Process parameter decision of tin smelting process based on data-driven multi-objective optimization

Abstract

The present application relates to tin smelting process parameter decision based on data-driven multi-objective optimization, belongs to intelligent optimization algorithm technical field, including the following steps: S1: data preprocessing: adopting local regression smoothing method reduces the noise in tin smelting process parameter data;S2: tin smelting process parameter optimization model construction;S3: multi-objective optimization solution;S4: front solution evaluation and decision-making: the obtained Pareto front solution is evaluated and decided by adopting the combination method based on AHP-TOPSIS.This application effectively overcomes the problem of incomplete, unbalanced, noisy data, so as to avoid misleading evolutionary search;The amount of historical data used for optimization is sufficient, which reduces the computing cost while ensuring the timeliness of the model, ensures the performance of the algorithm under the condition of meeting the limited function evaluation times;AHP-TOPSIS method shows significant superiority in decision analysis, is particularly effective when dealing with complex structure and criterion conflict decision-making problems, and is conducive to establishing the functional relationship between process parameters and product quality.

Description

Technical Field

[0001] This invention relates to the decision-making of process parameters in tin smelting based on data-driven multi-objective optimization, and belongs to the field of intelligent optimization algorithm technology. Background Technology

[0002] Tin smelting is the core step in the efficient extraction and purification of tin resources, and its technological level directly determines the purity of refined tin products and the comprehensive utilization rate of resources. Top-blown furnaces, due to their high processing efficiency and strong adaptability, have become the mainstream equipment in tin smelting. They achieve selective separation of impurity elements such as iron, arsenic, and antimony through precise control of thermodynamic conditions. However, top-blown furnaces involve numerous process parameters, as detailed in the instruction manual. Figure 11 The parameters shown (such as oxygen concentration at the furnace inlet, lance air pressure, coal-carrying air pressure, cooling water flow rate, etc.) will affect the entire reaction process, thereby affecting the primary yield of tin and energy consumption indicators. Existing tin smelting process parameter decisions mainly rely on operator experience or traditional mechanistic modeling methods, which have the following drawbacks: Tin smelting process parameter data is incomplete, unbalanced, and noisy, potentially misleading evolutionary searches; the amount of historical data available for optimization is insufficient, and acquiring new data is costly, requiring rapid and accurate tracking of dynamically changing optimal solutions through finite-order function evaluation; the tin smelting process mechanism is complex, and traditional mechanistic modeling methods struggle to establish the functional relationship between process parameters and product quality. Therefore, this invention provides a data-driven multi-objective optimization-based method for tin smelting process parameter decision-making. Summary of the Invention

[0003] In view of this, the present invention provides a data-driven multi-objective optimization-based decision-making method for tin smelting process parameters, effectively overcoming the problems of incomplete, unbalanced, and noisy data to avoid misleading the evolutionary search. Sufficient historical data is available for optimization, reducing computational overhead while ensuring the model's timeliness. The algorithm's performance is guaranteed while satisfying the limitation on the number of function evaluations. The AHP-TOPSIS method demonstrates significant superiority in decision analysis, particularly effective in handling complex decision problems with conflicting criteria, and is beneficial for establishing the functional relationship between process parameters and product quality.

[0004] This invention provides a data-driven multi-objective optimization-based decision-making method for tin smelting process parameters. The proposed technical solution includes the following steps: S1: Data preprocessing: Local regression smoothing method is used to reduce noise in tin smelting process parameter data; S2: Construction of tin smelting process parameter optimization model: Based on the preprocessed tin smelting process parameter data, a Kriging surrogate model is constructed separately for each objective function. The Kriging surrogate model is then used to reduce the number of actual evaluations in the optimization process and simulate the requirements of expensive optimization in actual production. S3: Multi-objective optimization solution: The multi-objective state transition algorithm based on Pareto dominance and penalty function method is used to solve the optimization model. Candidate solutions are generated through state transition operators, and new frontier solutions are obtained by combining non-dominated sorting and crowding calculation. The penalty function method is used to transform the constrained optimization problem into an unconstrained optimization problem. S4: Frontier Solution Evaluation and Decision-Making: The Pareto frontier solution obtained by optimization is evaluated and decided using the AHP-TOPSIS combined method. The 1-9 calibration method is used to quantify the decision-maker's preferences and calculate the weights of each objective function. The decision matrix is ​​constructed using the TOPSIS method. After vector normalization and weighting, the positive and negative ideal solutions are determined. The distances from each frontier solution to the positive and negative ideal solutions are calculated and sorted, and the optimal process parameter decision scheme is output.

