A method for predicting gallium and germanium leaching rate in zinc powder replacement slag under a composite external field and optimizing process parameters, a computer readable storage medium and a system

Abstract

The present application belongs to the technical field of hydrometallurgy, and specifically relates to a method for predicting gallium and germanium leaching rates in zinc powder replacement slag under a composite external field and optimizing process parameters, a computer readable storage medium and a system, comprising: constructing a data set; constructing a shrinkage core model of the external field correction of gallium and germanium, and solving the mechanism leaching characteristics of gallium and germanium; combining the process parameters with the mechanism leaching characteristics of gallium and germanium, and screening an optimal leaching rate prediction model; constructing an industrial feasible parameter space and a device gear mapping relationship according to the parameter boundaries of the leaching equipment; taking the optimal leaching rate prediction model as an evaluation model, performing multi-objective search on candidate process parameters, and obtaining a non-dominated solution set; standardizing and clustering the non-dominated solution set, and selecting representative process parameters. Compared with the prior art, the present application solves the problems of low leaching rate prediction accuracy and high cost and low efficiency caused by the dependence of multi-objective process parameter optimization on experience and trial and error. The present scheme can reduce the prediction deviation under the condition of a small sample.

Description

Technical Field

[0001] This invention belongs to the field of hydrometallurgical technology, specifically relating to a method for predicting gallium and germanium leaching rate and optimizing process parameters in zinc powder replacement slag under a composite external field, as well as a computer-readable storage medium and system. Background Technology

[0002] Gallium and germanium possess unique physicochemical properties and have important applications in high-tech fields such as semiconductors, optoelectronics, new energy, and aerospace. Gallium is a core raw material for manufacturing third-generation semiconductor materials such as gallium nitride and gallium arsenide, and is widely used in 5G communication base stations, power devices, and radio frequency chips; while germanium is a key material in infrared optics, fiber optic communication, solar cells, and nuclear radiation detection.

[0003] Gallium and germanium rarely form independent industrial deposits in nature; they are mostly found as associated deposits in non-ferrous metal mines such as bauxite, lead-zinc ore, and copper ore. Among these, zinc powder replacement slag, produced during zinc smelting, is an important secondary resource for gallium and germanium recovery. Zinc powder replacement slag is a solid waste generated in hydrometallurgical zinc smelting processes after zinc powder is added to purify zinc sulfate solution and remove impurities such as copper, cadmium, and cobalt. It typically contains 0.01%–0.5% gallium and 0.005%–0.3% germanium, possessing extremely high recovery value. The mainstream process for recovering gallium and germanium from zinc powder replacement slag is the hydrometallurgical process, which mainly includes unit operations such as acid leaching, alkaline leaching, extraction, ion exchange, and precipitation. Among these, leaching is the core of the entire recovery process, directly determining the overall recovery rate of gallium and germanium and the difficulty of subsequent processing steps. Traditional leaching processes mainly employ atmospheric pressure acid leaching or pressurized acid leaching. However, due to the complex occurrence state of gallium and germanium in zinc powder replacement slag, which often exists in mineral phases such as iron oxides and zinc sulfides in the form of isomorphous, adsorbed, or inclusions, the leaching kinetics are slow, the leaching rate is low, and the selectivity is poor.

[0004] To enhance the leaching process and improve the leaching efficiency of gallium and germanium, researchers have developed various composite external field enhanced leaching technologies in recent years, such as ultrasonic-assisted leaching, microwave-assisted leaching, magnetic field-assisted leaching, and composite external field leaching technologies with multiple coupled external fields. Patent CN116770079A discloses a method for ultrasonically enhanced leaching of gallium and germanium in zinc powder replacement slag, which significantly improves the leaching rate and extraction efficiency of gallium and germanium through the cavitation, acoustic flow, and mechanical disturbance effects of the ultrasonic field. Patent CN116790889A further discloses a magnetic field and ultrasonic composite enhanced leaching technology, which utilizes the regulatory effect of the magnetic field on ion migration, local flow regime, and the movement behavior of magnetic phases to improve the solid-liquid interface mass transfer conditions, and the synergistic effect with the ultrasonic field further accelerates the leaching rate. However, the leaching process under composite external fields is a complex nonlinear process with multiple factors, multiple variables, and strong coupling. Numerous factors affect the leaching rate, including leaching agent concentration, liquid-to-solid ratio, temperature, and external field intensity. In the process of extending composite field leaching technology from the laboratory to industrial applications, industrial production is subject to objective limitations from various factors such as equipment material and specifications, investment costs, energy consumption levels, safety and environmental protection requirements, and continuous production scale. There is a real need to adjust process parameters, making it difficult to directly adopt the best process parameters from the laboratory. It is necessary to seek the optimal solution within the local feasible domain.

