Ceramic slurry preparation process optimization method based on proxy model
By combining the KRIGING surrogate model and Sobol sensitivity analysis with the EGO algorithm, the problems of long experimental cycles and lack of theoretical models in the optimization of wet powder preparation process of ceramic slurry are solved. This achieves efficient and low-energy slurry performance prediction and process parameter optimization, and is applicable to a variety of production processes.
Patent Information
- Application Number
- CN202511556525.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-29
- Publication Date
- 2026-02-10
AI Technical Summary
Existing methods for optimizing wet-process ceramic slurry powder production suffer from problems such as long experimental cycles, high costs, and a lack of theoretical models, making it difficult to quickly and accurately predict slurry performance.
A data-driven approach combining the KRIGING surrogate model and Sobol sensitivity analysis with the EGO algorithm is adopted. By constructing a model using historical production data, the dominant factors affecting slurry performance are identified, the optimization search space is reduced, and global optimization is performed to achieve rapid and accurate prediction and optimization of process parameter selection.
It significantly improves process optimization efficiency, enables low-energy consumption and high-precision slurry performance prediction, shortens the optimization cycle, increases the success rate of industrialization conversion, and is adaptable to production equipment of different scales.
Smart Images
Figure CN121503209A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of ceramic production technology, and in particular to an optimization method for ceramic slurry preparation process based on a proxy model. Background Technology
[0002] In ceramic production processes, ball milling is a crucial step in raw material preparation, playing a key role in improving powder uniformity, particle size distribution, and stability. The ball milling stage, involving wet grinding of different materials, consumes the most energy. Therefore, improving grinding efficiency in this stage is of significant scientific and engineering value for energy conservation and emission reduction. Currently, the mainstream process optimization method in factories is experimental research, simulating the wet ball milling process using a small-scale ball mill and adjusting relevant parameters to control slurry properties. However, this method typically faces the following technical bottlenecks: 1. Long experimental cycle and high cost pressure: A large number of repeated experiments are required to screen parameters that have a significant impact on slurry performance. In addition, the high-hardness ball milling media required for ball milling are expensive and need to be replaced frequently after wear, which is time-consuming and material-intensive. 2. Lack of theoretical models: Traditional methods rely on empirical formulas or semi-empirical models, but the dominant factors that actually affect the performance of slurry are difficult to determine, making it difficult for traditional methods to quickly predict the performance of slurry.
[0003] Therefore, designing a ball milling process optimization method that is both efficient and capable of rapid and accurate prediction has become a key issue in the current optimization of wet powder production processes for ceramic slurries. Summary of the Invention
[0004] To address the above shortcomings, this invention provides a method for optimizing the ceramic slurry preparation process based on a surrogate model, which can solve the problems of existing experimental research methods requiring complex parameters and difficulty in determining the dominant factors affecting slurry performance.
[0005] To achieve the above objectives, the present invention adopts the following technical solution: A method for optimizing the ceramic slurry preparation process based on a surrogate model, characterized by comprising the following steps: Historical production data was collected to obtain data samples on ball milling technology, which were then divided into training and validation sets. Using the data samples from the training set, construct data samples with I input and O output. Based on this, build a surrogate model to form a mapping from input variables to output variables. Validate the model using data samples from the validation set. After the proxy model is constructed, sensitivity analysis is performed on the data samples to identify the degree of influence of each input variable on the output results, thereby revealing the dominant factors affecting the performance of the slurry. By setting variables with low influence as irrelevant variables and fixing these irrelevant variables, the optimization search space is reduced. Global optimization is then performed within the reduced optimization search space to achieve rapid prediction of the performance of the ball-milled slurry and to optimize the selection of ball milling process parameters.
[0006] Furthermore, the surrogate model is a KRIGING surrogate model, and the input parameters of the KRIGING surrogate model are M samples and N components q = ( ), m = 1, … , M, n = 1, … , N, and the corresponding output is represented as P (q), then the expression for the KRIGING proxy model is: ; In the formula, , is the general expression for the trend term. These are the coefficients of the regression model. yes The function, It is the variance of the Gaussian field. It is a stationary Gaussian random field with zero mean and unit variance.
