Dielectric constant measurement method based on open coaxial probe and neural network

Abstract

The application discloses a dielectric constant measurement method based on an open coaxial probe and a neural network, and specifically comprises the following steps: calculating a data set 1 of complex dielectric constants in a target range, and calculating a data set 2 of reflection coefficients corresponding to different sample thicknesses; dividing the data set 1 and the data set 2 obtained in step 1 into a training set and a test set; training an F-NN network with the data set 1 as output and the data set 2 as input, and saving the network with the best training and test effect; training an ID-NN network with the data set 2 as output and the data set 1 as input, and bringing the network into the F-NN network trained in step 3, and saving the network with the best training and test effect; and bringing a to-be-measured solution into the ID-NN network obtained in step 4 after measurement and calibration, so that the corresponding dielectric constant can be obtained. The application can quickly and accurately measure the relative complex dielectric constant of a to-be-measured object, the method is flexible to realize, and is suitable for measuring the dielectric coefficients of various substances.

Description

Technical Field

[0001] This invention relates to the field of dielectric constant measurement technology, and in particular to a dielectric constant measurement method based on an open coaxial probe and a neural network. Background Technology

[0002] The dielectric constant is a critical system design parameter for developing microwave diagnostic, imaging, and therapeutic devices, as well as RF / microwave circuits; its accuracy significantly impacts system reliability. Depending on the sample properties and the frequency of interest, different techniques can be employed to measure the dielectric constant. One widely used technique is the open-ended coaxial probe (OECP) method, which has been used for complex dielectric constant characterization of many different materials, including liquids, biological tissues, and concrete.

[0003] The main reason this technique is widely used is that it requires only complete contact between the analyte and the probe aperture, without the need for rigorous sample preparation procedures. Furthermore, this technique enables broadband measurement of the complex permittivity of the analyte. These advantages make it a widely preferred tool for measuring the complex permittivity; however, this method suffers from significant measurement errors. Sources of error include mathematical methods, calibration degradation, and sample heterogeneity. Since the permittivity is not a measurable quantity but is calculated from other measurable quantities, it can be inferred that mathematical methods are likely a major factor contributing to measurement errors.

[0004] In OECP technology, the reflected signal from the object under test is measured and converted into the complex permittivity. Retrieving the complex permittivity from the measured reflection coefficient has been achieved using various mathematical methods, including the full-wave method and the equivalent circuit model. The full-wave analysis method proposed by British scientist J.P. Grant provides higher accuracy results for broadband applications, but suffers from poor convergence and slow computational performance when handling large amounts of data. The equivalent circuit model proposed by IEEE scientist Maria Stuchly offers faster computation speeds, but suffers from low accuracy and limited bandwidth. Summary of the Invention

[0005] To overcome the aforementioned problems in the prior art, this invention proposes a dielectric constant measurement method based on an open coaxial probe and a neural network.

[0006] The technical solution adopted by this invention to solve its technical problem is: a dielectric constant measurement method based on an open coaxial probe and a neural network, comprising the following steps:

[0007] Step 1: Calculate the complex permittivity within the target range to obtain dataset 1, and calculate the reflection coefficient corresponding to different sample thicknesses to obtain dataset 2;

[0008] Step 2: Divide the dataset 1 and dataset 2 obtained in Step 1 into training set and test set;

[0009] Step 3: Using dataset 1 as output and dataset 2 as input, train the F-NN network using backpropagation and gradient descent. Add a ReLU activation function after each layer and save the network with the best training and testing results respectively.

[0010] Step 4: Using dataset 1 as input and dataset 2 as output, the backpropagation algorithm and gradient descent method are used to input the F-NN network trained in Step 3. The loss function of the F-NN network and the ID-NN network are combined to generate the loss function of the cascaded network. The ID-NN network is trained using the new loss function. After each layer, the ReLU activation function is added, and the network with the best training and testing performance is saved.

[0011] Step 5: After measurement and calibration, the solution to be tested is fed into the ID-NN network obtained in step 4 to obtain the corresponding dielectric constant.

