A method for predicting and quantifying process parameters of a scrapped photovoltaic silver-aluminum bimetallic wet recovery based on bayesian optimization catboost and SHAP

Abstract

The application provides a method for predicting and quantifying the process parameters of a scrapped photovoltaic silver-aluminum bimetallic wet recovery based on Bayesian optimization CatBoost and SHAP, and relates to the field of process mechanism quantification. The method comprises the following steps: obtaining test data to construct two independent data sets of silver and aluminum after cleaning; dividing the training set, the validation set and the test set and constructing a ten-fold cross-validation mechanism; screening the basic optimal model, taking the maximum average determination coefficient of the ten-fold cross-validation as the optimization target, and using the Bayesian hyperparameter optimization algorithm for iterative optimization; and using the SHAP explainability analysis method based on the optimized model to quantify the contribution weight and action law of each process parameter to the extraction rate of silver and aluminum. The application can lock the optimal process parameter combination without a large number of repeated tests, and provides a theoretical basis for the optimization of the silver-aluminum acid leaching process.

Description

Technical Field

[0001] This application relates to the field of process mechanism quantification technology, and in particular to a method for predicting and quantifying process parameters of wet recycling of silver-aluminum bimetallic waste photovoltaic materials based on Bayesian optimization CatBoost and SHAP. Background Technology

[0002] The recycling of waste crystalline silicon photovoltaic modules can achieve multiple benefits in terms of economy, environment and mineral security[1]. The mass fractions of aluminum and silver in a single commercial crystalline silicon module are 7.75% and 0.57%, respectively, and aluminum and silver account for 30% and 14% of the total recycling revenue, respectively; existing pilot data show that the return on investment of the complete recycling process can reach 113%. In terms of environment, standardized recycling can avoid the leakage of hazardous waste and reduce carbon emissions from the smelting of primary minerals. From the perspective of resource strategy, silver is a scarce key mineral. Every 1GW of waste photovoltaic modules recycled can recover 17 tons of silver and 9,000 tons of aluminum, which can effectively alleviate the pressure on the supply of primary minerals; the recycled high-purity aluminum and silver can be directly used for the preparation of photovoltaic frames and conductive silver paste, which can help the closed-loop development of the photovoltaic industry chain.

[0003] Currently, mainstream recycling technologies are divided into three main categories: pyrometallurgical, physical sorting, and hydrometallurgical. Hydrometallurgical acid leaching has become the core research direction for silver and aluminum recycling due to its superior metal selectivity and controllable product purity. The literature "Huang YF, Cheng TT, Chiueh P T, et al. Resource recovery from spent crystalline-silicon solar modules byusing microwave pyrolysis, acid leaching and chemical etching[J]. Process Safety and Environmental Protection, 2025, 194:47-57" describes a microwave pyrolysis pretreatment and a two-stage stepwise acid leaching process, using sulfuric acid to leach aluminum and nitric acid to leach silver. Under optimal conditions, the aluminum recovery rate is 94.90% (purity 99.63%) and the silver recovery rate is 95.74% (nearly 100%). If crushing and classification pretreatment is used, the precious metals are enriched in fine powder with a particle size <150μm (accounting for only 5% of the crushed material, with a silver content of 0.85wt%), and only the rich fine powder is leached with nitric acid, which greatly reduces acid consumption and transportation costs. To avoid the defects of inorganic strong acid pollution, organic acid leaching has become a cutting-edge direction. The literature "Luo SW, Chen XH, Lu JJ, et al. Selective separation and recovery of silver from end-of-life photovoltaic modules using organic acid leaching" describes this approach. The literature "[J]. Journal of Environmental Chemical Engineering, 2026, 14:122096" describes the construction of a methanesulfonic acid-hydrogen peroxide synergistic silver leaching system, combined with ascorbic acid reduction, achieving a silver leaching rate >99.7% and a purity >99.6%. The literature "[J]. Separation and Purification Technology, 2025, 359:130343" describes the development of a citric acid-hydrogen peroxide green leaching system, which, through chlorination precipitation, ammonia dissolution, and liquid-phase reduction, yields silver with an average particle size of 229.7 nm and a purity of 99%.85% nano-silver; the literature "Choi S, Kang H, Park E, et al. Pulse laser recovery of high purity colloidal silver spheres from end of life crystalline siliconsolar panels[J]. Separation and Purification Technology, 2025, 379:134842" uses nanosecond pulsed light to reduce silver oxide in nitric acid leaching solution, achieving a final total silver recovery rate of approximately 98%. Although various wet processes have been validated in the laboratory and pilot-scale, several technical bottlenecks still hinder industrialization.

[0004] Optimizing simultaneous acid leaching of aluminum and silver presents significant technical challenges: sulfuric acid leaching of aluminum follows pseudo-second-order kinetics, while nitric acid dissolution of silver is controlled by cylindrical diffusion. These differences in dissolution mechanisms lead to completely different response patterns to parameters such as temperature, acid concentration, and liquid-to-solid ratio. Leaching efficiency is influenced by a combination of factors, including pretreatment method, acid type, reagent concentration, temperature, solid-to-liquid ratio, and leaching time. Traditional single-factor and response surface methodology experiments are costly in terms of reagents, manpower, and experimentation. The composition of waste photovoltaic raw materials from different manufacturers and with varying service lives fluctuates greatly, with inconsistent aluminum and silver content, residual EVA impurities, and fragmentation particle size, making it difficult to adapt optimization parameters for multiple batches. Existing research primarily optimizes single-metal leaching processes for silver or aluminum, lacking efficient dual-metal simultaneous control schemes. Inorganic acid pollution is severe, and balancing the cost and leaching efficiency of organic acids is difficult. Traditional trial-and-error methods cannot clarify the coupling relationships among multiple parameters, hindering industrialization.

[0005] In recent years, machine learning has been widely applied in chemical engineering, environmental science, and hydrometallurgy due to its excellent nonlinear fitting, feature analysis, and global optimization capabilities. Leveraging massive experimental datasets, machine learning can establish quantitative prediction models for process parameters and leaching efficiency, quantifying the independent effects and interactions of various factors, and quickly identifying the optimal process combination while eliminating the need for numerous repetitive experiments. Currently, machine learning has been used to optimize the acid leaching process for waste printed circuit boards and waste zinc-manganese batteries, but related research rarely focuses on data-driven optimization of the synergistic acid leaching of waste crystalline silicon photovoltaic aluminum and silver bimetallic materials.

[0006] Therefore, existing technologies suffer from the problem that traditional experimental methods cannot quantitatively elucidate the multi-factor coupling correlation law of the simultaneous acid leaching system of aluminum and silver, and the process trial and error optimization cycle is lengthy and the R&D cost is high. Summary of the Invention

[0007] This application provides a method for predicting and quantifying process parameters in the wet recycling of silver and aluminum bimetals from waste photovoltaic systems based on Bayesian optimization using CatBoost and SHAP. Using pretreatment conditions, acid system type, and various process parameters as input features, and aluminum and silver leaching rates as dual output indicators, multiple machine learning models are constructed. By leveraging the analytical features' importance and parameter interaction patterns, the optimal acid leaching conditions that simultaneously achieve high aluminum and silver recovery rates are intelligently selected. This application aims to achieve green and efficient recycling of valuable metals from waste crystalline silicon using a data-driven approach, significantly reducing experimental costs and promoting the implementation of the photovoltaic solid waste recycling industry.

[0008] To achieve the above objectives, this application adopts the following technical solution: This application provides a method for predicting and quantifying process parameters in the wet recycling of silver-aluminum bimetallic materials from waste photovoltaic systems based on Bayesian optimization of CatBoost and SHAP. The method includes: Test data on the wet acid leaching recovery of silver and aluminum from waste crystalline silicon photovoltaic cells were obtained, and the test data was cleaned. Non-standard content was uniformly converted into missing values, while the blank missing fields of the original data were retained to obtain the original dataset. Based on the calculation logic of indicators for silver and aluminum metal recycling, silver datasets and aluminum datasets are constructed respectively. The silver dataset is constructed by coupling the silver leaching rate, silver precipitation rate and silver reduction rate to calculate the final silver extraction rate of the entire process. The aluminum dataset is constructed by using the aluminum acid leaching rate as an equivalent of the final aluminum extraction rate. Furthermore, the silver dataset and the aluminum dataset respectively remove the other metal-specific features to form their own independent feature systems. The silver dataset and the aluminum dataset are randomly divided into training set, validation set and test set, respectively, and a ten-fold cross-validation mechanism is constructed based on the training set; Multiple tree-based machine learning models were selected and trained on the silver dataset and the aluminum dataset respectively to obtain the prediction performance index of each basic model. The optimal basic model was selected based on the prediction performance index, wherein the prediction performance index includes the coefficient of determination, root mean square error and mean absolute error. With the goal of maximizing the average coefficient of determination of the 10-fold cross-validation of the training set, the Bayesian hyperparameter optimization algorithm is used to iteratively optimize the basic optimal model to obtain the optimal model after Bayesian optimization. Based on the optimal model after Bayesian optimization, the SHAP interpretability analysis method is used to quantify the contribution weight and effect of each process parameter on the silver extraction rate and aluminum extraction rate.

