Terahertz thermal barrier coating oxide layer thickness measuring method based on multimode characteristics and improved dung beetle optimization algorithm

Abstract

The invention discloses a terahertz thermal barrier coating oxide layer thickness measuring method based on multimode features and an improved dung beetle optimization algorithm, and the method comprises the steps: firstly collecting a signal through a terahertz time-domain spectroscopy system, and extracting the time domain, entropy, frequency domain and wavelet features of the signal; screening out a feature subset most relevant to the thickness by adopting a maximum mutual information coefficient; then, providing an improved dung beetle optimization algorithm: initializing a population through Logistic-Tent chaotic mapping, providing a dynamic convergence factor based on an arc tangent function for balancing global exploration and local development, and increasing a theft failure strategy to enhance the capability of jumping out of local optimum; and finally, optimizing hyper-parameters of the XGBoost model by using the improved algorithm, and constructing a high-precision thickness measurement model. According to the invention, the interference caused by terahertz wave multiple reflection is effectively overcome, the measurement precision and reliability of the thickness of the thin thermal growth oxide layer are obviously improved, and the method is suitable for nondestructive testing and life evaluation of the thermal barrier coating of the aero-engine.

Description

Technical fields:

[0001] This invention relates to the intersection of nondestructive testing technology and machine learning, particularly to the field of terahertz time-domain spectroscopy. Specifically, it is a high-precision method for measuring the thickness of the oxide layer of thermally grown thermal barrier coatings based on multi-mode feature extraction and an improved dung beetle optimization algorithm to optimize the XGBoost regression model. Background technology:

[0002] Thermal barrier coatings are widely used for thermal protection of aero-engine and gas turbine blades. Their service life largely depends on the growth of the internal thermally grown oxide layer. When the oxide layer thickness is less than 7 μm, it can protect the metal substrate from further oxidation. However, as the oxide layer thickness continues to increase, the internal thermal stress of the coating increases sharply, creating a risk of cracking near the oxide layer and threatening the service life of the thermal barrier coating. Therefore, accurate non-destructive testing of the oxide layer thickness is crucial.

[0003] Terahertz time-domain spectroscopy is an emerging non-contact non-destructive testing technique that utilizes the propagation characteristics of terahertz waves in a medium to invert the thickness and optical parameters of layered materials. However, in actual measurements, the multiple reflections of terahertz waves within thermal barrier coating samples can complicate the measurement signal and introduce significant errors. Traditional terahertz thickness measurement methods have poor anti-interference capabilities and are only suitable for measuring relatively thick coating samples, with severely insufficient measurement accuracy for thin layers (especially oxide layers).

[0004] In recent years, machine learning methods have been introduced to solve the problem of inversion of complex signals, but existing methods have the following limitations: (1) the feature construction is simple and fails to make full use of the comprehensive information in the time domain, frequency domain and other aspects of terahertz signals; (2) the model hyperparameters depend on empirical parameter tuning, making it difficult to obtain the global optimal solution and easy to fall into local optima, resulting in unstable prediction performance. Therefore, there is an urgent need for a high-precision thin oxide layer thickness measurement method that can effectively extract multimodal features and intelligently optimize the model. Summary of the Invention:

[0005] In view of the above-mentioned shortcomings of the prior art, the purpose of this invention is to provide a method for measuring the thickness of terahertz thermal barrier coating oxide layer based on multi-mode features and an improved dung beetle optimization algorithm. This method constructs a multi-mode feature set and uses the maximum mutual information coefficient for feature selection, and uses the improved dung beetle optimization algorithm to globally optimize the hyperparameters of the XGBoost regression model, ultimately achieving fast and high-precision non-destructive measurement of oxide layer thickness.

