Intelligent coating optimization method for surface treatment of quartz crucible

Abstract

The application belongs to the technical field of crucible coating optimization, and relates to an intelligent coating optimization method for surface treatment of a quartz crucible; the application collects coating material data, surface treatment environment data, coating process data and performance test data, takes the performance test data as a true result label of a training set, carries out denoising, missing value processing and normalization on the collected data, screens out a group of key features through a Pearson correlation coefficient and a principal component analysis method, reduces the data dimension, simultaneously retains main information affecting coating performance, enables a deep neural network model to be trained, predicts coating performance through the model, optimizes coating process parameters based on the predicted coating performance, can effectively search for an optimal parameter combination, avoids blindness and high cost of a traditional optimization method, forms a closed-loop intelligent coating optimization process, and significantly improves optimization efficiency and performance of the coating process.

Description

Technical Field

[0001] This application belongs to the field of crucible coating optimization technology, and more specifically, relates to an intelligent coating optimization method for the surface treatment of quartz crucibles. Background Technology

[0002] Currently, the production and manufacturing of quartz crucibles mainly adopts the high-temperature melting method, which involves melting high-purity quartz sand at high temperatures and then using specific molding processes, such as centrifugal casting and hot pressing, to produce crucibles with certain shapes and sizes. In order to improve the performance and lifespan of the crucibles, a coating treatment is usually required on the surface of the crucibles during the manufacturing process.

[0003] The specific implementation steps of the coating process are as follows:

[0004] Cleaning and pretreatment: First, clean the surface of the quartz crucible to remove oil, dust and other impurities, and then dry it.

[0005] Coating material selection: Select appropriate coating materials, such as ceramics, metals, oxides, etc., according to the crucible's usage environment and performance requirements.

[0006] Coating application: The coating material is evenly applied to the crucible surface using methods such as spraying, dipping, or brushing. Parameters such as coating thickness, uniformity, temperature gradient, spraying rate, and angle have a significant impact on coating performance.

[0007] Drying and curing: After the coating is applied, the crucible is dried and cured to ensure that the coating material is tightly bonded to the surface of the crucible and to improve the service life of the coating.

[0008] However, current optimization of coating processes relies on engineers' experience and experimental data, lacking systematicity and objectivity. Since the optimization of coating processes is often based on personal experience, it is highly subjective and lacks objective evaluation standards, making it difficult to ensure that the results of each optimization meet the optimal performance requirements. Summary of the Invention

[0009] This invention provides an intelligent coating optimization method for the surface treatment of quartz crucibles, which aims to solve the technical problem that the optimization results based on personal experience are difficult to meet the optimal performance requirements.

[0010] A smart coating optimization method for quartz crucible surface treatment, characterized by comprising the following steps:

[0011] Step 1: Collect coating material data, surface treatment environment data, coating process data, and performance test data during the surface treatment process of the quartz crucible, and use the performance test data as the true result label of the training set data;

[0012] Step 2: Denoise the collected data, identify and fill in missing values, and finally normalize the data.

[0013] Step 3: Based on the preprocessed data and the data after feature extraction, Pearson correlation coefficient and principal component analysis are used to screen features and obtain a set of key features;

[0014] Step 4: Train the deep neural network based on the obtained key features to obtain a trained deep neural network, and obtain the coating performance based on the trained deep neural network;

[0015] Step 5: Based on the predicted coating performance, the particle swarm optimization algorithm is used to optimize the coating process parameters to obtain the optimal combination of coating process parameters.

[0016] This invention proposes an intelligent coating optimization method for quartz crucible surface treatment. Addressing the problem that traditional coating process optimization based on personal experience often fails to meet optimal performance requirements, the method first collects coating material data, surface treatment environment data, coating process data, and performance test data, using the performance test data as the true result label for the training set. Next, the collected data undergoes denoising, missing value processing, and normalization to improve data quality and lay the foundation for subsequent model training. Then, using Pearson correlation coefficient and principal component analysis, a set of key features is selected, reducing data dimensionality while retaining the main information affecting coating performance. Utilizing these key features, a deep neural network model is trained, and the model predicts coating performance, achieving an intelligent transformation from data to performance prediction. Finally, based on the predicted coating performance, a particle swarm optimization algorithm is used to optimize the coating process parameters. This method effectively searches for the optimal parameter combination, avoiding the blindness and high cost of traditional optimization methods. In summary, by integrating data acquisition, preprocessing, feature selection, deep learning model training, and intelligent optimization algorithms, a closed-loop intelligent coating optimization process is formed, significantly improving the optimization efficiency and performance of the coating process and solving the technical problems of traditional methods.