[0005] To address this, researchers conducted numerous acid leaching optimization experiments. However, such repetitive experiments are time-consuming and labor-intensive, increasing recycling costs and environmental risks associated with wastewater treatment. Furthermore, when dealing with complex nonlinear leaching processes involving multiple factors, variables, and strong coupling under composite external fields, traditional methods suffer from limited prediction accuracy, insufficient generalization ability, and difficulty in obtaining globally optimal solutions. In existing technologies, CN121789809A discloses a method and system for germanane reactor slag recovery combining machine learning and process simulation. However, this method targets germanane reactor slag recovery, which differs significantly from the zinc powder replacement slag process under composite external fields. Moreover, this method fails to practically consider the objective physical limitations of the equipment, and the resulting optimization results still require further adjustment based on on-site conditions. CN117874465A discloses a method for predicting the leaching rate of rare earth elements in waste phosphor using machine learning. However, this method targets the leaching of rare earth elements in waste phosphor, which differs significantly from the zinc powder replacement slag process under composite external fields. Furthermore, this method also fails to practically consider the objective physical limitations of the equipment, making it difficult to meet the process parameter optimization needs in industrial production.

[0006] Therefore, developing a method that can fully utilize laboratory data to quickly and accurately predict the gallium-germanium leaching rate in zinc powder replacement slag under a composite external field, and that can map process parameters to adjustment levels of industrial production equipment, is of great theoretical significance and practical application value for promoting the industrial application of composite external field leaching technology, improving gallium-germanium recovery efficiency, and reducing production costs. Summary of the Invention

[0007] The purpose of this invention is to address at least one of the aforementioned problems by providing a method, computer-readable storage medium, and system for predicting gallium-germanium leaching rates and optimizing process parameters in zinc powder replacement slag under a composite external field. This addresses the issues of low leaching rate prediction accuracy and high cost and inefficiency caused by reliance on empirical trial-and-error for multi-objective optimization of process parameters in existing technologies. This solution integrates composite external field leaching kinetics, data-driven prediction, and equipment-constrained optimization into an interactive technical chain, which can reduce prediction bias under small sample conditions and provide an executable parameter decision-making basis for the gallium-germanium leaching process.

[0008] Machine learning technology possesses powerful nonlinear fitting and data mining capabilities, enabling it to learn complex underlying patterns from limited experimental data and establish high-precision predictive models. Using this model, high-accuracy leaching rate predictions can be quickly obtained simply by inputting process parameters. Furthermore, by combining this model with optimization algorithms, multi-objective optimization can be achieved within an industrially feasible parameter space, providing a new and effective approach to solving the aforementioned problems.

[0009] The objective of this invention is achieved through the following technical solution: The first aspect of this invention discloses a method for predicting gallium-germanium leaching rate and optimizing process parameters in zinc powder replacement slag under a composite external field, comprising the following steps: S1. Construct a dataset based on the process parameters and leaching results of zinc powder replacement slag; wherein the process parameters include at least temperature, liquid-to-solid ratio, sulfuric acid concentration, ultrasonic power and magnetic field strength, and the leaching results include gallium leaching rate and germanium leaching rate; S2. Construct the shrinking kernel model of gallium and germanium with external field correction, and solve the gallium mechanism leaching characteristics and germanium mechanism leaching characteristics respectively using the training set in the dataset constructed in step S1. S3. Combine the process parameters in step S1 with the gallium mechanism leaching characteristics and germanium mechanism leaching characteristics in step S2 to form an enhanced feature vector, and use the enhanced feature vector to train various different machine learning algorithm models. By evaluating the prediction accuracy of different models, the optimal leaching rate prediction model is selected. S4. Construct an industrial feasible parameter space based on the parameter boundaries of the leaching equipment, and construct the equipment level mapping relationship; using the optimal leaching rate prediction model in step S3 as the evaluation model, and taking gallium leaching rate and germanium leaching rate as optimization objectives, perform multi-objective search to obtain the non-dominated solution set. S5. Standardize and cluster the non-dominated solution set in step S4, select the solution with the minimum operating cost in each solution cluster as the representative process parameter, and output the representative process parameter and the gallium leaching rate prediction value and germanium leaching rate prediction value calculated by the optimal leaching rate prediction model under the representative process parameter; wherein, the operating cost is the weighted sum of the process parameters.

