor R branch.

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