[0017] Preferably, for data where a single feature exists at multiple measurement points in a sample, the Pearson correlation coefficient is used for feature selection as follows:

[0018] Calculate the Pearson correlation coefficient between the feature and the target variable based on the weighting factor and the smoothing factor:

[0019]

[0020] In the formula: r xy (j) represents the smoothed Pearson correlation coefficient between the j-th feature variable and the target variable; This represents the average value of the j-th feature variable in the i-th sample; Let y represent the average of the j-th feature variable across all samples; i This represents the value of the target variable for the i-th sample; w represents the mean of the target variable across all samples. ij α represents the average weighting factor of the j-th feature variable of the i-th sample; ij The average smoothing factor represents the j-th feature variable of the i-th sample;

[0021] The formula for calculating the smoothing factor is as follows:

[0022]

[0023] In the formula: α ik The residual represents the smoothing factor for the k-th measurement of the j-th feature of the i-th sample; ik The median(|residuals) represents the residual of the k-th measurement of the j-th feature of the i-th sample relative to the mean of the j-th feature variable of that sample; i |) represents the median of the absolute values ​​of the residuals of the characteristic variables measured in the i-th sample; e represents the base of the natural logarithm; M represents the number of measurements of the j-th characteristic variable in the i-th sample;

[0024] The formula for calculating the weighting factor is as follows:

[0025]

[0026] In the formula: w ik The weight factor represents the k-th measurement value of the j-th feature of the i-th sample; x ik The variance(x) represents the feature data value of the k-th measurement of the j-th feature of the i-th sample. ik The variance (x) represents the feature data variance of the k-th measurement of the j-th feature in the i-th sample; j ) represents the average variance of the data for the j-th feature across all samples;

[0027] The features corresponding to the top k Pearson correlation coefficients are selected as inputs for principal component analysis based on the absolute values ​​of the calculated Pearson correlation coefficients from highest to lowest.

[0028] Preferably, when a feature data point has only one measurement in a sample, the Pearson correlation coefficient is calculated as follows:

[0029]

[0030] In the formula: r xy The Pearson correlation coefficient represents the relationship between feature x and target variable y; x i y represents the feature value of the i-th sample; i This represents the target variable value for the i-th sample; This represents the mean of all samples for feature x. N represents the mean of all samples of the target variable y; N represents the number of samples.

[0031] The features corresponding to the top k Pearson correlation coefficients are selected as inputs for principal component analysis based on the absolute values ​​of the calculated Pearson correlation coefficients from highest to lowest.

[0032] Preferably, the deep neural network includes an input layer, a feature cross layer, an intermediate layer, and an output layer;

[0033] The input layer is used to receive feature vectors input to the deep neural network;

[0034] The feature cross layer generates new features by using inner product cross and multiplicative cross, and then outputs them to the intermediate layer after nonlinear transformation by the ReLU activation function.

[0035] The intermediate layer receives the features output by the feature cross layer and performs feature extraction based on multiple fully connected layers. Residual connections are added to each fully connected layer. The activation function uses the ReLU activation function to introduce nonlinearity, and a regularization term is introduced in the intermediate layer to prevent overfitting.

[0036] Output layer: A fully connected layer containing one neuron outputs the final predicted coating performance.

[0037] Preferably, the data processing steps of the feature cross layer are as follows:

[0038] Let the input feature vector be X = [x1, x2, ..., xn]. n ], where x i Let represent the i-th feature, and n represent the total number of features;

[0039] Inner product cross: for feature x i and x j Perform inner product crossover to generate new crossover features:

[0040]

[0041] In the formula: z ij Indicates feature x i and x j The features generated after performing inner product cross are then subjected to inner product cross for each pair of features.

[0042] Element-wise product cross: Perform element-wise product operation on all features to obtain cross features.

[0043] z=X⊙X=[x1·x2,x1·x3,…,x n-1 ·x n ];

[0044] In the formula: ⊙ represents element-wise multiplication;

[0045] Generate the cross feature matrix: Concatenate the results of the inner product cross and the element-wise product cross to generate a new feature matrix Z:

[0046] Z = [z 12 ,z 13 ,…,z ij ,z];

[0047] In the formula: Z represents the generated cross feature vector, which includes the inner product cross and element-wise product cross of all feature pairs;

[0048] The generated feature matrix Z is nonlinearly transformed using the ReLU activation function and then output to the intermediate layer.

[0049] Preferably, the loss function of the deep neural network is as follows:

[0050]

[0051] In the formula: L represents the value of the loss function; N represents the number of samples; y i This represents the true label value of the i-th sample; λ represents the predicted value of the i-th sample; λ represents the regularization coefficient; M represents the number of all weight parameters in the model; W j This represents the j-th weight parameter.

[0052] Preferably, step 5 includes the following steps:

[0053] Initialize the particle swarm: Assume the coating process parameters have d dimensions. Define each particle in the particle swarm as a d-dimensional vector, representing a set of process parameters; initialize the position and velocity of each particle in the particle swarm:

[0054] x i =(x i1 ,x i2 ,…,x id ),v i =(v i1 ,v i2 ,…,v id );

[0055] In the formula: i represents the particle index; d represents the dimension of the process parameter; xi Indicates the position of the i-th particle; v i x represents the velocity of the i-th particle; id v represents the position of the i-th particle in the d-th dimension; id This represents the velocity of the i-th particle in the d-th dimension;

[0056] Calculate the fitness of particles: Predict the coating performance of each particle based on the trained deep neural network, and calculate the fitness of each particle based on the predicted coating performance.