[0005] Furthermore, in step S1, local regression smoothing is used to reduce noise in the tin smelting process parameter data. The specific steps are as follows: First, using sample points... Centered on the boundary, cut a segment of length 1 to 2. The data, weighted for this data segment Perform a weighted linear regression, obtain the center point of the weighted regression line for each sample point, and fit a higher-order polynomial, as shown in the equation: The weights The value can be: , obtained That is The smoothed value.

[0006] Furthermore, in step S2, the Kriging model is a simple interpolation model, and the specific steps are as follows: First, the tin smelting process parameter data are sampled, and its decision variables are read. and the corresponding target response value And calculate using a linear weighted method. The estimated value As shown in the formula: For weights By introducing statistical assumptions, the unknown objective function is considered as a concrete realization of a certain Gaussian static stochastic process, as shown in the equation: ,in For unknown constants, representing The expected value of the mathematical value, The mean is 0 and the variance is The Gaussian random process is represented by covariance, as shown in the following equation: .

[0007] Furthermore, among them The relevant function is shown in the equation: Related functions The correlation decreases as the distance increases; hyperparameters , , The training is performed by maximizing the log-likelihood function, as shown in the equation: Then the newly generated data points The objective function calculated by the surrogate model is shown in the following equation: .

[0008] Furthermore, the decision variables include the oxygen concentration in the furnace, the lance air pressure, the coal-carrying air pressure, and the cooling water flow rate; the objective function includes molten tin, sulfur content of the roasted sand in the furnace, and fixed carbon in the anthracite.

[0009] Furthermore, in step S3, for a general constrained optimization problem, as shown in the equation: ,in, It is the objective function These are inequality constraints and equality constraints, respectively; the penalty function method transforms them into the following unconstrained problem for solution, as shown in the equation: ,in Let be the penalty function. If it is a very large positive number, it is called the penalty factor. To constrain the degree of violation.

[0010] Furthermore, in step S4, the quantification standard of the 1-9 calibration method is: using Indicator Factors With factors The ratio of importance of factors With factors The ratio of importance is .

[0011] Furthermore, in step S4, an initial decision matrix is ​​constructed based on the relationship between the frontier solution and the corresponding objective, as shown in the equation: , The normalized matrix is ​​obtained by using vector normalization, thus eliminating the influence of dimensions, i.e.: The weight vectors calculated in the AHP step are multiplied onto each column to obtain the weighted normalized matrix.

[0012] Furthermore, the ideal solution is determined based on the best and worst values ​​in each column. With negative ideal solution This allows us to calculate the distance from each solution to the ideal solution. and distance to the negative ideal solution Calculate the score according to the formula: , The closer it is to the ideal solution, The larger.

[0013] The beneficial effects of this invention are: This invention offers more accurate dynamic modeling, with an objective function that better aligns with actual needs. It effectively overcomes issues such as incomplete, unbalanced, and noisy data, preventing misleading evolutionary searches and outperforming traditional mechanistic modeling. The algorithm structure fits production requirements, optimizing searches more efficiently. Sufficient historical data for optimization reduces computational overhead while ensuring model immediacy, guaranteeing algorithm performance even with limited function evaluation times. Fast optimization response meets the real-time control requirements of top-blown furnace production. The AHP-TOPSIS method demonstrates significant superiority in decision analysis, particularly effective in handling complex, conflicting decision problems, and facilitates the establishment of functional relationships between process parameters and product quality. Attached Figure Description

[0014] Figure 1 This is a data-driven modeling diagram based on the agent model of the present invention.

[0015] Figure 2 This is the objective function and optimization direction table of the present invention.

[0016] Figure 3 This is the decision variable table for this invention.

