Terahertz Measurement Method for Ceramic Layer Thickness Based on Adaptive Transfer Learning

Abstract

The present invention is applicable to the field of terahertz measurement technology, and provides a terahertz measurement method for the thickness of a ceramic layer based on adaptive transfer learning, comprising the following steps: constructing an analytical model considering the terahertz signal of a material color thermal barrier coating, measuring the reflection signal of a silver mirror by using a terahertz time-domain spectroscopy system, inputting the reflection signal as a reference signal into the analytical model to establish a source domain data set; measuring the terahertz experimental signal at the corresponding position by using a terahertz time-domain spectroscopy system, carrying out a metallographic experiment to extract the accurate thickness value of a sample, and constructing a target domain data set; establishing a source domain convolutional neural network and a target domain convolutional neural network to form a transfer learning framework, and realizing the measurement of the thickness of the ceramic layer of the thermal barrier coating. By exploring the propagation mechanism of terahertz waves in the thermal barrier coating, the present invention constructs a terahertz signal analytical model to generate a source domain data set, replaces part of the experimental signals to complete the training of the convolutional neural network, avoids manufacturing a large number of layer samples, and reduces the training cost.

Description

Technical Field

[0001] The present invention relates to the technical field of terahertz measurement, and specifically relates to a method for measuring the thickness of a ceramic layer based on adaptive transfer learning using terahertz waves. Background Technique

[0002] Thermal barrier coatings, as an important heat-insulating material for aeroengines, can improve the high-temperature resistance and corrosion resistance of turbine blades. The commonly used thermal barrier coating structure includes a top ceramic layer, a middle bonding layer, and a bottom metal substrate. The ceramic layer is usually prepared by atmospheric plasma spraying technology. Ceramic powder is sent into a high-temperature plasma flame and impacts the surface of the substrate with a certain kinetic energy, forming a layered organizational structure composed of countless deformed particles intersecting and stacked in a wavy shape. As a result, there is a certain degree of uneven thickness distribution in the prepared ceramic layer. If the ceramic layer is prepared too thin, its heat-insulating performance will be reduced. If it is sprayed too thickly, the huge difference in the thermal expansion coefficients between the ceramic layer and the substrate will cause a significant increase in the interfacial stress of the coating. Coupled with the extremely large centrifugal force generated by the high-speed rotation of the blade, the bonding strength between the ceramic layer and the substrate is weakened, resulting in the coating being extremely prone to peeling off. In view of this, regularly detecting the thickness of the ceramic layer is an important part of ensuring the service performance of turbine blades.

[0003] Currently, the commonly used methods for detecting the thickness of ceramic layers mainly include metallography, electrochemical impedance spectroscopy, eddy current, ultrasonic, infrared thermal imaging, and ray methods. The thickness measurement result of the metallography method is accurate and intuitive, but it is a destructive test and requires cutting the ceramic layer, resulting in damage to the thermal barrier coating. Affected by the low conductivity of the bonding layer, the measurement accuracy of the eddy current detection method is reduced. The ultrasonic method requires the use of a coupling agent, which may corrode the ceramic layer. When using the infrared thermal imaging method to detect materials with a low thermal radiation coefficient, a graphite coating needs to be applied. The ionization energy of X-rays is higher than the human threshold and may cause harm to the health of the detection personnel.

[0004] Terahertz is a frequency range of 0.1 THz - 10 THz (1 THz = 10 12Electromagnetic waves in the range of [[Hz]] are between microwave and far-infrared bands. Their ionization energy is on the order of meV, which is much less than the human body ionization threshold and is harmless to the human body. At the same time, terahertz can propagate in the air to achieve non-contact detection. The above advantages have made terahertz non-destructive testing technology increasingly widely used in the detection of ceramic layer thickness. The main measurement methods are based on time of flight, model iteration, and machine learning. For the terahertz thickness measurement method based on time of flight, it is necessary to prepare a standard specimen to calibrate the refractive index, and extract the time of flight by positioning the reflection peak to calculate the ceramic layer thickness. Due to the large number of randomly distributed pores inside the ceramic layer, the refractive index changes with spatial position, resulting in a difference from the calibration result and reducing the measurement accuracy. The model iteration thickness measurement method needs to establish an analytical model of terahertz signals and use an optimization algorithm to iteratively solve the mathematical model to obtain the ceramic layer thickness, with high accuracy but high computational complexity and low measurement efficiency. The machine learning thickness measurement method needs to extract features from terahertz signals and input the obtained features into a machine learning algorithm to predict the ceramic layer thickness. However, this method requires a large number of data samples to train weights and biases to establish a mathematical mapping between input features and thickness. Since the thermal barrier coating is prepared by an atmospheric plasma spraying process, this process is relatively complex. In addition, constructing a complete training set requires non-destructive terahertz testing of samples to obtain experimental signals and using destructive testing methods such as metallographic method to obtain accurate thickness values, which significantly increases the training cost. Summary of the Invention