[0057] f(x i = -Predicted Performance(x) i );

[0058] In the formula: Predicted Performance(x) i ) represents the coating performance predicted by the deep neural network for each particle;

[0059] Update individual best position and global best position:

[0060] For each particle, record the optimal position p with the lowest historical fitness. i If the current fitness value is less than the historical best position p i If the fitness value is obtained, then the individual's optimal position is updated:

[0061] p i =x i ,if f(x i ) <f(p i );

[0062] Record the global best position g among all particles, that is, the position of the particle with the lowest fitness:

[0063]

[0064] Update the particle's velocity and position:

[0065]

[0066] In the formula: This represents the updated velocity of particle i in the d-th dimension; This represents the velocity of particle i in the d-th dimension before the update; This indicates the position of particle i in dimension d before the update; Let represent the position of particle i in d-dimensional space after the update; ω represents the inertia weight; c1 and c2 represent the acceleration constants, which control the degree to which the particle moves towards its individual optimal position and global optimal position, respectively; r1 and r2 represent random numbers uniformly distributed between [0,1]; p idG represents the optimal individual position of particle i in d dimensions; d This represents the d-th dimension value of the globally optimal position;

[0067] Convergence criteria: Set a maximum number of iterations. Stop iteration when the particle swarm reaches the maximum number of iterations or the improvement of the global optimal solution is less than the set threshold; output the optimal combination of coating process parameters.

[0068] The beneficial effects of this invention include:

[0069] This invention proposes an intelligent coating optimization method for quartz crucible surface treatment. Addressing the problem that traditional coating process optimization based on personal experience often fails to meet optimal performance requirements, the method first collects coating material data, surface treatment environment data, coating process data, and performance test data, using the performance test data as the true result label for the training set. Next, the collected data undergoes denoising, missing value processing, and normalization to improve data quality and lay the foundation for subsequent model training. Then, using Pearson correlation coefficient and principal component analysis, a set of key features is selected, reducing data dimensionality while retaining the main information affecting coating performance. Utilizing these key features, a deep neural network model is trained, and the model predicts coating performance, achieving an intelligent transformation from data to performance prediction. Finally, based on the predicted coating performance, a particle swarm optimization algorithm is used to optimize the coating process parameters. This method effectively searches for the optimal parameter combination, avoiding the blindness and high cost of traditional optimization methods. In summary, by integrating data acquisition, preprocessing, feature selection, deep learning model training, and intelligent optimization algorithms, a closed-loop intelligent coating optimization process is formed, significantly improving the optimization efficiency and performance of the coating process and solving the technical problems of traditional methods. Attached Figure Description

[0070] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0071] Figure 1 This is an overall step diagram provided for an embodiment of the present invention.

[0072] Figure 2 This is a schematic diagram of the execution flow of the particle swarm optimization algorithm provided in an embodiment of the present invention. Detailed Implementation

[0073] To make the technical problems, technical solutions, and beneficial effects to be solved by this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the scope of this application.

[0074] See Figure 1 As shown, an intelligent coating optimization method for the surface treatment of quartz crucibles is characterized by comprising the following steps:

[0075] Step 1: Collect coating material data, surface treatment environment data, coating process data, and performance test data during the surface treatment process of the quartz crucible, and use the performance test data as the true result label of the training set data;

[0076] The coating material data includes the type, composition, physical and chemical properties of the coating material; wherein the physical and chemical properties include the density, hardness, thermal conductivity, surface roughness and chemical stability of the coating material, wherein the chemically stable coating exhibits corrosion resistance and oxidation resistance under various environmental conditions;

[0077] The surface treatment environmental data includes the temperature, humidity, and air pressure during the coating application process;

[0078] The coating process data includes spraying rate, spraying angle, spraying time, coating thickness, coating roughness, and spraying angle.

[0079] Therefore, we detect temperature, humidity, coating thickness, and coating roughness by setting up multiple measurement points;

[0080] The performance test data is antioxidant test data;

[0081] Step 2: Denoise the collected data, identify and fill in missing values, and finally normalize the data.

[0082] Noise reduction processing:

[0083] For each data point, calculate its Z-score, which represents the standard deviation of the data point from the mean. If the Z-score of a data point is greater than 3 or less than -3, it is considered an outlier.

[0084] Specific implementation:

[0085] Assume the mean of the spraying rate is 100 and the standard deviation is 10. If a certain spraying rate data point is 500, its Z-score is: Z = (500 – 100) / 10 = 40. Since the absolute value of the Z-score is greater than 3, it indicates that the data point is an outlier and can be deleted or replaced with other reasonable values.

[0086] For other numerical data such as coating roughness and coating thickness, the same Z-score method is used to detect and remove outliers.

[0087] Imputation of missing values ​​in numerical data:

[0088] For numerical data such as spraying rate, spraying angle, and coating thickness, if there are missing values, we will fill them with the mean of the feature.

[0089] Example: Suppose a missing value for the spray rate is located at a certain position, and the mean of that column is 150. If the value for that data point is missing, it will be filled with 150.

[0090] Other numerical data, such as coating thickness and coating roughness, also use a similar mean-filling method.

