Ceramic sintering performance prediction method based on GA-BP neural network

Abstract

The invention discloses a ceramic firing performance prediction method based on a GA-BP neural network, and the method comprises the steps: data collection and preprocessing, gray correlation analysis and screening of key process parameters, construction of a GA-BP neural network model, model training and verification, prediction model testing, and firing performance index prediction. By means of unique intelligent algorithm fusion, the problems of high experience dependence, high experiment cost, long period, low efficiency, time consumption, energy consumption, high efficiency and the like of a method for judging the ceramic firing performance through artificial experience in actual ceramic firing production are effectively solved. The technical problem that multi-target collaborative optimization is difficult to realize at the same time in the prior art is solved, remarkable advantages are shown in the aspects of prediction precision, intelligent degree and the like, the requirements of intelligent, green and high-quality ceramic firing process optimization are met, and the method has wide application prospects and important practical value.

Description

Technical Field

[0001] This invention relates to the field of ceramic preparation technology, and in particular to a method for predicting ceramic firing performance based on GA-BP neural network. Background Technology

[0002] As a typical example of a high-energy-consuming and high-emission industry, the ceramics industry is facing unprecedented pressure to conserve energy and reduce emissions. Throughout the entire lifecycle of ceramic products, from raw materials to finished products, the firing process accounts for the largest share of energy consumption—exceeding 40% of the total energy consumption, and even reaching 60% for some product categories. This not only directly affects the production costs of enterprises but also becomes a key factor restricting the industry's green transformation. Therefore, systematically optimizing the firing process to achieve the dual goals of reducing energy consumption and improving production efficiency has become an essential question for the sustainable development of ceramic enterprises.

[0003] In the entire ceramic production process, the firing process is a crucial and energy-intensive step, making its optimization essential for energy conservation and emission reduction. The final properties of ceramics are determined by various process parameters. Traditional methods largely rely on manual experience to judge the firing performance of ceramics or to conduct performance tests on fired samples. These methods are not only inefficient and time-consuming, but also cannot guarantee the post-firing performance, exhibiting the following main technical bottlenecks: 1. Traditional firing methods rely on manual experience to subjectively adjust parameters such as firing temperature and firing time at each stage, lacking actual quantitative basis, which leads to large fluctuations in the performance of different batches of fired products; 2. Traditional methods rely on empirical formulas or semi-empirical models, but the actual firing effect is affected by a variety of factors, so traditional methods are difficult to accurately predict the firing performance. 3. Traditional methods require a large number of repeated experiments to screen process parameters that have a significant impact on firing performance. This experimental method has high cost per experiment and a cycle of 1-2 weeks, which is inefficient, time-consuming and energy-intensive.

[0004] Currently, obtaining the optimal range of ceramic firing performance using existing technologies requires repeated adjustments to process parameters and performance testing of fired ceramic samples, which consumes significant manpower, resources, and time. Therefore, there is an urgent need for a predictive method that can quickly and accurately predict firing performance to reduce the wasted manpower and resources in firing experiments. Summary of the Invention

[0005] To address the above shortcomings, this invention provides a method for predicting ceramic firing performance based on GA-BP neural network, which can solve the problems of strong reliance on experience, high experimental cost, long cycle, low efficiency, and high time and energy consumption in existing methods for judging ceramic firing performance by human experience.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for predicting the firing performance of ceramics based on GA-BP neural network includes the following steps: Historical data, including process parameters and performance indicators, is collected from the kiln production database. Grey relational analysis was used to reduce high-dimensional data to low-dimensional data, and the key process parameters corresponding to the performance indicators were selected by sorting according to the degree of correlation. A portion of the key process parameters was divided into training set and validation set, and the remaining portion was divided into test set. The training set of key process parameters is input into the BP neural network prediction model, initial weights and initial thresholds are set for training, and the BP neural network prediction model is iteratively updated through the GA algorithm to obtain the optimized GA-BP neural network prediction model. The training set of key process parameters is input into the optimized GA-BP neural network prediction model for further training and optimization, and the prediction model is validated using a validation set. The test set of key process parameters is input into the optimized GA-BP neural network prediction model for testing. The accuracy and quality of the sintering performance prediction of the optimized GA-BP neural network prediction model are evaluated based on the test results, thereby evaluating the generalization ability of the prediction model to unknown data. The firing process parameters to be performed are input into the GA-BP neural network prediction model to predict the firing performance, thereby achieving the prediction of firing performance indicators.

[0007] Furthermore, historical data is selected from production data that falls within the standardized range. The selected data is cleaned to remove obvious outliers caused by equipment failure or human error, and the KNN algorithm is used to fill in the missing data.

