CN118036414B - Coating thickness characterization method based on ultrasonic guided wave machine learning - Google Patents
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Abstract
The invention discloses a coating thickness characterization method based on ultrasonic guided wave machine learning, which aims to perform nondestructive evaluation on the thickness and uniformity of a non-uniform coating system by utilizing machine learning and deep learning technologies.
Description
Technical Field
The invention relates to a method for characterizing coating thickness by using guided waves based on machine learning and deep learning, belonging to the field of nondestructive testing.
Background
In modern industrial applications, coating technology plays a vital role. The coating not only provides physical protection against corrosion and abrasion, but also improves the aesthetics and specific functional properties of the material, such as thermal resistance, electrical insulation or specific optical properties. For example, in the aerospace and energy and military industries, coatings are used to improve the performance and durability of materials in extreme environments. In addition, thin film coatings in the microelectronics industry are critical to the manufacture of high performance and miniaturized electronic devices and the maintenance of military devices. However, the performance and function of the coating is largely dependent on its thickness and uniformity. Improper coating thickness may lead to performance degradation or even failure. Thus, accurate measurement and control of coating thickness is critical to ensuring product quality and performance. Conventional coating thickness measurement techniques include contact and non-contact measurements (e.g., X-ray fluorescence, infrared spectroscopy, and ultrasonic measurements). These methods each have advantages, but also have limitations such as dependency on specific materials, destructiveness of measurement processes, complexity of operation, or high cost.
With the development of material science and signal processing technology, non-destructive evaluation (NDE) techniques have been widely studied and applied to the measurement of coating thickness. In particular, ultrasound-based non-destructive evaluation techniques are of great interest because of their high sensitivity and non-destructive nature. Among these methods, the guided wave technique is a hot spot of research because it can propagate in a thin plate structure. Guided waves are elastic waves that propagate in a sheet material, whose propagation characteristics are affected by material properties and structural characteristics, and thus can be used to infer the thickness and uniformity of the coating. However, extracting accurate coating information from the guided wave signal is a complex problem. This is mainly because the guided waves are multimode and dispersive, i.e. the wave speed varies with frequency and mode changes. In addition, conventional signal processing methods face challenges in processing highly dispersive and multi-modal signals. To overcome these limitations, machine learning and deep learning techniques have been introduced for guided wave signal analysis. These advanced methods enable extraction of useful features from complex signals, improving the accuracy and efficiency of coating thickness characterization.
In summary, although some progress has been made in the prior art, there is room for further improvement in the non-destructive evaluation of coating thickness, particularly in terms of improved characterization accuracy, processing of complex signals, and cost reduction. Accordingly, the present invention aims to provide a more efficient and accurate method of characterizing coating thickness to meet the need for high quality and reliability in industrial applications.
Disclosure of Invention
The invention aims to provide a method for characterizing the thickness of a substrate material by using guided waves based on machine learning and deep learning.
The invention provides a method for accurately characterizing the thickness of a coating based on machine learning and deep learning technologies and combined with the application of guided waves. The method not only improves the accuracy of coating thickness measurement, but also can be applied to various layering systems, especially in coated plate samples, including coating materials and substrate materials. The core principle of the invention is that a physical model and a data driving method are combined, key information is extracted from the complexity of the multi-mode and frequency dispersion wave problem, uncertainty is reduced, and accurate representation of the thickness of the coating is realized.
The principle of the invention is to integrate a physical model and a data analysis method. The physical model simulates guided wave propagation using finite elements. Digital signal processing techniques are used to extract dispersion information from the time domain signal. Machine learning and deep learning models construct a map from the dispersion curve to the coating thickness based on the known dispersion curve and thickness data. The models replace the traditional physical model, and the measurement accuracy of the coating thickness is improved by learning the nonlinear relation. The method comprises the following steps:
1.1. A composite structure formed by two materials is established, the bottom layer is a zirconium alloy plate with the length L and the thickness D 1, and the upper layer is a chromium coating with the thickness D 2. N signal receiving points are arranged on the upper surface of the composite structure, and modulated sine wave excitation is applied to the upper left corner of the coating so as to simulate the propagation of guided waves in a sample. The excitation frequency is set to f, expressed as follows:
(1)
Where u (T) represents a time-varying displacement, A is the maximum amplitude of the signal, f is the signal frequency, T is the time variable, and T is the period. And a fixed boundary condition is set at the left side edge of the composite structure. The grid cell size should be less than 1/10 of the corresponding wavelength at the highest frequency.