[0009] As a preferred technical solution, based on the calculation logic of indicators for silver and aluminum metal recycling, silver datasets and aluminum datasets are constructed respectively, including: Test samples with valid silver leaching rate records are selected from the original dataset. For samples with missing precipitation rate and / or reduction rate fields, the conversion factor of the missing precipitation and reduction processes is assigned to 1, indicating that the missing process does not contribute to silver loss. The silver leaching rate is multiplied by the conversion factor of each process to obtain the final silver extraction rate of the entire process. The silver dataset is formed by the silver leaching rate, precipitation rate, reduction rate and final silver extraction rate of each sample. Test samples with valid aluminum leaching rate records are selected from the original dataset. The aluminum acid leaching rate is used as the final aluminum extraction rate. The aluminum dataset is formed by the aluminum acid leaching rate and process parameters of each sample. The aluminum-specific features in the silver dataset are kept as missing values, and the silver-specific features in the aluminum dataset are kept as missing values.

[0010] As a preferred technical solution, the various tree-based machine learning models include gradient boosting tree models, Bagging ensemble tree models, and single decision tree models; the gradient boosting tree models include CatBoost, XGBoost, and LightGBM; the Bagging ensemble tree models include random forests and extreme random trees; and the single decision tree models include single decision trees with maximum depths of 3, 5, and 10.

[0011] As a preferred technical solution, the determination coefficient The root mean square error and the mean absolute error Calculate according to the following formulas respectively: in, For the first The true metal extraction rate of each sample For the first The model prediction extraction rate for each sample. The average of the true extraction rates for all samples. This represents the total number of samples in the test set.

[0012] As a preferred technical solution, the basic optimal model is selected based on the predicted performance indicators, including: The determination coefficients of each base model on the silver dataset and the aluminum dataset are sorted respectively; The CatBoost model with the highest determination coefficient was selected as the base optimal model on both the silver dataset and the aluminum dataset.

[0013] As a preferred technical solution, a Bayesian hyperparameter optimization algorithm is used to iteratively optimize the basic optimal model to obtain the optimal model after Bayesian optimization, including: Obtain a set of candidate hyperparameter combinations for the basic optimal model, perform 10-fold cross-validation on the training set for the set of candidate hyperparameter combinations, and calculate the corresponding average coefficient of determination. Based on the evaluated combinations of candidate hyperparameters and their corresponding average coefficients of determination, a posterior probability distribution of the objective function is constructed using a Gaussian process to characterize the current confidence level in the region where the optimal hyperparameters are located. Based on the posterior probability distribution, the next set of candidate hyperparameter combinations to be evaluated is calculated using the acquisition function, so that the evaluation direction tends toward the global optimal region, wherein the acquisition function is used to measure the evaluation priority of each candidate hyperparameter combination. The next set of candidate hyperparameter combinations to be evaluated is substituted back into the basic optimal model for 10-fold cross-validation, the corresponding average coefficient of determination is calculated, and the newly obtained candidate hyperparameter combinations and their corresponding average coefficients of determination are added to the historical data to update the posterior probability distribution. Repeat the above evaluation and update process until the preset number of iterations is reached. Select the candidate hyperparameter combination with the highest average coefficient of determination in the historical data as the optimal hyperparameter configuration. Assign the optimal hyperparameter configuration to the basic optimal model to obtain the optimal model after Bayesian optimization.

[0014] As a preferred technical solution, based on the optimal model after Bayesian optimization, the SHAP interpretability analysis method is used to quantify the contribution weight and effect of each process parameter on the silver extraction rate and aluminum extraction rate, including: An interpreter adapted to the tree-based model is used. Based on the internal decision path of the optimal model after Bayesian optimization, the marginal contribution of each process parameter to the model prediction result relative to the baseline prediction value is calculated in each test sample, and the SHAP value of each process parameter on each sample is obtained. The absolute values ​​of the SHAP values ​​of each process parameter on all test samples were taken and the average value was calculated. This average value was used as the global importance of each process parameter. All process parameters in the entire process were sorted in descending order to determine the main control parameters and secondary parameters that affect the extraction rate. Based on the ranking of the global importance of the features, identify the top-ranking core control parameters and the bottom-ranking non-core influencing parameters in the silver extraction system and the aluminum extraction system. For the silver extraction system and the aluminum extraction system, SHAP feature importance bar charts are generated to horizontally display the global importance and ranking of each process parameter. SHAP colony distribution map is generated to correlate the SHAP value of each sample with the value of the corresponding process parameter, showing the changing trend of each process parameter in different value ranges, which has a positive promoting or negative inhibiting effect on the extraction rate. Generate a full-feature SHAP heatmap of silver and aluminum, with process parameters as the x-axis, metal type as the y-axis, and global importance of SHAP features as the fill color, and compare the differences in the contribution weight of the same process parameter in the silver extraction system and the aluminum extraction system.

[0015] As a preferred technical solution, the process parameters include EVA pretreatment parameters, acid leaching process parameters, precipitation process parameters, and reduction process parameters, wherein the acid leaching process parameters include solid-liquid ratio, acid concentration, acid leaching time, and acid leaching temperature.

[0016] As a preferred technical solution, after quantifying the contribution weight and effect of each process parameter on the silver extraction rate and aluminum extraction rate, the method further includes: Based on the ranking of the importance of the SHAP features, the top three process parameters in the silver extraction system are identified as the core control parameters, and the process parameters of the precipitation and reduction processes are identified as having a significant regulatory effect on the silver extraction rate. Based on the ranking of the importance of the SHAP features, the top three process parameters in the aluminum extraction system are identified as the core control parameters, and the precipitation process parameters and reduction process parameters are identified as having zero contribution weight to the aluminum extraction rate and therefore no regulatory effect.

[0017] As a preferred technical solution, after quantifying the contribution weights and effects of each process parameter on the silver and aluminum extraction rates, the following is also included: Based on the quantitative results of the SHAP interpretability analysis method, the core control parameters and priority rankings for the silver extraction system and the aluminum extraction system were determined respectively. The process control priority for the silver extraction system was set as follows: solid-liquid ratio takes precedence over acid concentration, and acid concentration takes precedence over acid leaching time. The process control priority for the aluminum extraction system was set as follows: acid leaching time takes precedence over reduction temperature, and reduction temperature takes precedence over acid leaching temperature. Based on the priority order, the control direction of each core control parameter is determined, resulting in the optimal combination of process parameters for the simultaneous and efficient recovery of silver and aluminum.

[0018] The method for predicting and quantifying process parameters for the wet recycling of silver-aluminum bimetallic waste photovoltaic cells based on Bayesian optimization CatBoost and SHAP provided in this application has at least the following beneficial effects: (1) This application constructs two sets of differentiated independent datasets for silver and aluminum, and selects the CatBoost model as the basic optimal model for the silver and aluminum bimetallic extraction rate prediction task based on a systematic comparison of eight types of tree-based models. Furthermore, with the maximization of the average determination coefficient of the ten-fold cross-validation of the training set as the optimization objective, the Bayesian hyperparameter optimization algorithm is used to iteratively optimize the basic optimal model, which can improve the prediction accuracy of all models and effectively overcome the overfitting or underfitting defects caused by the default hyperparameter configuration of the model. The entire modeling process relies on the random division of the training set, validation set and test set and the ten-fold cross-validation mechanism to ensure the stability and reproducibility of model training, validation and testing. At the same time, the selected tree-based machine learning model is naturally compatible with missing values, and there is no need to fill or remove blank missing fields in the original dataset. It can perfectly adapt to the current situation that the experimental data in the literature generally have missing fields, saving the tedious steps of filling missing values ​​and removing invalid samples in traditional data processing, and effectively avoiding subjective errors caused by human data correction. Therefore, this application can provide a standardized and reproducible technical reference paradigm for intelligent modeling of similar photovoltaic solid waste wet recycling.

