New method of measuring thickness of thermal barrier coating based on model pre-three peak value driving

Abstract

This invention proposes a novel terahertz thickness measurement method for thermal barrier coatings based on the first three peak values ​​driven by a model. The method includes the following steps: preparing thermal barrier coating samples, conducting terahertz nondestructive testing experiments, and acquiring time-domain signals; exploring the interaction mechanism between terahertz waves and the thermal barrier coating, and analyzing that the first three peak values ​​contain the refractive index and time of flight required for thickness measurement; constructing a terahertz signal analytical model and extracting the first three peak values ​​as the training set; designing a weight allocation layer to reduce the difference between experiments and simulations caused by terahertz wave scattering, and updating network parameters via backpropagation; extracting the first three peak values ​​of the experimental signal as the test set, and conducting performance testing of the model-driven neural network. This invention explores the terahertz propagation mechanism to demonstrate that the first three peak values ​​can be used for thermal barrier coating thickness measurement, ensuring a high degree of agreement between the experimental test set and the simulation training set. It achieves accurate terahertz thickness measurement of thermal barrier coatings using deep learning methods without requiring extensive sample destruction.

Description

Technical Field

[0001] This invention relates to the field of terahertz thickness measurement, specifically to a novel terahertz thickness measurement method for thermal barrier coatings based on the first three peak values ​​of a model. Background Technology

[0002] Aero engines, hailed as the "crown jewel of industry," are a crucial component of aircraft. To improve thrust-to-weight ratio, combustion chamber temperatures are constantly increasing, now far exceeding the melting point of turbine blades. To address this, thermal barrier coatings are applied to the blade surface to resist the erosion of high-temperature gases and particles. The thickness of the top ceramic layer is related to its thermal resistance, determining its insulation performance. However, the ceramic layers produced by current mainstream atmospheric plasma spraying methods exhibit a wavy, stacked structure with uneven thickness. If the thickness is too great, the ceramic layer is prone to detachment under the immense centrifugal force of the high-speed rotation of the blade. Conversely, thinner areas have lower thermal resistance and increased thermal conductivity, leading to higher temperatures on the blade substrate surface and increased susceptibility to damage. Therefore, regular ceramic layer thickness testing is critical for extending the service life of turbine blades.

[0003] Current methods for measuring the thickness of thermal barrier coatings are divided into destructive and non-destructive methods. Destructive methods such as metallography offer high accuracy but require damaging the ceramic layer, resulting in sample waste. Non-destructive methods mainly include ultrasonic, eddy current, infrared, and X-ray methods. When using ultrasonic methods to measure ceramic layer thickness, a coupling agent needs to be applied to the surface, which can easily contaminate the coating. Eddy current methods can detect ceramic layer thickness, but the adhesive layer material is a nickel-based alloy with low conductivity, affecting measurement accuracy. Infrared methods suffer from uneven thermal emission on the ceramic layer surface, increasing measurement errors. X-ray methods provide intuitive results, but their high ionizing radiation poses a potential health hazard.

[0004] In recent years, terahertz nondestructive testing methods have been widely used in the measurement of thermal barrier coating thickness. Terahertz waves, with frequencies ranging from 0.1 THz to 10 THz, possess strong penetrability to ceramic materials and enable non-contact, non-ionizing thickness measurement. Currently, terahertz-based ceramic layer thickness measurement methods mainly include the time-of-flight method, the inversion method, and machine learning. The time-of-flight method obtains the flight time by locating the first two reflection peaks and extracts the refractive index from a standard sample to achieve thickness measurement. However, the ceramic layer contains a large number of randomly distributed pores, resulting in inconsistent refractive indices in different regions, which increases the measurement error of the time-of-flight method. The inversion method, on the other hand, constructs an optimized algorithm to iteratively solve the model, reducing the residual between simulation and experimental signals, and achieving simultaneous measurement of refractive index and thickness, thus reducing the measurement error caused by the inhomogeneity of the ceramic layer's microstructure. However, this method requires a large number of iterative calculations for each thickness measurement, resulting in low efficiency. In contrast, the machine learning method optimizes weights and bias parameters through backpropagation, establishing a mathematical mapping between input features and thickness. After training, the machine learning method can predict the ceramic layer thickness without iterative calculations. However, reverse propagation is a fully supervised method, which requires destroying a large number of thermal barrier coating samples to obtain accurate thickness values ​​as labels, which can easily lead to sample waste and increased costs. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a novel terahertz thickness measurement method for thermal barrier coatings based on the first three peak values ​​driven by a model. This method overcomes the limitation of data-driven machine learning-based methods requiring extensive sample destruction. Instead, it uses an analytical model to generate a training set and explores the mathematical mapping relationship between the first three reflection peaks and the thickness. This relationship is then used as input to a convolutional neural network, reducing redundant information that deviates significantly from experimental results. Furthermore, considering the terahertz wave scattering caused by the ceramic layer material, a weight allocation layer is proposed to reduce the weight of the third peak, which has a poorer fit. This results in a terahertz thickness measurement method for thermal barrier coatings driven by the first three peak values ​​of a model, achieving efficient and high-precision measurement. This method has significant theoretical and engineering application value for online evaluation of blade coating manufacturing quality.

