CN117630049B - Material electromagnetic parameter extraction method based on machine learning gradient descent algorithm - Google Patents

Material electromagnetic parameter extraction method based on machine learning gradient descent algorithm Download PDF

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CN117630049B
CN117630049B CN202410101768.1A CN202410101768A CN117630049B CN 117630049 B CN117630049 B CN 117630049B CN 202410101768 A CN202410101768 A CN 202410101768A CN 117630049 B CN117630049 B CN 117630049B
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transmittance
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CN117630049A (en
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吴肖肖
李海涛
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Hong Kong University Of Science And Technology Guangzhou
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Abstract

The invention provides a material electromagnetic parameter extraction method based on a machine learning gradient descent algorithm, which comprises the following steps: s1, acquiring the transmissivity of a sample to be tested; s2, obtaining the refractive index and electromagnetic wave impedance expression of the sample to be tested according to the electromagnetic wave principle; s3, obtaining a transmissivity function according to the complex dielectric constant, the refractive index and the electromagnetic wave impedance; s4, obtaining a loss function according to the transmittance function and the transmittance; s5, solving the complex dielectric constant of the sample to be measured by using a machine learning gradient descent algorithm for the loss function. The electromagnetic parameter inverse algorithm is based on the gradient descent concept which is the most critical in the artificial intelligence field, is different from the NRW method based on algebraic algorithm, and can be combined with deep learning and a neural network to realize more flexible operation. Secondly, the NRW operation method needs to measure the transmissivity and the reflectivity of the sample, and the method only needs one parameter of the transmissivity, and in addition, the method can still work normally under the condition of oblique incidence.

Description

Material electromagnetic parameter extraction method based on machine learning gradient descent algorithm
Technical Field
The invention relates to the technical field of electromagnetism, in particular to a material electromagnetic parameter extraction method based on a machine learning gradient descent algorithm.
Background
The radio frequency electromagnetic parameter measurement and calibration of the material are the basis in radio frequency engineering and microwave engineering all the time, and are necessary paths in the design process of various radars and radio frequency circuits. The current mainstream test methods include: a centralized circuit method; a transmission line method; a resonant cavity method; free space methods and the like are needed to be carried out under certain experimental conditions, and the size of the required electromagnetic parameters is calculated by constructing different microwave networks and measuring corresponding scattering parameters, and each method has certain advantages and limitations. The most widely used transmission line method is used for example at present, and has the advantages of simple operation, higher precision and suitability for electromagnetic test of any frequency, and the scattering parameters (S21 and S11) measured by the transmission line method are usually extracted by inverse calculation of a Nicolson-Ross-Weir algorithm (NRW algorithm). The NRW method is an electromagnetic parameter calculation method proposed by three persons of Nicolson, ross and Weir in the 80S of the 20 th century, and the method obtains the relation between the transmission coefficient and the observability (S21 and S11) of the transmission coefficient and the reflection coefficient under a microwave network through S21 and S22 (both of which are functions of the scattering coefficient and the transmission coefficient in the microwave network) in a simultaneous scattering parameter matrix element, and finally the complex dielectric constant and the complex permeability of the material can be algebraically solved by directly measured scattering parameter data. However, this method has disadvantages in that, when the electromagnetic parameters are inversely calculated by using the NRW method, abnormality of S11 coefficient is caused due to physical phenomenon that half-wave resonance may exist inside the sample, thus generating an indistinct multi-value problem, and there is a specific and high precision requirement for the size and surface roughness of the sample, and precise characterization of the thin film and the surface roughened material is impossible. The algorithm of the invention ensures higher precision level on the basis of overcoming various limitations of a transmission line method and an NRW method, and is very hopeful to become a new method for measuring and calculating main stream electromagnetic parameters.
Disclosure of Invention
The invention aims at least solving the technical problems in the prior art, and particularly creatively provides a material electromagnetic parameter extraction method based on a machine learning gradient descent algorithm.