[0007] Furthermore, the construction of the KRIGING proxy model includes: Choose a suitable autocorrelation function model to determine the random term. , recorded as ,in, θ This represents its hyperparameters; Optimize hyperparameters to output optimal results θ ; Leave-one-out cross-validation is performed on the KRIGING model. In each iteration, only one sample is left as the test set, and the remaining m-1 samples are used to train the KRIGING model. This process is repeated m times until each sample has served as test data at least once. The root mean square error of all test points is then calculated. ; In the formula It is the response value to the m-th dataset obtained by training the model using the remaining dataset after removing the m-th dataset.
[0008] Furthermore, the hyperparameter optimization to output the optimal... θ The specific method is as follows: Estimate using the maximum likelihood method: ; In the formula, , ,and: ; At this point, the trend term in the expression of the KRIGING proxy model is represented by an equation: ,in From the formula The parameters are given. θ Formula The solution is replaced.
[0009] Furthermore, the collected historical production data covers key process parameters and slurry performance indicators. The key process parameters corresponding to input I include ball mill current, water flow rate, slurry moisture content, slurry flow rate, slurry specific gravity, and additive flow rate. The slurry performance indicators corresponding to output O include flow rate, specific gravity, and sieve residue.
[0010] Furthermore, after obtaining data samples on the ball milling process, data within the standardized range of production data are selected to ensure the quality of the data samples; then, data cleaning is performed to remove outliers; finally, the influence of dimensions is eliminated through Min-Max normalization, and the data is divided into training and validation sets.
[0011] Furthermore, sensitivity analysis of the data sample includes: generating a Sobol matrix sequence, setting the corresponding response values calculated through the surrogate model, calculating the estimated total variance and partial variance of the response values, and calculating the Sobol index from the partial variance and total variance to represent the degree of influence of the input variables on the output results.
[0012] Furthermore, before performing sensitivity analysis, a set of quasi-random, low-biased samples was generated based on the Sobol sequence, which automatically follows the order [0,1]. n Uniform distribution over the interval.
[0013] Furthermore, the optimization based on the EGO algorithm includes the following steps: Based on the established proxy model, the optimal sample points to be updated are searched using a combination of global search and local exploration. Based on the sample point filling criterion, the true response value of the updated sample point is obtained and used as a new data sample update proxy model. Determine if the iteration stopping condition has been met: Calculate whether the maximum value of the EI function of the sample points in the existing sample space is less than the set threshold. If it is less than the threshold, it means that the sample space is well optimized and the sample points are stopped being updated. If it is greater than the threshold, continue to update the sample points according to the error filling criterion for sample points until the iteration stopping condition is met. Finally, the optimal result is output, thus realizing the optimization process.
[0014] Compared with the prior art, the beneficial effects of the present invention are: 1. Significantly Improved Process Optimization Efficiency. The method of this invention significantly improves process optimization efficiency through data-driven modeling technology. Compared to the numerous sample points required for full-factor experiments, the surrogate model divides predicted response values into global trend terms and local bias terms, and combines this with Gaussian function fitting for response values. Only 20 or more sample points are needed to construct the surrogate model. Furthermore, leave-one-out cross-validation is used for model verification, further ensuring the model's stability and accuracy. This enables rapid and accurate prediction with small samples, requiring only a few model reconstructions to evaluate generalization performance, avoiding the resource consumption of additional test sets in traditional methods. This efficient modeling method greatly shortens the entire optimization cycle, providing technical support for rapid process debugging.
[0015] 2. Reliable Theoretical Model Support. This method, by integrating surrogate models and sensitivity analysis, profoundly reveals the complex mapping relationship between process parameters and slurry properties from both qualitative and quantitative dimensions. The established surrogate model, as a high-precision nonlinear response surface model, can accurately capture and reproduce complex physicochemical processes that traditional empirical formulas cannot describe, achieving high-precision prediction of ball milling results and effectively compensating for the shortcomings of the theoretical model. The surrogate model, combined with sensitivity analysis, uses data-driven analysis of the SOBOL index to obtain the degree of response of each input to each output. This not only quantitatively reveals the complex relationship between inputs and outputs but also significantly improves the interpretability of the surrogate model, facilitating rapid prediction of ball milling slurry properties and optimization of ball milling process parameter selection.