[0006] The technical solution of this invention is as follows:

[0007] Includes the following steps:

[0008] 1) Construct an analytical model of terahertz signals that takes into account the surface roughness of thermal barrier coatings. Use a terahertz time-domain spectroscopy system to measure the reflection signal of the silver total reflection mirror as a reference signal and input it into the analytical model. Set different parameters such as thickness, refractive index, and roughness to generate simulation signals and extract the first three peaks of each simulation signal to construct a training set.

[0009] 2) Prepare thermal barrier coating specimens, use a terahertz time-domain spectroscopy system to measure the time-domain signal at different locations of the sample, and extract the top three peak values; then, use a wire cutting method to destroy the sample, and use a metallographic microscope to obtain the accurate thickness value at each detection location to construct a test set;

[0010] 3) Establish a convolutional neural network structure with a weight allocation layer, update the parameters using the training set in step 1), and then verify the performance of the convolutional neural network using the test set in step 2) to realize online measurement of thermal barrier coating thickness.

[0011] Step 1) specifically includes:

[0012] 1.1) Based on the phenomenon of terahertz signal scattering caused by the surface roughness of the thermal barrier coating, which leads to a decrease in the amplitude of the reflection peak, this phenomenon is described using Kirchhoff's theory. Among them, R s Let R0 be the specular reflectivity of the rough surface, λ be the wavelength of the incident terahertz wave, σ be the roughness, and e be the surface roughness.

[0013] 1.2) Generating a terahertz simulation signal considering the surface roughness of the thermal barrier coating by utilizing the square relationship between reflectivity and reflection coefficient:

[0014] Among them, Y M For terahertz simulation signals, IFFT stands for Inverse Fourier Transform, r 01 r is the reflection coefficient of terahertz waves on the surface of the ceramic layer. 12 t represents the reflection coefficient of terahertz waves at the interface between the ceramic layer and the metal bonding layer. 01 t is the transmission coefficient of terahertz waves on the surface of the thermal barrier coating. 10 Let ω be the transmission coefficient of terahertz waves inside the thermal barrier coating, i be the imaginary unit, and E0(ω) be the frequency domain reference signal. d1 is the phase factor, c is the speed of light, ω is the angular velocity of the terahertz wave, and d1 is the thickness of the ceramic layer. as well as σ1 represents the complex refractive index of air, the ceramic layer, and the adhesive layer, respectively; κ is the extinction coefficient; n is the real part of the refractive index; t is the transmission coefficient; and r is the reflection coefficient. σ1 is the surface roughness of the ceramic layer, and σ2 is the interface roughness between the ceramic layer and the substrate.

[0015] Step 2) specifically includes:

[0016] 2.1) Locate the first reflection peak using the maximum value of the terahertz time-domain signal, and then locate the peak and valley values ​​by increasing the direction over time;

[0017] 2.2) Starting from the peak-valley time in step 2.1), locate the second reflection peak using the maximum signal value;

[0018] 2.3) Solve for the time delay between the first and second reflection peaks;

[0019] 2.4) Add the peak time of the second peak to the time delay in step 2.3), and determine whether the signal amplitude corresponding to the summation time is the minimum value of the nearby amplitude; if so, extract the third reflection peak; otherwise, locate the third peak based on the coordinates of the nearby minimum value.

[0020] 2.5) Establish the mapping relationship between the first three peaks and the thickness, and use the first three peak signals as input to the convolutional neural network to measure the thickness of the thermal barrier coating.