1.2. Time domain signals generated by the finite element model are acquired, including waveform data at different locations and points in time. And carrying out two-dimensional Fourier transform processing on the collected time domain signals. Firstly, denoising preprocessing is carried out on time domain signals received by N signal receiving points in the step 1.1, so as to obtain preprocessed signals s (t, x), wherein t represents time and x represents a spatial position. S (t, x) is converted to the frequency-wavenumber domain using a two-dimensional discrete fourier transform:
(2)
S (f, k) represents a signal of the frequency-wave number domain. s (t n,xm) is a discrete representation of the time domain signal, where t n and x m represent discrete temporal and spatial positions, respectively. f is frequency, k is wavenumber, and N and M represent the number of discrete points in time and space, respectively.
By the above two-dimensional fourier discrete transformation, the signal intensity at each frequency f and wave number k can be obtained. This intensity map is known as a dispersion map, where the bright lines or areas of concentrated intensity represent wave propagation modes in the material, which modes are related to the thickness and other physical properties of the material.
1.3. And (3) extracting key fluctuation characteristics from the dispersion map in the step (1.2) by using a non-maximum suppression technology, and reserving local maximum points for linear fitting. The specific flow of the steps is as follows:
For each pixel point on the dispersion map, a non-maximum suppression (NMS) technique is applied, which compares the intensity value of that point with its neighbors. If the intensity of a point is not the maximum value in the adjacent area, the intensity of the point is inhibited, only the local maximum value point is reserved, key fluctuation characteristics are highlighted, and the reserved local maximum value point is extracted, wherein the points represent the most obvious fluctuation mode in the dispersion graph. The high intensity value points extracted by NMS techniques are then linear fitted to build a mathematical model of the wave pattern. The fitting function takes the form:
(3)
Where a is the slope, b is the y-axis intercept, k is the wavenumber, and f (k) is the frequency corresponding to wavenumber k. The slope a is very sensitive to variations in coating thickness because it is directly related to the propagation velocity of the A0 mode. The result provides an accurate description of the different wave behaviors of thinner and thicker coatings.
1.4. And (3) classifying the coating sample by using a machine learning classifier part through the extracted characteristics, and judging whether the coating sample reaches a preset coating thickness standard or not. The coating thickness threshold was chosen to be H, based on which the coating samples were classified into two categories, "thick enough" and "thick not enough". This threshold setting is based on the test results and is applicable to different thickness criteria. The maximum intensity values extracted from the features extracted in step 1.3, which exhibit a high sensitivity over the range of coating thicknesses (x, y), are used for the linear fit.
Normalizing the input data to a characteristic value ranging from 0 to 1,
(4)
Where x n is the normalized eigenvalue, x is the original eigenvalue, x min is the minimum value of the eigenvalue in the dataset, and x max is the maximum value of the eigenvalue in the dataset.
A variety of machine learning classifiers are applied including k-nearest neighbor (kNN), single layer perceptrons, support vector machines, gaussian processes and feed forward neural networks. The classifier is k-fold cross-validated to evaluate its performance on different subsets of data. The general form of these classifiers can be represented as y=f (X; θ), where Y is the characterized class label, X is the input feature, and θ represents the model parameters. And then evaluating the model performance by using k-fold cross validation, and selecting an optimal model according to the cross validation result.
1.5. For uniform coating thickness, machine learning in step 1.4 was applied for characterization. For the non-uniform coating thickness, extracting the dispersion characteristic by using a two-dimensional Fourier transform method, adopting a deep learning network to design a corresponding CNN architecture, constructing a mapping relation between the dispersion curve and the non-uniform coating thickness, training a CNN model by adjusting super parameters such as a learning rate, a batch size, a loss function, an optimizer and the like, adopting cross verification to avoid over fitting, and optimizing the characterization performance of the CNN model.