[0016] 3. Low Energy Consumption for Effective Processing. Traditional ball milling processes have extremely low energy utilization. This method, through surrogate model construction and combined with the EGO optimization algorithm, can systematically perform global optimization in a multi-dimensional parameter space. This method not only considers slurry performance indicators but also takes energy consumption as an important optimization objective, accurately finding the parameter combination that minimizes energy consumption while achieving the best process effect. In this way, production can be directly guided to operate under optimal parameters from the operational strategy level, significantly increasing the proportion of energy used for effective ball milling and precisely allocating limited energy to the slurry preparation process.
[0017] 4. Significantly improved industrialization success rate. The surrogate model offers significant advantages in interpolation, effectively handling nonlinear problems. Leave-one-out cross-validation ensures the model's accuracy and robustness within the sample range, making the model's predictions closer to real-world conditions. Furthermore, this method can directly utilize real factory production data, effectively mitigating the differences between small-scale experiments and large-scale production, thus significantly improving the success rate and reliability of its industrialization transformation.
[0018] 5. Strong adaptability and scalability. The surrogate model based on KRIGING exhibits excellent adaptability to small sample data, and a reliable model can be established with a sample size of ≥20. This method is not only applicable to ball mill process optimization, but can also be extended to various production processes, such as press forming and tunnel kiln temperature optimization in firing processes. By adjusting the model parameters, it can adapt to production equipment of different scales. Attached Figure Description
[0019] 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.
[0020] Figure 1 This is a schematic flowchart of the ceramic slurry preparation process optimization method based on the proxy model of the present invention; Figure 2 The logic diagram for constructing the KRIGING proxy model in this invention is as follows; Figure 3 This is a flowchart of the EGO algorithm optimization process in this invention; Figure 4 This is a schematic diagram of the sensitivity analysis of input to output in this invention, where (a) corresponds to specific gravity, (b) corresponds to flow rate, and (c) corresponds to sieve residue. Detailed Implementation
[0021] 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.
[0022] 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.
[0023] 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.
[0024] Based on the technical bottlenecks mentioned in the background, this invention innovatively introduces a surrogate model based on KRIGING, the Sobol sensitivity analysis method, and the EGO algorithm for global optimization. It constructs a method that can obtain key process parameters affecting the performance of ball mill slurry and quickly and accurately predict parameters affecting the performance of ball mill slurry. This provides a better solution for optimizing the wet grinding process of ceramic slurry and also controls the quality of ceramic products from the source of raw materials.
[0025] The exemplary embodiment of this invention proposes a method for optimizing ceramic slurry preparation process based on a surrogate model, which mainly includes data collection and preprocessing, KRIGING surrogate model construction, Sobol sensitivity analysis, and EGO algorithm global optimization. These steps can be referred to... Figure 1 Specifically, the ceramic slurry preparation process optimization method based on the surrogate model of the present invention includes the following steps: Historical production data was collected to obtain data samples on ball milling technology, which were then divided into training and validation sets. Using the data samples from the training set, construct data samples with I input and O output. Based on this, build a surrogate model to form a mapping from input variables to output variables. Validate the model using data samples from the validation set. After the proxy model is constructed, sensitivity analysis is performed on the data samples to identify the degree of influence of each input variable on the output results, thereby revealing the dominant factors affecting the performance of the slurry. By setting variables with low influence as irrelevant variables and fixing these irrelevant variables, the optimization search space is reduced. Global optimization is then performed within the reduced optimization search space to achieve rapid prediction of the performance of the ball-milled slurry and to optimize the selection of ball milling process parameters.
[0026] The following is a more specific exemplary embodiment to illustrate the surrogate model-based method for optimizing ceramic slurry preparation process of the present invention.
[0027] First, historical data is collected from the ball mill production database. The data covers key process parameters (such as current, water flow rate, mud moisture content, mud flow rate, mud specific gravity, and additive flow rate of the five ball mills) and slurry performance indicators (flow rate, specific gravity, and sieve residue). Data within the standardized range of production data is selected to ensure the quality of the data sample. Then, data cleaning is performed to remove outliers caused by sensor anomalies or human recording errors.
[0028] Finally, Min-Max normalization was used to eliminate the influence of dimensions, laying the data foundation for subsequent modeling. The training and validation sets required for the model were divided according to a certain ratio to obtain the final data samples, thus laying the data foundation for subsequent modeling.