[0019] (2) Based on the optimal model after Bayesian optimization, this application uses the SHAP interpretability analysis method to calculate the SHAP value of each process parameter in each test sample through the interpreter of the adapted tree-based model. The average value of the absolute SHAP value of each process parameter is used as the global importance of the feature for ranking, thereby accurately quantifying the contribution weight and role of each process parameter to the silver and aluminum extraction rates. The SHAP quantification results reveal that there are significant differences in the main control parameters of the silver and aluminum recovery systems: the silver extraction rate is synergistically coupled and controlled by multiple processes such as solid-liquid ratio, acid concentration, acid leaching time, and reduction parameters, which is the result of the combined effect of multiple parameters in the whole process; the aluminum extraction rate is mainly determined by the acid leaching time and acid leaching temperature and other core acid leaching parameters in the acid leaching stage. The contribution weight of precipitation process parameters and reduction process parameters to the aluminum extraction rate is zero, and they have no regulatory effect. The direct contribution of EVA pretreatment parameters to the extraction rates of the two metals is low, and they can only play an auxiliary role in breaking the encapsulation structure. This application uses SHAP bee colony distribution diagrams to further demonstrate the changing trends of various process parameters in different value ranges, which can positively promote or negatively inhibit the extraction rate. This can achieve quantitative deconstruction of the multi-parameter coupling mechanism of wet acid leaching, and can make up for the shortcomings of traditional experimental methods in clarifying the multi-factor coupling relationship.

[0020] (3) The data-driven intelligent analysis system constructed in this application can quickly lock the optimal combination of process parameters for the simultaneous and efficient recovery of silver and aluminum without the need for extensive repetitive trial and error as required by traditional controlled variable experiments. This can significantly reduce the material and time costs of laboratory research and development. Specifically, based on the quantitative results of the SHAP interpretability analysis method, this application determines the core control parameters and priority order for the silver extraction system and the aluminum extraction system respectively: the process control priority for the silver extraction system is set as solid-liquid ratio first, acid concentration first, and acid concentration first, acid leaching time first; the process control priority for the aluminum extraction system is set as acid leaching time first, reduction temperature first, and reduction temperature first, acid leaching temperature first. The control direction of each core control parameter is determined according to the priority order. This technical solution can provide accurate data guidance and process control basis for the design of subsequent small-scale and pilot-scale test schemes, effectively reduce the blindness in the process development process, reduce the consumption of test materials and labor costs, accelerate the process optimization iteration speed, and provide a reliable theoretical basis and engineering reference for the industrialization of waste crystalline silicon photovoltaic resource utilization process. Meanwhile, this application can fill the research gap in intelligent modeling and parameter mechanism quantitative analysis of silver and aluminum bimetallic synergistic acid leaching, and can improve the technical system of photovoltaic solid waste resource recycling and circular economy. Attached Figure Description

[0021] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0022] Figure 1 A flowchart of a method for predicting and quantifying process parameters for wet recycling of silver-aluminum bimetallic waste photovoltaic cells based on Bayesian optimization CatBoost and SHAP is provided for embodiments of this application. Figure 2 The silver-based model R provided for the embodiments of this application 2 Ranking bar chart; Figure 3 The aluminum base model R provided for the embodiments of this application 2 Ranking bar chart; Figure 4 Scatter plot of prediction results for the CatBoost model provided in the embodiments of this application; Figure 5 Scatter plot of prediction results for the CatBoost optimal model for aluminum base provided in the embodiments of this application; Figure 6 Ranking graph of the optimized Silver Bayes model provided in the embodiments of this application; Figure 7 Ranking diagram of the aluminum Bayesian optimized model provided in the embodiments of this application; Figure 8Scatter plot of the optimal model after silver optimization (CatBoost) provided in the embodiments of this application; Figure 9 Scatter plot of the optimal aluminum-optimized model (CatBoost) provided in the embodiments of this application; Figure 10 This is a silver SHAP combination analysis diagram provided in the embodiments of this application; Figure 11 An analysis diagram of aluminum SHAP combinations provided in the embodiments of this application; Figure 12 The full-feature SHAP heatmap of silver and aluminum provided in the embodiments of this application.

[0023] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concepts of this application to those skilled in the art through reference to specific embodiments. Detailed Implementation

[0024] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0025] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0026] To address the limitations of traditional experimental methods in quantitatively elucidating the multi-factor coupling and correlation laws of simultaneous aluminum and silver acid leaching systems, and the lengthy trial-and-error optimization cycle and high R&D costs associated with such methods, this application, relying on a machine learning data-driven approach, provides a method for predicting and quantifying process parameters in the wet recycling of silver and aluminum bimetallic materials from waste photovoltaic systems based on Bayesian optimization of CatBoost and SHAP. This method enables intelligent prediction of valuable metals and quantitative analysis of parameter mechanisms within the wet acid leaching system of waste crystalline silicon photovoltaic systems. The method comprises six modules: literature data collection and screening, dataset construction, data standardization preprocessing, multi-tree-based machine learning model selection, Bayesian hyperparameter optimization, comprehensive model performance evaluation, and interpretable quantitative analysis of SHAP features. This application's method employs a multi-algorithm horizontal comparison, iterative hyperparameter tuning, optimal model selection, and a progressive analysis of the influence mechanisms of key process factors. By quantifying the independent effects and interactions of each variable through models, it provides comprehensive methodological support for accurate prediction of aluminum and silver leaching efficiency, intelligent selection of optimal acid leaching processes, and in-depth analysis of intrinsic reaction laws. All data cleaning, model training, parameter optimization, and feature analysis work is implemented programmatically using Python and mainstream open-source machine learning code libraries, ensuring standardization of the entire process and reproducibility of experimental results, laying the methodological foundation for subsequent intelligent optimization of acid leaching processes and industrial parameter selection.

[0027] like Figure 1 As shown, the method for predicting and quantifying process parameters of wet recycling of silver-aluminum bimetallic waste photovoltaic materials based on Bayesian optimization CatBoost and SHAP includes the following steps S10-S60.

[0028] S10: Obtain test data on the wet acid leaching recovery of silver and aluminum from waste crystalline silicon photovoltaic cells, clean the test data, convert non-standard content into missing values, retain the blank missing fields that are inherent in the original data, and obtain the original dataset.

[0029] For example, the original experimental data used in this embodiment were obtained by meta-analysis, which screened and compiled domestic and international journal articles and dissertations related to wet acid leaching recycling of waste photovoltaic modules within 15 years up to April 2026. The literature screening strictly followed the principle of matching research topics, retaining only experimental research data on wet acid leaching recycling of silver and aluminum metals, and eliminating irrelevant process literature such as pyrometallurgical recycling, physical sorting, and material modification. At the same time, invalid literature with incomplete experimental parameter records, missing key recycling indicators, and vague descriptions of experimental conditions was also screened out, so as to ensure the authenticity and validity of the original data to the greatest extent.

[0030] Based on the current state of experimental research, there are significant differences in the completeness of experimental procedures across different literature. Some studies only conduct basic EVA removal and acid leaching processes, recording only metal leaching rate data; a few complete experiments simultaneously complete the entire process of acid leaching, precipitation, and reduction, obtaining multi-stage recovery efficiency data for leaching, precipitation, and reduction. Due to limitations in existing experimental systems, aluminum metal recovery research mostly focuses on the acid leaching stage, with limited comprehensive precipitation and reduction experimental data. Therefore, aluminum extraction rate is modeled and analyzed solely based on acid leaching indicators. In contrast, silver metal recovery is supported by experimental data from the entire process, enabling the calculation and prediction modeling of the final extraction rate under multi-stage coupling.

[0031] Based on the differences in the characteristics of the two types of metal recycling data, this embodiment constructs two independent datasets for silver and aluminum to avoid interference from mixed parameters. The original dataset contains 23 process feature variables, fully covering the controllable process parameters of the entire EVA pretreatment, acid leaching, precipitation, and reduction process. It includes various data types such as categorical variables and continuous numerical variables, and the parameter units are uniformly standardized. Some experiments also include some silver- and aluminum-specific feature variables, which are uniformly set as missing values ​​in the other metal dataset. This ensures that the feature systems of the two datasets are independent and adapted to their respective recycling process characteristics, laying a data foundation for accurate prediction by multiple models in the future.

