Optimization method, device, equipment and medium for sustainable lithium recovery from waste lithium iron phosphate batteries

Abstract

The application provides a sustainable lithium recovery optimization method, device, equipment and medium for waste lithium iron phosphate battery, and relates to the technical field of resource recovery. The method comprises the following steps: obtaining historical leaching experiment data, constructing and preprocessing an associated database; training an adaptive physical information integrated model comprising a physical information neural network, CatBoost and K-nearest neighbors; inputting process parameters to be optimized into three models to obtain basic prediction values, determining adaptive weights of each model based on local neighborhood information, and obtaining a predicted lithium leaching rate through weighted summation; ensuring the prediction physical consistency through a loss function embedded with the Arrhenius kinetics law; calculating the energy value output rate through an energy value accounting module to quantify the resource conversion efficiency; and adopting Bayesian optimization for iterative optimization to obtain a high leaching rate candidate scheme set and select an optimal scheme. The method overcomes the defect of physical inconsistency of traditional models, and realizes the collaborative optimization of technical efficiency and ecological sustainability.

Description

Technical Field

[0001] This invention relates to the field of resource recycling technology, and in particular to an optimized method, apparatus, equipment, and medium for the sustainable lithium recycling of waste lithium iron phosphate batteries. Background Technology

[0002] The global transition to electric transportation has driven unprecedented demand for lithium-ion batteries. Due to their inherent safety and economic advantages, lithium iron phosphate (LiFePO4, LFP) batteries are currently generating over 400,000 tons of waste annually, a figure projected to exceed 1.5 million tons by 2030. This impending surge in waste urgently necessitates the development of highly scalable and efficient resource recycling strategies. Unlike nickel-rich cathodes, lithium extraction from waste LFP is hampered by the superior structural stability of the olivine lattice and the competitive kinetics of iron-phosphate precipitation. These chemical properties make the LFP leaching process a complex network of synergistic and antagonistic interactions. This systemic complexity imposes significant limitations on traditional optimization methods.

[0003] Methodological advancements in this field have progressed from traditional single-factor, one-off experimental (OFAT) designs to multivariate statistical optimization. Early research focused on identifying isolated parameter sensitivities by changing a single factor while keeping other factors constant. While these studies provided baseline trends, they inherently ignored the synergistic dependence of the effects of temperature or stoichiometry on the fundamental alteration of background acid concentration. Subsequent research employed response surface methodology (RSM), using quadratic polynomial fitting to capture the interactions between parameters. However, it is now widely recognized that RSM, limited by its dependence on predefined mathematical forms, cannot accommodate the nonlinear singularities and sharp stoichiometric thresholds observed in LFP dissolution. Detailed kinetic analyses confirm that leaching efficiency is governed by a strong dependence between activation energy and chemical equilibrium. This complexity necessitates a shift towards advanced data-driven modeling methods capable of internalizing these underlying physicochemical interdependencies without being constrained by rigid functions.

[0004] Against this backdrop, machine learning (ML) has emerged as a transformative tool, demonstrating immense potential in optimizing resource recycling processes. High-precision predictive models have been established for copper recycling from waste printed circuit boards and for zinc-manganese batteries. Specifically, regression-based predictions have been achieved for ternary cathode materials and lithium iron phosphate. However, these architectures typically operate as black boxes, failing to incorporate the fundamental chemical principles controlling metal dissolution. This lack of mechanistic foundation can lead to physically inconsistent predictions in data-sparse regions, such as violations of the Arrhenius dependence of reaction rates on temperature. These limitations hinder the reliability of model-based extrapolation, thus highlighting the critical need for a physical-information architecture that couples thermodynamic constraints with machine learning.

[0005] Beyond predictive fidelity, a common blind spot in current process optimization is the overemphasis on single-objective leaching yields while neglecting overall environmental costs. This performance-centric approach can lead to a sustainability paradox—minor technological improvements require aggressive reagent dosages, potentially offsetting the eco-benefits of material recovery. To address this, a comprehensive evaluation system is needed to reconcile technological gains with systemic environmental support. Emergy analysis provides a scientific framework for this by assessing the leverage effect between eco-economic inputs and recovered material outputs. Unlike traditional assessments, emergy accounting evaluates energy quality differences in solar joules (sej). However, emergy assessment has historically been a static and retrospective tool. A methodological gap remains in the proactive synergistic optimization of technology recovery and system performance efficiency, a capability crucial for identifying truly sustainable operational windows. Summary of the Invention

[0006] This invention provides an optimized method, apparatus, device, and medium for the sustainable lithium recycling of spent lithium iron phosphate batteries. It aims to ensure physical consistency by embedding mechanistic dynamics laws into a nonlinear machine learning model through the construction of an Adaptive Physical Information Integration (APIE) model. By coupling this predictive capability with a system performance value calculation module, it coordinates the technology recycling yield with the system performance value efficiency, effectively shifting the optimization focus from narrow performance indicators to overall resource conversion efficiency. Unlike univariate or purely data-driven methods, this invention provides analytical resolution that elucidates cross-system nonlinear dependencies and accurately assesses the leverage effect between eco-economic inputs and material outputs.