[0091] Imputation of missing values ​​in categorical data:

[0092] For categorical data, such as coating material type or spraying environment, we will use the mode of this column for population. The mode is the category that appears most frequently in this column.

[0093] Example: Suppose there are multiple categories in the coating material type column (e.g., "A", "B", "C"), and a missing value is located in a row. If the mode of the column is "A", then fill the missing value with "A".

[0094] Similarly, other categorical data (such as surface treatment environments) also use the mode filling method.

[0095] Z-score standardization: For each numerical feature, calculate its mean and standard deviation, then subtract the mean from each data point and divide by the standard deviation to obtain the standardized data.

[0096] Categorical data encoding: For categorical data, one-hot encoding is used to convert all categorical features into binary vector form.

[0097] The coating material type column contains multiple categories (such as "A", "B", "C"). We will create a binary variable for each category.

[0098] Example: For the "Coating Material Type" column, its categories "Material A", "Material B", and "Material C" will be converted into three binary features: "A" → [1,0,0]; "B" → [0,1,0]; "C" → [0,0,1]; other categorical data such as spraying environment also use the same one-hot encoding method. In this way, the original category information is transformed into numerical vectors, which facilitates subsequent model training.

[0099] It should be noted that the current spraying process is controlled based on pre-set fixed parameters. The parameters during the spraying process do not change frequently or continuously and do not depend on time continuity. Therefore, time series data is not considered in this embodiment.

[0100] Step 3: Based on the preprocessed data and the data after feature extraction, Pearson correlation coefficient and principal component analysis are used to screen features and obtain a set of key features;

[0101] For data where a single feature exists at multiple measurement points in a sample, the Pearson correlation coefficient is used for feature selection as follows:

[0102] Calculate the Pearson correlation coefficient between the feature and the target variable based on the weighting factor and the smoothing factor:

[0103]

[0104] In the formula: r xy (j) represents the smoothed Pearson correlation coefficient between the j-th feature variable and the target variable; This represents the average value of the j-th feature variable in the i-th sample; Let y represent the average of the j-th feature variable across all samples; i This represents the value of the target variable for the i-th sample; w represents the mean of the target variable across all samples. ij α represents the average weighting factor of the j-th feature variable of the i-th sample; ij The average smoothing factor represents the j-th feature variable of the i-th sample;

[0105] The formula for calculating the smoothing factor is as follows:

[0106]

[0107] In the formula: α ik The residual represents the smoothing factor for the k-th measurement of the j-th feature of the i-th sample; ik The median(|residuals) represents the residual of the k-th measurement of the j-th feature of the i-th sample relative to the mean of the j-th feature variable of that sample; i |) represents the median of the absolute values ​​of the residuals of the characteristic variables measured in the i-th sample; e represents the base of the natural logarithm; M represents the number of measurements of the j-th characteristic variable in the i-th sample;

[0108] The reason for introducing a smoothing factor in this embodiment is that in the analysis of coating uniformity (i.e. roughness), there may be some fluctuations caused by accidental factors, which are reflected in the residuals. Through the above formula, we assign a lower smoothing factor to data points with larger residuals, thereby reducing their impact on the analysis. For example, if the coating uniformity of a certain area becomes abnormal due to external interference (such as temperature changes), this abnormality will be reflected in the residuals, and the smoothing factor will be reduced accordingly to reduce the interference of this data point on the final analysis results.

[0109] The formula for calculating the weighting factor is as follows:

[0110]

[0111] In the formula: w ik The weight factor represents the k-th measurement value of the j-th feature of the i-th sample; x ik The variance(x) represents the feature data value of the k-th measurement of the j-th feature of the i-th sample. ik The variance (x) represents the feature data variance of the k-th measurement of the j-th feature in the i-th sample; j ) represents the average variance of the data for the j-th feature across all samples;

[0112] The reason for introducing weighting factors in this embodiment is as follows: For example, in coating thickness data, some measurement points may have greater fluctuations due to the special nature of their location (such as near the edge or seam). These measurement points have larger variances, so they should be given lower weights in correlation analysis to avoid their excessive influence on the overall trend. The above method ensures that data points with larger variances have lower weights, while data points with smaller variances have higher weights.

[0113] This embodiment considers the inherent characteristics of the data. The weighting factor focuses on the relative magnitude of fluctuations in the data points themselves, while the smoothing factor focuses on the consistency of the data points with the overall trend. By combining these two factors, key factors in the quartz crucible surface treatment process can be analyzed more accurately, and coating process parameters can be optimized. This method helps improve the interpretability of the data, thereby achieving better results in coating performance prediction and process optimization.

[0114] The features corresponding to the top k Pearson correlation coefficients are selected as inputs for principal component analysis based on the absolute values ​​of the calculated Pearson correlation coefficients from highest to lowest.

[0115] When a feature data point in a sample has only one measurement, the Pearson correlation coefficient is calculated as follows:

[0116]

[0117] In the formula: r xy The Pearson correlation coefficient represents the relationship between feature x and target variable y; x i y represents the feature value of the i-th sample; i This represents the target variable value for the i-th sample; This represents the mean of all samples for feature x. N represents the mean of all samples of the target variable y; N represents the number of samples.