In order to achieve the above object of the present invention, the present invention provides a method for extracting electromagnetic parameters of a material based on a machine learning gradient descent algorithm, comprising the steps of:
s1, acquiring electromagnetic wave transmittance of a sample to be detected;
s2, obtaining the refractive index and electromagnetic wave impedance expression of the sample to be tested according to the electromagnetic wave principle; wherein, for nonmagnetic materials, the refractive index and the electromagnetic wave impedance are both functions of complex dielectric constants;
s3, obtaining a transmissivity function according to the wave vector of the electromagnetic wave, the complex dielectric constant, the refractive index and the electromagnetic wave impedance;
s4, obtaining a loss function according to the transmittance function and the transmittance in the step S1;
s5, solving complex dielectric constants of the sample to be measured under different thicknesses by using a machine learning gradient descent algorithm for the loss function.
In a preferred embodiment of the present invention, the method for obtaining the transmittance of the sample to be measured in step S1 includes constructing a system for obtaining the transmittance of the sample to be measured, the system for obtaining the transmittance of the sample to be measured including an incident excitation source electromagnetic wave, the sample to be measured, and an electromagnetic wave receiving resolver;
the incident excitation source electromagnetic wave is used for emitting electromagnetic waves with the frequency of Freq;
the electromagnetic wave receiving analyzer is used for analyzing the received electromagnetic wave to obtain the transmissivity t of the sample to be detected 0 ；
The sample to be tested comprises a homogenizing plate, wherein the homogenizing plate can be made of resin, the homogenizing plate is rectangular, an incident excitation source electromagnetic wave is arranged at one end of the homogenizing plate, and an electromagnetic wave receiving analyzer is arranged at the opposite end of the homogenizing plate.
In a preferred embodiment of the present invention, the method further comprises placing the homogenizing plate horizontally on a horizontal table, so that the electromagnetic wave of the incident excitation source is incident along an incident angle θ, θ∈ (-pi/2, pi/2), where θ is an angle between the incident direction and the normal direction of the sample surface.
In a preferred embodiment of the present invention, θ=0;
the transmittance is expressed by:
t 0 =a+bj
wherein t is 0 Representing the transmittance obtained by experiment;
a represents the real part value of transmittance;
b represents the imaginary value of the transmittance;
j represents an imaginary unit.
In a preferred embodiment of the present invention, the method for obtaining the wave vector of the electromagnetic wave of the incident excitation source according to the frequency of the electromagnetic wave of the incident excitation source comprises the following steps:
k=2*np.pi*Freq/3E8
wherein k represents the wave vector of the electromagnetic wave of the incident excitation source;
2 represents a value of 2;
nppi represents the circumference ratio pi;
freq represents the frequency of the incident excitation source electromagnetic wave;
3E8 represents the propagation velocity of the incident excitation source electromagnetic wave.
In a preferred embodiment of the present invention, the complex permittivity expression of the sample to be measured in step S3 is:
EpsR=EpsRr+EpsRi*1j
wherein, epsR represents complex dielectric constant of the sample to be measured;
EpsRr represents the real part value of the complex permittivity;
EpsRi represents the imaginary value of the complex dielectric constant;
1 represents a value 1;
j represents an imaginary unit.
In a preferred embodiment of the present invention, the method for expressing the refractive index of the sample to be measured in step S2 is as follows:
n=jnp.sqrt(EpsR)
wherein n represents the refractive index of the sample to be measured;
jnp.sqrt () represents open square;
EpsR represents the complex permittivity of the sample to be measured;
in step S2, the method for representing electromagnetic impedance of the sample to be measured includes:
z=jnp.sqrt(1/EpsR)
wherein z represents the electromagnetic wave impedance of the sample to be measured;
jnp.sqrt () represents open square;
EpsR represents the complex permittivity of the sample to be tested.
In a preferred embodiment of the present invention, the expression of the transmittance function in step S3 is:
t(ε r )=2j*z/(2j*z*jnp.cos(n*d*k)+(1+z*z)*jnp.sin(n*d*k))=2j*jnp.sqrt(1/EpsR)/(2j*jnp.sqrt(1/EpsR)*jnp.cos(jnp.sqrt(EpsR)*d*2*np.pi*Freq/3E8)+(1+jnp.sqrt(1/EpsR)*jnp.sqrt(1/EpsR))*jnp.sin(jnp.sqrt(EpsR)*d*2*np.pi*Freq/3E8))
wherein t (ε) r ) Representing a transmittance function;
2 represents a value of 2;
j represents an imaginary unit;
z represents the electromagnetic wave impedance of the sample to be measured;
jnp.cos () represents a cosine function;
n represents the refractive index of the sample to be measured;
d represents the thickness of the sample to be measured;
k represents the wave vector of the electromagnetic wave of the incident excitation source;
1 represents a value 1;
jnp.sin () represents a sine function.