[0010] Preferably, in step S2: The external field-corrected shrinkage kernel model is as follows: ; In the formula, Let be a dimensionless time function of the leaching reaction. For leaching rate, Let be the apparent reaction rate constant under a combined external field. This refers to the leaching time; Apparent reaction rate constant under combined external fields for: ; In the formula, Pre-exponential factor, As the apparent activation energy, The gas constant is... For temperature, Liquid-to-solid ratio, This refers to the concentration of sulfuric acid. Ultrasonic power, The magnetic field strength, , and These are the exponential coefficients for the liquid-to-solid ratio, ultrasonic power, and magnetic field strength, respectively. The coupling coefficient between ultrasound and magnetic field; The gallium leaching mechanism characteristics are obtained by solving the inverse function separately. Germanium leaching mechanism characteristics .

[0011] Preferably, the pre-exponential factor in the apparent reaction rate constant under a combined external field The exponential coefficient of the liquid-solid ratio The exponential coefficient of ultrasonic power The exponential coefficient of magnetic field strength and the coupling coefficient between ultrasound and magnetic fields Constructing a set of dynamic parameters specific to the forming element ; The element-specific kinetic parameter sets of gallium and germanium were identified using the differential evolution algorithm based on the training set in the dataset constructed in step S1, and determined by minimizing the error between the mechanistic leaching rate and the measured leaching rate.

[0012] Preferably, in step S3: The machine learning algorithm models include random forest, extreme gradient boosting, lightweight gradient boosting machine, support vector regression, and neural networks.

[0013] Preferably, Bayesian optimization is used to tune the hyperparameters of each model during the process of using enhanced feature vectors to train various different machine learning algorithm models.

[0014] Preferably, in step S3: The optimal leaching rate prediction model was obtained through K-fold cross-validation.

[0015] Preferably, in step S4: The multi-objective search employs the NSGA-II algorithm to search for the Pareto front within the industrial feasible parameter space; The equipment gear mapping relationship is as follows: ; In the formula, The first generation generated by the NSGA-II algorithm One process parameter; For the first Each process parameter corresponds to the minimum executable parameter of the equipment; For the first Each process parameter corresponds to the adjustment step size of the equipment; For the first Each process parameter corresponds to an executable parameter of the equipment after gear mapping.

[0016] Preferably, in step S5: The clustering process uses the DBSCAN clustering algorithm. The cost function of each solution in each solution cluster is calculated as the operating cost of each solution, and the solution with the minimum operating cost in each solution cluster is selected as the representative process parameter. The cost function is: .

[0017] The second aspect of this invention discloses a computer-readable storage medium for predicting gallium-germanium leaching rate and optimizing process parameters in zinc powder replacement slag under a composite external field. The computer-readable storage medium stores one or more programs, which can be executed by one or more processors to implement the steps of the method for predicting gallium-germanium leaching rate and optimizing process parameters in zinc powder replacement slag under a composite external field as described in any of the preceding claims.

[0018] The third aspect of this invention discloses a system for predicting gallium and germanium leaching rates and optimizing process parameters in zinc powder replacement slag under a composite external field, comprising a processor and a memory for executable instructions. When the processor executes the instructions, it implements the steps of the method for predicting gallium and germanium leaching rates and optimizing process parameters in zinc powder replacement slag under a composite external field as described in any of the preceding claims.

[0019] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention employs a unified external-field modified shrinking core kinetic model to describe the leaching process of gallium and germanium, and sets separate sets of kinetic parameters for gallium and germanium. Thus, while maintaining consistency in the expression of the gallium and germanium leaching mechanism (external-field modified shrinking core model), it can characterize the differences between the two in terms of apparent activation energy, acid concentration response, liquid-solid ratio response, and ultrasonic and magnetic field enhancement responses, avoiding the distortion of mechanism characteristics caused by using the same set of kinetic parameters for both elements.

[0020] 2. This invention integrates process parameters such as temperature, liquid-to-solid ratio, sulfuric acid concentration, ultrasonic power, and magnetic field strength with the leaching characteristics of gallium and germanium mechanisms to construct a leaching rate prediction model. This model combines the determinism of classical physicochemical kinetics with the strong nonlinear mapping capability of data-driven models, eliminating the generalization limitations of pure theoretical models under complex multi-physics conditions, and correcting the generalization distortion caused by the lack of physical priors in pure data-driven models.

[0021] 3. This invention is guided by a multi-objective optimization approach to improve gallium and germanium leaching rates. It uses clustering to screen the optimization results, incorporating key factors such as temperature, acid consumption, liquid-to-solid ratio, ultrasonic energy consumption, and magnetic field energy consumption into a unified operational cost evaluation system. The aim is to find the optimal trade-off between leaching efficiency and production costs. This method effectively overcomes the inefficiencies of traditional orthogonal experiments or empirical trial-and-error methods, significantly shortening the process optimization cycle.