[0029] Using data samples from the training set, a surrogate model is built based on the KRIGING method. This model forms a mapping from input variables to output variables. The input parameters are M samples and N components q = ( ), m = 1, … , M, n =1, …, N, and the corresponding output is represented as P (q). Assume the surrogate model follows an implementation of a Gaussian stochastic process: ; (1) In the formula, , is the general expression for the trend term. These are the coefficients of the regression model. yes The function, It is the variance of the Gaussian field. It is a stationary Gaussian random field with zero mean and unit variance. In this method, we assume the trend term is an unknown constant, and the model is a standard Kriging model. More precisely, W =1 and ,therefore ,in k These are unknown parameters to be estimated.
[0030] For reference Figure 2 The specific steps for constructing the KRIGING proxy model include: First, choose a suitable autocorrelation function (ACF) model to determine the random terms. , recorded as ,in θ This represents its hyperparameters. This invention recommends using the Matérn function family, where... v =1.5, ,but ; (2) In the formula, and These are two sample points in the input space. l ={ l 1 , …, l n} represents the scale parameter to be estimated. θ The hyperparameters in the model are estimated using the maximum likelihood method. ; (3) In the formula, It is a correlation matrix. It is an information matrix, and ; (4) Formula (3) represents an unconstrained nonlinear optimization problem. This invention employs the BFGS quasi-Newton algorithm to solve for the minimum value of this objective function. After calculation using formula (4), the trend term in formula (1) is expressed by the equation: ,in The parameters are given by formula (4). θ Replaced by the solution of formula (3). For any new input parameters The proxy model based on KRIGING is as follows: ; (5) In the formula, and It is an M-dimensional vector used to calculate the correlation between new uncertain parameters and the input parameters used in Kriging modeling.
[0031] To ensure data validity, leave-one-out (LOO) cross-validation is performed on the KRIGING model using the validation set data samples. In each iteration, only one sample is kept as the test set, and the remaining m-1 samples are used to train the KRIGING model. This process is repeated m times until each sample has served as test data at least once. The root mean square error of all test points is then calculated. ; (6) In the formula, It is the response value to the m-th dataset obtained by training the model using the remaining dataset after removing the m-th dataset.
[0032] By using the above methods, the generalization ability of the model can be evaluated, making the most of the limited data and avoiding evaluation bias caused by the randomness of data partitioning.
[0033] After the surrogate model is constructed, sensitivity analysis is performed on the data samples to identify the degree of influence of each input variable on the output results, thereby revealing the dominant factors affecting the performance of the slurry.
[0034] After the KRIGING surrogate model was constructed, since such machine learning models are black-box models with poor interpretability, Sobol sensitivity analysis was introduced to explain the rationality of the KRIGING surrogate model and to obtain the degree of influence of each process parameter on the performance of each slurry. Sobol sensitivity analysis is a global sensitivity analysis method based on variance decomposition. It identifies key influencing factors by quantifying the contribution of input parameters to the uncertainty of output results.
[0035] Sobol sensitivity analysis can be used to identify the contribution of each input variable to the output result, thereby revealing the dominant factors affecting slurry performance. Before performing the sensitivity analysis, a set of quasi-random, low-biased samples is first generated based on the Sobol sequence, which automatically follows the range [0,1]. n A uniform distribution over the interval. The interval [0,1] is mapped to the target interval using a linear transformation. ; (7) This yields a uniformly distributed support set. parameters .
[0036] Based on the Sobol sequence method in Quasi-Monte Carlo (QMC) estimation, global sensitivity can be quantified using a variance-based Sobol sensitivity index. In this process, a Sobol sequence containing M×2N samples is generated, denoted as: ; (8) set up This represents the corresponding response value calculated through the surrogate model. P Mean estimation for: ; (9) Similarly, total variance It can be estimated as follows: ; (10) matrix The former N The column is denoted as matrix A, and the rest... N The column is denoted as matrix H, and both are... M × N Matrix. The first n Uncertain parameters The first-order Sobol exponent is: ; (11) This index is composed of total variance. and partial variance The estimate yielded: ;(12) In the formula, q ~n Indicates except q n The set of all variables other than A n Let be the matrix obtained by replacing the m-th column of the first sample set A with the m-th column of the second sample set H. It expresses expectation.
[0037] The Sobol index is a percentage representing the degree of influence of each input on each output. Obtaining the influence of each input on each output through Sobol sensitivity analysis significantly improves the interpretability of the Kriging surrogate model. By selecting key variables with significant impact on each output and fixing irrelevant variables with minimal impact at reasonable values (such as median values), the dimensionality of the global optimization problem is significantly reduced, which greatly improves optimization efficiency.