In a preferred embodiment of the present invention, the expression of the loss function in step S4 is:
f_loss(ε r ) T (∈) r )-t 0 I (I)
Where f_loss (ε) r ) Representing a loss function;
i represents an absolute value function;
t(ε r ) Representing a transmittance function;
t 0 the transmittance obtained by the experiment is shown.
In a preferred embodiment of the present invention, the solving means in step S5 includes the steps of:
s51, setting a complex dielectric constant of one sample to epsilon i As an initial value of the iteration; setting a learning rate L and a preset iteration number threshold;
s52, for the loss function f_loss (ε) r ) With respect to the variable epsilon r Differentiating df_loss (epsilon) r )=∂f_loss(ε r )/∂ε r Wherein ∂ represents a biased derivative;
s53, starting from the initial value epsilon of the complex permittivity of the sample i Starting iterative calculation:
ε i(n+1) =ε i(n) -L*df_loss(ε i(n) )
wherein ε i(n+1) Representing the complex dielectric constant obtained in the nth iteration and serving as an initial value of the (n+1) th iteration;
ε i(n) the initial value of the nth iteration is represented, and the initial value is also the complex dielectric constant obtained by the nth-1 iteration;
l represents a learning rate of machine learning;
when the loss function f_loss (epsilon) r ) When the value is smaller than the preset stop threshold value, orAnd stopping the loop when the iteration times are larger than a preset iteration times threshold.
In summary, by adopting the technical scheme, the electromagnetic parameter inverse algorithm is performed based on the gradient descent concept which is the most critical in the field of artificial intelligence, and the algorithm is different from the NRW method based on algebraic algorithm, and can be combined with deep learning and a neural network to realize more flexible operation. Secondly, the NRW operation method needs to measure the transmissivity and the reflectivity of the sample, and the method only needs one parameter of the transmissivity, and in addition, the method can still work normally under the condition of oblique incidence.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
The foregoing and/or additional aspects and advantages of the invention will become apparent and may be better understood from the following description of embodiments taken in conjunction with the accompanying drawings in which:
FIG. 1 is a schematic diagram of complex permittivity results calculated using the NRW method.
FIG. 2 is a graph showing the complex permittivity results calculated using the method of the present invention.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the invention.
The invention provides a material electromagnetic parameter extraction method based on a machine learning gradient descent algorithm, which comprises the following steps of:
s1, acquiring the transmissivity of a sample to be tested; in the embodiment of the invention, the method for acquiring the transmissivity of the sample to be measured comprises the steps of firstly constructing an acquisition system of the transmissivity of the sample to be measured, wherein the acquisition system of the transmissivity of the sample to be measured comprises an incident excitation source electromagnetic wave, the sample to be measured and an electromagnetic wave receiving analyzer;
the incident excitation source electromagnetic wave is used for emitting electromagnetic waves with the frequency of freq=10ghz;
the electromagnetic wave receiving analyzer is used for analyzing the received electromagnetic wave to obtain the transmissivity t0 of the sample to be detected;
the sample to be tested comprises homogenizing plates with different thicknesses, wherein the materials of the homogenizing plates are preferably resin materials, the advantage is that the magnetic permeability is 1+0j, the shape of the homogenizing plates is cuboid, the incident excitation source electromagnetic wave is arranged at one end of the homogenizing plates, and then the electromagnetic wave receiving analyzer is arranged at the opposite end of the homogenizing plates. When in test, the homogeneous plate is horizontally placed on a horizontal platform, so that the electromagnetic wave of the incident excitation source is incident along an incident angle theta, theta epsilon (-pi/2, pi/2), theta is the included angle between the incident direction and the horizontal direction, and the best horizontal incidence is theta=0.