[0118] Based on the absolute values ​​of the calculated Pearson correlation coefficients, the features corresponding to the top k Pearson correlation coefficients are sorted from high to low, and the features are selected as the input for principal component analysis (PCA). PCA itself will not be elaborated upon in this embodiment, but it is a well-known method for data dimensionality reduction and feature extraction. PCA was first proposed by Karl Pearson in 1901 and has since been further developed and popularized by other scholars. Therefore, given the specific implementation method, how to perform PCA based on the feature data output from the Pearson correlation coefficients is a conventional technique in this field, and will not be described in detail in this embodiment.

[0119] Step 4: Train the deep neural network based on the obtained key features to obtain a trained deep neural network, and obtain the coating performance based on the trained deep neural network;

[0120] The deep neural network includes an input layer, a feature cross layer, an intermediate layer, and an output layer;

[0121] The input layer is used to receive feature vectors input to the deep neural network;

[0122] The feature cross layer generates new features by using inner product cross and multiplicative cross, and then outputs them to the intermediate layer after nonlinear transformation by the ReLU activation function.

[0123] The data processing steps of the feature cross layer are as follows:

[0124] Let the input feature vector be X = [x1, x2, ..., xn]. n ], where x i Let represent the i-th feature, and n represent the total number of features;

[0125] Inner product cross: for feature x i and x j Perform inner product crossover to generate new crossover features:

[0126]

[0127] In the formula: zij Indicates feature x i and x j The features generated after performing inner product cross are then subjected to inner product cross for each pair of features.

[0128] Element-wise product cross: Perform element-wise product operation on all features to obtain cross features.

[0129] z=X⊙X=[x1·x2,x1·x3,…,x n-1 ·x n ];

[0130] In the formula: ⊙ represents element-wise multiplication;

[0131] Generate the cross feature matrix: Concatenate the results of the inner product cross and the element-wise product cross to generate a new feature matrix Z:

[0132] Z = [z 12 ,z 13 ,…,z ij ,z];

[0133] In the formula: Z represents the generated cross feature vector, which includes the inner product cross and element-wise product cross of all feature pairs;

[0134] The generated feature matrix Z is nonlinearly transformed using the ReLU activation function and then output to the intermediate layer.

[0135] The intermediate layer receives the features output by the feature cross layer and performs feature extraction based on multiple fully connected layers. Residual connections are added to each fully connected layer. The activation function uses the ReLU activation function to introduce nonlinearity, and a regularization term is introduced in the intermediate layer to prevent overfitting.

[0136] Multiple fully connected layers: The intermediate layers consist of multiple fully connected layers (MLP) to learn deeper feature relationships;

[0137] Residual connections: To avoid the vanishing or exploding gradient problems in deep networks, residual connections are used. In each layer, the original input is directly added to the output of that layer, thereby achieving efficient information transfer.

[0138] ReLU activation function: The output of each layer passes through the ReLU activation function, which increases the nonlinear mapping capability of the network;

[0139] The applications of regularization are as follows:

[0140] Suppose we use two fully connected layers, namely the first layer and the second layer, with weight matrices W1 and W2, and biases b1 and b2, respectively;

[0141] The weight matrix for the first layer is: Where m1 represents the number of parameters in the first-layer weight matrix W1; λ1 represents the regularization coefficient;

[0142] The weight matrix for the second layer is: Where m2 represents the number of parameters in the second-layer weight matrix W2; λ2 represents the regularization coefficient;

[0143] Output layer: Employs a fully connected layer containing one neuron, which outputs the final predicted coating performance;

[0144] For the weight matrix of the output layer: W in the output layer out L2 regularization will also be performed:

[0145]

[0146] Where: m out W represents the output layer weight matrix. out The number of parameters in the middle; λ out Represents the regularization coefficient of the output layer;

[0147] The loss function of the deep neural network is as follows:

[0148]

[0149] In the formula: L represents the value of the loss function; N represents the number of samples; y i This represents the true label value of the i-th sample; λ represents the predicted value of the i-th sample; λ represents the regularization coefficient; M represents the number of all weight parameters in the model; W j This represents the j-th weight parameter; This represents the L2 regularization term.

[0150] In summary, the complete form of the loss function is as follows:

[0151]

[0152] therefore:

[0153]

[0154] As can be seen from the above, the final form of the loss function L is related to the structure of the intermediate layer. Based on the above exemplary technical solution, the variation law of the loss function L has been clearly described, so it will not be repeated in this embodiment.

[0155] In this embodiment, the coating performance is antioxidant; however, this is not a limitation of this application. It can also be the prediction of coating hardness. The difference lies in the different labels used for the actual results, that is, the different target variables. The other solutions are the same. Therefore, based on the specific technical solution for predicting coating performance given above, replacing it with the prediction of coating hardness is a conventional alternative in the field. Therefore, it will not be described in detail in this embodiment.