[0007] In a first aspect, the present invention provides an optimized method for sustainable lithium recycling of spent lithium iron phosphate batteries, the method comprising: Historical leaching experiment data were obtained, and a correlation database including raw material parameters, process parameters and lithium leaching rate was constructed. The data in the correlation database were then cleaned and normalized to obtain a standardized dataset. Based on the standardized dataset, an adaptive physical information ensemble model is trained, which includes a physical information neural network, a CatBoost model, and a K-nearest neighbor model. The process parameters to be optimized are input into the trained adaptive physical information ensemble model to obtain the predicted lithium leaching rate. This includes: inputting the process parameters to be optimized into the physical information neural network, the CatBoost model, and the K-nearest neighbor model respectively to obtain their respective basic predicted values; determining the adaptive weights of the physical information neural network, the CatBoost model, and the K-nearest neighbor model based on the local neighborhood information of the process parameters to be optimized in the feature space; and weighting and summing the basic predicted values ​​of the physical information neural network, the CatBoost model, and the K-nearest neighbor model according to their respective adaptive weights to obtain the predicted lithium leaching rate. Based on the predicted lithium leaching rate, the energy value output rate is calculated by the energy value accounting module. The energy value output rate is the ratio of total energy value output to total energy value input. With the goal of maximizing the lithium leaching rate, a Bayesian optimization algorithm is used to generate candidate solutions for each acid system within the parameter feasible region. For each acid system, the upper quartile thresholds of the lithium leaching rate and energy yield of the candidate solutions are determined. Candidate solutions that are not lower than both thresholds are formed into a set of excellent performance candidates. The candidate solution with the highest lithium leaching rate in the set of excellent performance candidates is determined as the recommended optimal leaching solution for the acid system.

[0008] In one possible design, the training process of the physical information neural network includes: The semi-empirical kinetic model is embedded in the loss function of the physical information neural network. The semi-empirical kinetic model defines the rate of change of lithium leaching rate based on the reaction rate constant, reaction time, and reaction order. (1) in, It is the lithium leaching rate. It is the reaction time. It is the reaction order. , where is the reaction rate constant, T is the reaction temperature in °C, Cacid is the acid concentration in mol / L, and Cox is the molar ratio of oxidant to lithium, which in this example is the molar ratio of H2O2 / Li. Calculate the reaction rate constant using the following formula: (2) Where A is the pre-exponential factor, and exp is the natural exponential function. As the apparent activation energy, R The molar gas constant, a The reaction order is determined by the acid concentration. b The reaction order is the molar ratio of the oxidant to lithium. The total loss function for constructing the physical information neural network is expressed as follows: (3) in, Let E be the total loss function, E be the expectation operator (averaged across samples during batch training), and λ be the weighting coefficient between the data loss and the physical residual loss. For the predicted lithium leaching rate, For physical residuals, ; Based on the standardized dataset, the training of the physical information neural network is completed by minimizing the total loss function and simultaneously optimizing the network weights and the learnable physical parameters in the semi-empirical dynamics model.

[0009] In one possible design, based on the local neighborhood information of the process parameters to be optimized in the feature space, the adaptive weights of the physical information neural network, the CatBoost model, and the K-nearest neighbor model are determined respectively, including: For the target prediction point corresponding to the process parameter to be optimized, its K nearest neighbor samples are identified in the feature space, and the local determination coefficients of each base model in the physical information neural network, the CatBoost model, and the K nearest neighbor model on the nearest neighbor samples are calculated; the formula for calculating the local determination coefficients is: (4) in, It is the basic model The local coefficient of determination, It is the target prediction point. It is the set of K nearest neighbor samples. It is the true value of the sample. It is the basic model The predicted value, It is the average of the true values ​​within the set. Based on the local determination coefficients, calculate the adaptive weights for each base model; (5) in, Basic Model Adaptive weights, Indicates the index of the base model. This indicates taking the maximum value. Representation of the basic model The local coefficient of determination.

[0010] In one possible design, a model interpretation step is also included, which quantifies the impact of various process parameters on the lithium leaching rate, specifically including: The global importance of each process parameter is quantified based on normalized importance; the formula for calculating the global importance is as follows: (6) in, and It is a parameter and Importance metrics This is the total number of parameters; Based on the SHapley additive interpretation method, the marginal contribution value of each process parameter to a single predicted sample is calculated, and a summary attribution plot is generated to visualize the positive and negative influence direction of each process parameter on the lithium leaching rate. Based on the partial dependency graph analysis, the average response of the lithium leaching rate is simulated when a single process parameter changes, and the single-factor response curves of each process parameter are compared to identify the nonlinear influence of each process parameter.

[0011] In one possible design, the emergy accounting module calculates the emergy output rate using the following formula. : (7) in, For output energy value, Energy input; The formula for calculating the energy output value is as follows: (8) in, It is the lithium mass fraction in the black powder. This is the predicted lithium leaching rate. and These are the molar masses of lithium carbonate and lithium, respectively. It is the energy value per unit of production of primary lithium carbonate, g is the mass unit gram, 1 g means that 1 g of black powder is used as the accounting basis; The formula for calculating the input energy value is as follows: (9) in, This is the operating energy consumption value. It is the energy value of chemical reagent production. It is the environmental remediation cost energy value, which is calculated differently based on the characteristic pollutants of the acid leaching path.

[0012] In one possible design, with the objective of maximizing the lithium leaching rate, a Bayesian optimization algorithm is used to iteratively optimize within the feasible region of the parameters, including: Using the trained adaptive physical information ensemble model as an alternative objective function for Bayesian optimization, the optimization problem is defined according to the following formula: (10) in, It is an input vector that includes eight process parameters. It is the feasible region of the parameters. It is the predicted lithium leaching rate output by the adaptive physical information integration model; A probabilistic proxy model is constructed with a Gaussian process as the objective function, and the sampling function is improved by maximizing the expectation. The next sampling point is iteratively selected within the feasible region of the parameters to approximate the global optimal solution that maximizes the lithium leaching rate.