The specific steps of the step 1.5 are as follows:
1.5.1. the data size is reduced, and the dispersion map is converted into PNG format through lossless compression, and the formula is PNG (I), wherein I is an original dispersion image.
1.5.2. Setting a network structure, and a convolution layer: the input data x is processed by a two-dimensional convolution operation Conv2D using W l and b l as weights and offsets for each layer. After convolution, the nonlinearity is increased by the ReLU activation function. For each convolution layer, l, the formula is
(5)
Where x is the input data, conv2D represents a two-dimensional convolution operation, reLU is the activation function, W l is the weight of the first convolution layer, and b l is the bias of the first convolution layer.
Average pooling layer: the output of the convolution layer is processed by the averaging pooling layer P to reduce the feature dimension.
Using 2D averaging pooling, the formula is
(6)
Where P is the average pooling operation and x is the input data.
Full tie layer: the output of the average pooling layer is further processed through the full connection layer F l, again applying the ReLU activation function.
For each full connection layer, the formula is
(7)
Where F l is the first full-connection layer, x is the input data, dense is the full-connection operation, W l is the weight of the first convolution layer, and b l is the offset of the first convolution layer.
1.5.3. Loss function and training the network is trained using a negative log likelihood loss function L (θ). For a given input x i and tag y i, the loss is calculated and the network parameter θ is updated by gradient descent. Negative log likelihood loss formula:
(8)
Where L is the loss function and θ is the probability of the correct tag y i given the input x i and the network parameter θ, for the network parameter P (y i|xi; θ). Network training updates the formula:
(9)
Wherein theta new is updated network parameter, alpha is learning rate, Is the gradient of the loss function with respect to θ.
1.5.4. The accuracy of the network in identifying uniform and non-uniform coatings is assessed using the confusion matrix M ij (i is the true data and j is the number of samples characterizing the data) to assess the classification performance of the network. The actual thickness and the number of characterizing thicknesses for each category are calculated.
1.5.5. And (3) returning to the step 1.5.2 to adjust the network structure and the super parameters according to the performance results on the training and verification set. Including changing the number of convolutional layers, adjusting the number of neurons of the fully connected layers, or modifying the learning rate.
The beneficial technical effects of the invention are as follows: the invention combines finite element analysis, ultrasonic guided wave, machine learning and deep learning technologies to realize inversion characterization of uniform and non-uniform coating thickness. The advanced machine learning and deep learning algorithm is used, the accuracy of coating thickness characterization is remarkably improved, particularly when a non-uniform coating is processed, the traditional method is difficult to capture the fine change of the coating thickness, but the method can be accurately identified by a deep learning model, and the limitation of the traditional method applied to changeable and complex coating conditions is overcome. According to the invention, through an efficient calculation model, the requirement of experimental tests can be reduced, and a large amount of complex data can be processed by applying machine learning and deep learning, so that key features are extracted. The invention is not only suitable for specific coating materials, but also can be applied to inversion of the coating thickness of other types of materials by adjusting parameters and training data.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a finite element excitation signal diagram;
FIG. 3 is a finite element model diagram of a uniformly coated layer;
FIG. 4 is a finite element model diagram with a non-uniform coating;
FIG. 5 is a finite element simulated dispersion plot with a 200 μm thick coating;
FIG. 6 is a plot of inversion characteristics of a coating thickness threshold of 200 μm dispersion;
fig. 7 is a kNN (k=1) classifier graph;
FIG. 8 is a diagram of a Support Vector Machine (SVM) classifier;
FIG. 9 is a classification chart of 100 samples;
FIG. 10 is a training-validation loss value graph;
FIG. 11 is a training-validation accuracy graph;
Fig. 12 is a confusion matrix.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. The present embodiment is implemented on the premise of the technical scheme of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection scope of the present invention is not limited to the following examples.