The transmittance at different thicknesses can also be measured by adopting the existing mode, the obtained transmittance is split into a real part numerical value and an imaginary part numerical value, and the real part numerical value and the imaginary part numerical value are put into a TXT document, and the three-column form is generally adopted to represent the transmittance as shown in the table 1: the first column is the thickness of the homogenization plate, the second column is the real number and the third column is the imaginary number.
TABLE 1 real and imaginary parts of transmittance at different thicknesses
Sequence number Thickness (Unit mm) Real part numerical value Imaginary part value
01 1 0.5579 0.42709
02 1.2 0.48313 0.45151
03 1.4 0.41621 0.46818
04 1.6 0.35587 0.47981
05 1.8 0.30073 0.48839
06 2 0.2494 0.49497
07 2.2 0.20073 0.5
08 2.4 0.15358 0.50383
09 2.6 0.10694 0.50645
10 2.8 0.060058 0.50745
11 3 0.012295 0.50633
12 3.2 -0.036788 0.50228
13 3.4 -0.087367 0.49434
14 3.6 -0.13919 0.48138
15 3.8 -0.19165 0.46226
16 4 -0.24355 0.43594
17 4.2 -0.29336 0.40156
18 4.4 -0.3388 0.35942
19 4.6 -0.37797 0.30991
20 4.8 -0.40893 0.25453
21 5 -0.43037 0.1952
22 5.2 -0.44159 0.13423
23 5.4 -0.44287 0.074144
24 5.6 -0.4351 0.016936
25 5.8 -0.41966 -0.035921
26 6 -0.39807 -0.083401
27 6.2 -0.37202 -0.12516
28 6.4 -0.34275 -0.16116
29 6.6 -0.3115 -0.1917
30 6.8 -0.27907 -0.21719
31 7 -0.24597 -0.23819
32 7.2 -0.21272 -0.25509
33 7.4 -0.17952 -0.26833
34 7.6 -0.14647 -0.2782
35 7.8 -0.11373 -0.28492
36 8 -0.081361 -0.2887
37 8.2 -0.049335 -0.28948
38 8.4 -0.017856 -0.28738
39 8.6 0.012945 -0.28236
40 8.8 0.042924 -0.27436
41 9 0.071773 -0.26336
42 9.2 0.099109 -0.24937
43 9.4 0.1246 -0.2325
44 9.6 0.14779 -0.21291
45 9.8 0.16832 -0.19083
46 10 0.1858 -0.16669
Software reads the data in the TXT document and combines it into a transmittance at different thicknesses, e.g. 1mm thickness, t 0 =0.5579+0.42709 j; when the thickness is 1.2mm, the transmittance is t 0 =0.48313+0.45151j; when the thickness is 1.4mm, the transmittance is t 0 =0.41621+0.46818j; when the thickness is 1.6mm, the transmittance is t 0 =0.35587+0.47981j; the other thicknesses mentioned above are not listed here.
S2, obtaining the refractive index and electromagnetic wave impedance expression of the sample to be tested according to the electromagnetic wave principle;
s3, obtaining a transmissivity function according to the wave vector of the electromagnetic wave, the complex dielectric constant, the refractive index and the electromagnetic wave impedance;
s4, obtaining a loss function according to the transmittance function and the transmittance in the step S1;
s5, solving the complex dielectric constant of the sample to be measured by using a machine learning gradient descent algorithm for the loss function.
In a preferred embodiment of the present invention, the method for obtaining the wave vector of the electromagnetic wave of the incident excitation source according to the frequency of the electromagnetic wave of the incident excitation source comprises the following steps:
k=2*np.pi*Freq/3E8
wherein k represents the wave vector of the electromagnetic wave of the incident excitation source;
2 represents a value of 2;
nppi represents the circumference ratio pi;
freq represents the frequency of the incident excitation source electromagnetic wave;
3E8 represents the propagation velocity of the incident excitation source electromagnetic wave.
In a preferred embodiment of the present invention, the complex permittivity expression of the sample to be measured in step S3 is:
EpsR=EpsRr+EpsRi*1j
wherein, epsR represents complex dielectric constant of the sample to be measured;
EpsRr represents the real part value of the complex permittivity;
EpsRi represents the imaginary value of the complex dielectric constant;
1 represents a value 1;
j represents an imaginary unit.