[0013] In one possible design, the optimal leaching scheme is selected from the candidate scheme set based on the lithium leaching rate and energy yield according to the acid system, including: Multiple candidate process parameter combinations are generated for each acid system using a Bayesian optimization algorithm, forming a candidate scheme set for the corresponding acid system; Call the energy value calculation module to calculate the energy value output rate corresponding to each scheme in the candidate scheme set of each acid system; For each acid system, the upper quartile thresholds of lithium leaching rate and energy yield of candidate schemes are calculated. Candidate schemes that are not lower than both thresholds are formed into a set of excellent performance candidates. The candidate scheme with the highest lithium leaching rate in the set of excellent performance candidates is taken as the recommended optimal leaching scheme for the acid system.

[0014] Secondly, the present invention provides an optimized device for sustainable lithium recycling of spent lithium iron phosphate batteries, the device comprising: The data preprocessing module is configured to acquire historical leaching experiment data, construct a correlation database including raw material parameters, process parameters and lithium leaching rate, and clean and normalize the data in the correlation database to obtain a standardized dataset. The model training module is configured to train an adaptive physical information ensemble model based on the standardized dataset, the adaptive physical information ensemble model including a physical information neural network, a CatBoost model and a K-nearest neighbor model; The lithium leaching rate prediction module is configured to input the process parameters to be optimized into the trained adaptive physical information ensemble model to obtain the predicted lithium leaching rate. This includes: inputting the process parameters to be optimized into the physical information neural network, the CatBoost model, and the K-nearest neighbor model respectively to obtain their respective basic prediction values; determining the adaptive weights of the physical information neural network, the CatBoost model, and the K-nearest neighbor model based on the local neighborhood information of the process parameters to be optimized in the feature space; and performing a weighted summation of the basic prediction values ​​of the physical information neural network, the CatBoost model, and the K-nearest neighbor model based on their respective adaptive weights to obtain the predicted lithium leaching rate. The regrid output rate calculation module is configured to calculate the regrid output rate based on the predicted lithium leaching rate through the regrid accounting module, wherein the regrid output rate is the ratio of total regrid output to total regrid input. The optimal leaching scheme screening module is configured to generate candidate schemes for each acid system within the parameter feasible region using a Bayesian optimization algorithm with the objective of maximizing the lithium leaching rate. For each acid system, the upper quartile thresholds of the lithium leaching rate and energy yield of the candidate schemes are determined. Candidate schemes that are not lower than both thresholds are formed into an excellent performance candidate set, and the candidate scheme with the highest lithium leaching rate in the excellent performance candidate set is determined as the recommended optimal leaching scheme for the acid system.

[0015] Thirdly, embodiments of the present invention provide an electronic device, comprising: at least one processor and a memory; the memory storing computer execution instructions; the at least one processor executing the computer execution instructions stored in the memory, causing the at least one processor to perform the optimized method for sustainable lithium recycling of waste lithium iron phosphate batteries as described in the first aspect and various possible designs of the first aspect.

[0016] Fourthly, embodiments of the present invention provide a computer-readable storage medium storing computer-executable instructions. When a processor executes the computer-executable instructions, it implements the optimized method for sustainable lithium recycling of waste lithium iron phosphate batteries as described in the first aspect and various possible designs of the first aspect.

[0017] Fifthly, embodiments of the present invention provide a computer program product, including a computer program that, when executed by a processor, implements the optimized method for sustainable lithium recycling of waste lithium iron phosphate batteries as described in the first aspect and various possible designs of the first aspect.

[0018] The optimized method, apparatus, equipment, and medium for sustainable lithium recycling of spent lithium iron phosphate batteries provided by this invention have at least the following beneficial effects: (1) This invention trains an adaptive physical information ensemble model that includes a physical information neural network, a CatBoost model, and a K-nearest neighbor model. The process parameters to be optimized are input into the three models to obtain basic predicted values. The adaptive weights of each model are determined based on local neighborhood information, and the predicted lithium leaching rate is obtained by weighted summation. This invention utilizes a mechanistic model to ensure the physical consistency of sparse data regions and uses a data-driven model to capture global nonlinear interactions and local patterns, thereby improving the prediction accuracy (test set R). 2 The result is 0.9934, which aligns with the physical rationality.

[0019] (2) This invention embeds the semi-empirical dynamic model and its Arrhenius-type rate constant formula into the loss function of the physical information neural network, and uses the physical residual as a constraint term for network training, so that the model prediction strictly follows the laws of chemical reaction kinetics and avoids the defect of physical inconsistency prediction in the sparse data region.

[0020] (3) By introducing a model interpretation step, this invention uses normalized importance analysis, SHapley additive interpretation method and partial dependency graph analysis to quantify the global importance, local marginal contribution and nonlinear response and interaction of each process parameter on lithium leaching rate, providing an interpretable decision basis for process optimization.

[0021] (4) This invention calculates the ratio of output energy value to input energy value as energy value output rate through the energy value accounting module, and incorporates technology recovery efficiency and systematic ecological and economic input into a unified measurement framework, overcoming the limitation of traditional single-objective optimization that ignores environmental costs, and realizing the synergistic optimization of technology efficiency and ecological sustainability.