[0021] The establishment of the mapping relationship between the first three peak values ​​of the terahertz signal and the thickness of the thermal barrier coating specifically includes:

[0022] According to the terahertz thickness measurement formula Where Δt is the flight time, n1 is the refractive index of the ceramic layer, and c is the speed of light; the calculation of Δt only requires the time difference between the first two peaks, Δt = t peak1 -t peak2 Where Δt is the flight time, t peak1 The peak time of the first reflection peak, t peak2 The peak time of the second peak; n1 calculation requires extracting the first three peak times. E n (ω) is the frequency domain representation of the nth reflection peak, r 01 r is the reflection coefficient of terahertz waves on the surface of the ceramic layer. 12 t represents the reflection coefficient of terahertz waves at the interface between the ceramic layer and the metal bonding layer. 01 t is the transmission coefficient of terahertz waves on the surface of the thermal barrier coating. 10 The transmission coefficient of terahertz waves inside the thermal barrier coating; since the peak value is part of the reflection peak, it can be known that the peak values ​​of the first three peaks carry refractive index information.

[0023] Step 3) specifically includes:

[0024] 3.1) Construct a convolutional neural network structure, including a weight allocation layer, a convolutional layer, a batch normalization layer, an activation layer, and a fully connected layer, to form a complete thickness measurement framework;

[0025] 3.2) Use the three-peak simulation dataset to train the parameters of the convolutional neural network, establish the mathematical mapping between the three peaks and the thickness, and end the weight and bias update after the convergence condition is met.

[0026] 3.3) Input the experimental signals of the first three peaks into the trained convolutional neural network to predict the thickness value of the ceramic layer.

[0027] As a further aspect of this invention: In step 3.1), the weight allocation layer, due to the residual between simulation and experiment caused by terahertz wave dispersion, reduces the weight of the third peak, thereby improving the consistency between the simulation training set and the experimental test set. Furthermore, since the amplitude of the third peak is negative, the ratio of the sum of the amplitudes of the first three peaks to the sum of the absolute amplitudes of the first three peaks is used to limit its upper bound. This ensures that the larger the absolute amplitude of the third peak, the smaller its upper bound, guaranteeing the accuracy of the convolutional neural network in measuring the thickness of actual samples. Where Y represents the output of the adaptive weight layer, w3 is the third peak weight, and peak i Let m be the peak value of the m-th reflection peak, where m = 1, 2, 3.

[0028] As a further aspect of the present invention: Step 3.1) Constructing convolutional layers, batch normalization layers, activation layers, and fully connected layers, wherein the convolutional layer is represented as: Z i,j l =conv(Y,w)+b, where Z i,j l The output of the l-th convolutional layer is represented as follows: i and j are the dimensions of the output data, b is the bias, w is the weight, and conv represents the convolution operation; the activation layer is represented as: S l =σ(Z) i,j l ), where S l The output of the l-th activation layer is σ, where σ is the activation function; the batch normalization layer is represented as: In the formula, E() represents the expectation, and ε is a small positive number to ensure numerical stability. A fully connected expression is represented as F. l =W l F l-1 +B l , of which F l This is the output of the l-th fully connected layer.

[0029] To address the issue of traditional machine learning methods requiring extensive sample destruction, this invention employs a model-driven thickness measurement method. Specifically, it reduces the discrepancy between simulated and experimental signals by constructing a weighted distribution layer. Using simulated signals as the training set, a convolutional neural network is trained to establish a mathematical mapping between the top three peak values ​​and the thickness. Actual thermal barrier coating samples are prepared, and terahertz nondestructive testing and destructive experiments are conducted. Labeled experimental signals are then used as a test set to verify the performance.

[0030] Compared with existing detection methods, the present invention has the following advantages:

[0031] First, to address the problem that traditional machine learning training requires a large number of destroyed samples, a terahertz signal analytical model is constructed to generate simulated signals for training weights and bias parameters, thereby reducing costs.

[0032] 2. To explore the refractive index and flight time of the ceramic layer required for thickness measurement carried by the first three peaks of the terahertz signal, this can replace the complete signal, reduce redundant information input, ensure the similarity between the simulation and experimental datasets, and improve the algorithm's solution efficiency.