[0032] Considering the issues of disorganized formatting, missing fields, and non-standard annotations in literature review data, this embodiment utilizes the Pandas library for systematic data cleaning and preprocessing. It standardizes data conversion, converting non-standard content such as text annotations, garbled characters, and invalid symbols into missing values ​​while retaining the original blank fields from the literature. Unlike traditional data processing methods that require filling in missing values ​​or removing samples, this embodiment uses a tree-based model that is natively compatible with missing data. Therefore, missing value filling and invalid sample removal are not performed throughout the process, preserving the original distribution characteristics of the limited experimental data to the greatest extent possible, restoring the true engineering experimental patterns, and avoiding subjective errors caused by manual data correction.

[0033] S20: Based on the calculation logic of the indicators for silver and aluminum metal recycling, silver datasets and aluminum datasets are constructed respectively. The silver dataset is constructed by coupling the silver leaching rate, silver precipitation rate and silver reduction rate to calculate the final silver extraction rate of the whole process. The aluminum dataset is constructed by converting the aluminum acid leaching rate into the final aluminum extraction rate. Furthermore, the silver dataset and aluminum dataset respectively remove the other metal-specific features to form their own independent feature systems.

[0034] In this embodiment, the silver and aluminum datasets are constructed based on the original datasets obtained in step S10. Specifically, after data cleaning, independent datasets are constructed according to the calculation logic of the indicators for silver and aluminum metal recovery. The silver dataset is constructed based on valid silver leaching test samples, and the final extraction rate of the entire process is calculated by coupling the leaching rate, precipitation rate, and reduction rate. For samples lacking precipitation and reduction process data, a coefficient conversion method is used for unified standardization to ensure that all valid samples can participate in modeling. The aluminum dataset is based on the current research status, and the final extraction rate is equivalent to the acid leaching rate, completing the data standardization conversion. The two datasets respectively remove interference from the other metal-specific features to form a feature system adapted to their respective prediction tasks.

[0035] In some embodiments, based on the calculation logic of indicators for silver and aluminum metal recycling, silver datasets and aluminum datasets are constructed respectively through the following steps S201-S203.

[0036] S201: Select test samples with valid silver leaching rate records from the original dataset. For samples with missing precipitation rate and / or reduction rate fields, assign a value of 1 to the conversion factor of the missing precipitation and reduction processes, indicating that the missing process does not contribute to silver loss. Multiply the silver leaching rate by the conversion factor of each process to obtain the final silver extraction rate of the entire process. The silver dataset is formed by the silver leaching rate, precipitation rate, reduction rate and final silver extraction rate of each sample.

[0037] For example, suppose a test sample only records a silver leaching rate of 95%, but not the precipitation rate and reduction rate. Then, the conversion factor for the precipitation process and the reduction process for this sample are both set to 1, resulting in a final silver extraction rate of 95% × 1 × 1 = 95%. Suppose another test sample records a silver leaching rate of 90% and a precipitation rate of 98%, but not the reduction rate. Then, the conversion factor for the reduction process for this sample is set to 1, resulting in a final silver extraction rate of 90% × 98% × 1 = 88.2%. Through this conversion process, all samples with valid silver leaching rate records can be retained in the dataset for subsequent modeling, without needing to remove samples due to missing data for some processes. Therefore, given the current industry situation where existing literature generally lacks complete experimental data for precipitation and reduction processes, this approach maximizes the retention of limited valid test samples, expands the dataset size, and provides more sufficient sample support for subsequent model training.

[0038] S202: Select test samples with valid aluminum leaching rate records from the original dataset, use the aluminum acid leaching rate as the final aluminum extraction rate, and form an aluminum dataset from the aluminum acid leaching rate and process parameters of each sample.

[0039] Unlike the full-process recovery of silver, aluminum recovery research is mostly focused on the acid leaching stage, with limited comprehensive experimental data on precipitation and reduction. Therefore, using the acid leaching rate as the equivalent of the final extraction rate can maximize the coverage of existing aluminum recovery experimental data and avoid the rejection of a large number of samples due to a lack of data on post-processing steps.

[0040] S203: Keep the aluminum-specific features in the silver dataset as missing values, and keep the silver-specific features in the aluminum dataset as missing values.

[0041] For example, aluminum-specific features include process parameters applicable to aluminum acid leaching, such as sulfuric acid concentration, while silver-specific features include process parameters only related to silver precipitation and silver reduction processes, such as nitric acid concentration, precipitant dosage, and reducing agent dosage. When constructing the silver dataset, aluminum-specific feature fields such as sulfuric acid concentration are left blank, retaining them as missing values; similarly, when constructing the aluminum dataset, silver-specific feature fields such as nitric acid concentration, precipitant dosage, and reducing agent dosage are left blank, retaining them as missing values. Since the tree-based machine learning model subsequently selected in this application is naturally compatible with missing values, there is no need to fill in or remove samples from the aforementioned missing fields. Therefore, model training can be completed without introducing human interpolation errors, allowing the model to automatically learn the effective splitting rules of each feature.

[0042] Through the processing steps S201 to S203 described above, the experimental data containing a mixture of silver and aluminum in the original dataset were split into two datasets with independent feature systems and clear target value definitions. This not only makes full use of the fragmented experimental records of each process in the existing literature, but also avoids the interference of the unique features of different metals on model training, laying a data foundation for the accurate training of the subsequent extraction rate prediction models for the two types of metals.

[0043] S30: Randomly divide the silver dataset and aluminum dataset into training set, validation set and test set respectively, and build a ten-fold cross-validation mechanism based on the training set.

[0044] For example, to balance model training effectiveness and generalization performance verification, this embodiment uses an 8:1:1 partitioning ratio to randomly split the dataset into a training set, a validation set, and a test set. The training set is used for model fitting and hyperparameter optimization, while the test set is used to independently verify the model's generalization ability. A 10-fold cross-validation mechanism is constructed based on the training set to improve the stability of parameter optimization. All dataset partitioning operations use a fixed random seed to ensure reproducible experimental results, providing a unified data foundation for subsequent multi-model performance comparisons and hyperparameter optimization.

[0045] S40: Select multiple tree-based machine learning models and train them on the silver dataset and aluminum dataset respectively to obtain the prediction performance index of each basic model. Then, select the best basic model based on the prediction performance index, which includes the coefficient of determination, root mean square error and mean absolute error.

[0046] Given the characteristics of datasets containing a large number of random missing values ​​and the coupled correlation of multiple process parameters, traditional linear models and conventional machine learning models have poor adaptability. Therefore, tree-based models, which have strong compatibility with missing data and excellent ability to fit nonlinear laws, are uniformly selected for predictive modeling. To achieve the core research objective of horizontal comparison of multiple models and selection of the optimal suitable model, eight typical tree-based models are selected in an exemplary implementation, covering gradient boosting tree models, ensemble tree models, and single decision tree models of different complexities. Specifically, these include three mainstream gradient boosting tree models (CatBoost, XGBoost, and LightGBM), two bagging ensemble tree models (Random Forest and Extremely Random Tree), and three types of shallow, medium, and deep single decision tree models with maximum depths of 3, 5, and 10, forming a multi-gradient, multi-structure model comparison system.

[0047] All selected models possess the ability to natively handle missing values, adaptively learning the splitting patterns of missing features without manual preprocessing, and are highly adapted to the features of the dataset in this embodiment. The gradient boosting tree model continuously optimizes prediction accuracy through iterative fitting of residuals, while the ensemble tree model enhances generalization ability through multi-tree parallel voting. Single decision trees of different depths are used for comparative verification of the performance advantages of complex ensemble models. Through unified training and performance comparison of the eight models on silver and aluminum datasets, the optimal model suitable for predicting the recycling process of waste photovoltaic metals can be objectively selected, providing a reliable model carrier for subsequent hyperparameter optimization and feature interpretability analysis.