[0012] In the above-described dielectric constant measurement method based on an open coaxial probe and a neural network, the calculation formula for dataset 1 in step 1 is as follows:

[0013]

[0014] Where, ε c ε represents the complex permittivity of the test object, ω represents the angular frequency, and ε represents the angular frequency. s It is the static dielectric constant, ε ∞ τ is the dielectric constant of infinite frequency, τ is the characteristic relaxation time, and i represents the unit of the imaginary number;

[0015] By adjusting ε s ε ∞ The complex permittivity within the target range is obtained by taking values ​​of τ in different ranges and step sizes, i.e., dataset 1.

[0016] In the above-described dielectric constant measurement method based on an open coaxial probe and a neural network, the calculation formula for dataset 2 in step 1 is as follows:

[0017]

[0018]

[0019] Where Γ represents the reflection coefficient at the probe aperture, η1 represents the intrinsic impedance of the probe surface, a and b represent the inner and outer radii of the conductor, respectively, J0(-) represents the first-order Bessel function, d represents the thickness of the sample being measured, ω represents the angular frequency, ε0 ​​represents the vacuum permittivity, μ0 represents the vacuum permeability, ε1 represents the relative permittivity of the medium filling the coaxial probe, μ1 represents the relative permeability of the medium filling the coaxial probe, μc represents the permeability of the sample being measured, and ε c The complex permittivity of the analyte is represented by , where i represents the unit of the imaginary number, and k represents the unit of the imaginary number. c Represents continuous eigenvalues;

[0020] Substituting the complex permittivity obtained from dataset 1 into the calculation formula of dataset 2, we obtain the reflection coefficients corresponding to different sample thicknesses, i.e., dataset 2.

[0021] In the above-described dielectric constant measurement method based on an open coaxial probe and a neural network, the loss function of the F-NN network in step 3 is Loss. T for:

[0022]

[0023] Where n1 represents the number of samples in the training set of dataset 2, m represents the current sample, and Loss T Let ε represent the loss function of the F-NN network. cm Let ε′ represent the complex permittivity of the m-th element in the dataset. cm This represents the complex permittivity corresponding to the m-th reflection coefficient predicted by the F-NN network.

[0024] In the above-described dielectric constant measurement method based on an open coaxial probe and a neural network, the loss function Loss of the ID-NN network in step 4 is:

[0025] Loss = Loss T +h*Loss R

[0026]

[0027] Where n2 represents the number of samples in the training set of dataset 1, and Loss T Denotes the loss function of the F-NN network, Loss R Let h denote the additional loss function used for structural comparison, and h denote the equilibrium loss. T and Loss R Scale factor, Γ y Γ represents the reflection coefficient of the y-th element in database 2. y ′ represents the y-th reflection coefficient predicted by the ID-NN network.

[0028] The beneficial effects of this invention are as follows: Based on the design requirements for rapid and accurate measurement of the relative complex permittivity of the test object, this invention proposes a design scheme for a complex permittivity measurement network model that combines an open coaxial probe with a deep learning network, based on the Debye formula and the admittance electromagnetic model. The method is flexible and highly applicable. (1) The method of generating data using the Debye formula and the admittance formula replaces the traditional data collection process and can better cover the data in the target frequency domain, making it adaptable to more test objects in that frequency domain; (2) By comparing the predicted data of the network model with the target data, it achieves an accuracy similar to the traditional inversion method, which is suitable for measuring the dielectric constant of various materials; (3) This invention predicts the dielectric constant through the network model, which greatly reduces the required computing resources and time, and the network model is small in size, making it easy to use in engineering projects where complex calculations cannot be performed; (4) The results calculated by the deep learning model are compared with the calculated values ​​of the measurement data in the literature. The generated deep learning model has high accuracy and can be adapted to most scenarios of measuring the complex permittivity with an open coaxial probe, which is convenient for engineering implementation. Attached Figure Description

[0029] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0030] Figure 1 This is a flowchart of the present invention;

[0031] Figure 2 A comparison of the prediction results of the real and imaginary parts of the dimethyl sulfoxide solution of the present invention at the 8th frequency point with the results of the cited literature;

[0032] Figure 3 A comparison of the prediction results of the real and imaginary parts of the dimethyl sulfoxide solution of the present invention at the 21st frequency point with the results of the cited literature;

[0033] Figure 4 The prediction results of the real and imaginary parts of the ethanol solution at the 8th frequency point of this invention are compared with the results of the cited literature;

[0034] Figure 5 The prediction results of the real and imaginary parts of the ethanol solution at the 21st frequency point of this invention are compared with the results of the cited literature. Detailed Implementation

[0035] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0036] Based on the design requirement of rapid and accurate measurement of the relative complex permittivity of liquids, this invention proposes a design scheme for a complex permittivity measurement network model that combines an open coaxial probe with a deep learning network, based on the Debye formula and admittance electromagnetic model.