[0033] Therefore, this invention provides a novel model-driven method for measuring ceramic layer thickness, reducing significant coating damage. By generating a training set through analytical modeling and exploring the propagation mechanism of terahertz waves within thermal barrier coatings, the method analyzes how the first three peak values ​​replace the complete signal as input to the convolutional neural network, reducing redundant information that differs significantly from experimental signals. Furthermore, this invention innovatively constructs a weight allocation layer, reducing the residual between experimental and simulation results, improving measurement accuracy, and eliminating the need for large sample volumes, thus reducing thickness measurement errors caused by microstructural inhomogeneities. Attached Figure Description

[0034] Figure 1 This is a waveform diagram of the terahertz reference signal.

[0035] Figure 2 The waveform of a terahertz signal carrying information with a thickness of 200 μm and a refractive index of 5-0.05i.

[0036] Figure 3 The waveform of a terahertz signal carrying information with a thickness of 300 μm and a refractive index of 4-0.05i.

[0037] Figure 4 A diagram of a model-driven convolutional neural network framework.

[0038] Figure 5 This is a graph for evaluating model accuracy.

[0039] Figure 6 This is a graph for evaluating measurement accuracy.

[0040] Figure 7 This is a thickness distribution diagram of the thermal barrier coating ceramic layer sample. Detailed Implementation

[0041] To clearly illustrate the technical features of this patent, the following detailed description is provided through specific embodiments and in conjunction with the accompanying drawings.

[0042] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0043] like Figures 1 to 5 As shown, this embodiment of the invention provides a terahertz thickness measurement method for thermal barrier coatings based on the three peak values ​​driven by the model. The method includes the following steps:

[0044] 1) Construct an analytical model of terahertz signals considering the surface roughness of the ceramic layer. Measure the silver total internal reflection mirror using a terahertz time-domain spectroscopy system (e.g., TeraMetrix T-Ray 5000) to obtain the model input reference signal. Analyze the ceramic layer thickness, refractive index, and roughness range, and combine this with the reference signal input to the terahertz signal analytical model to generate a large number of simulation signals. Specifically, by changing the material parameters, obtain terahertz simulation signals carrying different thicknesses, refractive indices, and roughnesses (e.g., 50,000 signals with different refractive indices and thicknesses). Two of these terahertz simulation signals carry thickness information of 300 μm and 200 μm, refractive indices of 4-0.05i and 5-0.05i, and root mean square roughness of 5 μm and 10 μm, respectively.

[0045] To investigate the propagation law of terahertz waves in thermal barrier coatings, and to reveal the mechanism by which the first three peaks of the terahertz signal carry the key information required for thickness measurement, namely the flight time and refractive index, so as to realize the use of the first three peaks as input to a convolutional neural network instead of the complete signal.

[0046] 2) Prepare thermal barrier coating samples, measure the terahertz signal at the center of the sample, and destroy the sample by wire cutting. Measure the specific thickness using metallographic method, and evaluate the degree of agreement between the simulated first three peaks and the experimental first three peaks. The relative errors are 0.1%, 0.4%, and 23.9%, respectively. It can be seen that terahertz wave scattering will cause a decrease in the degree of agreement of the third peak.

[0047] 3) Establish a weight allocation layer combined with a convolutional neural network to form a deep learning thickness measurement framework to achieve ceramic layer thickness measurement.

[0048] In step 1), the construction of an analytical model considering the surface roughness of the ceramic layer specifically includes:

[0049] The phenomenon of terahertz signal scattering caused by the surface roughness of thermal barrier coatings leads to a decrease in the amplitude of the reflection peak, which is described by Kirchhoff's theory. Among them, R s R0 is the specular reflectivity of the rough surface, λ is the incident THz wavelength, and σ is the roughness.

[0050] A terahertz simulation signal considering the surface roughness of the thermal barrier coating was generated using the square relationship between reflectivity and reflection coefficient.

[0051] Where E0(ω) is the frequency domain reference signal, E R (ω) is the terahertz frequency domain simulation signal, E n (ω) represents the frequency domain representation of the nth reflection peak. d is the phase factor, c is the speed of light, ω is the angular velocity, and d1 is the thickness of the ceramic layer. j = 0, 1, 2, as well as σ1 represents the complex refractive index of air, the ceramic layer, and the adhesive layer, respectively; κ is the extinction coefficient; n is the real part of the refractive index; t is the transmission coefficient; and r is the reflection coefficient. σ1 is the surface roughness of the ceramic layer, and σ2 is the interface roughness between the ceramic layer and the substrate.