[0038] By setting variables with low influence as irrelevant variables and fixing these irrelevant variables, the optimization search space is reduced. Global optimization is then performed within the reduced optimization search space to achieve rapid prediction of the performance of the ball-milled slurry and to optimize the selection of ball milling process parameters.
[0039] In the Sobol sensitivity analysis, by fixing irrelevant variables, the optimization search space of the EGO algorithm was reduced, and global optimization based on the EGO algorithm was performed within the reduced optimization search space.
[0040] The EGO algorithm uses information provided by the established KRIGING surrogate model to sequentially update sample points to search for and optimize the original problem. By balancing global search (updating sample points in regions with few sample points) and local exploration (updating sample points near the current optimal solution), it selects the most promising points as the sample points for sequential updates. Compared to single-step modeling methods, the EGO algorithm can fully utilize the improvement potential of each updated sample point, typically requiring less computation in the objective and constraint functions to find the optimal solution. The sample points to be updated are selected according to the EI criterion, and the KRIGING surrogate model is updated; this process is repeated until the iteration terminates. Throughout the iteration process, the number of sample points and the constructed approximate model continuously change.
[0041] The general optimization process of the EGO algorithm is as follows: Figure 3 As shown. Includes the following steps: Based on the established proxy model, the optimal sample points to be updated are searched using a combination of global search and local exploration. Based on the sample point filling criterion, the true response value of the updated sample point is obtained and used as a new data sample update proxy model. Determine if the iteration stopping condition has been met: Calculate whether the maximum value of the EI function of the sample points in the existing sample space is less than the set threshold. If it is less than the threshold, it means that the sample space is well optimized and the sample points are stopped being updated. If it is greater than the threshold, continue to update the sample points according to the error filling criterion for sample points until the iteration stopping condition is met. Finally, the optimal result is output, thus realizing the optimization process.
[0042] The ceramic slurry preparation process optimization method based on the surrogate model of this invention can transform historical production data into the data foundation required for the model, construct the KRIGING surrogate model, and achieve rapid and accurate prediction of ball mill slurry performance and optimization of wet grinding process of ceramic slurry.
[0043] The following is a specific implementation example.
[0044] Taking a five-unit ball mill in a factory as an example, production data for three consecutive months was collected, including 10 process parameters (I inputs) for the five ball mills: current, slurry moisture content, slurry specific gravity, slurry flow rate, water flow rate, and additive flow rate, as well as corresponding slurry performance indicators (O outputs) such as flow rate, specific gravity, and sieve residue. Data within a standardized range was selected to ensure the quality of the data samples. Data cleaning was then performed to remove outliers caused by sensor anomalies or human error, resulting in 126 valid data samples. All parameters were then normalized using Min-Max to eliminate the influence of dimensions on the data sample quality. 120 data samples were randomly selected as the training set, and the remaining 6 were used as the validation set, forming the final data sample and laying the data foundation for subsequent model building.
[0045] The 10-input, 3-output data samples obtained in the previous stage are imported into MATLAB software as an EXCEL data table as the training set. The training set and validation set are divided according to the proportion of the data preprocessing stage. A suitable autocorrelation function (ACF) model is selected to describe spatial correlation. This invention recommends using the Matérn function family (…). v =1.5), construct the covariance matrix. Fit the hyperparameters using maximum likelihood estimation (MLE). θ The optimal solution is obtained by using the BFGS quasi-Newton algorithm. θThen, an optimized KRIGING surrogate model was constructed using the optimal hyperparameters. Leave-one-out cross-validation (LOO-CV) was performed on the optimized surrogate model to demonstrate its accuracy and the effectiveness of the data sample quantity and quality. During model building, special attention was paid to the interactions between input parameters, which were represented by the off-diagonal elements of the covariance matrix. This surrogate model can predict the performance of new process parameters within one second, greatly improving optimization efficiency.