[0156] Step 5: Based on the predicted coating performance, the particle swarm optimization algorithm is used to optimize the coating process parameters to obtain the optimal combination of coating process parameters;

[0157] See Figure 2 As shown, step 5 includes the following steps:

[0158] Initialize the particle swarm: Assume the coating process parameters have d dimensions. Define each particle in the particle swarm as a d-dimensional vector, representing a set of process parameters; initialize the position and velocity of each particle in the particle swarm:

[0159] x i =(x i1 ,x i2 ,…,x id ),v i =(v i1 ,v i2 ,…,v id );

[0160] In the formula: i represents the particle index; d represents the dimension of the process parameter; x i Indicates the position of the i-th particle; v i x represents the velocity of the i-th particle; id v represents the position of the i-th particle in the d-th dimension; id This represents the velocity of the i-th particle in the d-th dimension;

[0161] Calculate the fitness of particles: Predict the coating performance of each particle based on the trained deep neural network, and calculate the fitness of each particle based on the predicted coating performance.

[0162] f(x i = -Predicted Performance(x) i );

[0163] In the formula: Predicted Performance(x) i ) represents the coating performance predicted by the deep neural network for each particle;

[0164] Update individual best position and global best position:

[0165] For each particle, record the optimal position p with the lowest historical fitness. i If the current fitness value is less than the historical best position p i If the fitness value is obtained, then the individual's optimal position is updated:

[0166] p i =x i ,if f(x i ) <f(p i );

[0167] Record the global best position g among all particles, that is, the position of the particle with the lowest fitness:

[0168]

[0169] Update the particle's velocity and position:

[0170]

[0171] In the formula: This represents the updated velocity of particle i in the d-th dimension; This represents the velocity of particle i in the d-th dimension before the update; This indicates the position of particle i in dimension d before the update; Let represent the position of particle i in d-dimensional space after the update; ω represents the inertia weight; c1 and c2 represent the acceleration constants, which control the degree to which the particle moves towards its individual optimal position and global optimal position, respectively; r1 and r2 represent random numbers uniformly distributed between [0,1]; p id G represents the optimal individual position of particle i in d dimensions; d This represents the d-th dimension value of the globally optimal position;

[0172] Convergence criteria: Set a maximum number of iterations. Stop iteration when the particle swarm reaches the maximum number of iterations or the improvement of the global optimal solution is less than the set threshold; output the optimal combination of coating process parameters.

[0173] For example, the coating process parameters include four dimensions, with the data for the other dimensions remaining unchanged: x1: spraying temperature (unit: °C), x2: spraying humidity (unit: %), x3: coating thickness (unit: μm), and x4: spraying rate (unit: mm / s); therefore, the dimension d of the process parameter space is 4.

[0174] Initialize particle position and velocity: Each particle in the particle swarm is a d-dimensional vector representing a set of process parameters; initialize the position x of each particle in the particle swarm. i =(x i1 ,x i2 ,x i3 ,xi4 ) and velocity v i =(v i1 ,v i2 ,v i3 ,v i4 Initialization strategy: Initial position x i The upper and lower limits of various process parameters can be randomly set. For example, assuming the spraying temperature range is 50℃ to 150℃, the spraying humidity range is 40% to 80%, the coating thickness range is 10μm to 100μm, and the spraying rate range is 5mm / s to 20mm / s.

[0175] Initial velocity v i It can be randomly set within a reasonable range, usually a small interval, to avoid excessive jumps. For example, the speed can be initialized to a range of ±10% of the process parameters.

[0176] x i1 This represents the value of particle i in the spraying temperature dimension; for example, x i1 =120 indicates that the current spraying temperature of this particle is 120℃;

[0177] x i2 This represents the value of particle i in the spraying humidity dimension; for example, x. i2 =60 indicates that the current spraying humidity corresponding to this particle is 60%;

[0178] x i3 This represents the value of particle i in the coating thickness dimension; for example, x. i3 =50 indicates that the current coating thickness corresponding to this particle is 50μm;

[0179] x i4 This represents the value of particle i in the spraying rate dimension; for example, x. i4 =15 indicates that the current spraying rate of this particle is 15 mm / s;

[0180] x i1 This represents the velocity of particle i in the spraying temperature dimension, for example, x. i1 =2, which means that the position of particle i in the spraying temperature dimension will increase by 2℃ in each iteration cycle;

[0181] v i2 This represents the velocity of particle i in the spraying humidity dimension, for example, v. i2 =-3 means that the position of particle i in the spraying humidity dimension will decrease by 3% in each iteration cycle;

[0182] v i3 This represents the velocity of particle i in the coating thickness dimension, for example, v. i3=5 means that the position of particle i in the coating thickness dimension will increase by 5μm in each iteration cycle;

[0183] v i4 This represents the velocity of particle i in the spraying rate dimension, for example, v. i4 =-1 means that the position of particle i in the spraying rate dimension will decrease by 1 mm / s in each iteration cycle.

[0184] Initialize the individual's optimal position (p) i (g) and the global optimal position.

[0185] The individual optimal position p of each particle i It is the parameter position corresponding to the lowest fitness achieved by the particle in its history, and can be set as the initial position of the particle.

[0186] For example, p1 = x1 = (120, 60, 50, 15);

[0187] The global optimal position g is the parameter position corresponding to the lowest fitness value historically achieved by all particles. Initially, the fitness of all particles is predicted by a deep neural network, and the global optimal position is determined by the parameter position of the best particle.