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

[0007] This invention relates to a method for measuring the thickness of terahertz thermal barrier coating oxide layers based on multi-mode features and an improved dung beetle optimization algorithm, characterized by comprising the following steps:

[0008] Step S1: Obtain the terahertz signal; Step S2: Extract the multi-mode features of the signal; Step S3: Filter features using the maximum mutual information coefficient; Step S4: Divide the training set and the test set; Step S5: Improve the dung beetle optimization algorithm; Step S6: Optimize the XGBoost hyperparameters; Step S7: Train the prediction model; Step S8: Obtain the predicted oxide layer thickness.

[0009] Furthermore, step S1 involves obtaining terahertz signals through both simulation and preparation of thermal barrier coating samples; step S2 involves obtaining the time-domain signal of the test object using terahertz time-domain spectroscopy, extracting time-domain and entropy features, then using fast Fourier transform to obtain the frequency-domain signal, retaining the effective data from 0-2THz as the frequency-domain signal to extract frequency-domain features, and simultaneously using three-layer wavelet packet decomposition to divide the time-domain signal into 8 sub-bands, extracting the corresponding wavelet features, and finally constructing a multi-mode feature dataset; in step S4, for the simulated signal, the multi-mode features of different oxide layer thicknesses are divided into a test set and a training set, where the test set contains 30 signals, randomly selected from 59 signals in the 0-29μm range, and the training set consists of the remaining 120 signals.

[0010] Furthermore, the simulation method in step S1 is to use the finite integration technique of CST MicroWave Studio electromagnetic simulation software to simulate the propagation mechanism of terahertz waves in the thermal barrier coating. This simulation method uses the terahertz reference signal in the actual terahertz time-domain pulse detection system. The thickness of the ceramic layer is fixed at 200 μm, and THz time-domain simulation signals of the 0-120 μm oxide layer are obtained. The signals from 0-29 μm are obtained at 0.5 μm intervals, and the signals from 30-120 μm are obtained at 1 μm intervals, for a total of 150 sets of simulation signals. At the same time, each set of simulation signals is sampled at an interval of 30 points / ps to form a simulation dataset.

[0011] Furthermore, in step S1, the thermal barrier coating sample is prepared by preparing a thermal barrier coating sample containing an oxide layer. 91 sets of time-domain signals were acquired using a terahertz time-domain spectrometer. Each set of signals has a flight time of 100 ps and a length of 3000 data points. To acquire the 91 sets of time-domain signals, the sample was cut and polished according to the measurement position, and the true thickness of the oxide layer at the measurement position was observed using a field emission scanning electron microscope and an electron backscatter diffraction analysis system. Finally, 29 sets of signals with an oxide layer thickness of less than 20 μm, 12 sets of signals with an oxide layer thickness of 20 μm to 30 μm, and 50 sets of signals with an oxide layer thickness of more than 30 μm were measured.

[0012] Furthermore, step S3, the Maximum Information Coefficient (MIC), captures the complex linear, nonlinear, and periodic relationships between variables through normalization and dynamic mesh partitioning. Dynamic mesh partitioning divides the scatter plot of variables into grids of different granularities, calculating the mutual information values ​​under all possible partitions to improve the sensitivity of the mutual information coefficient to complex relationships. The specific calculation formula is as follows:

[0013]

[0014] Where X and Y are two random variables in the analysis; a and b are the number of grids in the X and Y directions, respectively; B is a predefined threshold to control the complexity of the grid; I(X; Y|a×b) refers to the mutual information of X and Y when X and Y are divided into a and b grids, respectively; log2min(a,b) is a normalization factor to ensure that the value of MIC is between [0,1]. The larger the mutual information, the stronger the dependence between the two variables.

[0015] Furthermore, step S5 involves replacing the original random initialization method of DBO with Logistic-Tent (LT) chaotic mapping. This method is a combined chaotic mapping method that combines the advantages of Logistic mapping and Tent mapping. The specific principle is shown in Formula 2.

[0016]

[0017] In the formula, x0 is a random number in (0, 1), n ​​is the initial population size, and r is a control parameter used to adjust the weights of the Logistic mapping and the Tent mapping in the combination.