[0037] An open-ended coaxial probe (OECP) consists of two concentric cylindrical conductors with a dielectric material between them. When using an OECP to obtain the dielectric properties of a analyte, the relationship between the complex dielectric constant of the analyte and the reflection coefficient of the probe is given by a classical electromagnetic model, as shown in equations (1) and (2):

[0038]

[0039]

[0040] Where Γ represents the reflection coefficient at the probe aperture, η1 represents the intrinsic impedance of the probe surface, a and b represent the inner and outer radii of the conductor, respectively, J0(-) represents the first-order Bessel function, d represents the thickness of the sample being measured, ω represents the angular frequency, ε0 ​​represents the vacuum permittivity, μ0 represents the vacuum permeability, ε1 represents the relative permittivity of the medium filling the coaxial probe, μ1 represents the relative permeability of the medium filling the coaxial probe, μc represents the permeability of the sample being measured, i represents the unit of the imaginary number, and k c ε represents continuous eigenvalues. c The complex permittivity of the test object can be expressed by the Debye formula, equation (3).

[0041]

[0042] Where, ε c ε represents the complex permittivity of the test object, ω represents the angular frequency, and ε represents the angular frequency. s It is the static dielectric constant, ε ∞ τ is the dielectric constant of infinite frequency, τ is the characteristic relaxation time, and i represents the unit of the imaginary number;

[0043] The Debye equation (3) can be used to generate the complex dielectric constant. Then, the reflection coefficient model (1) of the analyte is derived.

[0044] The Z-score formula in Equation (4) is used to normalize the data in the dataset so that they have balanced weights in the loss function. Data normalization can avoid data polarization, thus avoiding numerical problems, and at the same time, it can simplify the calculation process, thereby speeding up the calculation process. Here, x* is the normalization parameter, and x and σ represents the original data and their mean, and σ is the standard deviation of each parameter.

[0045]

[0046] In a fully connected cascaded network, the first step is to train a Forward Neural Network (F-NN). Using dataset 1 as the output and dataset 2 as the input, the network is trained using backpropagation and gradient descent. The loss function is updated in each iteration; as the number of iterations increases, the loss function decreases until a fitted state is reached, i.e., the gradient descent reaches its minimum. The hyperparameters are listed in Table 1. These values ​​were obtained after repeated training and testing of the network, and were manually adjusted.

[0047] number of floors 7 Number of neurons in each layer 2-100-300-200-100-50-20 Number of training iterations per session 200

[0048] The loss function of the feedforward neural network is shown in equation (5), which is used to calculate ε. c (The complex permittivity calculated by formula (3)) and ε′ i The mean absolute error (MAE) between the complex permittivity predicted by F-NN and the data training set, where n is the number of samples.

[0049]

[0050] Where n1 represents the number of samples in the training set of dataset 2, m represents the current sample, and Loss T Let ε represent the loss function of the F-NN network. cm Let ε′ represent the complex permittivity of the m-th element in the dataset. cm This represents the complex permittivity corresponding to the m-th reflection coefficient predicted by the F-NN network.

[0051] To demonstrate the accuracy of the trained F-NN, we choose an accuracy variable to represent it, which is calculated by formula (6):

[0052]

[0053] Then, the Inverse Design Neural Network (ID-NN) is trained. This is a key component of the cascaded network used to inversely design the device from a given desired spectrum. Using dataset 1 as input and dataset 2 as output, the backpropagation algorithm and gradient descent are applied to the F-NN network trained in step 3. The loss function of the cascaded network is generated by combining the loss functions of the F-NN and ID-NN networks. The ID-NN network is then trained using this new loss function. The loss function is iteratively updated until it reaches its minimum point through gradient descent. We can set its hyperparameters, as shown in Table 2, and manually adjust them, similar to the parameter selection process for the F-NN described earlier.