[0008] Furthermore, the KNN algorithm for filling missing data includes: calculating the Euclidean distance between each sample with missing values ​​and all complete samples, sorting them in ascending order of distance, and selecting the K nearest neighbor samples for filling. The Euclidean distance is calculated using the following formula: ; In the formula, x i For samples containing missing values, x j For a complete sample, m For feature dimensions.

[0009] Furthermore, the process parameters include heating rate, maximum temperature, cooling rate, body thickness, preheating zone temperature, firing zone temperature, quenching zone temperature, cooling zone temperature, preheating zone time, firing zone time, quenching zone time, and cooling zone time. Performance indicators include ceramic brick density, water absorption rate, coefficient of thermal expansion, and mechanical strength.

[0010] Furthermore, the screening of key process parameters specifically includes: Set performance metrics as a reference sequence x 0 Using process parameters as a comparison sequence x i For the standardized sequence, calculate the reference sequence. x 0 Comparison sequence x i At each moment k Correlation coefficient: ; In the formula ρ The resolution coefficient is set to 0.5. After obtaining the correlation coefficients, the mean of the correlation coefficients can be used to calculate the degree of correlation. .

[0011] Furthermore, the steps for optimizing the BP neural network prediction model using the GA algorithm include: Individual encoding and population initialization, fitness function setting, individual selection, crossover and mutation operations. After individual selection, crossover and mutation operations, a new generation of population is obtained. Then the fitness function setting, individual selection and crossover operations are repeated until a set of weights and biases that minimizes the error is finally obtained.

[0012] Furthermore, the training set of key process parameters is input into the BP neural network prediction model for training. Specifically, the weights and biases of the network are adjusted layer by layer from top to bottom based on the error between the network output and the true target using the error backpropagation algorithm, employing the gradient descent method. ; in, ŋ The learning rate controls the step size for each parameter update. E It is a loss function; It is the momentum factor; After each training cycle, the prediction model is validated using a validation set, and performance metrics, including the coefficient of determination, are calculated. ; in,n For the sample size, y i For the first i The true value of each sample y j For the first j The model prediction value for each sample. y This is the average of the true values ​​of all samples.

[0013] Furthermore, leave-one-out cross-validation is used on the GA-BP neural network model using the test set. In each iteration, only one sample is left as the test set, and the rest... m -1 sample was used entirely to train the GA-BP neural network model, repeating the process. m Calculate the root mean square error for all test points, repeating this process until each sample has served as test data once. ; In the formula, By removing the first m The model trained on the remaining dataset after the first dataset yields the model on the second dataset. m The response values ​​of each dataset.

[0014] Furthermore, when predicting firing performance, the new input parameters are first preprocessed, and the standardization or normalization rules used in the model training stage must be strictly followed to avoid the data distribution deviation from interfering with the prediction results. After the preprocessing is completed, the process parameters are input into the optimized BP neural network, and the prediction results are obtained only through the forward propagation process. This stage does not involve any parameter updates.

[0015] Furthermore, the predicted firing performance indicators are compared with the actual production values ​​to calculate the mean absolute error (MAE) and root mean square error (RMSE). The mean absolute error (MAE) is calculated as follows: ; n For the sample size, y i For the first i The true value of each sample y j For the first j The model prediction value for each sample; The root mean square error (RMSE) is calculated as follows: ; n For the sample size, y i For the first i The true value of each sample yj For the first j The model prediction value for each sample; The smaller the MAE, the higher the model prediction accuracy; the smaller the RMSE, the higher the model prediction stability and accuracy. The degree of agreement between the model prediction and the true value is evaluated through the above error calculation. If a significant deviation is found, the model is retrained by supplementing new sample data. The prediction accuracy is continuously improved through iterative optimization.

[0016] Compared with the prior art, the beneficial effects of the present invention are: This invention utilizes a genetic algorithm to optimize the weights and biases of a BP neural network, leveraging its global optimization characteristics to enable the neural network to quickly converge to the global optimum, avoiding getting trapped in local optima. This ensures the accuracy of the prediction of ceramic firing performance and improves the prediction precision and accuracy. This invention obtains training samples, validation samples, and test samples by ranking and partitioning the firing production dataset according to importance. It then trains and tests a BP neural network prediction model using a genetic algorithm to obtain weights and a weight-optimized BP neural network prediction model. This enables rapid prediction of firing performance, reduces reliance on manual trial and error, and reduces experimental costs and time. By using grey relational analysis, key process parameters are quickly screened from numerous process parameters, solving the multidimensional parameter optimization problem faced by traditional methods. Based on the screened key process parameters, a GA-BP high-precision prediction model is constructed to achieve accurate prediction of calcination process performance indicators. By deeply integrating genetic algorithms with BP neural networks, the prediction of firing performance has reached a high level of intelligence. Through the closed loop of the entire process from data acquisition, key process parameter screening, GA-BP prediction model construction to performance prediction, the need for manual intervention has been greatly reduced, and the production is highly intelligent. The GA-BP neural network model has excellent adaptability to small sample data. This method is not only applicable to the optimization of firing process, but can also be extended to other ceramic production processes, such as drying and raw material grinding, providing a flexible and effective solution for the optimization of various processes in ceramic production. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below.