[0022] Furthermore, compared to existing technologies, this invention establishes a predictive model based on actual industrial operating data and optimizes process parameters by combining equipment physical constraints, thereby improving the reliability of the prediction results and the engineering feasibility of the optimized parameters. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating the method for predicting gallium-germanium leaching rate and optimizing process parameters in this scheme.

[0024] Figure 2 This is a schematic diagram of the process for predicting the gallium-germanium leaching rate in Example 1 of this scheme.

[0025] Figure 3 This is a flowchart illustrating the multi-objective optimization and clustering of process parameters in Embodiment 1 of this scheme.

[0026] Figure 4 This is a schematic diagram of the graphical interface operation process of Embodiment 2 of this solution.

[0027] Figure 5 This is a graph showing the prediction results of the Ga leaching efficiency prediction model obtained by machine learning in Implementation Example 1 of this scheme on the test set.

[0028] Figure 6This is a graph showing the prediction results of the Ge leaching efficiency prediction model obtained by machine learning in Implementation Example 1 of this scheme on the test set.

[0029] Figure 7 Example 2 of this solution is a graphical user interface for single-point prediction developed based on the optimal model for leaching rate prediction in Example 1.

[0030] Figure 8 Example 2 of this solution is a multi-objective optimized graphical user interface developed based on the optimal model for leaching rate prediction in Example 1. Detailed Implementation

[0031] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0032] Example 1 Taking the comprehensive recovery of gallium and germanium from zinc powder replacement slag in a smelter as an example, the zinc powder replacement slag is an intermediate material containing gallium and germanium produced during the hydrometallurgical zinc smelting process. Gallium and germanium are leached using sulfuric acid. The leaching process relies on experience and experiments to determine parameters such as temperature, liquid-to-solid ratio, sulfuric acid concentration, ultrasonic power, and magnetic field strength. Furthermore, the gallium and germanium leaching rate is affected by multiple coupled factors, making it difficult to obtain the globally optimal solution through laboratory-scale tests or orthogonal experiments alone. The main problems faced on-site include the complexity of the leaching mechanism under composite external fields, the difficulty in quantifying the contribution of each parameter to the leaching rate, and the need for multi-objective optimization to control energy and acid consumption while ensuring a high leaching rate. Traditional methods are inefficient and have long cycles.

[0033] This invention addresses the problems of strong coupling of multiple factors, low accuracy in leaching rate prediction, reliance on empirical trial and error for process optimization, and high cost and low efficiency in composite external field leaching processes. It integrates the leaching reaction mechanism with machine learning to achieve accurate prediction of gallium and germanium leaching rates and multi-objective optimization of process parameters. For example... Figure 1 As shown, this invention first collects process parameters such as temperature, liquid-to-solid ratio, sulfuric acid concentration, ultrasonic power, and magnetic field strength under combined external field conditions, as well as gallium and germanium leaching rate data to construct a dataset. For gallium and germanium, separate external field correction and shrinkage kernel models are established to obtain the mechanistic leaching characteristics of gallium and germanium. Using enhanced features as input and bi-element leaching rate as output, machine learning models such as random forest and extreme gradient boosting are trained and optimized, combined with Bayesian optimization to improve prediction accuracy. An industrial feasible domain including the equipment's applicable domain and operating costs is constructed. For each candidate solution, a level mapping is performed, and the mechanistic features and prediction results are recalculated to obtain a combination of non-dominated process parameters. The non-dominated solution set is standardized, clustered, and its operating costs are evaluated to output representative process parameters with equipment executability.

[0034] See Figure 2 and Figure 3 This solution utilizes laboratory single-factor and multi-factor composite field test data to construct a mechanism-data fusion prediction model and integrates a multi-objective search (multi-objective optimization) algorithm to recommend processes, which can significantly reduce the cost of trial and error experiments for factories and improve the efficiency of rare and dispersed metal recycling.

[0035] Step S1 involves constructing a dataset using data obtained from laboratory single-factor (temperature, liquid-to-solid ratio, sulfuric acid concentration, ultrasonic power, and magnetic field strength) and multi-factor experiments. The dataset is grouped according to the material batches of the zinc powder replacement slag, and further divided into training, validation, and independent test sets based on each material batch.