In this embodiment, a finite element analysis model (as shown in FIG. 3) is first built,
Step one, a composite structure model formed by two materials is established, the bottom layer is a zirconium alloy plate with the length of 155mm and the thickness of 1mm, the upper layer is a chromium coating, a finite element model with a uniform coating is shown in fig. 3, a finite element model with a non-uniform coating is shown in fig. 4, the thickness of the coating is changed from 10 mu m to 600 mu m, the depth of a gap in the non-uniform coating model is changed from 0 mu m to 200 mu m, and the following example is the thickness of the coating which is 200 mu m, so that the influence of different coating thicknesses on the propagation of guided waves is simulated. Material properties of zirconium alloy plate: young's modulus E is 99.3GPa, poisson's ratio μ is 0.37, density ρ is 6.56 g/cm 3. Material properties of the chromium coating: young's modulus E is 279GPa, poisson's ratio mu is 0.21, and density ρ is 7.19 g/cm.
Step two, a modulating sine wave excitation signal (shown in fig. 2) is applied to the upper left corner of the coating, and the expression of the modulating sine wave is as follows:
(1)
where u (T) represents a time-varying displacement, A is the maximum amplitude of the signal, f is the signal frequency, T is the time variable, and T is the period. In this embodiment, the excitation frequency f is set to 25MHz, and the frequency value is substituted into the periodic formula t=1/f, and 0.04 μs is calculated, so that the expression of the modulated sine wave signal is:
(2)
The left boundary of the model is provided with a fixed boundary condition, all nodes are constrained in the in-plane direction, the receiving points are distributed along the surface of the coating sample, and according to the formula, the wavelength lambda=c/f is the speed, f is the frequency, lambda=5.1×10 -4 m is calculated, the distance between the receiving points is smaller than 1/10 of the wavelength, and 5×10 -5 m is taken. The mesh cell size should also be set to be less than 1/10 of the corresponding wavelength at the highest frequency, in the example 5 x 10 -5 m.
And step three, acquiring time domain signals generated by the finite element model, namely waveform data at different positions and time points. And carrying out two-dimensional Fourier transform processing on the collected time domain signals. Firstly, denoising preprocessing is carried out on time domain signals received by N=256 signal receiving points in the second step, so as to obtain preprocessed signals s (t, x), wherein t represents time and x represents a spatial position. S (t, x) is converted to the frequency-wavenumber domain using a two-dimensional discrete fourier transform:
(3)
s (f, k) represents a signal of the frequency-wave number domain. s (t n,xm) is a discrete representation of the time domain signal, where t n and x m represent discrete temporal and spatial positions, respectively. f is frequency, k is wavenumber, and N and M represent the number of discrete points in time and space, respectively. The range from 0 to 25MHz is selected in this example. For wavenumber k, the wavenumber range is selected to be 0 to 12500 1/m depending on the wavelength and material properties.
Further, by performing a two-dimensional fourier transform in a selected time and space range, the signal intensity at each frequency f and wave number k can be obtained. The intensity map is a dispersion map (as shown in fig. 5), and the bright lines or the areas with concentrated intensities in the dispersion map represent wave propagation modes in the material, and the fluctuation modes of the transformed data S (f, k) under different frequencies and wave numbers are analyzed to identify and interpret the dispersion characteristics.
And step four, analyzing the dispersion map by using a non-maximum suppression technique (NMS), and accurately acquiring key fluctuation information by identifying local maximum intensity values around the wave mode.
Further, for each pixel point s (x, y) on the dispersion map, the NMS technique compares the intensity value of that point with its neighboring points, suppresses s (x, y) to 0 if s (x, y) is not the maximum value in its neighboring region, retains only those points that have the maximum intensity value in its neighboring region, eliminates interference of non-critical points, and highlights critical features. Where s (x, y) is the intensity value at a point on the dispersion map, where x and y represent the position in the frequency-wavenumber domain, respectively.
Step five, extracting local maximum intensity value points (k 1,f1),(k2,f2),...,(kn,fn) of each wave mode identified by the NMS technology in step four, wherein k i and f i respectively represent wave numbers and frequencies, performing mathematical modeling on the points by applying a linear fitting algorithm, and the fitting function is in the form of f (k) =ak+b, wherein a is a slope, and b is an intercept. Key propagation characteristics a and b sensitive to variations in coating thickness are accurately obtained.