[0018] Figure 1 This is a schematic flowchart of the ceramic firing performance prediction method based on GA-BP neural network of the present invention. Figure 2 This is a schematic diagram showing the correlation between various process parameters and corresponding performance indicators obtained by grey relational analysis in this invention. Figure 3 This is a schematic diagram of the neural network structure in this invention; Figure 4 This is a schematic diagram of the process of using a genetic algorithm (GA) to optimize a backpropagation neural network in this invention; Figure 5 This is a schematic diagram of the genetic algorithm process. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0020] In the description of this invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0021] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances. Furthermore, the technical features involved in the different embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0022] The purpose of this invention is to provide a method for predicting ceramic firing performance based on a GA-BP neural network, solving the problems of traditional methods that rely on manual trial and error, have long experimental cycles, and are time-consuming and energy-intensive, thus achieving intelligent, precise, and efficient prediction of the firing process. This invention focuses on in-depth research into ceramic firing performance prediction based on a GA-BP neural network model. By performing grey relational analysis on numerous process parameters during firing, the degree of correlation between each parameter and the target performance is determined. Finally, key process parameters are obtained from these parameters. A genetic algorithm (GA algorithm) is used to optimize the weights and biases of the BP neural network, establishing a high-precision prediction model to achieve rapid and accurate prediction of ceramic firing performance.

[0023] An exemplary embodiment of the present invention provides a method for predicting ceramic firing performance based on a GA-BP neural network. Please refer to [link / reference]. Figure 1 The prediction method mainly includes the following steps.

[0024] Historical data, including process parameters and performance indicators, are collected from the kiln production database.

[0025] First, historical data is collected from the kiln production database, including process parameters such as heating rate, maximum temperature, cooling rate, body thickness, preheating zone temperature, firing zone temperature, quenching zone temperature, cooling zone temperature, preheating zone time, firing zone time, quenching zone time, and cooling zone time, as well as ceramic performance indicators such as brick density, water absorption rate, coefficient of thermal expansion, and mechanical strength. Data within the standardized range is selected from the production data to reflect actual production conditions and ensure data reliability. Next, the selected data is cleaned: obvious outliers caused by equipment failure or human error are removed, and the KNN algorithm is used to fill in missing data. The core steps of the KNN algorithm are: calculating the Euclidean distance between each sample with missing values ​​and all complete samples, sorting them in ascending order of distance, and selecting the K nearest neighbors for filling. The Euclidean distance calculation formula is: ; (1) In the formula, x i For samples containing missing values, x j For a complete sample, m For feature dimensions.

[0026] Finally, Min-Max normalization is used to eliminate the influence of dimensions, thus ensuring the reliability of the data once again.

[0027] Grey relational analysis was used to reduce high-dimensional data to low-dimensional data, and the key process parameters corresponding to the performance indicators were selected by sorting according to the degree of correlation. A portion of the key process parameters was divided into training set and validation set, and the remainder was divided into test set.

[0028] The original input data recorded in the factory has a high dimensionality, but not all data is helpful in solving the problem. High dimensionality also leads to higher computational costs. Therefore, grey relational analysis is used to reduce the high-dimensional data to a lower dimensionality and to sort and filter key process parameters based on their correlation. At the same time, most of the information in the original dataset is retained to ensure the accuracy of subsequent training.

[0029] Grey relational analysis is a multi-factor correlation analysis method suitable for systems with limited information. It quantifies the degree of correlation between factors by comparing the geometric similarity of data sequences. The specific steps are: extracting the pre-processed data sample from the first part, and setting performance indicators such as brick density, water absorption rate, coefficient of thermal expansion, and mechanical strength as reference sequences. x 0 All process parameters recorded by the factory, including: heating rate, maximum temperature, cooling rate, billet thickness, preheating zone temperature, firing zone temperature, quenching zone temperature, cooling zone temperature, preheating zone time, firing zone time, quenching zone time, and cooling zone time, are used as a comparison sequence. x i For the standardized sequence, calculate the reference sequence. x 0 Comparison sequence x i At each moment k Correlation coefficient: ; (2) In the formula ρ The resolution coefficient is set to 0.5 to adjust the sensitivity of the correlation coefficient difference; the numerator is the minimum difference between the two levels, and the denominator is the difference at the current point plus the maximum difference globally.