[0018] Furthermore, step S5 employs an improved dynamic convergence factor formula using the arctangent function:

[0019]

[0020] In the formula, R is the dynamic convergence factor; M is the maximum number of iterations; and t is the current number of iterations.

[0021] Furthermore, in step S5, a location update strategy is adopted for failed theft, where dung beetles that fail to steal are driven to the worst living environment in the population:

[0022]

[0023] Where, x i (t) represents the position of the i-th dung beetle in the t-th iteration, X b Let S be the global optimal position, S be a constant, g be a 1×D random vector following a normal distribution, and X be...* For the local optimal position, X ω Let r represent the worst-case position, and r2 be a random number in the range (0, 1). This strategy, while referencing the current best solution, expands the search range to the historical search interval of the population by driving a portion of the population toward the current worst-case solution, thereby increasing the likelihood of the algorithm escaping local optima.

[0024] Furthermore, step S7 employs an improved Punish-theft Dung Beetle Optimizer (PDBO) algorithm to optimize the three core hyperparameters of XGBoost: the number of iterations (num_trees), the tree depth (max_depth), and the learning rate (eta). This aims to improve the prediction accuracy and speed of XGBoost for oxide layer thickness, and to measure the root mean square error (RMSE), mean absolute error (MAE), and goodness of fit (R²). 2 () is used as an indicator to evaluate the performance of the model.

[0025] Furthermore, for the simulation signals, the multi-mode features with different oxide layer thicknesses were divided into a test set and a training set. The test set consisted of 30 signals, randomly selected from 59 signals in the 0-29μm range, while the training set consisted of the remaining 120 signals. The data was normalized so that each feature could be analyzed on the same scale, thereby improving the performance and stability of the machine learning model. The hyperparameters of XGBoost were optimized using DBO, PDBO, and MIC-PDBO respectively, and the optimal solution was found using 5-fold cross-validation.

[0026] Furthermore, the population size of the optimization algorithms was 30, the maximum number of iterations was 200, and the ranges of the number of iterations (num_trees), tree depth (max_depth), and learning rate (eta) were [100, 800], [3, 10], and [0.001, 0.3], respectively. The algorithms were run and compared in MATLAB R2024b. The results showed that DBO's prediction error ranged from -4 to 2.4, PDBO's from -1.3 to 1.5, and MIC-PDBO's from -1.1 to 1.1. All three methods achieved relatively small errors using multi-modal feature datasets, with MIC-PDBO exhibiting the smallest prediction error. The R-values ​​of DBO, PDBO, and MIC-PDBO were also compared. 2 The values ​​are 0.98176, 0.9916, and 0.994, respectively, all greater than 0.98.

[0027] The beneficial effects of this invention are:

[0028] (1) The invention method characterizes the signal from multiple aspects such as time domain, entropy, frequency domain and wavelet features, and the constructed multi-mode feature dataset completely and accurately contains the feature parameters of the oxide layer THz signal;

[0029] (2) The method of this invention uses MIC to select the features most related to thickness, providing high-quality input for the model and improving the model's prediction efficiency for oxide layer thickness.

[0030] (3) The invention improves the dung beetle optimization algorithm for the problem of oxide layer thickness prediction. The improved PDBO algorithm effectively avoids model overfitting and getting trapped in local optima, and improves the convergence accuracy of the algorithm.

[0031] (4) The invention overcomes multiple reflection interference, significantly improves the measurement accuracy of thin oxide layers, and solves the bottleneck problem of traditional methods;

[0032] (5) The invention method has been verified through simulation and physical sample experiments, and has higher feasibility. Attached image description:

[0033] Figure 1 This is a flowchart of the present invention;

[0034] Figure 2 This is a partial terahertz simulation signal;

[0035] Figure 3 This represents the terahertz signal of a portion of the sample.