[0036] Step S2: Establish a leaching rate mechanism model. First, a shrinking core model (shrinking core kinetic equation) is constructed: gallium and germanium in the zinc powder replacement slag are located inside the solid particles; during leaching, the leaching agent diffuses from the outside of the particles to the inside and reacts with the gallium and germanium-containing phases, while the unreacted area gradually shrinks. To describe this process, the zinc powder replacement slag particles are approximated with an initial radius of... Spherical particles. Let the leaching time be... At that time, the radius of the unreacted nucleus inside the particle is The leaching rate of the target element Since the amount of unreacted target element in the particle is directly proportional to the volume of the unreacted nucleus, we have: ; Therefore, we can conclude that: ; When the leaching process is mainly controlled by diffusion through the solid product layer, the diffusion rate of the leaching agent through the product layer can be expressed as follows, based on the quasi-steady-state diffusion relationship of the leaching agent within the spherical particle product layer: ; in, The molar rate of the leaching agent through the product layer. The effective diffusion coefficient of the leaching agent within the product layer. This represents the effective concentration of the leachate on the outer surface of the particles.

[0037] The diffusion rate and the consumption rate of unreacted nuclei are calculated using a material balance, starting from the initial state. Integral calculation of the unreacted kernel radius up to any time step ,get: ; Right now: ; in Let be a dimensionless time function of the leaching reaction. Let be the apparent reaction rate constant under a combined external field. For gallium and germanium, the same form of contracting nuclear kinetic equations are used, but element-specific apparent reaction rate constants are set. To characterize the differences in the occurrence states and leaching responses of the two elements.

[0038] Under the influence of a combined external field (temperature, ultrasound, magnetic field), the apparent reaction rate constant The reaction rate is influenced by a combination of factors, including temperature, liquid-to-solid ratio, sulfuric acid concentration, ultrasonic power, and magnetic field strength. According to the Arrhenius relation, the effect of temperature on the reaction rate is as follows: ; in Pre-exponential factor, As the apparent activation energy, , Temperature in Celsius This is for calculating thermodynamic temperature.

[0039] Sulfuric acid concentration and liquid-to-solid ratio jointly affect the amount of leaching agent supplied per unit unit of solid, the solid-liquid contact state, and the concentration gradient on the particle surface. To characterize this combined effect, acid solution conditional variables are defined as follows: ; in, Liquid-to-solid ratio, This refers to the sulfuric acid concentration, in units of... .

[0040] The ultrasonic field thins the liquid film, promotes diffusion within the product layer, and strips away the surface deposits through cavitation, acoustic flow, and mechanical disturbance. The magnetic field improves interfacial mass transfer by regulating ion migration, flow regime, and magnetic phase movement. Together, they constitute the ultrasonic-magnetic field interaction term. Furthermore, considering that the leaching reaction can still proceed spontaneously without an external field, the basic term in the composite external field condition variable is set to 1, and its form is: ; in, Ultrasonic power, unit: , Magnetic field strength, unit: .

[0041] Multiplying the temperature correction term, acid condition correction term, and combined external field correction term yields the apparent reaction rate constant: ; in, , , These are the exponential coefficients for the liquid-to-solid ratio (affecting the solid-liquid contact area), ultrasonic power, and magnetic field strength, respectively. This is the coupling coefficient between ultrasound and magnetic fields. Among them, the specific kinetic parameter set for gallium and germanium elements... Dedicated kinetic parameter sets were set for gallium and germanium respectively. The differential evolution algorithm is used to iteratively optimize the parameter set, that is, to substitute it into the mechanism model to calculate the mechanism leaching rate; and by minimizing the error between the mechanism leaching rate and the corresponding measured leaching rate, the optimal kinetic parameter set for the corresponding element is obtained.

[0042] From the fundamental dynamic relationship The inverse function is solved, and since the leaching time is fixed in the experiment, therefore... The default value is 1, and the final result is... Input any process parameters Two mechanistic characteristics can be obtained by solving. and This is then combined with the original five process parameters to form a 7-dimensional enhanced feature set. This is used for subsequent model predictions.

[0043] Step S3: Establish leaching rate prediction models by constructing machine learning models such as Random Forest (RF), Extreme Gradient Boosting (XGBoost), Support Vector Machine (SVR), and Medium LP (MLP). Bayesian optimization (Optuna) is used to fine-tune the hyperparameters of each model (in some other embodiments, Lightweight Gradient Boosting Machine (LightGBM) may also be considered). Simultaneously, an early stopping mechanism is implemented for models supporting iterative training, while cross-validation and hyperparameter range constraints are used to reduce overfitting risk for models that do not support early stopping). To evaluate the generalization ability of each model, five-fold cross-validation is performed on the training set, and the coefficient of determination for each fold is calculated. Mean absolute error Root mean square error Mean absolute percentage error (As indicators for evaluating model accuracy), the average value of each indicator is used to assess the overall performance of the model. (Comprehensive consideration) The higher, , , Following the principle of lower values, the model with the best overall performance is selected. The model is then retrained using the full training set and finally evaluated on an independent test set to prevent overfitting.