[0030] After obtaining the correlation coefficients, the mean of the correlation coefficients can be used to calculate the degree of correlation. (3) Then, the average correlation coefficients at all time points are used to obtain the overall correlation degree. γ (0≤) γ ≤1), γ The closer the value is to 1, the greater the impact of this factor on the target performance index (e.g., γ >0.8 indicates a strong correlation; conversely, <0.8 indicates a strong correlation. γ The greater the deviation of the value from 1, the smaller the impact of that factor on the target performance index. Finally, based on the correlation degree, eight key process parameters were selected from 12 process parameters—heating rate, maximum temperature, cooling rate, billet thickness, preheating zone temperature, firing zone temperature, quench zone temperature, cooling zone temperature, preheating zone time, firing zone time, quench zone time, and cooling zone time—resulting in eight key process parameters: preheating zone temperature, firing zone temperature, quench zone temperature, cooling zone temperature, preheating zone time, firing zone time, quench zone time, and cooling zone time. These can be referenced. Figure 2 Finally, 85% of the data samples from the factory production data will be divided into training and validation sets, and 15% of the data samples will be divided into test sets.

[0031] The training set of key process parameters is input into the BP neural network prediction model, initial weights and initial thresholds are set for training, and the BP neural network prediction model is iteratively updated through the GA algorithm to obtain the optimized GA-BP neural network prediction model.

[0032] For reference Figure 3 First, a three-layer backpropagation (BP) neural network structure is constructed. Training samples from the training set are input into the BP neural network prediction model, and initial weights and biases are set for training and validation. The learning process of the BP neural network mainly includes forward propagation of the input signal and backward propagation of the error. During forward propagation, the input signal is input from the input layer, processed by the hidden layers, and then passed to the output layer. If the actual output error of the output layer is too large, the backward propagation process begins. Backpropagation involves adjusting the weights layer by layer from the output layer to the input layer to reduce the error. The forward propagation of the input signal and the backward propagation of the error are performed cyclically. The training process of the BP neural network is a continuous adjustment of the weights and biases, which continues until the output objective function reaches convergence.

[0033] Then, the BP neural network prediction model is iteratively updated using a genetic algorithm (GA algorithm) to obtain an optimized GA-BP neural network prediction model. The GA-BP neural network mainly consists of three parts: an input layer, a hidden layer, and an output layer. The eight key process parameters that have the greatest impact on firing performance are used as input layer nodes; the output layer contains four performance evaluation indicators for measuring firing performance: brick density, water absorption rate, coefficient of thermal expansion, and mechanical strength. The genetic algorithm (GA) optimizes the BP neural network as follows: Figure 4 As shown.

[0034] Using a genetic algorithm (GA) to continuously update and optimize the weights and biases of a backpropagation (BP) neural network can improve the model's prediction accuracy and response speed. Furthermore, leveraging the global optimization characteristic of the GA enables the neural network to quickly converge to the global optimum, avoiding the network from getting trapped in local optima, thereby further ensuring the accuracy of firing performance predictions.

[0035] For reference Figure 5 The steps for optimizing the BP neural network prediction model using the GA algorithm include: individual encoding and population initialization, fitness function setting, individual selection, crossover operation and mutation operation. After individual selection, crossover operation and mutation operation, a new generation of population is obtained. Then, the fitness function setting, individual selection and crossover operation are repeated until a set of weights and biases that minimizes the error is finally obtained.

[0036] In the individual encoding, each individual contains all the values ​​and biases of the entire BP neural network. This invention encodes individuals using real numbers. The encoding length is: ; (4) in, m This represents the number of hidden layer nodes. n This represents the number of nodes in the input layer. l This represents the number of nodes in the output layer.

[0037] Population initialization involves randomly generating a set of initial potential solutions, called the "population," with each solution referred to as an "individual." This initialization process is analogous to randomly scattering points in the solution space. A key parameter in population initialization is the population size. The population size significantly impacts the global search capability of the genetic algorithm (GA) and also affects the model's convergence speed. Therefore, the population size should be chosen appropriately based on the specific problem. For example, N individuals can be randomly generated to form the initial population, with each individual representing a potential solution to the problem, and then the population can be initialized.

[0038] Fitness is used to evaluate how well each individual adapts to the environment, i.e., the quality of the solution. For maximization problems, the fitness function is... f(x) The objective function is usually used directly. g(x) ,Right now: ; (5) For the minimization problem, the fitness function... f(x) The objective function is usually chosen. g(x) The reciprocal of, that is: ,(Require g(x) >0); (6) Fitness function of this invention f(x) Set as the reciprocal of the sum of squared errors (SE) of the neural network: that is Here, SE is the sum of squared errors between the predicted output and the expected output of the neural network. As can be seen from the fitness function, the smaller the prediction error of the neural network, the larger the corresponding fitness function, and the better the adaptability.

[0039] The core idea of ​​individual selection is "survival of the fittest," preserving good genes, or better solutions. Based on an individual's fitness, superior individuals are selected from the current population to serve as parents for reproduction. Individuals with higher fitness have a greater probability of being selected. Individual selection can be based on probability values, i.e.: ; (7) in, P iIt is the probability that an individual is selected. f i For individuals i fitness value, k The number of individuals in the population.