[0036] Figure 4 To compare the function graphs of the dynamic convergence factor formula before and after improvement;

[0037] Figure 5 The flowchart for the improved dung beetle optimization algorithm;

[0038] Figure 6 The prediction performance of the MIC-PDBO-XGBoost algorithm on the simulated signal of the 200μm TC layer;

[0039] Figure 7 The prediction performance of the MIC-PDBO-XGBoost algorithm on the simulated signal of the 300μm TC layer;

[0040] Figure 8 The prediction performance of the MIC-PDBO-XGBoost algorithm on the sample signal;

[0041] Figure 9 The prediction performance of the MIC-PDBO-XGBoost algorithm on TGO sample signals below 20μm;

[0042] Figure 10The image shows the prediction residuals of TGO sample signals below 20 μm using the MIC-PDBO-XGBoost algorithm. Detailed implementation method:

[0043] This invention relates to a method for measuring the oxide layer thickness of terahertz thermal barrier coatings based on multi-mode features and an improved dung beetle optimization algorithm. The method comprises the following steps: Step S1, acquiring a terahertz signal; Step S2, extracting multi-mode features from the signal; Step S3, selecting features based on the maximum mutual information coefficient; Step S4, dividing the training set and the test set; Step S5, improving the dung beetle optimization algorithm; Step S6, optimizing the XGBoost hyperparameters; Step S7, training the prediction model; and Step S8, obtaining the predicted oxide layer thickness.

[0044] Step S1 involves acquiring the terahertz signal (terahertz signal acquisition):

[0045] Terahertz signals were obtained through two methods: simulation and fabrication of thermal barrier coating samples. The simulation method employed the finite integration technique in CSTMIcroWave Studio electromagnetic simulation software to simulate the propagation mechanism of terahertz waves within the thermal barrier coating. This simulation used a terahertz reference signal from an actual terahertz time-domain pulse detection system. The ceramic layer thickness was fixed at 200 μm, and THz time-domain simulation signals for the 0-120 μm oxide layer were acquired. To obtain more terahertz signals from thin oxide layers, signals were acquired at 0.5 μm intervals for the 0-29 μm range and at 1 μm intervals for the 30-120 μm range, resulting in a total of 150 sets of simulation signals. Each set of simulation signals was sampled at an interval of 30 points / ps to form a simulation dataset.

[0046] The method for preparing thermal barrier coating samples involved creating samples containing an oxide layer. Ninety-one time-domain signals were acquired using a terahertz time-domain spectrometer, each signal having a flight time of 100 ps and a length of 3000 data points. Specifically, the samples were cut and polished at the measurement locations, and the true thickness of the oxide layer at those locations was observed using a field emission scanning electron microscope and an electron backscatter diffraction analysis system. Ultimately, 29 signals with an oxide layer thickness below 20 μm, 12 signals between 20 μm and 30 μm, and 50 signals above 30 μm were measured.

[0047] Step S2 involves extracting multi-mode features of the signal:

[0048] Feature extraction is a core step in machine learning and data analysis. Its significance lies in transforming raw data into a more representative and easier-to-process form, thereby improving the performance, efficiency, and interpretability of the model. This invention integrates common feature extraction types and proposes a multi-mode feature dataset that includes time-domain features, entropy features, frequency-domain features, and wavelet features. Specifically, the time-domain signal of the test object is obtained through terahertz time-domain spectroscopy, and time-domain and entropy features are extracted. Then, the frequency-domain signal is obtained using fast Fourier transform, and the effective data from 0-2THz is retained as the frequency-domain signal for frequency-domain feature extraction. At the same time, the time-domain signal is divided into 8 sub-bands using three-level wavelet packet decomposition, and the corresponding wavelet features are extracted, ultimately forming a multi-mode feature dataset. This dataset contains 55 signal features, including the maximum, minimum, peak, mean, absolute mean, root square amplitude, variance, standard deviation, root mean square, kurtosis, skewness, waveform factor, crest factor, impulse factor, margin factor, gap factor, and energy of time-domain signals; the sample entropy, permutation entropy, fuzzy entropy, approximate entropy, energy entropy, and information entropy of signals; the average frequency, centroid frequency, root mean square frequency, standard deviation frequency, maximum frequency, minimum frequency, skewness frequency, kurtosis frequency, frequency amplitude, waveform factor, impulse factor frequency, margin frequency, and energy of frequency-domain signals; and the wavelet energy entropy, singular spectrum entropy, wavelet energy ratio of the 8 sub-bands, and wavelet scale entropy of wavelet signals.