It should be noted that EpsRr and EpsRi in the complex permittivity expression of the sample to be measured are unknowns, which are two numbers to be solved.
In a preferred embodiment of the present invention, the method for expressing the refractive index of the sample to be measured in step S2 is as follows:
n=jnp.sqrt(EpsR)
wherein n represents the refractive index of the sample to be measured;
jnp.sqrt () represents open square;
EpsR represents the complex permittivity of the sample to be measured;
in step S2, the method for representing electromagnetic impedance of the sample to be measured includes:
z=jnp.sqrt(1/EpsR)
wherein z represents the electromagnetic wave impedance of the sample to be measured;
jnp.sqrt () represents open square;
EpsR represents the complex permittivity of the sample to be tested.
In a preferred embodiment of the present invention, the expression of the transmittance function in step S3 is:
t(ε r ) =2j×jnp.cos (n×d×k) + (1+z×z) ×jnp.sin (n×d×k))=2j×jnp.sqrt (1/EpsR)/(2j×jnp.sqrt (1/EpsR) ×jnp.cos (jnp.sqrt (EpsR) ×d×2×np.freq/3E 8)), where t (ε) r ) Can be written as t (EpsRr, epsRi), i.e. epsilon r EpsRr, epsRi, the purpose of which is to solve for EpsRr and EpsRi.
Wherein t (ε) r ) Representing a transmittance function;
2 represents a value of 2;
j represents an imaginary unit;
z represents the electromagnetic wave impedance of the sample to be measured;
jnp.cos () represents a cosine function;
n represents the refractive index of the sample to be measured;
d represents the thickness of the sample to be measured;
k represents the wave vector of the electromagnetic wave of the incident excitation source;
1 represents a value 1;
jnp.sin () represents a sine function.
In a preferred embodiment of the present invention, the expression of the loss function in step S4 is:
f_loss(ε r ) T (∈) r )-t 0 I (I)
Where f_loss (ε) r ) Representing a loss function;
i represents an absolute value function;
t(ε r ) Representing a transmittance function;
t 0 the transmittance obtained by the experiment is shown.
In a preferred embodiment of the present invention, the solving means in step S5 includes the steps of:
s51, setting a complex dielectric constant of one sample to epsilon i As an initial value of the iteration; setting a learning rate L and a preset iteration number threshold; here ε i B+vj, b being the real value of the set complex permittivity of the sample and v being the imaginary value of the set complex permittivity of the sample;
s52, for the loss function f_loss (ε) r ) With respect to the variable epsilon r Differentiating df_loss (epsilon) r )=∂f_loss(ε r )/∂ε r Wherein ∂ represents a biased derivative;
s53, starting from the initial value epsilon of the complex permittivity of the sample i Starting iterative calculation:
ε i(n+1) =ε i(n) -L*df_loss(ε i(n) )
wherein ε i(n+1) Representing the complex dielectric constant obtained in the nth iteration and serving as an initial value of the (n+1) th iteration;
ε i(n) representing the initial value of the nth iteration and the complex dielectric constant obtained by the nth-1 iteration；
L represents a learning rate of machine learning;
when the loss function f_loss (epsilon) r ) And stopping the loop when the number of iterations is smaller than a preset stopping threshold or when the number of iterations is larger than a preset iteration number threshold (1001). General loss function f_loss (ε) r ) Less than a preset stop threshold may be a loss function f_loss (ε) r ) Near 0 (0.001) is taken as a stop condition.
As shown in fig. 1, the complex permittivity of the sample to be measured having a complex permittivity of 7+3j and a permeability of 1+0j shows that dispersion phenomenon occurs in the complex permittivity as the thickness of the sample to be measured gradually increases from 1mm to 10 mm.
As shown in fig. 2, the complex permittivity of the sample to be measured having a complex permittivity of 7+3j and a permeability of 1+0j shows that the complex permittivity does not exhibit any dispersion phenomenon during the gradual increase of the thickness of the sample to be measured from 1mm to 10 mm.