[0040] The purpose of crossover is to combine desirable traits and explore new solution regions. This is the most important operation in genetic algorithms, simulating sexual reproduction in organisms. A pair of parent individuals is randomly selected, and their genes are exchanged in some way to produce one or two new offspring. The optimal individual is not crossovered but directly copied into the next generation. For other individuals, crossover probability is used. Pc (Usually between 0.6 and 0.9) Perform a crossover operation on two individuals to generate two new individuals.

[0041] The core idea of ​​mutation is to maintain population diversity and expand the search space. With a very small probability (the mutation probability Pm is typically a very small value, such as 0.001~0.05; too high a Pm would turn the algorithm into a random search), the value of one or more genes in an individual is randomly changed. This introduces new genetic material into the population, increasing its diversity and preventing the algorithm from getting trapped in local optima prematurely. Similarly, the best individual is not mutated but directly copied to the next generation. For other individuals, mutation is performed using the mutation probability to generate new individuals.

[0042] Repeat the above operations: After selection, crossover, and mutation, we obtain a new generation of population. Then, we repeat the setting of the fitness function, the selection of individuals, and the crossover operation until we finally obtain a set of weights and biases that minimize the error, and then terminate the above operations.

[0043] The following is an exemplary implementation of using a genetic algorithm (GA) to optimize weights and biases: First, define the objective function and its independent variable parameters. The independent variable parameters of the objective function include weights and biases. The objective function is used to calculate the fitness values ​​corresponding to the weights and biases. In this invention, the fitness value is the validation set error. Then, use the trained weights and thresholds as a set of independent variable parameters. Based on this set of independent variable parameters, multiple sets of independent variable parameters can be randomly obtained. Calculate the fitness value of each set of independent variable parameters, and use the first minimum fitness value corresponding to these multiple sets of independent variable parameters as the minimum fitness value of the objective function. Record the independent variable parameter corresponding to the first minimum fitness value. Next, perform global optimization on the multiple sets of independent variable parameters and calculate the fitness values ​​of the multiple sets of independent variable parameters after global optimization to obtain the second minimum fitness value corresponding to the multiple sets of independent variable parameters after global optimization. Compare the minimum fitness value of the objective function with the second minimum fitness value, update the minimum fitness value of the objective function, and record the value corresponding to the updated minimum fitness value of the objective function. The process involves: determining the independent variable parameters; performing local optimization on multiple sets of independent variable parameters after global optimization, calculating the fitness values ​​of these parameters, and determining the third minimum fitness value corresponding to each set; comparing the minimum fitness value of the objective function with the third minimum fitness value, updating the minimum fitness value of the objective function, and obtaining the independent variable parameters corresponding to the updated minimum fitness value; comparing the updated minimum fitness value of the objective function with the preset fitness value to determine if the termination condition has been met; if the termination condition has been met, ending the optimization of the independent variable parameters, and using the independent variable parameters corresponding to the minimum fitness value of the objective function as weights and thresholds in the BP neural network; if the termination condition has not been met, generating multiple sets of independent variable parameters based on the updated minimum fitness value of the objective function; repeating the steps of local optimization on multiple sets of independent variable parameters and updating the minimum fitness value of the objective function until the termination condition is met; finally, iterating with the optimized weights and biases to obtain the updated GA-BP neural network model.

[0044] The training set of key process parameters is input into the optimized GA-BP neural network prediction model for further training and optimization, and the prediction model is validated using a validation set.

[0045] After the optimal weights and biases are obtained through genetic algorithm (GA) optimization, these parameters are fed into a backpropagation (BP) neural network for supervised training. This stage uses 85% of the actual firing production data samples (i.e., data samples containing both training and validation sets, including 8 key process parameters and 4 final performance indicators). The training set is used for the core learning process of the model. Through the error backpropagation algorithm, the network weights and biases are adjusted layer by layer from top to bottom based on the error between the network output and the true target, using gradient descent. ; (8) in, ŋ The learning rate controls the step size for each parameter update. E It is a loss function; It is the momentum factor.

[0046] By introducing weight and bias updates, convergence is effectively accelerated and the model is helped to escape local minima. Meanwhile, the validation set plays a crucial role in this process; the validation set error is a key indicator for judging whether the model is overfitting and for assessing convergence. After each training epoch, the prediction model is validated using the validation set, and performance metrics such as the coefficient of determination are calculated. ; (9) in, n For the sample size, y i For the first i The true value of each sample y j For the first j The model prediction value for each sample. y This is the average of the true values ​​of all samples. R 2 The closer the value is to 1, the better the model fits.