[0049] To improve the computational efficiency of the model by selecting effective features, the Maximum Information Coefficient (MIC) is used for feature selection (i.e., feature selection using the MIC in step S3). MIC captures complex relationships between variables, such as linear, nonlinear, and periodic relationships, through normalization and dynamic grid partitioning. Compared with the original mutual information, the normalization added by MIC improves the comparability of the results, and the dynamic grid partitioning divides the scatter plot between variables into grids of different granularities, calculating the mutual information values ​​under all possible partitions, effectively improving the sensitivity of the mutual information coefficient to complex relationships. The specific calculation formula is as follows:

[0050]

[0051] Here, X and Y are two random variables in the analysis; a and b are the number of grids in the X and Y directions, respectively; B is a predefined threshold to control the complexity of the grid; I(X; Y|a×b) refers to the mutual information of X and Y when X and Y are divided into a and b grids, respectively. log2min(a,b) is a normalization factor to ensure that the value of MIC is between [0,1]. The larger the mutual information, the stronger the dependency between the two variables.

[0052] The mutual information values ​​of each feature were calculated based on the MIC, and the top 30 features with strong correlation to oxide layer thickness were extracted. The specific extracted features are shown in Table 1.

[0053] Table 1. 30 features extracted from mutual information

[0054]

[0055] Step S5 involves improving the dung beetle optimization algorithm:

[0056] This invention addresses the shortcomings of the Dung Beetle Optimizer (DBO) algorithm in predicting oxide layer thickness, aiming to improve the algorithm's optimization convergence accuracy.

[0057] The improved dung beetle optimization algorithm first replaces the original random initialization method of DBO with Logistic-Tent (LT) chaotic mapping. This method is a combined chaotic mapping method that combines the advantages of Logistic mapping and Tent mapping. It can generate a more uniform initial population within the exploration range. The specific principle is shown in Equation 2.

[0058]

[0059] In the formula, x0 is a random number in (0, 1), n ​​is the initial population size, and r is a control parameter used to adjust the weights of the Logistic mapping and the Tent mapping in the combination.

[0060] In the early stages, optimization algorithms need to expand the exploration scope as much as possible, while in the later stages, they focus on exploring around local optima. The dynamic convergence factor of the dung beetle optimization algorithm decreases linearly and does not favor different stages of the problem. Therefore, this invention proposes an improved dynamic convergence factor formula using the arctangent function:

[0061]

[0062] In the formula, R is the dynamic convergence factor; M is the maximum number of iterations; and t is the current number of iterations.

[0063] The improved convergence factor maintains a large value in the early stages of iteration, keeping the algorithm's exploration range broad and preventing it from getting stuck in local optima in the early stages. In the later stages of iteration, the convergence factor decreases rapidly, allowing the algorithm to focus on exploring the vicinity of the existing optimal solution and further searching for better solutions.

[0064] Finally, this invention proposes a location update strategy for failed theft attempts, based on the original strategy: dung beetles that fail to steal are driven to the worst living environment in the population.

[0065]

[0066] Where, x i (t) represents the position of the i-th dung beetle in the t-th iteration, X b Let S be the global optimal position, S be a constant, g be a 1×D random vector following a normal distribution, and X be... * For the local optimal position, X ω Let r represent the worst-case position, and r2 be a random number in the range (0, 1). This strategy, while referencing the current best solution, expands the search range to the historical search interval of the population by driving a portion of the population toward the current worst-case solution, further increasing the possibility of the algorithm escaping local optima.