The code of the invention is as follows:
import numpy as np
import matplotlib.pyplot as plt
import jax
import jax.numpy as jnp
import pandas as pd
Freq = 10E9
rowdata = pd.read_csv('E:\slab transmission\data\homo_slab\\sweepd.txt',sep='\t',names=['d','real','imag'])
d_G=rowdata['d']
t_real=rowdata['real']
t_imag=rowdata['imag']
t_complex=t_real+t_imag*1j
d_start=d_G[0]
d_stop=d_G.iat[-1]
print(d_start,d_stop)
d_G=d_G*1E-3
data=pd.DataFrame({
"d":d_G,
"t":t_complex
})
print(data)
def t(EpsRr,EpsRi,d):
k = 2*np.pi*Freq/3E8
EpsR=EpsRr+EpsRi*1j
n = jnp.sqrt(EpsR)
z = jnp.sqrt(1/EpsR)
t_val = 2j*z/(2j*z*jnp.cos(n*d*k)+(1+z*z)*jnp.sin(n*d*k))
return t_val
def loss(EpsRr,EpsRi,d,t_COMSOL):
t_pred = t(EpsRr,EpsRi,d)
lossr_val = jnp.abs(t_pred-t_COMSOL)
return lossr_val
D_lossr = jax.grad(loss,0)
D_lossi = jax.grad(loss,1)
Lr = 1e-1 # The learning rate for real part
Li = 1e-1 # The learning rate for imag part
epochs = 1001 # The number of iterations to perform gradient descent
EpsR_init = complex(6,2)
EpsR = EpsR_init
d_points=len(d_G)
index=0
d_axes=np.linspace(d_start,d_stop,d_points)
ii=1
Epslionr=[]
Epslioni=[]
for i in range(d_points):
d=d_G[i]
t0=t_complex[i]
D_lossr_val = D_lossr(jnp.real(EpsR),jnp.imag(EpsR),d,t0).item()
D_lossi_val = D_lossi(jnp.real(EpsR),jnp.imag(EpsR),d,t0).item()
EpsR = EpsR_init
EpsR = EpsR - complex(Lr*D_lossr_val,Li*D_lossr_val)
ii=1
while jnp.abs(Lr*D_lossr_val)>0.001 or jnp.abs(Li*D_lossi_val)>0.001:
D_lossr_val = D_lossr(jnp.real(EpsR),jnp.imag(EpsR),d,t0).item()
D_lossi_val = D_lossi(jnp.real(EpsR),jnp.imag(EpsR),d,t0).item()
EpsR = EpsR - complex(Lr*D_lossr_val,Li*D_lossi_val)
ii += 1
if ii>epochs:
break
Epslionr.append(jnp.real(EpsR))
Epslioni.append(jnp.imag(EpsR))
Eps=pd.DataFrame({
"real":Epslionr,
"imag":Epslioni
})
print(Eps)
plt.plot(d_axes,Epslionr,d_axes,Epslioni)
plt.show()
while embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.

Claims (3)

1. The material electromagnetic parameter extraction method based on the machine learning gradient descent algorithm is characterized by comprising the following steps of:
s1, acquiring electromagnetic wave transmittance of a sample to be detected;
s2, obtaining the refractive index and electromagnetic wave impedance expression of the sample to be tested according to the electromagnetic wave principle;
s3, obtaining a transmissivity function according to the wave vector of the electromagnetic wave, the complex dielectric constant, the refractive index and the electromagnetic wave impedance; the expression of the transmittance function is:
t(ε r )=2j*z/(2j*z*jnp.cos(n*d*k)+(1+z*z)*jnp.sin(n*d*k))
wherein t (ε) r ) Representing a transmittance function;
2 represents a value of 2;
j represents an imaginary unit;
z represents the electromagnetic wave impedance of the sample to be measured;
jnp.cos () represents a cosine function;
n represents the refractive index of the sample to be measured;
d represents the thickness of the sample to be measured;
k represents the wave vector of the electromagnetic wave of the incident excitation source;
1 represents a value 1;
jnp.sin () represents a sine function;
s4, obtaining a loss function according to the transmittance function and the transmittance in the step S1;
s5, solving the complex dielectric constant of the sample to be tested by using a machine learning gradient descent algorithm;
the method for acquiring the transmissivity of the sample to be detected in the step S1 comprises the steps of constructing a system for acquiring the transmissivity of the sample to be detected, wherein the system for acquiring the transmissivity of the sample to be detected comprises an incident excitation source electromagnetic wave, the sample to be detected and an electromagnetic wave receiving analyzer;
the incident excitation source electromagnetic wave is used for emitting electromagnetic waves with the frequency of Freq;
the electromagnetic wave receiving analyzer is used for analyzing the received electromagnetic wave to obtain the transmissivity t of the sample to be detected 0 ；