[0017] Figure 4 This is a flowchart of the data-driven state transition algorithm of the present invention.

[0018] Figure 5 This is the 1-9 calibration method quantification standard table of the present invention.

[0019] Figure 6 This is an overall conceptual diagram of the present invention.

[0020] Figure 7 This is the target variable data range table for this invention.

[0021] Figure 8 This is the optimal process parameter sequence table for the present invention.

[0022] Figure 9 This is a comparison diagram of the three multi-objective optimization methods of the present invention.

[0023] Figure 10 This is a table showing the optimal process parameters for this invention.

[0024] Figure 11 This diagram illustrates the process parameters and their impact on the production process of a top-blown furnace using existing technology. Detailed Implementation

[0025] The preferred embodiments of the present invention will now be described in detail.

[0026] This invention provides a data-driven multi-objective optimization-based decision-making method for tin smelting process parameters, which includes the following steps: S1: Data Preprocessing: To avoid the surrogate model trained with incomplete, unbalanced, and noisy data being too far removed from the actual working conditions and thus misleading the evolutionary algorithm search process, a local regression smoothing method is used to reduce the noise in the tin smelting process parameter data. In step S1, the specific steps for reducing noise in the tin smelting process parameter data by using local regression smoothing are as follows: First, using sample points... Centered on the boundary, cut a segment of length 1 to 2. The data, weighted for this data segment Perform a weighted linear regression, obtain the center point of the weighted regression line for each sample point, and fit a higher-order polynomial, as shown in the equation: The weights The value can be: , obtained That is The smoothed value.

[0027] S2: Construction of Optimization Model for Tin Smelting Process Parameters: (Refer to the appendix in the instruction manual) Figure 1 , 2 As shown in Figure 3, based on the preprocessed tin smelting process parameter data, a Kriging surrogate model is constructed separately for each objective function. The Kriging surrogate model is then used to reduce the number of actual evaluations in the optimization process, simulating the requirements of expensive optimization in actual production. The decision variables include the oxygen concentration in the furnace, the lance air pressure, the coal-carrying air pressure, and the cooling water flow rate. The objective functions include molten tin, the sulfur content of the calcined sand in the furnace, and the fixed carbon of the anthracite. Using an overly complex surrogate model as the objective function would increase the time consumption of the optimization process, which is not in line with the speed and immediacy of industrial production. The Kriging model mentioned is a simple interpolation model, and the specific steps are as follows: First, the tin smelting process parameter data are sampled, and its decision variables are read. and the corresponding target response value And calculate using a linear weighted method. The estimated value As shown in the formula: For weights By introducing statistical assumptions, the unknown objective function is considered as a concrete realization of a certain Gaussian static stochastic process, as shown in the equation: ,in For unknown constants, representing The expected value of the mathematical value, The mean is 0 and the variance is The Gaussian random process is represented by covariance, as shown in the following equation: ,in The relevant function is shown in the equation: Related functions The correlation decreases as the distance increases; hyperparameters , , The training is performed by maximizing the log-likelihood function, as shown in the equation: Then the newly generated data points The objective function calculated by the surrogate model is shown in the following equation: The Kriging model, as a classic surrogate-assisted multi-objective evolutionary algorithm, fully considers the distribution characteristics of solutions, ensuring the performance of the algorithm. On the other hand, it constructs a separate Kriging model for each objective function and selects multiple solutions for re-evaluation in each fill sampling. These strategies effectively reduce computational overhead and improve optimization efficiency.