[0067] Step S7 involves training the prediction model (i.e., constructing the prediction model):

[0068] An improved Punish-theft Dung Beetle Optimizer (PDBO) algorithm was used to optimize the three core hyperparameters of XGBoost: the number of iterations (num_trees), the tree depth (max_depth), and the learning rate (eta). This improved the prediction accuracy and speed of XGBoost for oxide layer thickness. The results were evaluated using root mean square error (RMSE), mean absolute error (MAE), and goodness of fit (R²). 2 () is used as an indicator to evaluate the performance of the model.

[0069] For the simulation signals, the multi-mode features with different oxide layer thicknesses were divided into a test set and a training set. The test set consisted of 30 signals, randomly selected from 59 signals in the 0-29 μm range. The training set consisted of the remaining 120 signals. Data normalization was performed to allow each feature to be analyzed on the same scale, thereby improving the performance and stability of the machine learning model. The hyperparameters of XGBoost were optimized using DBO, PDBO, and MIC-PDBO, respectively, and 5-fold cross-validation was used to find the optimal solution. The population size of the above optimization algorithms was 30, the maximum number of iterations was 200, and the ranges of the number of iterations (num_trees), the tree depth (max_depth), and the learning rate (eta) were [100, 800], [3, 10], and [0.001, 0.3], respectively. The algorithms were run and compared in MATLAB R2024b.

[0070] Ultimately, the prediction errors of DBO, PDBO, and MIC-PDBO ranged from -4 to 2.4, respectively. All three methods achieved relatively small errors using the multi-modal feature dataset, with MIC-PDBO exhibiting the smallest prediction error. The R-squared values ​​for DBO, PDBO, and MIC-PDBO were also observed. 2The values ​​are 0.98176, 0.9916, and 0.994, respectively, all greater than 0.98. This result further verifies the superiority of the multi-modal feature dataset proposed in this invention for predicting TGO thickness. Meanwhile, the PDBO algorithm proposed in this invention outperforms DBO in terms of accuracy in predicting TGO thickness, but requires more iterations and a smaller learning rate, resulting in longer prediction time. The MIC-PDBO-XGBoost algorithm, proposed after combining data dimensionality reduction methods, achieves the highest prediction accuracy and the shortest prediction time, enabling more accurate and efficient prediction of oxide layer thickness.

[0071] To verify the universality of MIC-PDBO-XGBoost in predicting TGO thickness, this study added a simulation experiment with a 300μm TC layer and obtained 59 sets of THz time-domain simulation signals for 0-29μm TGO layers. The signals were randomly divided into a test set and a training set, with 10 sets of signals in the test set and 49 sets in the training set. After repeating the experimental procedure, the prediction error range was found to be [-1.25, 1.03], RMSE was 0.65179μm, MAE was 0.58382μm, and R... 2 The value was 0.99273 and the running time was 0.44184s, indicating that the method can be applied to different TC layer thickness ranges.

[0072] For the thermal barrier coating sample signals, they were randomly divided into a training set and a test set. The training set contained 71 data sets, and the test set contained 20 data sets, ensuring that more than 10 data sets in the test set were below 20 μm. Thickness prediction was performed using MIC-PDBO-XGBoost. The overall prediction results showed an RMSE of 3.4327 μm, a MAE of 2.3901 μm, and a R... 2 The accuracy was 0.94638, the prediction time was 0.58345s, and the prediction accuracy for data thickness below 20μm was high. The mean residual was -0.13μm, and the minimum error was only 0.155μm, achieving accurate and efficient prediction of oxide layer thickness below 20μm.