[0022] (5) This invention uses Bayesian optimization algorithm with adaptive physical information integration model as alternative objective function for iterative optimization, and combines energy value output rate to screen candidate schemes. It can efficiently identify the optimal process scheme with high leaching rate and high resource conversion efficiency within a small number of evaluations, and provide a reliable technical template for the sustainable design of hydrometallurgical recycling process. Attached Figure Description

[0023] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0024] Figure 1 The following is a schematic diagram of the mechanism and operation framework of a Sustainable Leach Evaluation and Optimization (SLEO) system for realizing a sustainable lithium recycling optimization method for waste lithium iron phosphate batteries, provided in an embodiment of the present invention. Figure 2The optimized base model and APIE framework provided in this embodiment of the invention are used to verify the prediction performance on a test dataset. Figure 3 This is a schematic diagram of global feature importance and local attribution analysis performed by SHAP according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the one-dimensional partial dependency response of eight features provided in an embodiment of the present invention; Figure 5 A schematic diagram illustrating the trade-off between acid differences and lithium leaching efficiency and energy yield (EYR) provided for embodiments of the present invention; Figure 6 A schematic diagram highlighting the non-dominated solution for sustainable lithium recovery in the identification of the Pareto optimal front provided in this embodiment of the invention; Figure 7 A detailed parameter analysis diagram of the superior performance region provided in the embodiments of the present invention; Figure 8 This is a schematic diagram of the violin plot distribution of various numerical features in the lithium iron phosphate leaching dataset provided in this embodiment of the invention; Figure 9 A schematic diagram of the Spearman rank correlation matrix showing the relationship between various features provided in an embodiment of the present invention; Figure 10 A schematic diagram showing the comparison between predicted and observed values ​​of lithium leaching rate using 14 machine learning algorithms provided in this embodiment of the invention. Figure 11 This is a schematic diagram illustrating the predictive performance of each hyperparameter-optimized model for lithium leaching rate provided in the embodiments of the present invention. Figure 12 This is a structural diagram of the optimized device for sustainable lithium recycling of spent lithium iron phosphate batteries provided in an embodiment of the present invention.

[0025] The accompanying drawings have illustrated specific embodiments of the invention, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the invention in any way, but rather to illustrate the concept of the invention to those skilled in the art through reference to specific embodiments. Detailed Implementation

[0026] 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 numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of apparatuses and methods consistent with some aspects of the invention as detailed in the appended claims.

[0027] In the technical solution of this invention, the collection, storage, use, processing, transmission, provision and disclosure of relevant data and information comply with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0028] It should be noted that in the embodiments of the present invention, certain software, components, models and other existing solutions in the industry may be mentioned. These should be regarded as exemplary and are only intended to illustrate the feasibility of implementing the technical solution of the present invention. However, they do not mean that the inventor has used or necessarily used the solution.

[0029] The technical solution of the present invention and how the technical solution of the present invention 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 the present invention will now be described with reference to the accompanying drawings.

[0030] This invention provides an optimized method for sustainable lithium recycling of spent lithium iron phosphate batteries, based on the following... Figure 1 The Sustainable Leach Assessment and Optimization (SLEO) system demonstrated is implemented to achieve multidimensional optimization of technology recovery and resource conversion efficiency in lithium iron phosphate (LFP) recycling. The system aims to reconcile industrial performance with environmental sustainability through three main objectives: (1) establishing a mechanism-data hybrid prediction core to ensure physical consistency in complex leaching environments; (2) implementing high-resolution emergy assessment to quantify resource quality and remediation service costs; and (3) achieving automatic identification of optimal leaching schemes to balance recovery efficiency with system performance footprint. As an integrated methodology, the SLEO framework can serve as an adaptive template for the sustainable design of hydrometallurgical processes.

[0031] like Figure 1 As shown in (a), SLEO integrates an Adaptive Physical Information Integration (APIE) prediction core with a system performance value accounting module. The APIE architecture couples three mathematically distinct family of models selected through system screening: Physical Information Neural Network (PINN), ensuring dynamic consistency through Arrhenius's law; CatBoost, capturing global nonlinear feature interactions; and K-Nearest Neighbors (KNN), for local pattern recognition. This integration minimizes the bias of individual algorithms and ensures the physical plausibility of predictions in sparse data regions. In the specific context of LFP recycling, the framework evaluates the sustainability of leaching paths through an emergy-based output rate (EYR) emergy value accounting module. This module compares the total emergy output (in terms of the recovered...)... The value represented by replacing primary production and the total energy input quantify the systemic resource conversion efficiency. Input accounting covers the consumption of major resources and the cost of ecosystem services required to remediate characteristic pollutants, specifically including sulfate ions (…). ), nitrogen oxides ( This method allows for a unified assessment of technical leaching performance and the systemic resource intensity required to achieve specific recovery objectives, including chemical oxygen demand (COD).

[0032] Specifically, the operation process of the SLEO framework is as follows: (1) Database construction, which involves the collection and standardization of experimental records to ensure data consistency; (2) APIE model training, which combines the mechanism constraints of PINN with the data-driven capabilities of the selected model to build an integrated prediction model; (3) Mechanism interpretation, which uses SHAP and one-dimensional PDP to quantify the importance of features and nonlinear response; (4) Technology-environment coupling, which associates the prediction results with the emergy module to evaluate the emergy input of different leaching paths; (5) Optimization and sustainability screening, which uses the Bayesian method to generate candidate conditions for each acid system, calculates the upper quartile thresholds of lithium leaching rate and EYR respectively, and uses the conditions that simultaneously reach the two thresholds to form the excellent performance zone, and selects the condition with the highest lithium leaching rate in each excellent performance zone as the recommended optimal solution.

[0033] The empirical basis for this embodiment is a database containing 2,820 independent experimental records from publications between 2010 and 2023. WebPlotDigitizer was used to extract data points from published leaching curves to maintain high fidelity. The SLEO framework was implemented in a Python environment, using PyTorch to build PINN, the CatBoost library for gradient boosting, and Scikit-learn for KNN and preprocessing. Although 14 models (including linear regression, SVR, and MLP) were initially selected, these specific libraries constituted the final architecture of the framework. Multi-objective optimization and hyperparameter tuning were performed using the Optuna library (Akiba et al., 2019). All energy conversion factors were derived from authoritative life cycle assessment databases and up-to-date unity energy (UEV) repositories to ensure rigorous quantification of sustainability metrics.