[0028] S3: Multi-objective optimization solution: Refer to the appendix in the instruction manual. Figure 4 As shown, unlike traditional particle swarm optimization and genetic algorithms, the state transition algorithm treats each solution as a state. The introduced state transition operator demonstrates significant versatility and powerful capabilities in global, local, and heuristic search. The Pareto-dominated multi-objective state transition algorithm can quickly and effectively evaluate the merits of different process parameter schemes and obtain the Pareto front for subsequent decision-making, meeting the speed and immediacy requirements of industrial problems. Building upon excellent state transition algorithm operators, the Pareto-dominated multi-objective state transition algorithm introduces non-dominated sorting and crowding calculation to ensure the optimality and distribution of solutions, resulting in higher efficiency and better results in solving multi-objective problems. The optimization model is solved using a multi-objective state transition algorithm based on Pareto dominance and penalty function. Candidate solutions are generated through state transition operators, and new front solutions are obtained by combining non-dominated sorting and crowding calculation. The penalty function method is used to transform the constrained optimization problem into an unconstrained optimization problem. Constraint optimization using the penalty function method involves constructing a new objective function (i.e., a penalty function) by adding a "penalty term" to the original objective function. This penalty term "penalizes" solutions that violate the constraints; the more severe the violation, the greater the penalty. By finding the minimum value of this penalty function, the solution to the original constraint problem can be approximated. For general constraint optimization problems, as shown in the equation: ,in, It is the objective function These are inequality constraints and equality constraints, respectively; the penalty function method transforms them into the following unconstrained problem for solution, as shown in the equation: ,in Let be the penalty function. If it is a very large positive number, it is called the penalty factor. This method addresses constraint violation; it designs constraints as new objective functions, making the concept intuitive and the implementation simple.

[0029] S4: Frontier Solution Evaluation and Decision Making: The Analytic Hierarchy Process (AHP) is a widely used and classic decision-making method in management science, engineering, and business that considers decision-makers' preferences. It quantifies the subjective judgments of decision-makers through pairwise comparisons, thereby providing clear solutions for multi-objective and multi-criteria decision-making problems to meet the different preferences of enterprises for different objectives in actual production. The Pareto frontier solution obtained by optimization is evaluated and decided using the AHP-TOPSIS combined method. The 1-9 calibration method is used to quantify decision-makers' preferences and calculate the weights of each objective function. The decision matrix is ​​constructed using the TOPSIS method. After vector normalization and weighting, the positive and negative ideal solutions are determined. The distances from each frontier solution to the positive and negative ideal solutions are calculated and ranked, and the optimal process parameter decision scheme is output. Combined with the instructions Figure 5 As shown, the quantification standard of the 1-9 calibration method is: using Indicator Factors With factors The ratio of importance of factors With factors The ratio of importance is Calculate the eigenvectors of this matrix to obtain the weights of the three objectives in the decision-making process parameters for tin smelting. Traditional AHP methods calculate scores for different solutions using a linear weighting approach after determining the weights, then decide on the optimal solution based on the scores. However, this linear weighting method can lead to incorrect judgments if the objective function value of a high-weighted solution is too large. In actual production, decision-makers often prefer a balanced solution rather than one with an exceptionally good or bad objective. TOPSIS, on the other hand, argues that the optimal solution should not be merely a simple sum of scores, but rather the solution closest to the positive ideal solution and furthest from the negative ideal solution, which aligns better with human decision-making patterns. TOPSIS simulates the human mind's image of an "ideal perfect solution" and a "completely failed solution," selecting the realistic solution closest to the former and furthest from the latter. Furthermore, it uses vectorization to transform numerical measures into distance measures in a high-dimensional space, avoiding the drawbacks of linear weighting in one-dimensional space. Based on the relationship between the frontier solution and the corresponding objective, an initial decision matrix is ​​constructed, as shown in the equation: The normalized matrix is ​​obtained by using vector normalization to eliminate the influence of dimensions. Right now: The weight vectors calculated in the AHP step are multiplied by each column to obtain the weighted normalized matrix. The positive ideal solution is then determined based on the best and worst values ​​in each column. With negative ideal solution This allows us to calculate the distance from each solution to the ideal solution. Distance to the negative ideal solution Calculate the score according to the formula: , The closer it is to the ideal solution, The larger the score, the better; based on the ranking of scores, a decision-making scheme is derived.