Claims

1. A method for measuring the thickness of terahertz thermal barrier coating oxide layers based on multi-mode features and an improved dung beetle optimization algorithm, characterized in that, Includes the following steps: Step S1: Obtain the terahertz signal; Step S2: Extract the multi-mode features of the signal; Step S3: Filter features using the maximum mutual information coefficient; Step S4: Divide the training set and the test set; Step S5: Improve the dung beetle optimization algorithm; Step S6: Optimize the XGBoost hyperparameters; Step S7: Train the prediction model; Step S8: Obtain the predicted oxide layer thickness.

2. The method for measuring the oxide layer thickness of terahertz thermal barrier coatings based on multi-mode features and an improved dung beetle optimization algorithm according to claim 1, characterized in that, Step S1 involves obtaining terahertz signals through two methods: simulation and preparation of thermal barrier coating samples. Step S2 involves obtaining the time-domain signal of the test object through terahertz time-domain spectroscopy, extracting time-domain features and entropy features, then using fast Fourier transform to obtain the frequency-domain signal, retaining the effective data from 0-2THz as the frequency-domain signal to extract frequency-domain features, and using three-layer wavelet packet decomposition to divide the time-domain signal into 8 sub-bands, extracting the corresponding wavelet features, and finally forming a multi-mode feature dataset. In step S4, for the simulation signal, the multi-mode features of different oxide layer thicknesses are divided into a test set and a training set. The test set consists of 30 sets of signals, which are randomly selected from 59 sets of signals in the 0-29μm range. The training set consists of the remaining 120 sets of signals.

3. The method for measuring the oxide layer thickness of terahertz thermal barrier coatings based on multi-mode features and an improved dung beetle optimization algorithm according to claim 2, characterized in that, The simulation method for step S1 is to use the finite integration technique of CST Microwave Studio electromagnetic simulation software to simulate the propagation mechanism of terahertz waves in thermal barrier coatings. This simulation method uses the terahertz reference signal in an actual terahertz time-domain pulse detection system; the ceramic layer thickness is fixed at 200μm, and THz time-domain simulation signals of the 0-120μm oxide layer are obtained. The 0-29μm layer is obtained at 0.5μm intervals, and the 30-120μm layer is obtained at 1μm intervals, for a total of 150 sets of simulation signals. At the same time, each set of simulation signals is sampled at an interval of 30 points / ps to form a simulation dataset. In step S1, the thermal barrier coating sample was prepared by preparing a thermal barrier coating sample containing an oxide layer. 91 sets of time-domain signals were acquired using a terahertz time-domain spectrometer. Each set of signals had a flight time of 100 ps and a length of 3000 data points. To acquire the 91 sets of time-domain signals, the sample was cut and polished according to the measurement position. The actual thickness of the oxide layer at the measurement position was observed using a field emission scanning electron microscope and an electron backscatter diffraction analysis system. Finally, 29 sets of signals with an oxide layer thickness of less than 20 μm, 12 sets of signals with an oxide layer thickness of 20 μm to 30 μm, and 50 sets of signals with an oxide layer thickness of more than 30 μm were measured.

4. The method for measuring the oxide layer thickness of terahertz thermal barrier coatings based on multi-mode features and an improved dung beetle optimization algorithm according to claim 2, characterized in that, Step S3, the Maximum Information Coefficient (MIC), captures complex linear, nonlinear, and periodic relationships between variables through normalization and dynamic mesh partitioning. Dynamic mesh partitioning divides the scatter plot of variables into grids of different granularities, calculating the mutual information values ​​under all possible partitions to improve the sensitivity of the mutual information coefficient to complex relationships. The specific calculation formula is as follows: Where X and Y are two random variables in the analysis; a and b are the number of grids in the X and Y directions, respectively; B is a predefined threshold to control the complexity of the grid; I(X; Y|a×b) refers to the mutual information of X and Y when X and Y are divided into a and b grids, respectively; log2min(a,b) is a normalization factor to ensure that the value of MIC is between [0,1]. The larger the mutual information, the stronger the dependence between the two variables.