And step six, inputting the extracted characteristics into a machine learning classifier to realize effective classification of the coating thickness. The coating samples were classified as thick enough and not thick enough, labeled as two categories, and the threshold value for coating thickness h=200um was chosen as a boundary for discriminating between thick enough and not thick enough in this example, and the features extracted from the previous step (40 data), i.e., slope a and intercept b from the linear fit, were used as inputs to a machine-learned classifier, with each data point corresponding to a sample with the corresponding coating thickness (as shown in fig. 6). In this example, first, feature data x and corresponding tag data y are collected and processed, normalization processing is performed on the input feature values, the feature values are normalized to a range of 0 to 1, and a machine learning classifier is selected: k-nearest neighbor algorithm (kNN), support Vector Machine (SVM), gaussian Process (GP), or feed forward neural network.
Further, training the selected classifier, using the extracted features as training data, for example, adopting a k-nearest neighbor (kNN) algorithm, initializing KNeighborsClassifier, setting the number of adjacent points 1 as a parameter, and inputting the normalized feature data x and the corresponding label y into the classifier for training by using a fit method. And adopting a Support Vector Machine (SVM), creating a support vector machine model by using the SVC, setting radial basis functions and regularization parameters, inputting the processed data set into the model, and executing a fit method to complete training. The results after cross-validation show that the accuracy of the support vector machine with radial basis function is up to 95.4% (as shown in fig. 8) and the accuracy of the nearest neighbor classifier (1 NN) is up to 90.3% (as shown in fig. 7) but exceeds 90% in the data set with 40 simulated uniform coated plates.
And step seven, applying a deep learning method to the non-uniform coating thickness. Simulation experiments with different parameters (coating thickness and gap depth) were performed 200 times using ABAQUS software, with different coating thicknesses h c and gap depths h g as measures of coating non-uniformity, with gap depths varying between 0-200 μm, to generate data sets for training CNN.
Step eight, developing a Convolutional Neural Network (CNN), wherein the network comprises a convolutional layer, an average pooling layer and a fully-connected layer. The convolution layer learns spatial features of the input data through a plurality of filters, increases nonlinearities using a ReLU activation function, and applies maximum pooling to reduce the spatial dimensions of the features. The first layer of the network uses 64 filters, the second layer uses 70 filters, the third layer uses 500 filters, each layer is followed by a ReLU activation function and a max pooling operation. A random discard layer and a bulk normalization layer are also applied after the last convolutional layer.
The averaging pooling layer then further reduces the feature dimension of the convolutional layer output to reduce the computational burden of the subsequent fully-connected layer. The full connection layer in the network is responsible for integrating the learned features and performing final classification characterization. A ReLU activation function and random discard layer is also applied after these layers to increase the generalization ability of the model.
After defining the network architecture and loss function (negative log likelihood loss), model training is performed. Training environment configurations include input dimensions (1024 x 1024), data paths, model save paths, batch sizes (25), and optimizer settings. The learning rate (5 e -4), weight decay (1.1 e -3), and momentum (1 e -7) were configured using an Adam optimizer, and data enhancement and normalization processes were performed.
Step nine, inputting data, firstly storing a dispersion map as a PNG format, randomly disturbing the created PNG image, and distributing the PNG image to a training set and an evaluation set, wherein 70% of the data are used for training. 30% of the data was used for testing, in this example training using a batch of input images, with a batch size of 32. And loading random batch images, transmitting the images through a network, and calculating the loss of each image. This example captures subtle changes in the image using an input resolution of 1024 x 1024. Training cycles are performed by neural network training and evaluation to set the number of training cycles 200, and the trained model weights and training statistics are saved using a function (as shown in fig. 10 and 11). The classification performance of the network for 100 samples is shown in fig. 9, and the accuracy of the network in identifying uniform and non-uniform coatings is assessed by adjusting the hyper-parameters and optimizing the model performance using cross-validation techniques (as shown in fig. 10).
The invention has been described above schematically with reference to the accompanying drawings and examples, but the invention is not limited to the examples described above, and the changes and modifications of the technical solution shown in the drawings are only one of the examples of the invention, and the scope of the invention is to be understood as being included in the scope of the invention, and the scope of the invention is to be defined by the claims. Various modifications or improvements may be made to the above examples, and such modifications, improvements or equivalents are intended to be included within the scope of the invention.