[0046] Global sensitivity analysis of Sobol was performed based on the established KRIGING model. The results are as follows: Figure 4 As shown, the percentages represent the degree of influence of each parameter on the performance index. Among them, Q a For additive flow rate, Q m For mud flow rate, L m For mud specific gravity, w m For mud moisture content, Q w For water flow, I 1 For the first ball mill current, I 2 For the second ball mill current, I 3 For the current of the third ball mill, I 4 For the current of the fourth ball mill, I 5 This represents the current of the fifth ball mill; corresponding to the three outputs. L For specific gravity, T For flow rate, S For sieve residue, 120 sets of data samples were randomly selected as the training set, and the remaining 6 sets were used as the test set (validation set) to form the final data sample, laying the data foundation for subsequent model building. For specific gravity, mud flow rate and water flow rate had the greatest impact, accounting for 25.17% and 19.89% respectively; for flow velocity, mud flow rate and additive flow rate had the greatest impact, accounting for 23.3% and 17.7% respectively; for sieve residue, mud flow rate and the current of the fourth ball mill had the greatest impact, accounting for 22.46% and 20.07% respectively. This provides good interpretability for the optimized KRIGING surrogate model and can directly point out the major influencing factors for adjusting slurry performance indicators (flow velocity, specific gravity, sieve residue), thus enabling more efficient and targeted adjustments.
[0047] Based on the high-precision Kriging surrogate model constructed in the second stage and the Sobol sensitivity analysis results in the third stage, the Efficient Global Optimization (EGO) algorithm is used to intelligently optimize the production process of the five-unit ball mill. The algorithm aims to maximize the comprehensive evaluation score function of slurry performance and performs sequential optimization on the key process parameters identified by the Sobol analysis. During the iteration process, the algorithm fully utilizes the predicted values and uncertainty estimates provided by the Kriging model, intelligently balancing local fine-grained search and global exploration by maximizing the expected improvement (EI) function, and sequentially recommending the most promising new combination of process parameters. After efficient iteration, the maximum value of EI drops below the threshold, the algorithm converges, and outputs the optimal solution.
[0048] In summary, the surrogate model-based optimization method for ceramic slurry preparation, as presented in this invention, achieves efficient, intelligent, and stable operation throughout the entire process through the coordinated operation of its various components, including data acquisition and preprocessing, KRIGING model construction, Sobol sensitivity analysis, and global optimization using the EGO algorithm. Leveraging its unique data-driven approach and the fusion of multiple methods, it effectively overcomes the technical bottlenecks of traditional experimental research. It demonstrates significant advantages in process efficiency optimization, theoretical model support, low-energy consumption implementation, industrialization, and adaptive expansion, meeting the demands for intelligent, green, and high-quality optimization of wet ceramic slurry powder preparation processes. This method possesses broad application prospects and significant practical value.
[0049] This invention innovatively employs a ball milling process optimization method based on a fusion of multiple algorithms: KRIGING surrogate model, Sobol sensitivity analysis, and EGO global optimization. The method includes surrogate model establishment and a complete process optimization process. The EGO algorithm relies on a constructed high-precision KRIGING surrogate model for sequential optimization. This model, with its unique covariance structure, effectively captures the complex nonlinear and interactive relationships between process parameters and performance indicators. Its prediction accuracy error, verified by the leave-one-out method, is ≤10%, far exceeding traditional polynomial models. Furthermore, it innovatively uses Sobol global sensitivity analysis as a pre-process step for EGO optimization. Through quantitative evaluation, it accurately identifies and fixes key process parameters with minimal impact on ball milling process indicators, thereby reducing the complex multivariate optimization problem to a low-dimensional space. This significantly improves the search efficiency of the EGO algorithm, enabling rapid and accurate location of the global optimum. The innovative approach employs a surrogate model based on the KRIGING method. Its unique covariance matrix construction method enables accurate fitting of nonlinear relationships, and the model is validated using leave-one-out cross-validation (LOO-CV), achieving a prediction error of ≤10%, a 20% improvement in accuracy compared to polynomial models. Furthermore, the innovative Sobol sensitivity analysis method is used to determine the degree of influence of each parameter on each performance index. By identifying and fixing irrelevant variables through Sobol analysis, the complexity of the optimization problem is directly reduced, resulting in an exponential increase in optimization speed. This transforms optimization from a "black box" blind search process. Engineers can clearly understand which process parameters are most important and how they interact, leading to a deeper understanding and greater confidence in the optimization results.