[0048] In some embodiments, to quantitatively evaluate the predictive performance of different models before and after optimization and to objectively select the optimal predictive model, this embodiment selects three core evaluation indicators commonly used in regression tasks: the coefficient of determination. Root mean square error Mean absolute error .in It is used to characterize the model's ability to explain the overall variation pattern of the dataset. The closer the value is to 1, the better the model fits and the stronger its explanatory power. and These three indicators are used to quantify the deviation between model predictions and actual experimental values. A smaller value indicates a smaller prediction error and higher stability. They complement each other, comprehensively reflecting the model's fitting accuracy and generalization ability, providing a unified and objective quantitative standard for cross-model comparisons and performance difference analysis before and after optimization. The calculation formulas for these indicators are as follows: in, For the first The true metal extraction rate of each sample For the first The model prediction extraction rate for each sample. The average of the true extraction rates for all samples. This represents the total number of samples in the test set.

[0049] Based on three evaluation metrics, this embodiment uses a unified visualization standard to draw the basic model and the Bayesian optimized model respectively. The ranking bar chart and the scatter plot of measured values ​​versus predicted values ​​of the best model at each stage intuitively present the hierarchical pattern of model performance and the effect of optimization, providing visual support for subsequent results analysis.

[0050] S50: With the goal of maximizing the average coefficient of determination of the 10-fold cross-validation of the training set, the Bayesian hyperparameter optimization algorithm is used to iteratively optimize the basic optimal model to obtain the optimal model after Bayesian optimization.

[0051] To address the issues of insufficient adaptability of default hyperparameters in models, leading to underfitting and overfitting, and to further explore the optimal performance of each model and maximize model accuracy, this embodiment introduces a Bayesian hyperparameter optimization algorithm to perform refined iterative optimization of the initially selected model. Compared to traditional optimization methods such as grid search and random search, Bayesian optimization relies on a Gaussian process to construct the posterior probability distribution of the objective function. It can dynamically update the optimization direction using historical iteration information, efficiently locking in the optimal hyperparameter combination within a limited number of iterations. Its optimization efficiency and accuracy are better suited to the modeling and optimization needs of this embodiment.

[0052] This embodiment focuses on maximizing the average coefficient of determination (R²) of the training set through 10-fold cross-validation. It performs targeted hyperparameter optimization on models with rich parameter spaces, such as CatBoost, XGBoost, LightGBM, and Random Forest. The optimization range is defined around key parameters like learning rate, maximum tree depth, and number of base learners, and a fixed number of 50 iterations is used for global optimization. For single-decision-tree and extreme random-tree models with simple structures and limited adjustable parameters, a fixed optimal parameter configuration is used for modeling. Hyperparameter optimization is performed independently on the silver and aluminum datasets to ensure the optimization results are adapted to the characteristics of their respective datasets. The core purpose of this optimization process is to overcome the performance bottleneck of default parameters, achieve iterative performance improvements for all models, and finally determine the unified optimal model for both datasets through horizontal comparison of the optimized models.

[0053] S60: Based on the optimal model after Bayesian optimization, the SHAP interpretability analysis method is used to quantify the contribution weight and effect of each process parameter on the silver extraction rate and aluminum extraction rate.

[0054] Machine learning models often suffer from the "black box problem," meaning that relying solely on prediction accuracy cannot reveal the intrinsic mechanism between process parameters and metal extraction rates, making it difficult to guide actual experimental optimization. To address this issue, this embodiment, based on the optimal model selected through Bayesian optimization, introduces the SHAP interpretability analysis method to quantitatively analyze the key process parameters affecting silver and aluminum metal recovery. The core objective is to clarify the weight and dynamic relationship of each process characteristic on the final recovery efficiency, providing theoretical guidance for subsequent experimental optimization and process control.

[0055] This embodiment employs the TreeExplainer interpreter, adapted to a tree-based model, to calculate SHAP values. It quantifies the marginal contribution of individual process parameters to the prediction results of a single sample, using the average absolute SHAP value to characterize the global importance of features and accurately prioritize the impact of all process parameters. The study also generates SHAP feature importance bar charts, swarm distribution maps, and silver-aluminum feature heatmaps. These not only visually display the core control parameters of a single metal recovery system but also allow for horizontal comparison of the differentiated impacts of similar parameters on silver and aluminum recovery, revealing the multi-parameter coupling mechanism from both qualitative and quantitative perspectives. This method provides core technical support for process parameter mechanism analysis and experimental optimization guidance, and is a key technical difference between this embodiment and traditional single-prediction modeling.

[0056] In some embodiments, step S60 specifically includes the following steps S601-S605.

[0057] S601: An interpreter that adopts an adapted tree-based model calculates the marginal contribution of each process parameter to the model prediction result relative to the baseline prediction value in each test sample based on the internal decision path of the optimal model after Bayesian optimization, and obtains the SHAP value of each process parameter on each sample.

[0058] S602: Take the absolute value of the SHAP value of each process parameter on all test samples and calculate the average value. Use this average value as the global importance of each process parameter. Sort all process parameters in the whole process in descending order to determine the main control parameters and secondary parameters that affect the extraction rate.

[0059] In this embodiment, the process parameters include EVA pretreatment parameters, acid leaching process parameters, precipitation process parameters, and reduction process parameters, wherein the acid leaching process parameters include solid-liquid ratio, acid concentration, acid leaching time, and acid leaching temperature.

[0060] S603: Based on the ranking of global importance of features, identify the top-ranking core control parameters and the bottom-ranking non-core influencing parameters in the silver extraction system and aluminum extraction system.

[0061] S604: For the silver extraction system and the aluminum extraction system respectively, generate SHAP feature importance bar charts to horizontally display the global importance and ranking of each process parameter; generate SHAP colony distribution map to correlate the SHAP value of each sample with the value of the corresponding process parameter, and show the changing trend of each process parameter in different value ranges, which has a positive promoting or negative inhibiting effect on the extraction rate. S605: Generate a full-feature SHAP heatmap of silver and aluminum, with process parameters as the horizontal axis, metal type as the vertical axis, and global importance of SHAP features as the fill color, to compare the differences in the contribution weight of the same process parameter in the silver extraction system and the aluminum extraction system.

[0062] Through the aforementioned processes S601 to S605, this application achieves a quantitative deconstruction of the multi-parameter coupling mechanism of wet acid leaching. The independent influence of each process parameter on the recovery rate is quantitatively separated from the complex multi-parameter coupling system, clarifying the primary and secondary control parameters for silver and aluminum recovery systems. Furthermore, the differential effects of the same process parameter in the two systems can be directly compared. This quantitative analysis not only verifies the different response characteristics of silver and aluminum due to differences in dissolution kinetics but also provides clear guidance for subsequent process optimization. Researchers can prioritize the control of high-ranking core parameters based on the global importance ranking of features, avoiding unnecessary experimental resources invested in non-core influencing parameters, thereby improving process optimization efficiency and reducing research and development costs.

[0063] In some embodiments, the method further includes: identifying the top three process parameters in the silver extraction system as core control parameters based on the ranking of SHAP feature importance, and identifying the process parameters of the precipitation and reduction processes as having a significant regulatory effect on the silver extraction rate; identifying the top three process parameters in the aluminum extraction system as core control parameters based on the ranking of SHAP feature importance, and identifying the precipitation and reduction process parameters as having a zero contribution weight to the aluminum extraction rate and no regulatory effect.

[0064] In this embodiment, the core directions for process optimization of each metal recovery system can be accurately identified by ranking the global importance of the SHAP feature. Specifically, for the silver extraction system, the solid-liquid ratio, acid concentration, and acid leaching time rank as the top three, indicating that the adjustment of these three parameters has the most significant impact on the overall silver recovery efficiency. The parameters of the precipitation and reduction processes also have a significant regulatory effect, because the overall silver recovery process involves three chemical reaction processes: leaching, precipitation, and reduction. Fluctuations in the parameters of each process will be transmitted along the process and accumulate, affecting the final extraction rate. For the aluminum extraction system, acid leaching time, reduction temperature, and acid leaching temperature rank as the top three, and the SHAP values ​​of the precipitation and reduction process parameters are close to zero. This indicates that aluminum recovery is entirely determined by the single-stage acid leaching reaction, and fluctuations in the parameters of the post-treatment processes will not have a real impact on the aluminum extraction rate, which is highly consistent with the process characteristics of aluminum, which only involves acid dissolution and has no subsequent precipitation or reduction losses. Therefore, researchers can focus on their respective core process links based on the differentiated main control parameter characteristics of different metals, avoiding the dispersion of experimental resources on ineffective control parameters.