Claims (5)
1. A coating thickness characterization method based on ultrasonic guided wave machine learning is characterized by comprising the following steps of: the method comprises the following steps:
Step 1, a composite structure finite element simulation model formed by two materials is established, the bottom layer is a zirconium alloy plate with the length L and the thickness D 1, the upper layer is a chromium coating with the thickness D 2, N signal receiving points are arranged on the upper surface of the composite structure, modulated sine wave excitation is applied to the upper left corner of the coating so as to simulate the propagation of guided waves in the structure, a time domain signal is obtained, wherein the excitation frequency is set to be f, and the expression is as follows:
，
Wherein u (T) represents a displacement which changes with time, A is the maximum amplitude of the signal, f is the frequency of the signal, T is the time variable, T is the period, and a fixed boundary condition is set on the left boundary of the composite structure, and the size of the grid unit is smaller than 1/10 of the corresponding wavelength at the highest frequency;
step 2, carrying out two-dimensional Fourier transform processing on the time domain signals obtained in the step 1 to obtain the signal intensity of each frequency and each wave number, namely a frequency dispersion diagram;
Step 3, extracting key fluctuation features from the dispersion map in the step 2 by applying a non-maximum suppression technology, and reserving local maximum points to establish a mathematical model of a wave mode and performing linear fitting;
Step 4, inputting the features extracted in the step 3 into a machine learning classifier, training the classifier, and applying the machine learning classifier part to judge whether the features reach a preset coating thickness standard or not;
and 5, for the non-uniform coating thickness condition, applying a deep learning method, and using a convolutional neural network CNN to perform classification characterization on the data set.
2. The ultrasonic guided wave machine learning-based coating thickness characterization method of claim 1, wherein: in step 2, acquiring time domain signals generated by a finite element model, including waveform data at different positions and time points, performing two-dimensional fourier transform processing on the collected time domain signals, firstly, for time domain signals s (t, x) received by N signal receiving points in step 1, where t represents time and x represents a spatial position, performing denoising preprocessing, and converting the preprocessed signals s (t, x) into a frequency-wave number domain, where the expression of the two-dimensional discrete fourier transform is:
，
S (f, k) represents a signal in the frequency-wave domain, S (t n,xm) is a discrete representation of a signal in the time domain, where t n and x m represent discrete time and space positions, respectively, f is frequency, k is wave number, N and M represent the number of discrete points in time and space, respectively,
The signal intensity at each frequency f and wave number k can be obtained by the two-dimensional discrete Fourier transform, and the intensity graph is a dispersion graph.
3. The ultrasonic guided wave machine learning-based coating thickness characterization method of claim 1, wherein: in step 3, a non-maximum suppression technique is applied to extract key fluctuation features from the dispersion map in step 2, local maximum points are reserved to establish a mathematical model of a wave mode and perform linear fitting, and the fitting function adopts a form f (k) =ak+b, wherein a is a slope, b is a y-axis intercept, k is a wave number, and f (k) is a frequency corresponding to the wave number k.
4. The ultrasonic guided wave machine learning-based coating thickness characterization method of claim 1, wherein: in step 4, the extracted features are input into a machine learning classifier, the classifier is trained, a machine learning classifier part is applied, a coating sample is classified according to the extracted features, whether the coating sample meets a preset coating thickness standard or not is judged, a coating thickness threshold value is selected as H, the coating sample is classified into two categories of 'enough thickness' and 'not enough thickness' according to the standard, and the threshold value is set based on a test result and is suitable for different thickness standards.
5. The ultrasonic guided wave machine learning-based coating thickness characterization method of claim 1, wherein: in step 5, for the non-uniform coating thickness situation, a deep learning method is applied, a convolutional neural network CNN is used for classifying a data set, a neural network model is developed, tiny changes in input data are captured by minimizing the number of parameters to realize inversion of the coating thickness, a network training environment is configured, including setting input dimensions, defining data paths, model storage paths and batch processing sizes, the network is trained by using an Adam optimizer, model training and evaluation are performed by using the deep learning network, and model performance is optimized by adjusting super-parameters and applying a cross-validation technique.
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