[0050] 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 optimizing the ceramic slurry preparation process based on a surrogate model, characterized in that, It includes the following steps: Historical production data was collected to obtain data samples on ball milling technology, which were then divided into training and validation sets. Using the data samples from the training set, construct data samples with I input and O output. Based on this, build a surrogate model to form a mapping from input variables to output variables. Validate the model using data samples from the validation set. After the proxy model is constructed, sensitivity analysis is performed on the data samples to identify the degree of influence of each input variable on the output results, thereby revealing the dominant factors affecting the performance of the slurry. By setting variables with low influence as irrelevant variables and fixing these irrelevant variables, the optimization search space is reduced. Global optimization is then performed within the reduced optimization search space to achieve rapid prediction of the performance of the ball-milled slurry and to optimize the selection of ball milling process parameters.
2. The method for optimizing ceramic slurry preparation process based on a surrogate model according to claim 1, characterized in that, The surrogate model is the KRIGING surrogate model, and the input parameters of the KRIGING surrogate model are M samples and N components q = ( ), m = 1, … , M, n = 1, … , N, and the corresponding output is represented as P (q), then the expression for the KRIGING proxy model is: ； In the formula, , is the general expression for the trend term. These are the coefficients of the regression model. yes The function, It is the variance of the Gaussian field. It is a stationary Gaussian random field with zero mean and unit variance.
3. The method for optimizing ceramic slurry preparation process based on a surrogate model according to claim 2, characterized in that, The construction of the KRIGING proxy model includes: Choose a suitable autocorrelation function model to determine the random term. , recorded as ,in, θ This represents its hyperparameters; Optimize hyperparameters to output optimal results θ ; Leave-one-out cross-validation is performed on the KRIGING model. In each iteration, only one sample is left as the test set, and the remaining m-1 samples are used to train the KRIGING model. This process is repeated m times until each sample has served as test data at least once. The root mean square error of all test points is then calculated. ； In the formula It is the response value to the m-th dataset obtained by training the model using the remaining dataset after removing the m-th dataset.
4. The method for optimizing ceramic slurry preparation process based on a surrogate model according to claim 3, characterized in that, The hyperparameter optimization is performed to output the optimal value. θ The specific method is as follows: Estimate using the maximum likelihood method: ； In the formula, , ,and: ； At this point, the trend term in the expression of the KRIGING proxy model is represented by an equation: ,in From the formula The parameters are given. θ Formula The solution is replaced.
5. The method for optimizing ceramic slurry preparation process based on a surrogate model according to claim 1, characterized in that, The collected historical production data covers key process parameters and slurry performance indicators. The key process parameters corresponding to input I include ball mill current, water flow rate, slurry moisture content, slurry flow rate, slurry specific gravity, and additive flow rate. The slurry performance indicators corresponding to output O include flow rate, specific gravity, and sieve residue.
6. The method for optimizing ceramic slurry preparation process based on a surrogate model according to claim 5, characterized in that, After obtaining data samples on the ball milling process, data within the standardized range of production data were selected to ensure the quality of the data samples; then data cleaning was performed to remove outliers; finally, the influence of dimensions was eliminated by Min-Max normalization, and the data was divided into training and validation sets.
7. The method for optimizing ceramic slurry preparation process based on a surrogate model according to claim 1, characterized in that, Sensitivity analysis of the data sample includes: generating a Sobol matrix sequence, setting the corresponding response values calculated through the surrogate model, calculating the estimated total variance and partial variance of the response values, and calculating the Sobol index from the partial variance and total variance to represent the degree of influence of the input variables on the output results.
8. The method for optimizing ceramic slurry preparation process based on a surrogate model according to claim 7, characterized in that, Before sensitivity analysis, a set of quasi-random, low-biased samples was generated based on the Sobol sequence, which automatically follows the range [0,1]. n Uniform distribution over the interval.
9. The method for optimizing ceramic slurry preparation process based on a surrogate model according to claim 1, characterized in that, The optimization based on the EGO algorithm includes the following steps: Based on the established proxy model, the optimal sample points to be updated are searched using a combination of global search and local exploration. Based on the sample point filling criterion, the true response value of the updated sample point is obtained and used as a new data sample update proxy model. Determine if the iteration stopping condition has been met: Calculate whether the maximum value of the EI function of the sample points in the existing sample space is less than the set threshold. If it is less than the threshold, it means that the sample space is well optimized and the sample points are stopped being updated. If it is greater than the threshold, continue to update the sample points according to the error filling criterion for sample points until the iteration stopping condition is met. Finally, the optimal result is output, thus realizing the optimization process.