[0030] Experimental verification: To verify the effectiveness of this invention, process parameter optimization experiments were conducted on 500 samples of actual tin smelting process parameters and historical product quality data. The data range is as shown in the appendix to the specification. Figure 7 As shown, the first-generation surrogate model is trained using historical data. The rotation, translation, scaling, and axial operations in the state transition algorithm are used to generate candidate solutions. The non-dominated sorting and crowding distance methods are used to filter out candidate solutions for real function evaluation. The surrogate model is updated once every 50 real function evaluations. Here, we assume a maximum allowed number of evaluations of the true function of 1000, and the optimal sequence is shown in the appendix to the manual. Figure 8 As shown; The solutions were compared with the frontier solutions obtained by the classic multi-objective optimization algorithms NSGA-II and SPEA2. Based on the weighting results of AHP, two objective functions were selected for comparison: molten metal tin and fixed carbon content of anthracite. The results are shown in the appendix of the manual. Figure 9 As shown (the coordinate axes have been processed for easier representation of the minimization problem); The decision matrix is ​​obtained by quantification using the AHP method, the weights are calculated, and the optimal solution is determined using the TOPSIS method, as shown in the appendix of the instruction manual. Figure 10 As shown, the decision variables and objective function values ​​all satisfy the constraints, and the optimal solution is obtained quickly and well within a limited number of evaluations of the real function, demonstrating the stability and superiority of the algorithm.

[0031] In summary, the present invention has the following advantages: Dynamic modeling is more accurate, and the objective function is more in line with actual needs: Compared with the fixed traditional mechanism model, the data-driven Kriging surrogate model, combined with local regression smoothing preprocessing, effectively overcomes the problems of incomplete, unbalanced, and noisy data, so as to avoid misleading the evolutionary search. The data-driven model dynamic update method can more accurately characterize the impact of process parameters, which is better than traditional mechanism modeling. The algorithm structure aligns with production needs, making optimization and search more efficient: The data-driven multi-objective state transition algorithm adopted in this invention features an excellent candidate solution generation mechanism, environment selection mechanism, and surrogate model filling mechanism. While the amount of historical data for tin smelting process parameters used for optimization is insufficient, the algorithm's performance is guaranteed under the condition of limited function evaluation times. Multiple operators balance local depth exploration and global mining capabilities; the environment selection mechanism under non-dominated sorting and penalty function methods ensures the optimality of the solution under the constraints; and the surrogate model filling mechanism reduces computational overhead while ensuring the model's immediacy. The optimized response speed meets the real-time control requirements of top-blown furnace production: Compared with generative networks, the data-driven multi-objective state transition algorithm proposed in this invention takes into account both the requirements of fast response and stable efficiency through the "from frugality to luxury" proxy model update strategy; under the same computing resources, it can quickly find the optimal solution and suboptimal solution sequence of process parameters, providing timely and effective production suggestions for actual production, and ensuring the real-time availability of the algorithm in the top-blown furnace production process; The AHP-TOPSIS method demonstrates significant advantages in decision analysis: the analytic hierarchy process quantifies the decision-maker's experience and judgment into a scientific weighting system, ensuring the consistency and rationality of the relative importance among criteria; TOPSIS compares the merits of different options based on absolute distance, avoiding excessive reliance on the ideal solution setting for option ranking and enhancing the robustness of the results; this combined framework takes into account both the decision-maker's subjective preferences and the inherent laws of objective data, ensuring the logical rigor of the decision-making process while improving the discrimination and accuracy of option evaluation, making this decision-making method particularly effective in dealing with complex decision problems with conflicting criteria, and facilitating the establishment of a functional relationship between process parameters and product quality.

[0032] The present invention and its embodiments have been described above. This description is not restrictive, and the accompanying drawings are only one embodiment of the present invention; the actual structure is not limited thereto. In conclusion, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the invention, such designs should fall within the protection scope of the present invention.