[0044] Coefficient of determination ( This measures the extent to which a model explains the variance of the data, reflecting the goodness of fit between predicted and actual values. Its definition formula is as follows: ; in, This represents the average of all true values. For the first The true value of each sample For predicted values, The total number of samples.

[0045] Mean absolute error ( The average of the absolute values ​​of the prediction error is used to measure the degree of deviation between the predicted result and the actual result. Its definition formula is as follows: .

[0046] Among them, root mean square error ( The standard deviation of the prediction error measures the volatility and accuracy of the predicted value. Its definition is as follows: .

[0047] Among them, the mean absolute percentage error ( The average relative deviation of the predicted value from the true value is used to measure the overall relative error level and fitting effect of the model's predictions.

[0048] .

[0049] The leaching rate prediction performance of each model on the training set is compared in Tables 1 and 2 below.

[0050] Table 1. Performance comparison of different models for Ga leaching rate Table 2 Comparison of performance of different models for Ge leaching rate During the implementation process and Using the zinc powder replacement slag as the primary evaluation metric, the Limiting Gradient Boosting (XGBoost) model was determined to have the best predictive performance for gallium-germanium leaching rate. The trained XGBoost model was then evaluated on an independent test set, and its prediction results on the test set are as follows: Figure 5 and Figure 6 As shown. By Figure 5 and Figure 6 It can be seen that, on the independent test set, the predicted values ​​of gallium and germanium leaching rates show good consistency with the actual values, and the leaching rates of gallium and germanium are... All values ​​were above 0.9, indicating that the XGBoost model has high predictive accuracy and generalization ability for the leaching rates of gallium and germanium in zinc powder replacement slag, and can provide a reliable predictive basis for the parameter optimization of actual leaching processes.

[0051] In step S4, the user sets upper and lower limits for temperature, liquid-to-solid ratio, sulfuric acid concentration, ultrasonic power, magnetic field strength, and leaching time based on the design capacity of the leaching equipment, material tolerance conditions, safe operation requirements, and actual adjustment methods. Simultaneously, the user sets the corresponding equipment adjustment step size (equipment level) for each parameter, such as a magnetic field strength adjustment step size of 10T. Using the optimal leaching rate prediction model from step S3 as the evaluation model, and taking gallium leaching rate and germanium leaching rate as dual maximization objectives, the NSGA-II algorithm searches for the Pareto front within the user-specified boundary. The NSGA-II algorithm randomly initializes a set of process parameter combinations as the initial population; then, through selection, crossover, and mutation operations, it generates a offspring population. After merging the parent and offspring generations, it performs non-dominated sorting, dividing the solutions into non-dominated fronts of different levels. In this embodiment, the solution with simultaneously high gallium and germanium leaching rates is selected. Simultaneously, the crowding distance of each solution is calculated to measure its density in the target space, prioritizing solutions with high non-dominated levels and large crowding distances for the next generation. After a specified number of iterative optimizations, the algorithm outputs a Pareto front consisting of non-dominated solutions.

[0052] Because the NSGA-II algorithm generates continuous candidate process parameters, these parameters need to be mapped to the actual adjustable settings of the equipment before leaching rate prediction and objective function evaluation. For the first... Each process parameter, with its corresponding gear mapping, is as follows: ; in, The first generation generated by the NSGA-II algorithm One process parameter; For the first Each process parameter corresponds to the minimum executable parameter of the equipment; For the first Each process parameter corresponds to the adjustment step size of the equipment; For the first Each process parameter corresponds to an executable parameter of the equipment after gear mapping. Parameters exceeding the upper and lower limits after mapping are boundary-corrected, that is, parameters exceeding the allowable range of the equipment are truncated to the corresponding upper and lower limits, thereby obtaining a discrete process parameter combination that satisfies the actual constraints of the equipment, and thus completing the search for the non-dominated solution set.

[0053] After obtaining the Pareto front solution set through a multi-objective optimization algorithm, this embodiment further normalizes the predicted values ​​of gallium and germanium leaching rates, and then uses the DBSCAN clustering algorithm to cluster the Pareto solution set. DBSCAN is a density-based spatial clustering algorithm that automatically divides clusters based on the density of sample point distribution. This embodiment sets the neighborhood radius. and minimum neighborhood sample number =1, then for each sample point in the Pareto solution set (using the leaching rates of gallium and germanium as two-dimensional spatial coordinates), count the number of sample points contained within its neighborhood radius, and then count the number of sample points. Points that are not core points are marked as core points. Then, starting from a core point, all sample points within its neighborhood radius are grouped into the same cluster and recursively expanded outwards until no further expansion is possible. Finally, sample points that are neither core points nor within the neighborhood radius of any core point are discarded as noise points. After clustering, the Pareto front solution set is divided into N clusters. Since solutions within the same cluster are close to each other in the leaching rate target space, they can be considered equivalent schemes with similar leaching effects in engineering practice.