[0034] Specifically, the optimized method for sustainable lithium recycling of spent lithium iron phosphate batteries includes the following steps S10-S50.

[0035] S10: Obtain historical leaching experiment data, construct a correlation database including raw material parameters, process parameters and lithium leaching rate, and clean and normalize the data in the correlation database to obtain a standardized dataset.

[0036] The method described in this embodiment aims to recover lithium from waste LiFePO4 (LFP) cathode material via hydrometallurgical processes. This process involves proton-induced dissolution of the olivine structure, requiring precise redox control, typically achieved by adding... The process converts Fe(II) to Fe(III) and prevents the redeposition of insoluble ferrous phosphate. The key lies in the fact that leaching efficiency is affected by the acid dissociation constant (…). The strong nonlinear dependence between oxidant dosage and thermodynamic variables governs this. For example, The optimal concentration is highly sensitive to specific acid systems and reaction temperatures, creating a high-dimensional operating space. Traditional single-factor, one-time experiments (OFAT) are inherently limited in addressing this complexity, often failing to achieve the global optimum with the minimum reagent strength for maximum recovery. Furthermore, high leaching rates in the laboratory do not always correspond to system sustainability; excellent recovery rates may be offset by excessive energy consumption or the environmental burden of wastewater generated during treatment. Therefore, a comprehensive database encompassing diverse chemical and physical environments is crucial. This foundational data enables the framework to map coupled interactions and provides a quantitative basis for multidimensional optimization that balances the efficiency of technology recovery with resource conversion.

[0037] In an exemplary embodiment, step S10 specifically includes the following steps S101-S103.

[0038] S101: Data sources and collection.

[0039] This embodiment integrates two distinct data streams as its experimental foundation. First, a primary dataset containing 2,820 independent records was compiled from peer-reviewed literature (2010–2023), mapping published leaching curves using WebPlotDigitizer. This extensive dataset serves as the basis for model training and hyperparameter tuning. Second, independent laboratory experiments were conducted to generate high-fidelity benchmarks for the final model validation. In these experiments, lithium concentration in the leachate was precisely determined by ICP-MS, ensuring that the model's predictive performance was validated under controlled, original experimental evidence, rather than solely relying on historical literature.

[0040] S102: Feature definition and selection.

[0041] To establish a physically interpretable input vector, candidate features were initially identified based on the LiFePO4 leaching mechanism. Fourteen parameters representing the chemical and physical environments were initially considered. To ensure model stability and unbiased evaluation of feature importance, statistical collinearity analysis was performed to address information redundancy. The analysis showed a high positive correlation between acid concentration and the acid / lithium molar ratio. Therefore, the acid / lithium molar ratio was excluded, and the more fundamental acid concentration was retained as a representative variable for proton availability.

[0042] The final input vector consists of eight key process parameters: (1) the mass fraction of lithium in the raw material (%), representing the material composition; (2) the acid concentration (mol / L) and (3) , representing acid strength and proton-donating capacity; (4) / Li molar ratio, defining the redox environment; (5) liquid-solid ratio (mL / g); (6) reaction temperature (°C); (7) reaction time (min); (8) stirring speed (rpm). The target variable for all prediction models is lithium leaching rate ( ,%).

[0043] S103: Data preprocessing.

[0044] The original dataset underwent systematic cleaning to remove outliers and duplicate entries, ultimately retaining 2,820 records. A hierarchical random partitioning method with `random_state=123` was used to divide the dataset into a training set of 1,692 records (60%) and a test set of 1,128 records (40%). For models requiring a uniform feature scale, such as K-nearest neighbors and neural networks, standardized parameters were fitted only on the training set and then applied to the test set; tree models retained their original feature scale. The test set was used only to report prediction performance on unseen samples.

[0045] S20: Train an adaptive physical information ensemble model based on a standardized dataset. The adaptive physical information ensemble model includes a physical information neural network, a CatBoost model, and a K-nearest neighbor model.

[0046] In this embodiment, the development process of the adaptive physical information ensemble model is provided. Specifically, a systematic performance screening was performed on 14 candidate machine learning algorithms, which were divided into four mathematical families: (1) Linear and generalized linear models: linear regression, ridge regression, Lasso regression, and ElasticNet. (2) Ensemble tree models: random forest, gradient boosting decision tree (GBDT), XGBoost, LightGBM, CatBoost, and AdaBoost. (3) Distance and kernel models: support vector regression (SVR) and k-nearest neighbors (KNN). (4) Neural network architectures: multilayer perceptron (MLP) and physical information neural network (PINN).

[0047] All models were evaluated using 5-fold cross-validation on a standardized dataset. Benchmark results show that linear models are insufficient for this task. Nonlinear ensembles and distance models show significant predictive potential. Therefore, three best-performing models from different mathematical families were retained for the final ensemble: (1) PINN, which ensures mechanistic consistency; (2) CatBoost, which excels at capturing global nonlinear feature interactions; and (3) KNN, which provides accurate local pattern interpolation.

[0048] In one exemplary embodiment, to ensure that the model predictions follow the fundamental laws of chemical kinetics, PINN was constructed by embedding the apparent leaching kinetic equation as a constraint. The reaction rate is defined based on a semi-empirical kinetic model: (1) in, It is the lithium leaching rate. It is the reaction time. It is the reaction order. Here, is the reaction rate constant, T is the reaction temperature in °C, Cacid is the acid concentration in mol / L, and Cox is the molar ratio of oxidant to lithium, which in this example is the H₂O₂ / Li molar ratio. Rate constant Following the Arrhenius form of expression: (2) Where A is the pre-exponential factor, and exp is the natural exponential function. Let R be the apparent activation energy, and R be the molar gas constant. a The reaction order is determined by the acid concentration. b denoted as the reaction order of the oxidant and lithium in molar ratio.