Claims

1. A data-driven multi-objective optimization-based decision-making method for tin smelting process parameters, characterized by: Includes the following steps: S1: Data preprocessing: Local regression smoothing method is used to reduce noise in tin smelting process parameter data; S2: Construction of tin smelting process parameter optimization model: Based on the preprocessed tin smelting process parameter data, a Kriging surrogate model is constructed separately for each objective function. The Kriging surrogate model is then used to reduce the number of actual evaluations in the optimization process and simulate the requirements of expensive optimization in actual production. S3: Multi-objective optimization solution: The multi-objective state transition algorithm based on Pareto dominance and penalty function method is used to solve the optimization model. Candidate solutions are generated through state transition operators, and new frontier solutions are obtained by combining non-dominated sorting and crowding calculation. The penalty function method is used to transform the constrained optimization problem into an unconstrained optimization problem. S4: Frontier Solution Evaluation and Decision-Making: The Pareto frontier solution obtained by optimization is evaluated and decided using the AHP-TOPSIS combined method. The 1-9 calibration method is used to quantify the decision-maker's preferences and calculate the weights of each objective function. The decision matrix is ​​constructed using the TOPSIS method. After vector normalization and weighting, the positive and negative ideal solutions are determined. The distances from each frontier solution to the positive and negative ideal solutions are calculated and sorted, and the optimal process parameter decision scheme is output.

2. The tin smelting process parameter decision based on data-driven multi-objective optimization according to claim 1, characterized in that: In step S1, the specific steps for reducing noise in the tin smelting process parameter data by using local regression smoothing are as follows: First, using sample points... Centered on the boundary, cut a segment of length 1 to 2. The data, weighted for this data segment Perform a weighted linear regression, obtain the center point of the weighted regression line for each sample point, and fit a higher-order polynomial, as shown in the equation: The weights The value can be: , obtained That is The smoothed value.

3. The tin smelting process parameter decision based on data-driven multi-objective optimization according to claim 1, characterized in that: In step S2, the Kriging model is a simple interpolation model, and the specific steps are as follows: First, the tin smelting process parameter data are sampled, and its decision variables are read. and the corresponding target response value And calculate using a linear weighted method. The estimated value As shown in the formula: For weights By introducing statistical assumptions, the unknown objective function is considered as a concrete realization of a certain Gaussian static stochastic process, as shown in the equation: ,in For unknown constants, representing The expected value of the mathematical value, The mean is 0 and the variance is The Gaussian random process is represented by covariance, as shown in the following equation: .

4. The tin smelting process parameter decision based on data-driven multi-objective optimization according to claim 3, characterized in that: in The relevant function is shown in the equation: Related functions The correlation decreases as the distance increases; hyperparameters , , The training is performed by maximizing the log-likelihood function, as shown in the equation: Then the newly generated data points The objective function calculated by the surrogate model is shown in the following equation: .

5. The tin smelting process parameter decision based on data-driven multi-objective optimization according to claim 3, characterized in that: The decision variables include the oxygen concentration at the furnace feed, the lance air pressure, the coal-carrying air pressure, and the cooling water flow rate; the objective function includes molten tin, the sulfur content of the roasted sand at the furnace feed, and the fixed carbon content of the anthracite.

6. The tin smelting process parameter decision based on data-driven multi-objective optimization according to claim 1, characterized in that: In step S3, for a general constrained optimization problem, as shown in the equation: ,in, It is the objective function These are inequality constraints and equality constraints, respectively; the penalty function method transforms them into the following unconstrained problem for solution, as shown in the equation: ,in Let be the penalty function. If it is a very large positive number, it is called the penalty factor. To constrain the degree of violation.

7. The tin smelting process parameter decision based on data-driven multi-objective optimization according to claim 1, characterized in that: In step S4, the quantification standard of the 1-9 calibration method is: using Indicator Factors With factors The ratio of importance of factors With factors The ratio of importance is .

8. The tin smelting process parameter decision based on data-driven multi-objective optimization according to claim 1, characterized in that: In step S4, based on the relationship between the frontier solution and the corresponding objective, an initial decision matrix is ​​constructed, as shown in the equation: ， The normalized matrix is ​​obtained by using vector normalization, thus eliminating the influence of dimensions, i.e.: The weight vectors calculated in the AHP step are multiplied onto each column to obtain the weighted normalized matrix.

9. The tin smelting process parameter decision based on data-driven multi-objective optimization according to claim 8, characterized in that: Determine the ideal solution based on the best and worst values ​​in each column. With negative ideal solution This allows us to calculate the distance from each solution to the ideal solution. Distance to the negative ideal solution Calculate the score according to the formula: , The closer it is to the ideal solution, The larger.

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