[0054] Within each cluster, the solution with the minimum cost is selected as the representative process parameter using a cost function. This cost function considers economic conditions, namely temperature. Lowest, liquid-to-solid ratio ( Minimum, sulfuric acid concentration ( (lowest) ultrasonic power ( The lowest magnetic field strength () The lowest cost function is defined as follows: ; Calculate each solution separately within each cluster. Value, select The solution with the smallest value is taken as the representative process parameter of the cluster, and after rounding, it can be directly used for production guidance.

[0055] This invention integrates composite external field leaching kinetics, data-driven prediction, and equipment constraint optimization into an interactive technology chain, which can reduce prediction bias under small sample conditions and provide executable parameter decision-making basis for gallium-germanium leaching process.

[0056] Example 2 See Figure 4 Building upon Example 1, this example further designs a graphical user interface (GUI) to facilitate easy use and timely adjustment of process parameters by factory operators. This example utilizes the Tkinter framework in Python to construct the graphical interface for the metallurgical process optimization system. The interface adopts a tabbed (notebook) structure and is divided into two modules: "Single-point Prediction" and "Multi-objective Optimization."

[0057] In the single-point prediction module, the user sequentially inputs five process parameters: temperature, liquid-to-solid ratio, sulfuric acid concentration, ultrasonic power, and magnetic field strength. After clicking the "Predict Leaching Rate" button, the system automatically calls the mechanism characteristic calculation step S2 and the optimal model in S3, outputting the predicted leaching rates of gallium and germanium in real time, clearly displayed in a result box with borders and icons. Figure 7 A graphical interface for single-point prediction.

[0058] In the multi-objective optimization module, users can set the lower and upper limits for each process parameter, and adjust the population size, generation number, and random seed. After clicking "Start Optimization," the system runs the NSGAII algorithm in the background, displaying the optimization progress with a progress bar. Once optimization is complete, the interface displays the filtered Pareto optimal process parameter combinations and their corresponding predicted leaching rates in a table format. It supports one-click saving as a CSV file, allowing users to easily export the results for production guidance. Figure 8 A graphical interface diagram for the multi-objective optimization module.

[0059] This embodiment integrates the prediction model and optimization algorithm described in Embodiment 1 into a visual operating platform by constructing a graphical user interface. Plant operators do not need to have professional knowledge of machine learning or optimization algorithms; they can obtain the predicted leaching rate or the optimal combination of process parameters simply by inputting parameters and clicking buttons. The interface effectively lowers the barrier to entry for using advanced prediction and optimization technologies, providing an intuitive and convenient engineering tool for real-time control and parameter optimization of the zinc powder replacement slag leaching process.

[0060] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0061] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0062] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0063] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0064] The above description of the embodiments is provided to enable those skilled in the art to understand and use the invention. It will be apparent to those skilled in the art that various modifications can be made to these embodiments, and the general principles described herein can be applied to other embodiments without inventive effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made by those skilled in the art based on the disclosure of the present invention without departing from the scope of the invention should be within the protection scope of the present invention.

Claims

1. A method for predicting gallium-germanium leaching rate and optimizing process parameters in zinc powder replacement slag under a composite external field, characterized in that, The steps include the following: S1. Construct a dataset based on the process parameters and leaching results of zinc powder replacement slag; wherein the process parameters include at least temperature, liquid-to-solid ratio, sulfuric acid concentration, ultrasonic power and magnetic field strength, and the leaching results include gallium leaching rate and germanium leaching rate; S2. Construct the shrinking kernel model of gallium and germanium with external field correction, and solve the gallium mechanism leaching characteristics and germanium mechanism leaching characteristics respectively using the training set in the dataset constructed in step S1. S3. Combine the process parameters in step S1 with the gallium mechanism leaching characteristics and germanium mechanism leaching characteristics in step S2 to form an enhanced feature vector, and use the enhanced feature vector to train various different machine learning algorithm models. By evaluating the prediction accuracy of different models, the optimal leaching rate prediction model is selected. S4. Construct an industrial feasible parameter space based on the parameter boundaries of the leaching equipment, and construct the equipment level mapping relationship; using the optimal leaching rate prediction model in step S3 as the evaluation model, and taking gallium leaching rate and germanium leaching rate as optimization objectives, perform multi-objective search to obtain the non-dominated solution set. S5. Standardize and cluster the non-dominated solution set in step S4, select the solution with the minimum operating cost in each solution cluster as the representative process parameter, and output the representative process parameter and the gallium leaching rate prediction value and germanium leaching rate prediction value calculated by the optimal leaching rate prediction model under the representative process parameter; wherein, the operating cost is the weighted sum of the process parameters.