[0065] In some embodiments, the method further includes: based on the quantitative results of the SHAP interpretability analysis method, determining the core control parameters and priority order of the silver extraction system and the aluminum extraction system respectively; setting the process control priority of the silver extraction system as solid-liquid ratio priority over acid concentration and acid concentration priority over acid leaching time, and setting the process control priority of the aluminum extraction system as acid leaching time priority over reduction temperature and reduction temperature priority over acid leaching temperature; determining the control direction of each core control parameter according to the priority order to obtain the optimal combination of process parameters for simultaneous and efficient recovery of silver and aluminum.

[0066] In this embodiment, based on the ranking of the contribution weights of each parameter and the changing trends of their positive and negative contributions revealed by the SHAP quantification results, the quantitative global importance of the features is further transformed into an operable process control strategy. For the silver extraction system, the control priority is configured in the order of solid-liquid ratio → acid concentration → acid leaching time, that is, the maximum recovery rate gain is obtained first by adjusting the solid-liquid ratio, and then the acid concentration and acid leaching time are optimized for fine adjustment. For the aluminum extraction system, the priority is configured in the order of acid leaching time → reduction temperature → acid leaching temperature. This priority ranking allows researchers to debug the parameters one by one in descending order of contribution weight when conducting process optimization experiments, and quickly lock the optimal process window with limited experimental resources. At the same time, combined with the positive and negative correlation between the values ​​of each parameter and the SHAP contribution in the SHAP swarm distribution diagram, the optimal control direction of each core control parameter can be further determined, and finally, an optimized combination scheme of process parameters for silver and aluminum can be formed, providing an executable technical path for the simultaneous and efficient recovery of silver and aluminum.

[0067] The feasibility and progressiveness of the method proposed in this application will be further illustrated below with specific experiments.

[0068] Specifically, this embodiment conducts a layer-by-layer pattern analysis based on the dataset preprocessing results, the performance indicators of the basic model and the Bayesian optimized model, and the SHAP feature parsing results. Combined with the accompanying visualization images, it analyzes the experimental patterns from three dimensions: data distribution, model performance evolution, and the influence mechanism of process parameters. The scientific validity of the method in this application is verified by relying on quantitative data and image information.

[0069] Analysis of dataset preprocessing results: After literature screening, illegal data cleaning, and dataset splitting, the silver and aluminum datasets exhibited data distribution patterns that closely matched the experimental characteristics of the original literature. In terms of sample composition, the silver dataset retained only experimental entries with valid silver leaching rate records. Samples with randomly missing precipitation and reduction rate fields were calculated according to predetermined conversion rules, with missing processes automatically assigned a conversion factor of 1, ensuring no valid experimental records were removed throughout the process. The aluminum dataset, constructed based on valid aluminum leaching data, lacked precipitation and reduction information due to limitations in existing literature data; the extraction rate was directly calculated from acid leaching indicators. In both datasets, dissimilar metal-specific features were uniformly filled with missing values, avoiding interference from irrelevant features on model training from the data source.

[0070] Analysis of the missing data distribution characteristics revealed a high proportion of missing parameters in EVA pretreatment and the entire precipitation and reduction process. The data completeness of core acid leaching process parameters such as acid leaching temperature, acid concentration, solid-liquid ratio, and acid leaching time was significantly better than that of parameters in preceding and subsequent processes. However, there were few systematic experiments conducted for precipitation and reduction, resulting in a significant lack of records for related process parameters. This embodiment employs a method of retaining missing values ​​and selecting a tree model suitable for the missing data. This method fully preserves the data missing characteristics inherent in the literature. Compared to preprocessing methods that involve censoring samples or interpolation for completion, it can objectively restore the distribution characteristics of real experimental data, ensuring that subsequent model training closely matches the actual process experimental patterns.

[0071] Analysis of Experimental Results of Basic Machine Learning Models: This embodiment utilizes eight tree models with default hyperparameter configurations to fit the silver and aluminum datasets and perform performance evaluation on the test set, combined with model R. 2 The ranking bar chart and the scatter plot of the best model prediction show that the prediction performance of different models in the two datasets exhibits a clear stratification pattern.

[0072] from Figure 2 Based on the ranking results, the silver-based model R 2 From highest to lowest: CatBoost > Random Forest > XGBoost > Medium Decision Tree > LightGBM > Shallow Decision Tree > Extremely Random Tree > Deep Decision Tree; Figure 3 Aluminum Basic Model R 2 The ranking is as follows: CatBoost > XGBoost > Extremely Random Tree > Random Forest > Deep Decision Tree > LightGBM > Medium Decision Tree > Shallow Decision Tree. CatBoost consistently ranks first in both the silver and aluminum datasets, becoming the best prediction model in the basic stage.

[0073] Overall, the three gradient boosting methods combined with the ensemble tree-like model in R... 2 Numerical performance consistently ranks among the top of all models. Random forest and extreme random tree performance are at a moderate level. The three single decision tree models with limited depth have the weakest overall fitting effect. Single decision trees, constrained by their simple model structure and limited fitting ability, struggle to capture the coupling relationships between multiple process parameters, ultimately exhibiting lower prediction accuracy. A horizontal comparison of the overall performance metrics of the models on the silver and aluminum datasets shows that the average R-value of each model on the aluminum side is... 2 The aluminum extraction rate is generally higher than that of the silver-side model. This phenomenon is caused by the difference in the definition of the target indicators of the two datasets. The aluminum extraction rate is determined by only the single acid leaching process, the variable coupling relationship is simple, and the inherent laws of the data are easy for the model to learn. The silver extraction rate involves three processes in series: leaching, precipitation and reduction. The multiple parameters are mutually constrained, the data coupling complexity is higher, and the fitting is more difficult under the same model conditions.

[0074] from Figure 4 , Figure 5 The distribution characteristics of the measured-predicted scatter points of the optimal base model are shown. The blue scatter points representing the training set mostly closely match the ideal predicted diagonal of y=x, indicating that CatBoost performs well on the training dataset under default parameters. In the silver test set, the red scatter points have a few isolated outliers in the range of 0.1 to 0.6, with excellent clustering in the high extraction rate range of 0.8 to 1.0. The overall deviation of the scatter points in the aluminum test set is much lower than that of the silver samples, with only a few isolated points slightly deviating from the baseline, further confirming the simple patterns and easier accurate prediction characteristics of aluminum recycling data. The local discrete deviations of the test samples demonstrate that the model has slight underfitting or overfitting issues under the default initial hyperparameter configuration. The hyperparameters have not yet adapted to the data characteristics of the photovoltaic recycling dataset, and there is still room for improvement in the model's generalization performance. This also provides necessary support for subsequent Bayesian hyperparameter optimization work.

[0075] Analysis of model performance changes after Bayesian hyperparameter optimization: like Figure 6 As shown, the optimized silver model R 2 Ranking: CatBoost > Random Forest > XGBoost > Extremely Random Tree > Shallow Decision Tree > Deep Decision Tree > Medium Decision Tree > LightGBM; Figure 7The ranking of the optimized aluminum dataset is shown as follows: CatBoost > XGBoost > Extremely Random Tree > Random Forest > Deep Decision Tree > LightGBM > Medium Decision Tree > Shallow Decision Tree. After optimization, CatBoost maintains its position as the best model across both datasets, while Gradient Boosting Tree and Ensemble Tree remain firmly in the top four. Analysis of the magnitude of metric changes shows that the overall performance improvement of all optimized models on the silver dataset is greater than that on the aluminum dataset. This is because the complex data features resulting from the multi-process coupling on the silver side are more sensitive to hyperparameters, with a larger deviation between default and optimal parameters, making the optimization effect more significant. The aluminum dataset has simpler data logic, and the default model parameters already achieve a good fit, limiting the performance improvement potential of hyperparameter optimization.

[0076] Comparison of measured-predicted scatter plots of the optimal model before and after optimization ( Figure 4 , Figure 5 , Figure 8 , Figure 9 As can be seen, the initial CatBoost model using the framework's default hyperparameters is limited by unreasonable configurations of key parameters such as learning rate, decision tree depth, and subsample sampling ratio. Furthermore, the inherent differences in the reaction mechanisms and data distributions of silver and aluminum wet acid leaching lead to overfitting and underfitting issues in different operating conditions before optimization. After 50 rounds of Bayesian iteration optimization to refine the parameters, the clustering of the red scatter points corresponding to the measured and predicted values ​​in the silver and aluminum test sets towards the ideal diagonal of y=x was significantly improved.