The sample to be tested comprises a homogenizing plate, wherein an incident excitation source electromagnetic wave is arranged at one end of the homogenizing plate, and an electromagnetic wave receiving analyzer is arranged at the opposite end of the homogenizing plate;
the method for obtaining the electromagnetic wave vector of the incident excitation source according to the frequency of the electromagnetic wave of the incident excitation source comprises the following steps:
k=2*np.pi*Freq/3E8
wherein k represents the wave vector of the electromagnetic wave of the incident excitation source;
2 represents a value of 2;
nppi represents the circumference ratio pi;
freq represents the frequency of the incident excitation source electromagnetic wave;
3E8 represents the propagation speed of the incident excitation source electromagnetic wave;
in step S3, the complex permittivity expression of the sample to be measured is:
EpsR=EpsRr+EpsRi*1j
wherein, epsR represents complex dielectric constant of the sample to be measured;
EpsRr represents the real part value of the complex permittivity;
EpsRi represents the imaginary value of the complex dielectric constant;
1 represents a value 1;
j represents an imaginary unit;
in step S2, the method for expressing the refractive index of the sample to be measured includes:
n=jnp.sqrt(EpsR)
wherein n represents the refractive index of the sample to be measured;
jnp.sqrt () represents open square;
EpsR represents the complex permittivity of the sample to be measured;
in step S2, the method for representing electromagnetic impedance of the sample to be measured includes:
z=jnp.sqrt(1/EpsR)
wherein z represents the electromagnetic wave impedance of the sample to be measured;
jnp.sqrt () represents open square;
EpsR represents the complex permittivity of the sample to be measured;
the expression of the loss function in step S4 is:
f_loss(ε r ) T (∈) r )-t 0 I (I)
Where f_loss (ε) r ) Representing a loss function;
i represents an absolute value function;
t(ε r ) Representing a transmittance function;
t 0 representing the transmittance obtained by experiment;
the solving method in step S5 includes the steps of:
s51, setting a complex dielectric constant of one sample to epsilon i As an initial value of the iteration; setting a learning rate L and a preset iteration number threshold;
s52, for the loss function f_loss (ε) r ) With respect to the variable epsilon r Differentiating df_loss (epsilon) r )=∂f_loss(ε r )/∂ε r Wherein ∂ represents a biased derivative;
s53, starting from the initial value epsilon of the complex permittivity of the sample i Starting iterative calculation:
ε i(n+1) =ε i(n) -L*df_loss(ε i(n) )
wherein ε i(n+1) Representing the complex dielectric constant obtained in the nth iteration and serving as an initial value of the (n+1) th iteration;
ε i(n) the initial value of the nth iteration is represented, and the initial value is also the complex dielectric constant obtained by the nth-1 iteration;
l represents a learning rate of machine learning;
when the loss function f_loss (epsilon) r ) And stopping the loop when the number of iterations is smaller than a preset stopping threshold value or when the number of iterations is larger than a preset iteration number threshold value.
2. The method for extracting electromagnetic parameters of a material based on a machine learning gradient descent algorithm according to claim 1, further comprising horizontally placing a homogenizing plate on a horizontal table, so that an incident excitation source electromagnetic wave is incident along an incident angle θ, θ e (-pi/2, pi/2), θ being an angle between an incident direction and a horizontal direction.
3. The method for extracting electromagnetic parameters of a material based on a machine learning gradient descent algorithm according to claim 2, wherein θ=0;
the transmittance is expressed by:
t 0 =a+bj
wherein t is 0 Representing the transmittance obtained by experiment;
a represents the real part value of transmittance;
b represents the imaginary value of the transmittance;
j represents an imaginary unit.
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