2. The method for predicting gallium and germanium leaching rates and optimizing process parameters in zinc powder replacement slag under a composite external field as described in claim 1, characterized in that, In step S2: The external field-corrected shrinkage kernel model is as follows: ； In the formula, Let be a dimensionless time function of the leaching reaction. For leaching rate, Let be the apparent reaction rate constant under a combined external field. This refers to the leaching time; Apparent reaction rate constant under combined external fields for: ； In the formula, Pre-exponential factor, As the apparent activation energy, The gas constant is... For temperature, Liquid-to-solid ratio, This refers to the concentration of sulfuric acid. Ultrasonic power, The magnetic field strength, , and These are the exponential coefficients for the liquid-to-solid ratio, ultrasonic power, and magnetic field strength, respectively. The coupling coefficient between ultrasound and magnetic field; The gallium leaching mechanism characteristics are obtained by solving the inverse function separately. Germanium leaching mechanism characteristics .

3. The method for predicting gallium and germanium leaching rate and optimizing process parameters in zinc powder replacement slag under a composite external field as described in claim 2, characterized in that, Pre-exponential factor in apparent reaction rate constant under combined external fields The exponential coefficient of the liquid-solid ratio The exponential coefficient of ultrasonic power The exponential coefficient of magnetic field strength and the coupling coefficient between ultrasound and magnetic fields Constructing a set of dynamic parameters specific to the forming element ; The element-specific kinetic parameter sets of gallium and germanium were identified using the differential evolution algorithm based on the training set in the dataset constructed in step S1, and determined by minimizing the error between the mechanistic leaching rate and the measured leaching rate.

4. The method for predicting gallium and germanium leaching rates and optimizing process parameters in zinc powder replacement slag under a composite external field as described in claim 1, characterized in that, In step S3: The machine learning algorithm models include random forest, extreme gradient boosting, lightweight gradient boosting machine, support vector regression, and neural networks.

5. The method for predicting gallium and germanium leaching rate and optimizing process parameters in zinc powder replacement slag under a composite external field as described in claim 4, characterized in that, In the process of using enhanced feature vectors to train various machine learning algorithm models, Bayesian optimization is used to tune the hyperparameters of each model.

6. The method for predicting gallium and germanium leaching rate and optimizing process parameters in zinc powder replacement slag under a composite external field as described in claim 1, characterized in that, In step S3: The optimal leaching rate prediction model was obtained through K-fold cross-validation.

7. The method for predicting gallium and germanium leaching rates and optimizing process parameters in zinc powder replacement slag under a composite external field as described in claim 1, characterized in that, In step S4: The multi-objective search employs the NSGA-II algorithm to search for the Pareto front within the industrial feasible parameter space; The equipment gear mapping relationship is as follows: ； In the formula, The first generation generated by the NSGA-II algorithm One process parameter; For the first Each process parameter corresponds to the minimum executable parameter of the equipment; For the first Each process parameter corresponds to the adjustment step size of the equipment; For the first Each process parameter corresponds to an executable parameter of the equipment after gear mapping.

8. The method for predicting gallium and germanium leaching rate and optimizing process parameters in zinc powder replacement slag under a composite external field as described in claim 1, characterized in that, In step S5: The clustering process uses the DBSCAN clustering algorithm. The cost function of each solution in each solution cluster is calculated as the operating cost of each solution, and the solution with the minimum operating cost in each solution cluster is selected as the representative process parameter. The cost function is: 。 9. A computer-readable storage medium for predicting gallium-germanium leaching rate and optimizing process parameters in zinc powder replacement slag under a composite external field, characterized in that... The computer-readable storage medium stores one or more programs, which can be executed by one or more processors to implement the steps of the method for predicting gallium and germanium leaching rate and optimizing process parameters in zinc powder replacement slag under a composite external field as described in any one of claims 1 to 8.

10. A system for predicting gallium and germanium leaching rates and optimizing process parameters in zinc powder replacement slag under a composite external field, characterized in that, The device includes a processor and a memory for executing instructions. When the processor executes the instructions, it implements the steps of the method for predicting gallium and germanium leaching rates and optimizing process parameters in zinc powder replacement slag under a composite external field as described in any one of claims 1 to 8.

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