[0047] By monitoring the changing trend of the validation set error in real time, the convergence state of the model can be accurately determined, and signs of overfitting can be identified in a timely manner. That is, when the training set error continues to decrease while the validation set error begins to increase, it means that the model may be overfitting, thus providing a key basis for deciding whether to terminate training early.

[0048] The test set of key process parameters is input into the optimized GA-BP neural network prediction model for testing. The accuracy and quality of the sintering performance prediction of the optimized GA-BP neural network prediction model are evaluated based on the test results, thereby evaluating the generalization ability of the prediction model to unknown data.

[0049] Test samples (i.e., the test set, containing 8 key process parameters and 4 final performance indicators) are input into the optimized GA-BP neural network prediction model for testing. The accuracy and quality of the sintering performance prediction are evaluated based on the test results, thereby assessing the model's generalization ability to unknown data. To evaluate the model's generalization ability, avoid evaluation bias caused by the randomness of data partitioning, and maximize the use of limited data, the remaining 15% of the data samples (which also contain 8 key process parameters and 4 final performance indicators) are used for leave-one-out (LOO) cross-validation of the GA-BP neural network model. That is, only one sample is retained as the test set in each iteration, and the rest... m -1 sample was used entirely to train the GA-BP neural network model, repeating the process. m Calculate the root mean square error for all test points, repeating this process until each sample has served as test data once. ; (10) In the formula, By removing the first m The model trained on the remaining dataset after the first dataset yields the model on the second dataset. m The response values ​​of each dataset.

[0050] Based on the established high-precision GA-BP neural network prediction model and the analysis results of key process parameters, the Particle Swarm Optimization (PSO) algorithm can also be used for intelligent optimization of the ceramic firing process. The algorithm aims to maximize four performance indicators of ceramic firing (brick density, water absorption, coefficient of thermal expansion, and mechanical strength), and iteratively optimizes eight key process parameters selected through grey relational analysis. During the optimization process, the algorithm fully utilizes the precise fitting capability of the BP neural network to the mapping relationship between parameters and performance. It achieves efficient searching of the parameter space through the collective cooperation mechanism of the particle swarm—each particle represents a set of process parameter combinations, dynamically adjusting its search direction by tracking its own historical optimal solution and the global optimal solution of the group. Simultaneously, an adaptive strategy of inertial weights is introduced to balance local refined search and global space exploration, gradually approaching the optimal parameter range. As iteration progresses, the improvement rate of the global optimal performance indicators of the particle swarm gradually narrows. When the improvement amount for multiple consecutive generations is lower than a preset threshold, the algorithm converges and outputs the final optimized combination of process parameters.

[0051] The firing process parameters to be performed are input into the GA-BP neural network prediction model to predict the firing performance, thereby achieving the prediction of firing performance indicators.

[0052] Once the model has passed validation and testing, it can be used for actual prediction. In actual prediction, the new input parameters must first be preprocessed, strictly adhering to the standardization or normalization rules used during model training. This means using the mean, standard deviation, and other statistical measures of the training set to avoid data distribution shifts interfering with the prediction results. After preprocessing, the process parameters are input into the optimized BP neural network, and the prediction results are calculated solely through the forward propagation process; no parameter updates are involved in this stage. If the input parameters were standardized or normalized during model training, the obtained prediction results must be denormalized to restore them to values ​​with actual physical meaning (e.g., converting the predicted value in the [0,1] interval into the actual unit of ceramic strength, MPa). The firing process parameters to be predicted (only 8 key process parameters are input) are then input into the GA-BP neural network prediction model for firing performance prediction. This allows for rapid and accurate prediction of properties such as brick density, water absorption, coefficient of thermal expansion, and mechanical strength (the model directly outputs the results), thus achieving ceramic firing performance prediction.

[0053] In practice, the predicted firing performance indicators can be compared with the actual production values ​​to verify the accuracy of the prediction model. This is achieved by calculating quantitative evaluation indicators such as Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). The formula for Mean Absolute Error (MAE) is: ; (11) n For the sample size, y i For the first i The true value of each sample y j For the first j The model prediction value for each sample; The root mean square error (RMSE) is calculated as follows: ;(12) n For the sample size, y i For the first i The true value of each sample y j For the first j The model prediction value for each sample.

[0054] A smaller MAE indicates higher model prediction accuracy, while a smaller RMSE indicates higher model stability and accuracy. The degree of agreement between the model's predicted values ​​and the actual values ​​is evaluated through error calculation. If a significant deviation is found, the model is retrained with new sample data, and prediction accuracy is continuously improved through iterative optimization. This continuous improvement in prediction accuracy provides data support for subsequent model optimization. By inputting process parameters into the model, output results can be obtained directly, significantly reducing experimental costs and ultimately achieving precise control of the ceramic tile firing process and stable improvement in production quality.