[0054] number of floors 6 Number of neurons in each layer 20-150-500-150-50-2 Number of training iterations per session 200

[0055] During training, if only the Loss in formula (5) is used... T To calculate the simulated target response ε cm and ε′ after concatenated NN deletion cm If the MAE between these parameters is low, then the trained ID-NN may produce an unreasonable GC structure, because for a given effective ε... cm There are no restrictions on its Γ' deletion. Therefore, to improve the accuracy of ID-NN during training, we can modify the loss function, as shown in formula (6). Simultaneously consider structural parameters and transmission response. Loss T It is given by formula (5), Loss R The MAE between the reflection coefficient Γ in the dataset and the ID-NN predicted Γ′ is given by equations (7) and (8), and the loss is... R This is an additional loss function used for structural comparison. Here, h is the loss function in the balanced total loss function. R and Loss T The scaling factor. If the normalization methods for the complex permittivity and the reflection coefficient are different, then h must be adjusted accordingly. If the data in the two training sets are normalized simultaneously, then it can be set to 1. Otherwise, it should be adjusted according to the accuracy value of equation (6) during the training process, and the value that maximizes the accuracy value should be selected.

[0056] Loss = Loss T +h*Loss R (7)

[0057]

[0058] Where n2 represents the number of samples in the training set of dataset 1, and Loss T Denotes the loss function of the F-NN network, Loss R Let h denote the additional loss function used for structural comparison, and h denote the equilibrium loss. T and Loss R Scale factor, Γ y Let Γ′ represent the reflection coefficient of the y-th element in database 2. y This represents the y-th reflection coefficient predicted by the ID-NN network.

[0059] The steps for implementing this invention are as follows: Figure 1 As shown, it specifically includes:

[0060] (1) First, use formula (2) to evaluate ε s ε ∞ By taking values ​​of τ within different ranges and step sizes, the relative complex permittivity ε within the target range can be obtained.c That is, dataset 1, now let ε c Substituting into formula (1), we can calculate the reflection coefficient corresponding to each complex permittivity at different thicknesses of the sample, i.e., dataset 2.

[0061] (2) For all samples in dataset 1 and dataset 2, 85% are used for network training and the remaining 15% are used for testing, thus completing the division of the dataset;

[0062] (3) The generated dataset of dielectric constants and dataset 1 are used as outputs, and the dataset of reflection coefficients, i.e. dataset 2, is used as inputs. The F-NN network is trained using formula (4) as the loss function. The network with the best training and testing results is saved respectively.

[0063] (4) Take the generated dielectric constant dataset (dataset 1) as input and the reflection coefficient dataset (dataset 2) as output, and substitute them into the F-NN network trained in step (3). Use formula (6) as the loss function to start training the ID-NN network and save the network with the best training and testing results.

[0064] (5) After the solution to be tested is calibrated by measurement, it is substituted into the ID-NN model trained in step (4) to obtain the corresponding dielectric constant.

[0065] This invention uses two solutions, dimethyl sulfoxide and ethanol, as examples. The complex permittivity obtained by calibrating the measured reflectance coefficients and inputting them into a network model is compared with data provided in the literature. There are 21 frequency points ranging from 0.5 GHz to 6 GHz, with one network at each frequency point. The data closest to each frequency point is input into the network trained at that frequency point. The networks at the 8th and 21st frequency points are selected to process the two solutions. The results are then compared with those in the literature. Figure 2 and Figure 3 The data referenced is provided by Tuba Yilmaz et al. in their 2019 paper, "Microwave Dielectric Spectroscopy of Renal Calculi: A Large Scale Study on Dielectric Properties from 500 MHz to 18 GHz," which has been cited multiple times.

[0066] For dimethyl sulfoxide solution, the results are as follows: Figure 2-3 As shown, the prediction error is around 6% at both the 8th and 21st frequency points, while for the ethanol solution, the result is as follows: Figure 4-5As shown, the prediction error at the two frequency points is about 10%, which meets our requirements for the accuracy of the dielectric constant and achieves the design expectation.