[0077] From the perspective of reaction mechanism, the silver recovery process involves a series of chemical reactions including acid leaching, chlorination precipitation, and liquid-phase reduction. The low extraction rate range is susceptible to disturbances from complex operating conditions such as insufficient reagents, side reactions, and particle agglomeration, resulting in higher data dispersion. The initial model struggled to accurately characterize the reaction patterns under these boundary conditions, leading to a large number of isolated outliers in the low extraction range before optimization. After global adaptation of hyperparameters, the model fully learned the reaction characteristics under low recovery conditions, significantly reducing the number of outliers in this range. In contrast, aluminum extraction relies solely on a single-step acid dissolution reaction, resulting in a simpler reaction path, fewer interfering factors, and stronger data distribution regularity. After optimization, the overall dispersion was further narrowed, with only a very few outliers remaining due to raw material impurities and localized experimental errors. Prediction biases for both systems were effectively controlled. From the perspective of optimization mechanism, Bayesian optimization relies on Gaussian processes to construct the posterior distribution of the objective function, fully reuses the model feedback information of each iteration to dynamically narrow the search range of optimal hyperparameters. Unlike blind grid traversal and random search, it can accurately match the different reaction inherent laws of the silver and aluminum systems, fundamentally improving the defects of underfitting (incomplete capture of reaction laws in key process intervals) and overfitting (overfitting data noise and random experimental errors) caused by parameter imbalance, and substantially improving the generalization prediction stability of the model on unfamiliar test samples.

[0078] Based on the above optimization results, this embodiment ultimately selects the optimal CatBoost model after Bayesian optimization as the basic carrier for SHAP quantization analysis. Thanks to the fact that the internal splitting logic of the CatBoost gradient boosting tree is highly adapted to the metallurgical reaction characteristics of multi-parameter nonlinear coupling in wet acid leaching, and that the model is natively adapted to the TreeExplainer solution framework, it can accurately decompose the marginal contribution of a single process parameter to the extraction rate. Based on this model, the analysis of feature importance and action mechanism can be carried out, which can ensure that the quantization results are consistent with the actual acid leaching reaction law to the greatest extent, and the conclusions obtained have reliable theoretical and engineering reference value.

[0079] SHAP Feature Interpretability Analysis: The SHAP quantitative analysis based on the optimized CatBoost model reveals the regulation law of the whole process parameters on the metal extraction rate from two dimensions: single metal feature ranking and horizontal comparison of silver and aluminum parameters. Combining the single metal SHAP combination diagram and the silver-aluminum shared thermogram enables both qualitative and quantitative analysis.

[0080] For silver extraction systems, from Figure 10The bar chart on the left side of the SHAP composite diagram, along with the numerical values ​​annotated on the heat map, clearly shows that the solid-liquid ratio (0.0484), acid concentration (0.0471), and acid leaching time (0.0463) are the top three core process parameters affecting the overall silver extraction rate. Reduction time and acid concentration follow closely behind. The importance of EVA removal-related process parameters and basic acid leaching parameters is in the medium range. The average SHAP values ​​of precipitation and stirring processes are generally low. The swarm diagram on the right side visually illustrates the trend of extraction rate changes caused by the rise and fall of different parameter values. For some process parameters, an increase in value within a reasonable range corresponds to a positive SHAP contribution, promoting improved silver extraction efficiency. However, exceeding the suitable range results in a negative contribution, inhibiting metal dissolution and enrichment. This provides a quantitative reference for the range control of process parameters.

[0081] like Figure 11 As shown, the SHAP analysis results of the aluminum extraction system are consistent with the aluminum data structure. The acid leaching time (0.0598), reduction temperature (0.0467), and acid leaching temperature (0.0415) are the three parameters with the highest weight in aluminum extraction, followed by the solid-liquid ratio and the concentration of acid. Since almost all of the precipitation and reduction-related features are missing values ​​in the entire dataset, the average SHAP value is close to 0, and they have basically no regulatory effect on the aluminum extraction rate. This result confirms the research premise that the aluminum extraction rate is completely determined by the acid leaching process from a data perspective, which is also consistent with the current situation that the original literature lacks experimental data on aluminum precipitation and reduction.

[0082] like Figure 12 As shown, the SHAP heatmap of silver and aluminum summarizes the quantitative contribution values ​​of all process parameters in the same visual chart. By comparing the strength of the same parameter in the two systems, it can be found that the SHAP values ​​of common acid leaching parameters such as acid leaching time and acid leaching temperature are generally higher for aluminum extraction than for silver extraction. The final recovery rate of silver is affected by the precipitation and reduction processes, which share the weight of the influence of acid leaching. Aluminum has no subsequent process losses, and the influence of acid leaching parameters is reflected entirely in the final extraction rate. The precipitation and reduction process parameters only have a significant SHAP contribution on the silver side, while the values ​​on the aluminum side are infinitely close to zero. The contribution of EVA pretreatment-related parameters to the extraction of both silver and aluminum is low. EVA removal only breaks the photovoltaic module encapsulation structure and does not directly participate in the acid dissolution reaction of the metal. Therefore, its direct control effect on the final extraction efficiency is limited, which is completely consistent with the reaction mechanism of hydrometallurgy.

[0083] In summary, this embodiment focuses on the core objective of predicting the entire process of wet recycling of silver and aluminum from waste photovoltaic modules. It completes a comprehensive methodology, from multi-source literature data preprocessing, multi-model comparative training, Bayesian hyperparameter optimization to feature interpretability analysis. The value of this application lies in two core aspects: model optimization and quantitative analysis of process parameters, effectively addressing the shortcomings of existing intelligent prediction and quantitative research on process mechanisms in photovoltaic metal recycling. Regarding model iteration and optimization, this embodiment addresses the common industry pain point of datasets containing a large number of random missing values. It uniformly employs eight types of tree-based models that are natively compatible with missing data to complete the prediction modeling for both silver and aluminum datasets. Through initial training and performance ranking of the basic models, the adaptability advantage of the ensemble tree model in photovoltaic recycling process prediction scenarios is preliminarily verified. Based on this, a Bayesian hyperparameter optimization algorithm is introduced to perform refined parameter iteration and optimization on all models. The results are compared before and after optimization. 2 A horizontal comparison of the three core evaluation indicators, RMSE and MAE, clearly demonstrates that hyperparameter optimization can effectively overcome the performance bottleneck of default model parameters, comprehensively improve the generalization ability and prediction accuracy of various models, and finally select the unified optimal model for predicting the extraction rate of silver and aluminum bimetals—CatBoost—through multi-dimensional performance comparison. This provides a high-precision and high-reliability model carrier for subsequent feature importance analysis and also provides a standardized reference paradigm for the selection and optimization of machine learning models in the field of photovoltaic wet recycling.

[0084] At the level of process research and engineering guidance, this embodiment abandons the limitations of traditional machine learning models that "only predict and do not explain." Based on the optimized CatBoost model, it conducts a systematic SHAP interpretability analysis, accurately quantifying the influence weights and patterns of the entire set of process parameters on the final extraction rates of silver and aluminum, and clearly distinguishing the core controlled parameters and secondary influencing parameters of the two metal recovery systems. The overall silver extraction efficiency is synergistically regulated by multiple process variables such as solid-liquid ratio, acid concentration, acid leaching time, and reduction parameters, exhibiting complex response characteristics of multi-process coupling. Aluminum extraction efficiency is mainly dominated by the core acid leaching process parameters, with subsequent precipitation and reduction processes having no significant impact. This quantitative result accurately reveals the differentiated control mechanisms of the silver and aluminum wet recovery processes. Compared to traditional single-control variable experiments that can only qualitatively determine the influence of parameters, this embodiment achieves precise ranking of the importance of process parameters through SHAP numerical quantification, clarifying the core focus and secondary directions for subsequent experimental optimization.

[0085] In summary, the method presented in this application not only achieved optimal iteration and performance verification of the prediction model for the entire process of silver-aluminum extraction from photovoltaic modules, but more importantly, it resolved the ambiguity of the multi-parameter coupling mechanism in wet recycling through interpretability analysis, and quantitatively identified key process control factors. This method can provide clear data guidance for the experimental design, parameter tuning, and process optimization of subsequent acid leaching recycling of waste photovoltaic modules, effectively reducing experimental blindness, lowering experimental costs, and improving the efficiency of recycling process optimization. Simultaneously, it fills the research gap in intelligent modeling and quantitative analysis of parameter mechanisms for the entire photovoltaic metal recycling system, providing a feasible technical approach for subsequent research on intelligent prediction and process optimization of similar solid waste resource utilization.