[0055] The ceramic firing performance prediction method of this invention, through steps such as data acquisition and preprocessing, gray relational analysis to screen key process parameters, GA-BP neural network model construction, model training and verification, prediction model testing, and prediction of firing performance indicators, achieves efficient, rapid, reliable, and stable prediction of firing performance indicators. With its unique intelligent algorithm fusion, it effectively solves the technical problems of strong experience dependence, high experimental costs, long cycles, low efficiency, and time and energy consumption in actual ceramic firing production, which make it difficult to simultaneously achieve multi-objective collaborative optimization. It exhibits significant advantages in prediction accuracy and intelligence, meeting the needs of intelligent, green, and high-quality ceramic firing process optimization, and has broad application prospects and important practical value.

[0056] This invention presents a ceramic firing performance prediction method based on a GA-BP neural network. Addressing the problems of traditional firing trial-and-error methods, such as large experimental volume, long cycle, high cost, low efficiency, and strong dependence on verification, this invention innovatively proposes a data-driven method for selecting key process parameters. This method utilizes a grey relational analysis algorithm to calculate the correlation between each process parameter and product performance indicators. γThis invention establishes a quantitative evaluation system for the importance of process parameters. Compared to traditional full-factor experimental design, this method can reduce the experimental sample size by more than 70% while ensuring that no key process parameters are missed. This intelligent screening method not only significantly reduces experimental costs and time but also lays a reliable data foundation for subsequent optimization. To address the problems of slow convergence speed and susceptibility to local optima in complex process optimization using traditional single BP neural networks, this invention introduces a high-precision prediction model based on a genetic algorithm (GA) optimized GA-BP neural network. This model optimizes the weights and thresholds of the BP neural network using a genetic algorithm (GA), leveraging its global optimization characteristics to enable the BP neural network to quickly converge to the global optimum, thereby further ensuring the accuracy of firing performance prediction. Through rigorous testing and verification, the model's prediction error is extremely small, improving accuracy by more than 20% compared to traditional single BP neural networks. This model can complete the performance prediction of new process parameters within 5 seconds, providing powerful tool support for rapid process debugging. Meanwhile, the firing performance prediction method of the present invention, which integrates GA and BP algorithms, is a technical solution for multi-algorithm fusion optimization. By organically combining grey relational analysis, genetic algorithm and BP neural network, a complete ceramic firing process optimization system is constructed. This innovative architecture of multi-algorithm fusion not only gives full play to the advantages of each method, but also significantly improves the overall optimization effect through the synergistic effect between algorithms, so that the process parameter configuration reaches the global optimum.

[0057] In summary, this invention utilizes a genetic algorithm to optimize the weights and biases of a BP neural network, leveraging its global optimization characteristic to enable the network to quickly converge to the global optimum, avoiding getting trapped in local optima. This ensures the accuracy of ceramic firing performance prediction and improves prediction precision and accuracy. By prioritizing and partitioning the firing production dataset, training, validation, and test samples are obtained. The BP neural network prediction model is then trained and tested using a genetic algorithm to obtain the optimized weights and weights, enabling rapid prediction of firing performance. This reduces reliance on manual trial and error, lowering experimental costs and time. Furthermore, grey relational analysis is used to quickly select key process parameters from numerous process parameters, solving the problem of... Traditional methods face the challenge of multidimensional parameter optimization. A high-precision GA-BP prediction model is constructed based on selected key process parameters to accurately predict firing process performance indicators. By deeply integrating genetic algorithms with BP neural networks, firing performance prediction achieves a high level of intelligence. The closed-loop process from data acquisition, key process parameter selection, GA-BP prediction model construction to performance prediction significantly reduces the need for manual intervention, resulting in a high degree of production intelligence. The GA-BP neural network model exhibits excellent adaptability to small sample data. This method is not only applicable to firing process optimization but can also be extended to other ceramic production processes, such as drying and raw material grinding, providing a flexible and effective solution for optimizing various processes in ceramic production.

[0058] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for predicting the firing performance of ceramics based on a GA-BP neural network, characterized in that, Includes the following steps: Historical data, including process parameters and performance indicators, is collected from the kiln production database. Grey relational analysis was used to reduce high-dimensional data to low-dimensional data, and the key process parameters corresponding to the performance indicators were selected by sorting according to the degree of correlation. A portion of the key process parameters was divided into training set and validation set, and the remaining portion was divided into test set. The training set of key process parameters is input into the BP neural network prediction model, initial weights and initial thresholds are set for training, and the BP neural network prediction model is iteratively updated through the GA algorithm to obtain the optimized GA-BP neural network prediction model. The training set of key process parameters is input into the optimized GA-BP neural network prediction model for further training and optimization, and the prediction model is validated using a validation set. The test set of key process parameters is input into the optimized GA-BP neural network prediction model for testing. The accuracy and quality of the sintering performance prediction of the optimized GA-BP neural network prediction model are evaluated based on the test results, thereby evaluating the generalization ability of the prediction model to unknown data. The firing process parameters to be performed are input into the GA-BP neural network prediction model to predict the firing performance, thereby achieving the prediction of firing performance indicators.