[0188] Calculate the fitness of particles: Calculate the fitness of each particle based on the fitness calculation formula;

[0189] Example: Suppose we predict using a deep neural network:

[0190] The coating performance of particle 1 is 90% (i.e., the predicted performance value is 0.9), and the fitness f(x1) = -0.9;

[0191] The coating performance of particle 2 is 85% (i.e., the predicted performance value is 0.85), and the fitness f(x2) = -0.85;

[0192] For each particle i, we check if the current fitness is lower than the historical fitness (i.e., if the coating performance is better). If so, we update the individual's optimal position p. i ,For example:

[0193] If the fitness of particle 1, f(x1) = -0.9, is lower than the historical fitness, f(x2) = -0.85, then update p1 = x1.

[0194] The global optimal position g records the position of the particle with the lowest fitness; for example, assuming particle 1 has the best coating performance (lowest fitness) among all particles, then g = p1

[0195] Update particle position and velocity: Update particle position and velocity based on the particle velocity and position update formula;

[0196] Convergence criteria: Set a maximum number of iterations (e.g., 1000), or stop iteration when the improvement of the global optimal solution is less than a set threshold (e.g., 0.01);

[0197] At the end of the iteration, the parameter position of the particle with the best fitness in the output particle swarm, i.e., the global best position g, corresponds to the optimal combination of coating process parameters, as shown in the following example:

[0198] Optimal coating process parameter combination: g=(118,63,55,16); spraying temperature: 118℃; spraying humidity: 63%; coating thickness: 55μm; spraying rate: 16mm / s.

[0199] This invention proposes an intelligent coating optimization method for quartz crucible surface treatment. Addressing the problem that traditional coating process optimization based on personal experience often fails to meet optimal performance requirements, the method first collects coating material data, surface treatment environment data, coating process data, and performance test data, using the performance test data as the true result label for the training set. Next, the collected data undergoes denoising, missing value processing, and normalization to improve data quality and lay the foundation for subsequent model training. Then, using Pearson correlation coefficient and principal component analysis, a set of key features is selected, reducing data dimensionality while retaining the main information affecting coating performance. Utilizing these key features, a deep neural network model is trained, and the model predicts coating performance, achieving an intelligent transformation from data to performance prediction. Finally, based on the predicted coating performance, a particle swarm optimization algorithm is used to optimize the coating process parameters. This method effectively searches for the optimal parameter combination, avoiding the blindness and high cost of traditional optimization methods. In summary, by integrating data acquisition, preprocessing, feature selection, deep learning model training, and intelligent optimization algorithms, a closed-loop intelligent coating optimization process is formed, significantly improving the optimization efficiency and performance of the coating process and solving the technical problems of traditional methods.

[0200] The above are merely preferred embodiments of this application and are not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. An intelligent coating optimization method for the surface treatment of quartz crucibles, characterized in that, Includes the following steps: Step 1: Collect coating material data, surface treatment environment data, coating process data, and performance test data during the surface treatment process of the quartz crucible, and use the performance test data as the true result label of the training set data; Step 2: Denoise the collected data, identify and fill in missing values, and finally normalize the data. Step 3: Based on the preprocessed data, Pearson correlation coefficient and principal component analysis are used to screen features and obtain a set of key features; For data where a single feature exists at multiple measurement points in a sample, the Pearson correlation coefficient is used for feature selection as follows: Calculate the Pearson correlation coefficient between the feature and the target variable based on the weighting factor and the smoothing factor: In the formula: r xy (j) represents the smoothed Pearson correlation coefficient between the j-th feature variable and the target variable; This represents the average value of the j-th feature variable in the i-th sample; Let y represent the average of the j-th feature variable across all samples; i This represents the value of the target variable for the i-th sample; w represents the mean of the target variable across all samples. ij α represents the average weighting factor of the j-th feature variable of the i-th sample; ij The average smoothing factor represents the j-th feature variable of the i-th sample; The formula for calculating the smoothing factor is as follows: In the formula: α ik The residual represents the smoothing factor for the k-th measurement of the j-th feature of the i-th sample; ik The median(|residuals) represents the residual of the k-th measurement of the j-th feature of the i-th sample relative to the mean of the j-th feature variable of that sample; i |) represents the median of the absolute values ​​of the residuals of the characteristic variables measured in the i-th sample; e represents the base of the natural logarithm; M represents the number of measurements of the j-th characteristic variable in the i-th sample; The formula for calculating the weighting factor is as follows: In the formula: w ik The weight factor represents the k-th measurement value of the j-th feature of the i-th sample; x ik The variance(x) represents the feature data value of the k-th measurement of the j-th feature of the i-th sample. ik The variance (x) represents the feature data variance of the k-th measurement of the j-th feature in the i-th sample; j ) represents the average variance of the data for the j-th feature across all samples; Based on the absolute values ​​of the calculated Pearson correlation coefficients, the features corresponding to the top k Pearson correlation coefficients are sorted from high to low, and the features are selected as inputs for principal component analysis. When a feature data point in a sample has only one measurement, the Pearson correlation coefficient is calculated as follows: In the formula: r xy The Pearson correlation coefficient represents the relationship between feature x and target variable y; x i y represents the feature value of the i-th sample; i This represents the target variable value for the i-th sample; This represents the mean of all samples for feature x. N represents the mean of all samples of the target variable y; N represents the number of samples. Based on the absolute values ​​of the calculated Pearson correlation coefficients, the features corresponding to the top k Pearson correlation coefficients are sorted from high to low, and the features are selected as inputs for principal component analysis. Step 4: Train the deep neural network based on the obtained key features to obtain a trained deep neural network, and obtain the coating performance based on the trained deep neural network; Step 5: Based on the predicted coating performance, the particle swarm optimization algorithm is used to optimize the coating process parameters to obtain the optimal combination of coating process parameters.