[0005] To overcome the deficiency that the traditional machine learning-based thermal barrier coating thickness measurement method requires a large amount of experimental data, this invention proposes to use a terahertz analytical model to generate simulation signals to replace part of the experimental signals for network training based on the idea of transfer learning. To improve the transfer effect, an adaptive weight layer is innovatively designed to construct a terahertz measurement method for ceramic layer thickness based on adaptive transfer learning, which has the characteristics of low training cost and high accuracy. It can quantitatively evaluate the ceramic layer thickness and has important theoretical significance and engineering application value for accurately evaluating the manufacturing quality of blade coatings.

[0006] The present invention is implemented as follows. A terahertz measurement method for ceramic layer thickness based on adaptive transfer learning, the method comprising the following steps:

[0007] Construct an analytical model considering the terahertz signal of the material color thermal barrier coating. Use a terahertz time-domain spectroscopy system to measure the reflection signal of a silver mirror, and input the reflection signal as a reference signal into the analytical model. According to the actual ceramic layer thickness range, use the analytical model to simulate the propagation law of terahertz waves in the thermal barrier coating with different ceramic layer thicknesses, obtain a large number of terahertz signals with different simulated thicknesses, and establish a source domain dataset;

[0008] Prepare a thermal barrier coating sample, determine the position to be measured, apply a terahertz time-domain spectroscopy system to measure the terahertz experimental signal at the corresponding position, then conduct a metallographic experiment to extract the accurate thickness value of the sample, and construct a target domain dataset;

[0009] Establish a source domain convolutional neural network and a target domain convolutional neural network to form a transfer learning framework to achieve the measurement of the thickness of the ceramic layer of the thermal barrier coating.

[0010] As a further solution of the present invention: The steps of constructing an analytical model for considering the terahertz signal of the color-dispersive thermal barrier coating specifically include:

[0011] According to the phenomenon that the reflection peak of the terahertz signal is broadened due to the dispersion of the ceramic material, a linear approximation model is deduced to characterize the phenomenon, , where is the slope, is the initial value of the dielectric constant of the dense ceramic layer, is the initial value of the dielectric constant of the porous ceramic layer, ω is the angular velocity;

[0012] According to the square relationship between the initial value of the dielectric constant of the porous ceramic layer and the refractive index, the refractive index of the ceramic considering dispersion is deduced as , where is the refractive index of the ceramic layer;

[0013] Generate a terahertz simulation signal by using the relationship between the reference signal, the reflection coefficient, and the transmission coefficient: , where E 0( ω ) is the frequency-domain reference signal, E R ( ω ) is the terahertz frequency-domain simulation signal, E n (ω) is the frequency-domain representation of the n reflection peak, is the phase factor, c is the speed of light, ω is the angular velocity, is the thickness of the ceramic layer, , j =1, 2, 3, , and are the complex refractive indices of air, the ceramic layer, and the bonding layer respectively, is the extinction coefficient, n is the real part of the refractive index, t is the transmission coefficient, r is the reflection coefficient.

[0014] As a further solution of the present invention, the steps of establishing a source domain convolutional neural network and a target domain convolutional neural network to form a transfer learning framework specifically include:

[0015] According to the Fresnel formula, determine the mathematical mapping relationship between the first three reflection peaks and the refractive index;

[0016] Construct a source domain convolutional neural network and a target domain convolutional neural network. Both the source domain convolutional neural network and the target domain convolutional neural network include the same adaptive weight layer, convolutional layer, pooling layer and fully connected layer to form a complete transfer learning framework;

[0017] Use the source domain dataset to train the source domain convolutional neural network. After the training is completed, transfer the parameters of the convolutional layer, pooling layer and activation layer to the target domain convolutional neural network;

[0018] Use the target domain dataset to train the parameters of the adaptive weight layer and the fully connected layer of the target domain convolutional neural network, establish the mathematical mapping between the experimental signal and the thickness, and measure the actual thickness of the ceramic layer.