2. The method for predicting ceramic firing performance based on GA-BP neural network according to claim 1, characterized in that, Historical data is selected from production data that falls within the standardized range. The selected data is cleaned to remove obvious outliers caused by equipment failure or human error, and the KNN algorithm is used to fill in the missing data.

3. The method for predicting ceramic firing performance based on GA-BP neural network according to claim 2, characterized in that, The KNN algorithm is used to fill in missing data. This involves calculating the Euclidean distance between each sample with missing values ​​and all complete samples, sorting them in ascending order of distance, and selecting the K nearest neighbors for filling. The Euclidean distance is calculated using the following formula: ； In the formula, x i For samples containing missing values, x j For a complete sample, m For feature dimensions.

4. The method for predicting ceramic firing performance based on GA-BP neural network according to claim 1, characterized in that, Process parameters include heating rate, maximum temperature, cooling rate, body thickness, preheating zone temperature, firing zone temperature, quenching zone temperature, cooling zone temperature, preheating zone time, firing zone time, quenching zone time, and cooling zone time. Performance indicators include ceramic brick density, water absorption rate, coefficient of thermal expansion, and mechanical strength.

5. The method for predicting ceramic firing performance based on GA-BP neural network according to claim 1, characterized in that, The specific steps for screening key process parameters include: Set performance metrics as a reference sequence x 0 Using process parameters as a comparison sequence x i For the standardized sequence, calculate the reference sequence. x 0 Comparison sequence x i At each moment k Correlation coefficient: ； In the formula ρ The resolution coefficient is set to 0.

5. After obtaining the correlation coefficients, the mean of the correlation coefficients can be used to calculate the degree of correlation. 。 6. The method for predicting ceramic firing performance based on GA-BP neural network according to claim 1, characterized in that, The steps for optimizing a BP neural network prediction model using the GA algorithm include: Individual encoding and population initialization, fitness function setting, individual selection, crossover and mutation operations. After individual selection, crossover and mutation operations, a new generation of population is obtained. Then the fitness function setting, individual selection and crossover operations are repeated until a set of weights and biases that minimizes the error is finally obtained.

7. The method for predicting ceramic firing performance based on GA-BP neural network according to claim 1, characterized in that, The training set of key process parameters is input into the BP neural network prediction model for training. Specifically, the weights and biases of the network are adjusted layer by layer from top to bottom based on the error between the network output and the true target using the error backpropagation algorithm, employing the gradient descent method. ； in, ŋ The learning rate controls the step size for each parameter update. E It is a loss function; It is the momentum factor; After each training cycle, the prediction model is validated using a validation set, and performance metrics, including the coefficient of determination, are calculated. ； in, n For the sample size, y i For the first i The true value of each sample y j For the first j The model prediction value for each sample. y This is the average of the true values ​​of all samples.

8. The method for predicting ceramic firing performance based on GA-BP neural network according to claim 1, characterized in that, Leave-one-out cross-validation is used to test the GA-BP neural network model, where only one sample is left as the test set in each iteration, and the rest... m -1 sample was used entirely to train the GA-BP neural network model, repeating the process. m Calculate the root mean square error for all test points, repeating this process until each sample has served as test data once. ； In the formula, By removing the first m The model trained on the remaining dataset after the first dataset yields the model on the second dataset. m The response values ​​of each dataset.

9. The method for predicting ceramic firing performance based on GA-BP neural network according to claim 1, characterized in that, When predicting firing performance, the new input parameters must first be preprocessed, and the standardization or normalization rules used in the model training stage must be strictly followed to avoid the data distribution shift from interfering with the prediction results. After preprocessing, the process parameters are input into the optimized and trained BP neural network, and the prediction results are obtained only through the forward propagation process. This stage does not involve any parameter updates.

10. The method for predicting ceramic firing performance based on GA-BP neural network according to claim 1, characterized in that, The predicted firing performance indicators are compared with the actual production values ​​to calculate the mean absolute error (MAE) and root mean square error (RMSE). The mean absolute error (MAE) is calculated as follows: ； n For the sample size, y i For the first i The true value of each sample y j For the first j The model prediction value for each sample; The root mean square error (RMSE) is calculated as follows: ； n For the sample size, y i For the first i The true value of each sample y j For the first j The model prediction value for each sample; The smaller the MAE, the higher the model prediction accuracy; the smaller the RMSE, the higher the model prediction stability and accuracy. The degree of agreement between the model prediction and the true value is evaluated through the above error calculation. If a significant deviation is found, the model is retrained by supplementing new sample data. The prediction accuracy is continuously improved through iterative optimization.

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