[0049] The PINN architecture consists of a 7-layer fully connected network. The total loss function ( It integrates data-driven loss and physical residual loss: (3) in, Let E be the total loss function, E be the expectation operator (averaged across samples during batch training), λ be the weighting coefficient between data loss and physical residual loss, and η^ be the predicted lithium leaching rate. This refers to the physical residual.

[0050] Physical residuals Automatic differentiation calculation is used to... By minimizing Network weights and learnable physical parameters ( This allows for simultaneous optimization, ensuring that the model remains physically plausible even in data-sparse operational regions.

[0051] S30: Input the process parameters to be optimized into the trained adaptive physical information ensemble model to obtain the predicted lithium leaching rate, including: inputting the process parameters to be optimized into the physical information neural network, the CatBoost model, and the K-nearest neighbor model respectively to obtain their respective basic predicted values; determining the adaptive weights of the physical information neural network, the CatBoost model, and the K-nearest neighbor model respectively based on the local neighborhood information of the process parameters to be optimized in the feature space; and weighting and summing the basic predicted values ​​of the physical information neural network, the CatBoost model, and the K-nearest neighbor model according to their respective adaptive weights to obtain the predicted lithium leaching rate.

[0052] In one exemplary embodiment, an adaptive physical information integration (APIE) strategy is implemented to leverage the complementary strengths of mechanistic PINN and high-performance data-driven models. This adaptive weighting and integration strategy employs a sample-based weighting mechanism that is based on local capabilities rather than fixed global weights. For each target prediction point... The framework is identified in the feature space. The nearest neighbors. Each base model The local reliability is determined by the local determination coefficient ( Quantification: (4) in, It is the basic model The local coefficient of determination, It is the target prediction point. It is the set of K nearest neighbor samples. It is the true value of the sample. It is the basic model The predicted value, It is the average of the true values ​​within the set.

[0053] Adaptive weights for each model By truncating the negative The value is calculated using normalized contributions: (5) in, Basic Model Adaptive weights, Indicates the index of the base model. This indicates taking the maximum value. Representation of the basic model The local coefficient of determination.

[0054] The final ensemble prediction is a weighted sum: This strategy enables the framework to intelligently prioritize the dynamic constraints of PINN in regions of high uncertainty, or rely on pattern recognition of CatBoost / KNN in regions of abundant data.

[0055] In one exemplary embodiment, a multi-layered interpretability framework was implemented to elucidate the impact of individual process parameters on lithium leaching rate and system sustainability. This analysis bridges the gap between the APIE model algorithm output and the physical behavior of the LFP leaching system through global importance ranking, local attribution, and nonlinear response mapping.

[0056] The relative contribution of each process variable was first quantified through standardized importance analysis. Normalized importance score ( The result is determined by aggregating the impurity reduction and permutation-based rinsing results from the integrated base model. The calculation is as follows: (6) in, and It is a parameter and Importance metrics This is the total number of parameters.

[0057] This stage identifies the dominant control variables, such as reagent dosage and acid properties, providing a priority focus for subsequent dual-objective optimization.

[0058] In one exemplary embodiment, the Shapley Additive Explanation (SHAP) method is employed to characterize the direction and magnitude of parameter effects at the individual sample level. SHAP values, derived from cooperative game theory, attribute predictions to the marginal contribution of each parameter relative to the average model output. This embodiment utilizes a summary attribution plot to rank parameters by mean absolute SHAP value and employs a bee colony graph to visualize the correlation between parameter magnitude and its positive or negative impact on recovery. This ensures that the model's internal logic aligns with known LiFePO4 dissolution chemistry trends.

[0059] The marginal response of lithium leaching rate to a specific parameter is quantified using a one-dimensional partial dependency plot (PDP). The partial dependency function simulates the average predicted response of lithium leaching rate as a single parameter varies within its experimental range, while marginalizing the distribution of other variables. In this embodiment, the one-dimensional response curves of eight input features are compared to identify their nonlinear effects.

[0060] S40: Based on the predicted lithium leaching rate, the emergy output rate is calculated through the emergy accounting module. The emergy output rate is the ratio of total emergy output to total emergy input.

[0061] Step S40 corresponds to the technology-environment coupling phase of the SLEO framework. In this phase, the predictions from the APIE model are combined with system performance value analysis (sej) to assess ecological productivity. This coupling enables the framework to transform heterogeneous material and energy inputs into a unified metric, thereby determining the emergy output rate (EYR) as the primary indicator of resource conversion efficiency.

[0062] In one exemplary embodiment, EYR measures the ability of a recycling system to replace virgin material production with resource inputs. It is defined as the ratio of gross energy output to gross energy inputs: (7) in, This represents the energy value of virgin lithium carbonate production avoided through product recycling. EYR represents the cumulative energy required for all materials, energy, and ecosystem services. An EYR value greater than 1 indicates that the process provides a net ecological benefit to the socio-economic system.

[0063] The coupling mechanism involves bilateral accounting of outputs and inputs: (1) Output energy value ( The output energy value is determined by the mass of recovered lithium, which replaces lithium carbonate ( The original production of ) . For 1 gram of black powder functional units, The calculation is as follows: (8) in It is the lithium mass fraction in the black powder. It is the predicted leaching rate from the APIE model. and These are the corresponding molar masses. It is the original production The unit energy value (UEV).