[0052] In step 2), the localization of the constructed reflection peak specifically includes:

[0053] 2.1) Locate the first reflection peak using the maximum value of the terahertz time-domain signal, and locate the peak and valley values ​​by increasing the time.

[0054] 2.2) Starting from the peak-valley time in step 2.1), locate the second reflection peak with the maximum signal value.

[0055] 2.3) Solve for the time delay between the first and second reflection peaks.

[0056] 2.4) Add the peak time of the second peak to the time delay in step 2.3), and determine whether the signal amplitude corresponding to the summed time is the minimum amplitude in the vicinity. If so, extract the third reflection peak; otherwise, locate the third peak based on the coordinates of the nearest minimum value.

[0057] 2.5) Establish the mapping relationship between the first three peaks and the thickness, and use the first three peak signals as input to the convolutional neural network to measure the thickness of the thermal barrier coating.

[0058] In step 2), establishing the mapping relationship between the first three peak values ​​of the terahertz signal and the thickness of the thermal barrier coating specifically includes:

[0059] According to the terahertz thickness measurement formula Where Δt is the flight time, n1 is the refractive index of the ceramic layer, and c is the speed of light. The calculation of Δt only requires the time difference between the first two peaks: Δt = t peak1 -t peak2 Where Δt is the flight time, t peak1 The peak time of the first reflection peak, t peak2 This represents the peak time of the second peak. The calculation of n1 requires extracting the first three peak times. E n (ω) represents the frequency domain of the nth reflection peak. Since the peak value is part of the reflection peak, it can be known that the peak values ​​of the first three peaks carry refractive index information.

[0060] Step 3), the construction of the convolutional neural network with weight allocation layers specifically includes:

[0061] 3.1) Construct a convolutional neural network structure, including a weight allocation layer, a convolutional layer, a batch normalization layer, an activation layer, and a fully connected layer, to form a complete thickness measurement framework;

[0062] 3.2) Use the three-peak simulation dataset to train the parameters of the convolutional neural network, establish the mathematical mapping between the three peaks and the thickness, and end the weight and bias update after the convergence condition is met.

[0063] 3.3) Input the experimental signals of the first three peaks into the trained convolutional neural network to predict the thickness value of the ceramic layer.

[0064] In step 3.1), the weight allocation layer specifically includes:

[0065] Because terahertz wave dispersion causes residuals between simulation and experiment, reducing the weight of the third peak improves the fit between the simulation training set and the experimental test set. Furthermore, since the amplitude of the third peak is negative, the ratio of the sum of the amplitudes of the first three peaks to the sum of their absolute amplitudes limits its weight. This ensures that the larger the absolute amplitude of the third peak, the smaller its weight upper bound, guaranteeing the accuracy of the convolutional neural network in measuring the thickness of actual samples. Where Y represents the output of the adaptive weight layer, w3 is the third peak weight, and peak i Let m be the peak value of the m-th reflection peak, where m = 1, 2, 3.

[0066] In step 3.1), the construction of the convolutional layer, batch normalization layer, activation layer, and fully connected layer specifically includes:

[0067] A convolutional layer is represented as: Z i,j l =conv(Y,w)+b, where Z i,j l The output of the l-th convolutional layer is represented as follows: i and j are the dimensions of the output data, b is the bias, w is the weight, and conv represents the convolution operation; the activation layer is represented as: S l =σ(Z) i,j l ), where S l The output of the l-th activation layer is σ, where σ is the activation function; the batch normalization layer is represented as: In the formula, E() represents the expectation, and ε is a small positive number to ensure numerical stability. A fully connected expression is represented as F. l =W l F l-1 +B l , of which F l This is the output of the l-th fully connected layer. Specifically, the constructed convolutional neural network structure includes one weight allocation layer, four convolutional layers, four batch normalization layers, four activation layers, one pooling layer, and two fully connected layers. The input signal size is 400×1, the learning rate is 0.05, the batch size is 512, and the maximum number of rounds is 500. The specific parameters of each layer are shown in the table below:

[0068] Convolutional Neural Network Parameter Setting Table with Weighted Layers

[0069] Floor names parameter Weighting layer One weight, with a value ranging from [0, 0.1]. Convolutional layer 1 The convolution kernel size is 7×1, with 1 channel and 16 kernels. Batch Normalization Layer 1 <![CDATA[ε is set to 10 -5 > Activation layer 1 ReLU activation function Convolutional layer 2 The convolution kernel size is 5×1, with 1 channel and 16 nodes. Batch Normalization Layer 2 <![CDATA[ε is set to 10 -5 > Activation layer 2 Using the ReLU activation function, the learnable parameter range is [0,1]. Convolutional layer 3 The convolution kernel size is 3×1, with 1 channel and 16 nodes. Batch normalization layer 3 <![CDATA[ε is set to 10 -5 > Activation layer 3 Using the ReLU activation function, the learnable parameter range is [0,1]. Convolutional layer 4 The convolution kernel size is 1×1, with 1 channel and 16 nodes. Batch Normalization Layer 1 <![CDATA[ε is set to 10 -5 > Activation layer 4 ReLU activation function Pooling layer 1 The pooling layer size is 4×1 Fully connected layer 2 Number of neurons 10 Fully connected layer 3 The number of neurons is 1

[0070] like Figure 5 and Figure 6 As shown in this embodiment of the invention, 17 actual thermal barrier coating samples with inconsistent thicknesses were prepared. The thickness of each sample was measured at its center, with a scanning step of 2 mm and 3 sampling points per sample, totaling 51 experimental signals as the test set. These signals were then input into a trained convolutional neural network, and the average relative error of the thickness measurement was 1.05%. Finally, the thermal barrier coating was scanned point by point using a terahertz time-domain spectroscopy system (e.g., TeraMetrix T-Ray 5000), and the terahertz experimental signals at all locations of the sample were input into the network, enabling the determination of the thickness value at each detection location without iterative calculation.

[0071] This invention constructs a model-driven convolutional neural network (CNN) thickness measurement framework. Based on a terahertz signal analytical model, it generates a large number of simulation training sets and explores how the first three peaks of the signal can measure refractive index and time-of-flight, replacing the complete signal as input and reducing redundant information that differs significantly from experimental signals. Simultaneously, the dispersion phenomenon of terahertz waves leads to poor agreement of the third peak. An innovative weight allocation layer is designed to intelligently reduce the weight of the third peak, improving the similarity between the training and test sets and ensuring the accuracy of the CNN in measuring the thickness of actual ceramic layers. The proposed method can update the weights and bias parameters of the CNN without extensive sample destruction, reducing training costs. This invention enables efficient non-contact detection of thickness at various locations on the sample, accurately measuring the thickness of microstructure-inhomogeneous thermal barrier coatings while avoiding significant sample waste. This has important theoretical significance and engineering application value for coating quality assessment during the preparation stage.

[0072] The above description only details the preferred embodiments of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0073] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the disclosure in the specification and embodiments. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the claims.

Claims

1. A terahertz thickness measurement method for thermal barrier coatings based on the first three peak values ​​of a model, characterized in that, The method includes the following steps: 1) Construct an analytical model of terahertz signals that takes into account the surface roughness of thermal barrier coatings. Use a terahertz time-domain spectroscopy system to measure the reflection signal of the silver total reflection mirror as a reference signal and input it into the analytical model. Set different thickness, refractive index and roughness parameters to generate simulation signals and extract the first three peaks of each simulation signal to construct a training set. 2) Prepare thermal barrier coating specimens, use a terahertz time-domain spectroscopy system to measure the time-domain signal at different locations of the sample, and extract the top three peak values; then, use a wire cutting method to destroy the sample, and use a metallographic microscope to obtain the accurate thickness value at each detection location to construct a test set; 3) Establish a convolutional neural network structure with a weight allocation layer, update the parameters using the training set in step 1), and then verify the performance of the convolutional neural network using the test set in step 2) to realize online measurement of thermal barrier coating thickness.