[0067] The above embodiments are merely exemplary embodiments of the present invention and are not intended to limit the present invention. The scope of protection of the present invention is defined by the claims. Those skilled in the art can make various modifications or equivalent substitutions to the present invention within its spirit and scope of protection, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of the present invention.

Claims

1. A method for measuring dielectric constant based on an open coaxial probe and a neural network, characterized in that: Includes the following steps: Step 1: Calculate the complex permittivity within the target range to obtain dataset 1, and calculate the reflection coefficient corresponding to different sample thicknesses to obtain dataset 2; Step 2: Divide the dataset 1 and dataset 2 obtained in Step 1 into training set and test set; Step 3: Using dataset 1 as output and dataset 2 as input, train the F-NN network using backpropagation and gradient descent. Add a ReLU activation function after each layer and save the network with the best training and testing results respectively. Step 4: Using dataset 1 as input and dataset 2 as output, the backpropagation algorithm and gradient descent method are used to input the F-NN network trained in Step 3. The loss function of the F-NN network and the ID-NN network are combined to generate the loss function of the cascaded network. The ID-NN network is trained using the new loss function. After each layer, the ReLU activation function is added, and the network with the best training and testing performance is saved. Step 5: After measurement and calibration, the solution to be tested is fed into the ID-NN network obtained in step 4 to obtain the corresponding dielectric constant.

2. The dielectric constant measurement method based on an open coaxial probe and neural network according to claim 1, characterized in that, The calculation formula for dataset 1 in step 1 is as follows: Where, ε c ε represents the complex permittivity of the test object, ω represents the angular frequency, and ε represents the angular frequency. s It is the static dielectric constant, ε ∞ τ is the dielectric constant of infinite frequency, τ is the characteristic relaxation time, and i represents the unit of the imaginary number; By adjusting ε s ε ∞ The complex permittivity within the target range is obtained by taking values ​​of τ in different ranges and step sizes, i.e., dataset 1.

3. The dielectric constant measurement method based on an open coaxial probe and neural network according to claim 2, characterized in that, The calculation formula for dataset 2 in step 1 is as follows: Where Γ represents the reflection coefficient at the probe aperture, η1 represents the intrinsic impedance of the probe surface, a and b represent the inner and outer radii of the conductor, respectively, J0(-) represents the first-order Bessel function, d represents the thickness of the sample being measured, ω represents the angular frequency, ε0 ​​represents the vacuum permittivity, μ0 represents the vacuum permeability, ε1 represents the relative permittivity of the medium filling the coaxial probe, μ1 represents the relative permeability of the medium filling the coaxial probe, μc represents the permeability of the sample being measured, and ε c The complex permittivity of the analyte is represented by , where i represents the unit of the imaginary number, and k represents the unit of the imaginary number. c Represents continuous eigenvalues; Substituting the complex permittivity obtained from dataset 1 into the calculation formula of dataset 2, we obtain the reflection coefficients corresponding to different sample thicknesses, i.e., dataset 2.

4. The dielectric constant measurement method based on an open coaxial probe and neural network according to claim 1, characterized in that, The loss function of the F-NN network in step 3 is Loss T for: Where n1 represents the number of samples in the training set of dataset 2, m represents the current sample, and Loss T Let ε represent the loss function of the F-NN network. cm Let ε′ represent the complex permittivity of the m-th element in the dataset. cm This represents the complex permittivity corresponding to the m-th reflection coefficient predicted by the F-NN network.

5. The dielectric constant measurement method based on an open coaxial probe and neural network according to claim 1, characterized in that, The loss function Loss of the ID-NN network in step 4 is: Loss=Loss T +h*Loss R Where n2 represents the number of samples in the training set of dataset 1, and Loss T Denotes the loss function of the F-NN network, Loss R Let h denote the additional loss function used for structural comparison, and h denote the equilibrium loss. T and Loss R Scale factor, Γ y Γ represents the reflection coefficient of the y-th element in database 2. y ′ represents the y-th reflection coefficient predicted by the ID-NN network.

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