[0064] (2) Input energy value ( To quantify the intensity of systemic resources, input energy values ​​summarize operational energy consumption ( Chemical reagent production ) and environmental remediation costs ( ): (9) Input accounting for the ecoservice costs of characteristic pollutants specific to each acid leaching pathway ( Differential assessments were implemented: 1) Sulfate system: residual 1) Rainwater energy required to dilute to a safe concentration. 2) Nitrate system: used for atmospheric dilution. 3) Organic acid system: Chemical energy value of dissolved oxygen required to oxidize residual chemical oxygen demand (COD). 4) Ammonium salt system: Chemical energy value of ammonia nitrogen (… The oxygen energy required for nitrification.

[0065] S50: With the goal of maximizing lithium leaching rate, a Bayesian optimization algorithm is used to generate candidate schemes for each acid system within the parameter feasible region. For each acid system, the upper quartile thresholds of lithium leaching rate and energy yield of the candidate schemes are determined. Candidate schemes that are not lower than both thresholds are formed into a set of excellent performance candidates. The candidate scheme with the highest lithium leaching rate in the set of excellent performance candidates is determined as the recommended optimal leaching scheme for the acid system.

[0066] In one exemplary embodiment, to transform a validated predictive model into a practical tool for process design, we employ a Bayesian optimization (BO) algorithm to intelligently search the multidimensional parameter space to find the optimal combination of process conditions that maximizes lithium leaching rate. Bayesian optimization is an efficient global optimization method, particularly suitable for "black box" problems where objective function evaluation is costly (e.g., running physical experiments) or lacks analytical gradients.

[0067] In this embodiment, the trained adaptive ensemble model (10) in It is an input vector of eight process parameters. This is the feasible domain of these parameters.

[0068] Boolean Optimization (BO) iteratively approximates the optimal solution by constructing a probabilistic alternative model (typically a Gaussian process (GP)) of the objective function. In each iteration, the algorithm selects the next most promising evaluation point by maximizing a harvest function (e.g., Expected Improvement (EI)). This function intelligently balances exploitation (searching in areas known to produce good results) and exploration (probing areas of high uncertainty), thus enabling the discovery of the global optimum with a minimal number of evaluations. Using this approach, we can efficiently generate a set of recommended high leaching process parameters for different acid systems (identified by pKa), providing data-driven guidance for subsequent experimental design and industrial applications.

[0069] The final stage of the SLEO framework involves identifying optimal operating conditions through a two-step optimization and evaluation sequence. To efficiently navigate the high-dimensional parameter space, Bayesian optimization (BO) is first employed to maximize the lithium leaching rate (…). The trained APIE model is used as a substitute objective function. The Gaussian process (GP) models the response surface and uses the expected improvement (EI) acquisition function to balance the utilization of known high-leaching regions with the exploration of uncertain regions.

[0070] Through this iterative search, a set of high-performance candidate solutions is generated for each acid system (e.g., In the second step, the emergy accounting module is applied to the population to calculate the emergy yield (EYR) for each candidate scheme. By evaluating the EYR distribution within the high-recovery subset, the framework identifies specific operating windows that achieve the leaching target with the highest resource conversion efficiency. This two-stage approach ensures that the recommended process conditions are technically reliable and ecologically sustainable.

[0071] The feasibility and progressiveness of the method of this invention will be further illustrated below with experimental verification and analysis.

[0072] To verify the adaptability of the SLEO framework, this embodiment used three representative types of spent LiFePO4 batteries: retired electric vehicle batteries (LFP-1), retired energy storage system batteries (LFP-2), and waste electronic device batteries (LFP-3). All samples underwent standardized pretreatment, including discharge, manual disassembly, crushing, and physical sorting, to obtain battery black powder. The elemental composition of the black powder was determined using inductively coupled plasma optical emission spectrometry (ICP-OES), and the results showed significant differences in lithium content and impurity distribution among the three sources.

[0073] This embodiment designed a systematic experimental matrix to verify the Pareto optimal conditions derived from the model. For each raw material, three sets of comparative experiments were performed: (1) conditions optimized for maximizing lithium recovery; (2) conditions optimized for maximizing energy efficiency; and (3) reference conditions determined by the traditional univariate method.

[0074] The experiment was conducted in a standardized 250 mL three-necked flask reactor equipped with precise temperature control. The system includes a digital mechanical stirrer. Energy consumption (electricity and heat) and reagent usage are monitored in real time during each leaching test, providing raw data for the subsequent validation of the emergy calculation module.

[0075] After leaching, through 0.45 Membrane filtration separation of solution. Lithium concentration in the leachate ( The leaching rate was determined by ICP-MS. The actual leaching rate was calculated as follows: (11) in It is the volume of the leachate. It's about the quality of the black powder. This refers to the lithium mass fraction. For the verification of sustainability indicators, the actual energy input for each experiment (…) The measured energy consumption data is aggregated with the unit energy value (UEV) defined in stage (4). The measured EYR is then compared with the EYR predicted by APIE to assess the reliability of the model in identifying the optimal sustainability options.

[0076] As shown in Table 1 and Figure 10 As shown, the initial benchmark performance of the 14 machine learning algorithms varies significantly: KNN's test set R 2 The R value is 0.9818 for XGBoost, LightGBM, GBDT, CatBoost, and PINN on the test set. 2 The values ​​range from 0.9145 to 0.9479, while the test set R for the four linear or regularized linear models is... 2 All are below 0.15. Figure 9 Further analysis shows that the absolute values ​​of the univariate Spearman rank correlation coefficients between all candidate input features and the target lithium leaching rate are all below 0.3; meanwhile, the feature correlation coefficient between acid concentration and the acid / Li molar ratio is approximately 0.697. These results indicate that univariate linear correlation is insufficient to describe the leaching process, and a model capable of characterizing nonlinear relationships is needed.