5. The method for measuring the oxide layer thickness of terahertz thermal barrier coatings based on multi-mode features and an improved dung beetle optimization algorithm according to claim 2, characterized in that, Step S5 involves replacing the original random initialization method of DBO with Logistic-Tent (LT) chaotic mapping. This method is a combined chaotic mapping method that combines the advantages of Logistic mapping and Tent mapping. The specific principle is shown in Formula 2. In the formula, x0 is a random number in (0, 1), n ​​is the initial population size, and r is a control parameter used to adjust the weights of the Logistic mapping and the Tent mapping in the combination.

6. The method for measuring the oxide layer thickness of terahertz thermal barrier coatings based on multi-mode features and an improved dung beetle optimization algorithm according to claim 5, characterized in that, The dynamic convergence factor formula improved by the arctangent function is used in step S5: In the formula, R is the dynamic convergence factor; M is the maximum number of iterations; and t is the current number of iterations.

7. The method for measuring the oxide layer thickness of terahertz thermal barrier coatings based on multi-mode features and an improved dung beetle optimization algorithm according to claim 5, characterized in that, In step S5, a location update strategy is used for failed thefts. Dung beetles that fail to steal are driven to the worst living environment in the population. Where, x i (t) represents the position of the i-th dung beetle in the t-th iteration, X b Let S be the global optimal position, S be a constant, g be a 1×D random vector following a normal distribution, and X be... * For the local optimal position, X ω Let r represent the worst-case position, and r2 be a random number in the range (0, 1). This strategy, while referencing the current best solution, expands the search range to the historical search interval of the population by driving a portion of the population toward the current worst-case solution, thereby increasing the likelihood of the algorithm escaping local optima.

8. The method for measuring the oxide layer thickness of terahertz thermal barrier coatings based on multi-mode features and an improved dung beetle optimization algorithm according to claim 5, characterized in that, Step S7 employs the improved Punish-theft Dung Beetle Optimizer (PDBO) algorithm to optimize the three core hyperparameters of XGBoost: the number of iterations (num_trees), the tree depth (max_depth), and the learning rate (eta). This aims to improve the prediction accuracy and speed of XGBoost for oxide layer thickness, and to measure the root mean square error (RMSE), mean absolute error (MAE), and goodness of fit (R²). 2 () is used as an indicator to evaluate the performance of the model.

9. The method for measuring the oxide layer thickness of terahertz thermal barrier coatings based on multi-mode features and an improved dung beetle optimization algorithm according to claim 8, characterized in that, For the simulation signals, the multi-mode features with different oxide layer thicknesses were divided into a test set and a training set. The test set consisted of 30 signals, randomly selected from 59 signals in the 0-29μm range, while the training set consisted of the remaining 120 signals. The data were normalized so that each feature could be analyzed on the same scale, thereby improving the performance and stability of the machine learning model. The hyperparameters of XGBoost were optimized using DBO, PDBO, and MIC-PDBO, respectively, and the optimal solution was found using 5-fold cross-validation.

10. The method for measuring the oxide layer thickness of terahertz thermal barrier coatings based on multi-mode features and an improved dung beetle optimization algorithm according to claim 9, characterized in that, The optimization algorithms all used a population size of 30 and a maximum number of iterations of 200. The ranges for the number of iterations (num_trees), tree depth (max_depth), and learning rate (eta) were [100, 800], [3, 10], and [0.001, 0.3], respectively. The algorithms were run and compared in MATLAB R2024b. The results showed that DBO's prediction error ranged from -4 to 2.4, PDBO's from -1.3 to 1.5, and MIC-PDBO's from -1.1 to 1.

1. All three methods achieved relatively small errors using a multi-modal feature dataset, with MIC-PDBO exhibiting the smallest prediction error. The R-squared values ​​for DBO, PDBO, and MIC-PDBO were also compared. 2 The values ​​are 0.98176, 0.9916, and 0.994, respectively, all greater than 0.98.

Images