2. The intelligent coating optimization method for quartz crucible surface treatment according to claim 1, characterized in that, The deep neural network includes an input layer, a feature cross layer, an intermediate layer, and an output layer; The input layer is used to receive feature vectors input to the deep neural network; The feature cross layer generates new features by using inner product cross and multiplicative cross, and then outputs them to the intermediate layer after nonlinear transformation by the ReLU activation function. The intermediate layer receives the features output by the feature cross layer and performs feature extraction based on multiple fully connected layers. Residual connections are added to each fully connected layer. The activation function uses the ReLU activation function to introduce nonlinearity, and a regularization term is introduced in the intermediate layer to prevent overfitting. Output layer: A fully connected layer containing one neuron outputs the final predicted coating performance.

3. The intelligent coating optimization method for quartz crucible surface treatment according to claim 2, characterized in that, The data processing steps of the feature cross layer are as follows: Let the input feature vector be X = [x1, x2, ..., xn]. n ], where x i Let represent the i-th feature, and n represent the total number of features; Inner product cross: for feature x i and x j Perform inner product crossover to generate new crossover features: In the formula: z ij Indicates feature x i and x j The features generated after performing inner product cross are then subjected to inner product cross for each pair of features. Element-wise product cross: Perform element-wise product operation on all features to obtain cross features. z=X⊙X=[x1·x2,x1·x3,…,x n-1 ·x n ]: In the formula: ⊙ represents element-wise multiplication; Generate the cross feature matrix: Concatenate the results of the inner product cross and the element-wise product cross to generate a new feature matrix Z: Z=[z 12 ,With 13 ,…,With ij ,With]; In the formula: Z represents the generated cross feature vector, which includes the inner product cross and element-wise product cross of all feature pairs; The generated feature matrix Z is nonlinearly transformed using the ReLU activation function and then output to the intermediate layer.

4. The intelligent coating optimization method for quartz crucible surface treatment according to claim 2, characterized in that, The loss function of the deep neural network is as follows: In the formula: L represents the value of the loss function; N represents the number of samples; y i This represents the true label value of the i-th sample; λ represents the predicted value of the i-th sample; λ represents the regularization coefficient; M represents the number of all weight parameters in the model; W j This represents the j-th weight parameter.

5. The intelligent coating optimization method for quartz crucible surface treatment according to claim 1, characterized in that, Step 5 includes the following steps: Initialize the particle swarm: Assume the coating process parameters have d dimensions. Define each particle in the particle swarm as a d-dimensional vector, representing a set of process parameters; initialize the position and velocity of each particle in the particle swarm: x i =(x i1 ,x i2 ,…,x id ),v i =(v i1 ,v i2 ,…,v id ); In the formula: i represents the particle index; d represents the dimension of the process parameter; x i Indicates the position of the i-th particle; v i x represents the velocity of the i-th particle; id v represents the position of the i-th particle in the d-th dimension; id This represents the velocity of the i-th particle in the d-th dimension; Calculate the fitness of particles: Predict the coating performance of each particle based on the trained deep neural network, and calculate the fitness of each particle based on the predicted coating performance. f(x i )=-Predicted Performance(x i ); In the formula: Predicted Performance(x) i ) represents the coating performance predicted by the deep neural network for each particle; Update individual optimal position and global optimal position: For each particle, record the optimal position p with the lowest historical fitness. i If the current fitness value is less than the historical best position p i If the fitness value is obtained, then the individual's optimal position is updated: p i =x i ,if f(x i )<f(p i ); Record the global best position g among all particles, that is, the position of the particle with the lowest fitness: Update the particle's velocity and position: In the formula: This represents the updated velocity of particle i in the d-th dimension; This represents the velocity of particle i in the d-th dimension before the update; This indicates the position of particle i in dimension d before the update; Let represent the updated position of particle i in d dimensions; ω represents the inertia weight; c1 and c2 represent acceleration constants, controlling the degree to which the particle moves towards its individual optimal position and global optimal position, respectively; r1 and r2 represent random numbers uniformly distributed between [0,1]; p id G represents the optimal individual position of particle i in d dimensions; d This represents the d-th dimension value of the globally optimal position; Convergence criteria: Set a maximum number of iterations. Stop iteration when the particle swarm reaches the maximum number of iterations or the improvement of the global optimal solution is less than the set threshold; output the optimal combination of coating process parameters.

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