[0019] As a further solution of the present invention, in the step of determining the mathematical mapping relationship between the first three reflection peaks and the refractive index, it includes constructing an adaptive weight layer to assign different coefficients to the peaks to reduce the measurement error caused by the deformation of the reflection peaks, , where, Y represents the output of the adaptive weight layer, x i is the i element of the input terahertz time-domain signal, peak j is the j peak position coordinate, j = 1, 2, 3.

[0020] As a further solution of the present invention, the convolutional layer is expressed as: , where, represents the output of the l convolutional layer, i and j are the output data dimensions, b is the bias, w is the weight, and conv represents the convolution operation; the activation layer is expressed as: , where, is the output of the l activation layer, is the activation function; the pooling layer is expressed as: , where, is the output of the l pooling layer, and are the element coordinates, k is the pooling kernel size.

[0021] In the present invention, aiming at the propagation law of terahertz waves in thermal barrier coatings, an adaptive transfer learning method is used to measure the thickness of the ceramic layer without damaging a large number of samples. In this method, the measurement error caused by the deformation of the reflection peak is mainly reduced by constructing an adaptive weight, and the simulation signal is generated by the analytical model as the source domain data set, and then part of the experimental signal is used to train the convolutional neural network. At the same time, considering the difference between the simulation and experimental signals, by preparing thermal barrier coating samples, terahertz non-destructive testing experiments and metallographic experiments are carried out, and the experimental signals carrying thickness marks are obtained as the target domain data set, and only the adaptive weight layer and the fully connected layer of the target convolutional neural network are trained, and the parameters of the remaining layers are migrated from the source domain neural network, so as to complete the measurement of the thickness of the ceramic layer of the actual sample.

[0022] Compared with the existing detection methods, the present invention has the following advantages:

[0023] 1. By exploring the propagation mechanism of terahertz waves in thermal barrier coatings, an analytical model of terahertz signals is constructed to generate a source domain data set, and part of the experimental signals are used to complete the training of the convolutional neural network, which can avoid the production of a large number of layer samples and reduce the training cost;

[0024] 2. Due to the uneven microstructure of the thermal barrier coating and the difference in refractive index, the present invention can generate a source domain data set carrying different refractive index information through the analytical model to train the network parameters, reduce the influence of microstructure transformation on the thickness measurement accuracy, and has a higher measurement accuracy than the time-of-flight method of preparing standard samples to calibrate the refractive index;

[0025] 3. By constructing an adaptive weight layer, different weights can be intelligently assigned to the peaks according to the prediction error to reduce the refractive index extraction error caused by the deformation of the reflection peak, and improve the thickness measurement accuracy and transfer effect.

[0026] Therefore, the present invention provides a new method for efficient and intelligent detection of the thickness of the ceramic layer in the preparation process of thermal barrier coatings. Based on the idea of transfer learning, by generating a source domain data set through an analytical model to replace part of the experimental signals for training the parameters of the convolutional neural network, the thickness measurement of the ceramic layer of the actual thermal barrier coating can be realized, avoiding the large-scale preparation and destruction of samples, and there is no need to use an optimization algorithm for time-consuming iterative solution. At the same time, the present invention is constructed based on a convolutional neural network framework containing an adaptive weight layer, has strong learning ability and generalization ability, can reduce the influence of reflection peak deformation on thickness measurement, and can be extended to the thickness measurement problems of other non-polar materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a waveform diagram of a terahertz reference signal.

[0028] Figure 2It is a waveform diagram of a terahertz signal carrying information with a thickness of 200 μm and a refractive index of 5 - 0.05i.

[0029] Figure 3 It is a waveform diagram of a terahertz signal carrying information with a thickness of 300 μm and a refractive index of 4 - 0.05i.

[0030] Figure 4 It is a framework diagram of adaptive transfer learning.

[0031] Figure 5 It is a diagram for evaluating measurement accuracy.

[0032] Figure 6 It is a thickness distribution diagram of the ceramic layer sample of the thermal barrier coating. Specific embodiments

[0033] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0034] The following describes the specific implementation of the present invention in detail with reference to specific embodiments.