[0086] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A method for predicting and quantifying process parameters in the wet recycling of silver-aluminum bimetallic waste photovoltaic cells based on Bayesian optimization CatBoost and SHAP, characterized in that, The method includes: Test data on the wet acid leaching recovery of silver and aluminum from waste crystalline silicon photovoltaic cells were obtained, and the test data were cleaned. Non-standard content was uniformly converted into missing values, while the blank missing fields of the original data were retained to obtain the original dataset. Based on the calculation logic of indicators for silver and aluminum metal recycling, silver datasets and aluminum datasets are constructed respectively. The silver dataset is constructed by coupling the silver leaching rate, silver precipitation rate and silver reduction rate to calculate the final silver extraction rate of the entire process. The aluminum dataset is constructed by using the aluminum acid leaching rate as an equivalent of the final aluminum extraction rate. Furthermore, the silver dataset and the aluminum dataset respectively remove the other metal-specific features to form their own independent feature systems. The silver dataset and the aluminum dataset are randomly divided into training set, validation set and test set, respectively, and a ten-fold cross-validation mechanism is constructed based on the training set; Multiple tree-based machine learning models were selected and trained on the silver dataset and the aluminum dataset respectively to obtain the prediction performance index of each basic model. The optimal basic model was selected based on the prediction performance index, wherein the prediction performance index includes the coefficient of determination, root mean square error and mean absolute error. With the goal of maximizing the average coefficient of determination of the 10-fold cross-validation of the training set, the Bayesian hyperparameter optimization algorithm is used to iteratively optimize the basic optimal model to obtain the optimal model after Bayesian optimization. Based on the optimal model after Bayesian optimization, the SHAP interpretability analysis method is used to quantify the contribution weight and effect of each process parameter on the silver extraction rate and aluminum extraction rate.

2. The method according to claim 1, characterized in that, Based on the calculation logic of indicators for silver and aluminum metal recycling, silver datasets and aluminum datasets are constructed respectively, including: Test samples with valid silver leaching rate records are selected from the original dataset. For samples with missing precipitation rate and / or reduction rate fields, the conversion factor of the missing precipitation and reduction processes is assigned to 1, indicating that the missing process does not contribute to silver loss. The silver leaching rate is multiplied by the conversion factor of each process to obtain the final silver extraction rate of the entire process. The silver dataset is formed by the silver leaching rate, precipitation rate, reduction rate and final silver extraction rate of each sample. Test samples with valid aluminum leaching rate records are selected from the original dataset. The aluminum acid leaching rate is used as the final aluminum extraction rate. The aluminum dataset is formed by the aluminum acid leaching rate and process parameters of each sample. The aluminum-specific features in the silver dataset are kept as missing values, and the silver-specific features in the aluminum dataset are kept as missing values.

3. The method according to claim 1, characterized in that, The various tree-based machine learning models include gradient boosting tree models, Bagging ensemble tree models, and single decision tree models; the gradient boosting tree models include CatBoost, XGBoost, and LightGBM; the Bagging ensemble tree models include random forests and extreme random trees; and the single decision tree models include single decision trees with maximum depths of 3, 5, and 10.

4. The method according to claim 1, characterized in that, The coefficient of determination The root mean square error and the mean absolute error Calculate according to the following formulas respectively: in, For the first The true metal extraction rate of each sample For the first The model prediction extraction rate for each sample. The average of the true extraction rates for all samples. This represents the total number of samples in the test set.

5. The method according to claim 3, characterized in that, The basic optimal model is selected based on the aforementioned predictive performance metrics, including: The determination coefficients of each base model on the silver dataset and the aluminum dataset are sorted respectively; The CatBoost model with the highest determination coefficient was selected as the base optimal model on both the silver dataset and the aluminum dataset.

6. The method according to claim 1, characterized in that, The basic optimal model is iteratively optimized using a Bayesian hyperparameter optimization algorithm to obtain the optimal Bayesian model, including: Obtain a set of candidate hyperparameter combinations for the basic optimal model, perform 10-fold cross-validation on the training set for the set of candidate hyperparameter combinations, and calculate the corresponding average coefficient of determination. Based on the evaluated combinations of multiple candidate hyperparameters and their corresponding average coefficients of determination, a posterior probability distribution of the objective function is constructed using a Gaussian process to characterize the current confidence level in the region where the optimal hyperparameters are located. Based on the posterior probability distribution, the next set of candidate hyperparameter combinations to be evaluated is calculated using the acquisition function, so that the evaluation direction tends toward the global optimal region, wherein the acquisition function is used to measure the evaluation priority of each candidate hyperparameter combination. The next set of candidate hyperparameter combinations to be evaluated is substituted back into the basic optimal model for 10-fold cross-validation, the corresponding average coefficient of determination is calculated, and the newly obtained candidate hyperparameter combinations and their corresponding average coefficients of determination are added to the historical data to update the posterior probability distribution. Repeat the above evaluation and update process until the preset number of iterations is reached. Select the candidate hyperparameter combination with the highest average coefficient of determination in the historical data as the optimal hyperparameter configuration. Assign the optimal hyperparameter configuration to the basic optimal model to obtain the optimal model after Bayesian optimization.

7. The method according to claim 1, characterized in that, Based on the optimal model after Bayesian optimization, the SHAP interpretability analysis method is used to quantify the contribution weight and effect of each process parameter on the silver extraction rate and aluminum extraction rate, including: An interpreter adapted to the tree-based model is used. Based on the internal decision path of the optimal model after Bayesian optimization, the marginal contribution of each process parameter to the model prediction result relative to the baseline prediction value is calculated in each test sample, and the SHAP value of each process parameter on each sample is obtained. The absolute values ​​of the SHAP values ​​of each process parameter on all test samples were taken and the average value was calculated. This average value was used as the global importance of each process parameter. All process parameters in the entire process were sorted in descending order to determine the main and secondary parameters that affect the extraction rate. Based on the ranking of the global importance of the features, identify the top-ranking core control parameters and the bottom-ranking non-core influencing parameters in the silver extraction system and the aluminum extraction system. For the silver extraction system and the aluminum extraction system, SHAP feature importance bar charts are generated to horizontally display the global importance and ranking of each process parameter. SHAP colony distribution map is generated to correlate the SHAP value of each sample with the value of the corresponding process parameter, showing the changing trend of each process parameter in different value ranges, which has a positive promoting or negative inhibiting effect on the extraction rate. Generate a full-feature SHAP heatmap of silver and aluminum, with process parameters as the x-axis, metal type as the y-axis, and global importance of SHAP features as the fill color, and compare the differences in the contribution weight of the same process parameter in the silver extraction system and the aluminum extraction system.

8. The method according to claim 7, characterized in that, The process parameters include EVA pretreatment parameters, acid leaching process parameters, precipitation process parameters, and reduction process parameters, wherein the acid leaching process parameters include solid-liquid ratio, acid concentration, acid leaching time, and acid leaching temperature.

9. The method according to claim 8, characterized in that, After quantifying the contribution weights and effects of each process parameter on the silver and aluminum extraction rates, the method further includes: Based on the ranking of the importance of the SHAP features, the top three process parameters in the silver extraction system are identified as the core control parameters, and the process parameters of the precipitation and reduction processes are identified as having a significant regulatory effect on the silver extraction rate. Based on the ranking of the importance of the SHAP features, the top three process parameters in the aluminum extraction system are identified as the core control parameters, and the precipitation process parameters and reduction process parameters are identified as having zero contribution weight to the aluminum extraction rate and therefore no regulatory effect.

10. The method according to claim 1, characterized in that, After quantifying the contribution weights and effects of each process parameter on silver and aluminum extraction rates, the following is also included: Based on the quantitative results of the SHAP interpretability analysis method, the core control parameters and priority rankings for the silver extraction system and the aluminum extraction system were determined respectively. The process control priority for the silver extraction system was set as follows: solid-liquid ratio takes precedence over acid concentration, and acid concentration takes precedence over acid leaching time. The process control priority for the aluminum extraction system was set as follows: acid leaching time takes precedence over reduction temperature, and reduction temperature takes precedence over acid leaching temperature. Based on the priority order, the control direction of each core control parameter is determined, resulting in the optimal combination of process parameters for the simultaneous and efficient recovery of silver and aluminum.

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