2. The terahertz thickness measurement method for thermal barrier coatings based on the first three peak values ​​of a model, as described in claim 1, is characterized in that... Step 1) specifically includes: 1.1) Based on the phenomenon of terahertz signal scattering caused by the surface roughness of the thermal barrier coating, which leads to a decrease in the amplitude of the reflection peak, this phenomenon is described according to Kirchhoff's theory. Among them, R s R0 is the specular reflectivity of the rough surface, λ is the incident THz wavelength, and σ is the roughness. 1.2) Generating a terahertz simulation signal considering the surface roughness of the thermal barrier coating by utilizing the square relationship between reflectivity and reflection coefficient: Among them, Y M For terahertz simulation signals, IFFT stands for Inverse Fourier Transform, r 01 r is the reflection coefficient of terahertz waves on the surface of the ceramic layer. 12 t represents the reflection coefficient of terahertz waves at the interface between the ceramic layer and the metal bonding layer. 01 t is the transmission coefficient of terahertz waves on the surface of the thermal barrier coating. 10 Let ω be the transmission coefficient of terahertz waves inside the thermal barrier coating, i be the imaginary unit, and E0(ω) be the frequency domain reference signal. d1 is the phase factor, c is the speed of light, ω is the angular velocity of the terahertz wave, and d1 is the thickness of the ceramic layer. as well as σ1 represents the complex refractive index of air, ceramic layer, and adhesive layer, respectively; κ is the extinction coefficient; n is the real part of the refractive index; t is the transmission coefficient; r is the reflection coefficient; σ1 is the surface roughness of the ceramic layer; and σ2 is the interface roughness between the ceramic layer and the substrate.

3. The terahertz thickness measurement method for thermal barrier coatings based on the first three peak values ​​of a model, as described in claim 1, is characterized in that... Step 2) specifically includes: 2.1) Locate the first reflection peak using the maximum value of the terahertz time-domain signal, and then locate the peak and valley values ​​by increasing the direction over time; 2.2) Starting from the peak-valley time in step 2.1), locate the second reflection peak using the maximum signal value; 2.3) Solve for the time delay between the first and second reflection peaks; 2.4) Add the peak time of the second peak to the time delay in step 2.3), and determine whether the signal amplitude corresponding to the summation time is the minimum value of the nearby amplitude; if so, extract the third reflection peak; otherwise, locate the third peak based on the coordinates of the nearby minimum value. 2.5) Establish the mapping relationship between the first three peaks and the thickness, and use the first three peak signals as input to the convolutional neural network to measure the thickness of the thermal barrier coating.

4. The terahertz thickness measurement method for thermal barrier coatings based on the first three peak values ​​of the model as described in claim 1, characterized in that, Step 3) specifically includes: 3.1) Construct a convolutional neural network structure, including a weight allocation layer, a convolutional layer, a batch normalization layer, an activation layer, and a fully connected layer, to form a complete thickness measurement framework; 3.2) Use the three-peak simulation dataset to train the parameters of the convolutional neural network, establish the mathematical mapping between the three peaks and the thickness, and end the weight and bias update after the convergence condition is met. 3.3) Input the experimental signals of the first three peaks into the trained convolutional neural network to predict the thickness value of the ceramic layer.

5. The terahertz thickness measurement method for thermal barrier coatings based on the first three peak values ​​driven by the model, as described in claim 1, is characterized in that... Step 3.1) constructs a weight allocation layer. Due to the residual between simulation and experiment caused by terahertz wave dispersion, the weight of the third peak is reduced, thereby improving the fit between the simulation training set and the experimental test set. In addition, since the amplitude of the third peak is negative, the ratio of the sum of the amplitudes of the first three peaks to the sum of the absolute amplitudes of the first three peaks is used to limit its upper bound. This ensures that the larger the absolute amplitude of the third peak, the smaller its upper bound, thus guaranteeing the thickness measurement accuracy of the convolutional neural network for actual samples. Y = w3·peak3 Where Y represents the output of the adaptive weight layer, w3 is the third peak weight, and peak i Let m be the peak value of the m-th reflection peak, where m = 1, 2, 3.

6. The terahertz measurement method for ceramic layer thickness based on convolutional neural networks according to claim 1, characterized in that, Step 3.1) Construct convolutional layers, batch normalization layers, activation layers, and fully connected layers, where the convolutional layer is represented as: Z i,j l =conv(Y,w)+b, where Z i,j l The output of the l-th convolutional layer is represented as follows: i and j are the dimensions of the output data, b is the bias, w is the weight, and conv represents the convolution operation; the activation layer is represented as: S l =σ(Z) i,j l ), where S l The output of the l-th activation layer is σ, where σ is the activation function; the batch normalization layer is represented as: In the formula, E() is the expectation, and ε is a small positive number to ensure numerical stability; the fully connected expression is represented as F. l =W l F l-1 +B l , of which F l This is the output of the l-th fully connected layer.

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