[0035] As Figures 1 to 3 shown, an embodiment of the present invention provides a terahertz measurement method for the thickness of a ceramic layer based on adaptive transfer learning. The method includes the following steps:

[0036] S100, construct an analytical model considering the terahertz signal of the material color thermal barrier coating, use a terahertz time-domain spectroscopy system (for example: TeraMetrix T-Ray 5000) to obtain the reflection signal of the terahertz wave vertically incident on a full-silver mirror as a reference signal, input the reference signal into the analytical model, and according to the actual ceramic layer thickness range, apply the analytical model to simulate the propagation law of the terahertz wave in the thermal barrier coating with different ceramic layer thicknesses, obtain a large number of terahertz signals with different simulated thicknesses, and establish a source domain dataset; specifically, by changing the thickness and refractive index parameters, obtain terahertz simulation signals carrying different thicknesses and refractive indices (for example, 10,000 signals with different refractive indices and thicknesses) as the source domain dataset, where two terahertz simulation signals carry thickness information of 300 μm and 200 μm respectively, and refractive indices of 4 - 0.05i and 5 - 0.05i;

[0037] S200, prepare a thermal barrier coating sample, determine the position to be measured, use a terahertz time-domain spectroscopy system to measure the terahertz experimental signal at the corresponding position, and then conduct a metallographic experiment to extract the accurate thickness value of the sample, and construct a target domain dataset;

[0038] S300. Establish a source domain convolutional neural network and a target domain convolutional neural network to form a transfer learning framework for realizing the measurement of the thickness of the ceramic layer of the thermal barrier coating.

[0039] In the embodiment of the present invention, the steps of constructing an analytical model for considering the terahertz signal of the material color-dispersive thermal barrier coating specifically include:

[0040] According to the phenomenon that the reflection peak of the terahertz signal is broadened due to the dispersion of the ceramic material, a linear approximation model is deduced to characterize the phenomenon, , where is the slope, is the initial value of the dielectric constant of the dense ceramic layer, is the initial value of the dielectric constant of the porous ceramic layer, ω is the angular velocity;

[0041] According to the square relationship between the initial value of the dielectric constant of the porous ceramic layer and the refractive index, the refractive index of the ceramic considering dispersion is deduced as , where is the refractive index of the ceramic layer;

[0042] Generate a terahertz simulation signal by using the relationship between the reference signal, the reflection coefficient, and the transmission coefficient: , where E 0( ω ) is the frequency-domain reference signal, E R ( ω ) is the terahertz frequency-domain simulation signal, E n ( ω ) is the frequency-domain representation of the nth reflection peak, is the phase factor, c is the speed of light, ω is the angular velocity, is the thickness of the ceramic layer, , j = 1, 2, 3, , and are the complex refractive indices of air, the ceramic layer, and the bonding layer respectively, is the extinction coefficient, n is the real part of the refractive index, t is the transmission coefficient, r is the reflection coefficient.

[0043] As Figure 4 shown, in the embodiment of the present invention, the steps of establishing a source domain convolutional neural network and a target domain convolutional neural network to form a transfer learning framework specifically include:

[0044] According to the Fresnel formula, the mathematical mapping relationship between the first three reflection peaks and the refractive index is determined. When the first three reflection peaks are not deformed, the formula can be used to measure the refractive index. However, affected by the Fabry - Perot effect, peak aliasing will occur, and it is necessary to obtain the first three reflection peaks after de - aliasing. However, this process will cause pulse - width compression distortion and amplitude change. Therefore, when constructing the mathematical mapping between the first three reflection peaks and the refractive index, it is necessary to build an adaptive weight layer to assign different coefficients to the peaks, reducing the measurement error caused by the deformation of the reflection peaks, , where, Y represents the output of the adaptive weight layer, x i is the i element of the input terahertz time - domain signal, peak j is the j peak position coordinate, j = 1, 2, 3.

[0045] Build a source - domain convolutional neural network and a target - domain convolutional neural network. Both the source - domain convolutional neural network and the target - domain convolutional neural network contain the same adaptive weight layer, convolutional layer, pooling layer, and fully - connected layer, forming a complete transfer learning framework. Among them, the convolutional layer can be expressed as: , where, represents the output of the l convolutional layer, i and j are the output data dimensions, b is the bias, w is the weight, and conv represents the convolution operation; the activation layer can be expressed as: , where, is the output of the l - th activation layer, is the activation function; the pooling layer can be expressed as: , where, is the output of the l pooling layer, and are the element coordinates, k is the pooling kernel size; specifically, both the source - domain convolutional neural network and the target - domain convolutional neural network each contain 1 adaptive weight layer, 5 convolutional layers, 5 activation layers, 2 pooling layers, and 3 fully - connected layers. The input signal size is 4096×1, the learning rate is selected as 0.01, the batch size is 128, and the maximum number of iteration steps is 500. The specific parameters of each layer are shown in the following table:

[0046] Table of parameter settings for the adaptive weight layer convolutional neural network

[0047] Names of each layer Parameter Adaptive weight layer 3 weights, and the value range of each is [0, 1] Convolutional layer 1 Convolution kernel size is 5×1, number of channels is 1, and the number is 32 Activation layer 1 Adopts the PReLu activation function, and the learnable parameter range is [0, 1] Convolutional layer 2 Convolution kernel size is 5×1, number of channels is 1, and the number is 16 Activation layer 2 Adopts the PReLu activation function, and the learnable parameter range is [0, 1] Convolutional layer 3 Convolution kernel size is 3×1, number of channels is 1, and the number is 16 Activation layer 3 Adopts the PReLu activation function, and the learnable parameter range is [0, 1] Convolutional layer 4 Convolution kernel size is 3×1, number of channels is 1, and the number is 8 Activation layer 4 Adopts the PReLu activation function, and the learnable parameter range is [0, 1] Convolutional layer 5 Convolution kernel size is 3×1, number of channels is 1, and the number is 8 Activation layer 5 Adopts the PReLu activation function, and the learnable parameter range is [0, 1] Pooling layer 1 Pooling layer size is 4×1 Pooling layer 2 Pooling layer size is 2×1 Fully connected layer 1 Number of neurons is 50 Fully connected layer 2 Number of neurons is 10 Fully connected layer 3 Number of neurons is 1

[0048] The source domain convolutional neural network is trained using the source domain dataset. After the training is completed, the parameters of the convolutional layer, pooling layer, and activation layer are migrated to the target domain convolutional neural network.

[0049] The adaptive weight layer and fully connected layer parameters of the target domain convolutional neural network are trained using the target domain dataset to establish a mathematical mapping between the experimental signal and the thickness, and the actual thickness of the ceramic layer is measured.

[0050] As Figure 5 and Figure 6 shown, in the embodiment of the present invention, 6 terahertz experimental signals with known thickness are selected and input into the trained transfer learning network to evaluate the method accuracy, and the mean absolute error is 1.78 μm. The newly prepared thermal barrier coating is scanned point by point through a terahertz time-domain spectroscopy system (for example: TeraMetrix T-Ray 5000), and the terahertz experimental signals at all positions of the specimen are input into the trained target domain convolutional neural network, and the thickness values at each detection position can be directly solved.

[0051] The present invention constructs an adaptive transfer learning framework, uses a terahertz signal analysis model to generate a source domain dataset to train the source domain convolutional neural network, and migrates the parameters of its convolutional layer, activation layer, and pooling layer, so as to realize the training of the adaptive weight layer and fully connected layer parameters of the target domain convolutional neural network with only a small amount of target domain dataset, and complete the measurement of the actual thickness of the ceramic layer. The method proposed by the present invention avoids the preparation of a large number of standard specimens. After the training of the target domain convolutional neural network is completed, the thickness measurement of the ceramic layer can be realized without iterative calculation, which can reduce the influence of the reflection peak deformation on the measurement accuracy, and form an accurate and efficient intelligent thickness measurement method. The present invention can realize the rapid measurement of the thickness of the ceramic layer at each position in a non-destructive manner, reduce the influence of the non-uniform microstructure of the ceramic layer on the thickness measurement accuracy, and has important theoretical significance and engineering application value for accurately evaluating the manufacturing quality of the blade coating.

[0052] The above only describes the preferred embodiments of the present invention in detail, and does not limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0053] After considering the specification and the disclosure of the embodiments, those skilled in the art will readily think of other embodiments of the present disclosure. This application is intended to cover any variations, uses, or adaptations of the present disclosure, which follow the general principles of the present disclosure and include the common general knowledge or conventional technical means in the technical field not disclosed in the present disclosure. The specification and the embodiments are only regarded as exemplary, and the true scope and spirit of the present disclosure are pointed out by the claims.

Claims

1. A terahertz measurement method for the thickness of a ceramic layer based on adaptive transfer learning, characterized in that, The method includes the following steps: Construct an analytical model considering the terahertz signal of the material-color thermal barrier coating, measure the reflection signal of the silver mirror using a terahertz time-domain spectroscopy system, input the reflection signal as a reference signal into the analytical model, and according to the actual ceramic layer thickness range, use the analytical model to simulate the propagation law of terahertz waves in the thermal barrier coating with different ceramic layer thicknesses, obtain a large number of terahertz signals with different simulated thicknesses, and establish a source domain dataset; Prepare a thermal barrier coating sample, determine the position to be measured, measure the terahertz experimental signal at the corresponding position using a terahertz time-domain spectroscopy system, then conduct a metallographic experiment to extract the accurate thickness value of the sample, and construct a target domain dataset; Establish a source domain convolutional neural network and a target domain convolutional neural network to form a transfer learning framework to achieve the measurement of the ceramic layer thickness of the thermal barrier coating.

2. The terahertz measurement method for the thickness of a ceramic layer based on adaptive transfer learning according to claim 1, wherein The steps of constructing the analytical model considering the terahertz signal of the material-color thermal barrier coating specifically include: Based on the phenomenon that the reflection peak of the terahertz signal broadens due to the dispersion of the ceramic material, a linear approximation model is derived to characterize this phenomenon. , where is the slope, is the initial value of the dielectric constant of the dense ceramic layer, is the initial value of the dielectric constant of the porous ceramic layer, ω is the angular velocity; Based on the square relationship between the initial value of the dielectric constant and the refractive index of the porous ceramic layer, the refractive index of the ceramic considering dispersion is deduced as , where is the refractive index of the ceramic layer; Generate a terahertz simulation signal using the relationship between the reference signal, reflection coefficient, and transmission coefficient: , where E 0( ω ) is the frequency-domain reference signal, E R ( ω ) is the terahertz frequency-domain simulation signal, E n ( ω ) is the frequency-domain representation of the n th reflection peak, is the phase factor, c is the speed of light, ω is the angular velocity, is the thickness of the ceramic layer, , j = 1, 2, 3, , and are the complex refractive indices of air, ceramic layer, and bonding layer respectively, is the extinction coefficient, n is the real part of the refractive index, t is the transmission coefficient, r is the reflection coefficient.

3. The terahertz measurement method for the thickness of a ceramic layer based on adaptive transfer learning according to claim 1, wherein The steps of establishing a source domain convolutional neural network and a target domain convolutional neural network to form a transfer learning framework specifically include: According to the Fresnel formula, determine the mathematical mapping relationship between the first three reflection peaks and the refractive index; Construct a source domain convolutional neural network and a target domain convolutional neural network. Both the source domain convolutional neural network and the target domain convolutional neural network include the same adaptive weight layer, convolutional layer, pooling layer, and fully connected layer to form a complete transfer learning framework; Use the source domain dataset to train the source domain convolutional neural network. After the training is completed, transfer the parameters of the convolutional layer, pooling layer, and activation layer to the target domain convolutional neural network; Use the target domain dataset to train the parameters of the adaptive weight layer and the fully connected layer of the target domain convolutional neural network, establish the mathematical mapping between the experimental signal and the thickness, and measure the actual thickness of the ceramic layer.

4. The terahertz measurement method for the thickness of a ceramic layer based on adaptive transfer learning according to claim 3, characterized in that The step of determining the mathematical mapping relationship between the first three reflection peaks and the refractive index includes constructing an adaptive weight layer to assign different coefficients to the peaks to reduce the measurement error caused by the deformation of the reflection peaks. ,in, Y represents the output of the adaptive weight layer, x i The input terahertz time domain signal i element, peak j For the j The peak position coordinates, j= 1, 2, 3.

5. The terahertz measurement method for the thickness of a ceramic layer based on adaptive transfer learning according to claim 3, characterized in that The convolutional layer is expressed as: , where represents the output of the l convolutional layer, i and j are the output data dimensions, b is the bias, w is the weight, and conv represents the convolution operation; the activation layer is expressed as: , where is the output of the l activation layer, is the activation function; the pooling layer is expressed as: , where is the output of the l pooling layer, and are the element coordinates, k is the pooling kernel size.

Images