[0077] Table 1 Performance Comparison of 14 Machine Learning Models

[0078] To characterize the nonlinear leaching relationship, hyperparameter optimization was performed on KNN, PINN, CatBoost, XGBoost, GBDT, and LightGBM (Table 2). Figure 11 Among them, the test set R for KNN, PINN, and CatBoost is... 2 The R values ​​are 0.9919, 0.9892, and 0.9865, respectively. Based on the same 1,128 test samples, the R... 2 The RMSE is 0.9934, the RMSE is 1.2425%, and the MAE is 0.7068%; compared with the single model KNN with the lowest RMSE on the test set, the RMSE is reduced by about 9.9%. Figure 2 The three basic models and APIE in the table are all plotted using the original test samples that are not aggregated by observations, so their graphical indicators are consistent with those in Table 2.

[0079] Table 2. Performance of the optimized base model and APIE

[0080] like Figure 3The diagram illustrates the global feature importance and local attribution analysis performed using SHAP. The left panel displays the mean absolute SHAP value, identifying the main determinants of lithium recovery; the right-hand swarm diagram illustrates the directionality and contextual dependence of parameter influence.

[0081] like Figure 4 The diagram shows the response relationship of process parameters analyzed by a one-dimensional partial dependence plot (PDP). Each panel displays the response of the average predicted lithium leaching rate when eight mold entry characteristics change, highlighting the nonlinear changes in chemical parameters such as acid concentration and the smaller response amplitude of stirring speed.

[0082] To transform the predictive power of the APIE framework into interpretable parametric information, SHAP and a one-dimensional partial dependency graph (PDP) are combined to quantify parameter contributions and their response relationships. Figure 3 and Figure 4 ). Figure 3 The average absolute SAP values ​​show that acid concentration (2.365) and H₂O₂ / Li molar ratio (1.786) were the two features contributing the most to the calculations. The average absolute SAP values ​​for liquid-to-solid ratio, raw material lithium content, temperature, time, pKa₁, and stirring speed were 0.829, 0.718, 0.664, 0.519, 0.495, and 0.185, respectively. This ranking is consistent with... Figure 9 The results that the absolute values ​​of the univariate Spearman rank correlation coefficients of all candidate input features with respect to the target lithium leaching rate are all below 0.3 are not contradictory, indicating that the model captures nonlinear and conditionally dependent effects. Figure 4 The results show that the average predicted value increases rapidly below approximately 0.7 mol / L, then the gain slows down, reaching a high level around 3.2 mol / L, and then remains approximately stable or decreases slightly when the acid concentration continues to increase.

[0083] Figure 4 The H₂O₂ / Li molar ratio exhibits a steep positive response at lower values, followed by a decrease in gain. The average predicted lithium leaching rate at the liquid-to-solid ratio continues to rise from 81.16% at approximately 2.54 mL / g to 92.52% at approximately 102.08 mL / g, with the high liquid-to-solid ratio range showing a decrease in marginal gain rather than a complete plateau after 20 mL / g. The PDP span corresponding to stirring speed is approximately 1.65 percentage points, indicating a relatively small average response amplitude within the current data range; these results are used to describe the model response and are not considered as causal evidence for determining the mass transfer or chemical reaction control steps.

[0084] like Figure 5The diagram illustrates the trade-offs between acid differences and lithium leaching efficiency and energy yield (EYR). The scatter plot shows the systemic resource conversion efficiency across the ten acid systems, highlighting the inherent tension between technology recovery and environmental-economic sustainability.

[0085] like Figure 6 The diagram shows a Pareto nondominated front for candidate sustainable lithium recovery schemes. The front depicts the performance boundary between lithium leaching rate and energy yield in each acid system, used to identify candidate operating windows that balance both objectives.

[0086] To assess resource conversion efficiency within the SLEO framework, the energy yield (EYR) was used to quantify the system performance of ten acid leaching pathways. Figure 5 An emergy assessment was performed on 5,000 Bayesian optimization candidate solutions. EYR is defined as the ratio of the emergy output corresponding to the replacement of primary Li₂CO₃ production to the emergy input of the recycling process. Emergy input includes acid and H₂O₂ production, electricity consumption, and environmental remediation services such as SO₄, NO₃, and COD. A higher EYR indicates higher resource conversion efficiency under the system boundary and conversion factor of this embodiment.

[0087] Figure 6 The Pareto front is used to characterize the non-dominated trade-off between lithium leaching rate and EYR. After taking the intersection of the upper quartile thresholds of lithium leaching rate and EYR for each acid, the excellent region for ammonium sulfate has a lithium leaching rate of 98.75%–99.40% and an EYR of 0.34–1.30. The recommended points selected based on the highest lithium leaching rate within this intersection are 99.40% and 0.40, with a total energy consumption of 267.67 kJ. Under the same rules, the recommended points for sulfuric acid are 99.99% and 0.20, and for nitric acid are 99.99% and 0.31. Although the recommended points for oxalic acid and citric acid reach lithium leaching rates of 99.99% and 99.54% respectively, their EYRs are 0.08 and 0.01, with the total energy consumption for citric acid at the recommended point being 8,537.56 kJ. The above comparisons are only applicable to the system boundary, candidate set, and energy conversion factor used in this embodiment.

[0088] Table 3 Recommended operating conditions and performance indicators for each acid system

[0089] Figure 5 The data distribution shows that in several acid systems, increasing the lithium leaching rate is accompanied by an increase in reagent or energy consumption, thereby reducing the EYR, but the magnitude of the change is not the same for different acid systems. Figure 6 By identifying other candidate schemes that do not simultaneously improve lithium leaching rate and EYR through the Pareto front, a basis is provided for selecting a compromise point based on specific engineering constraints.

[0090] like Figure 7 The diagram shown is a detailed parameter analysis of the high-performance region, displaying the optimal operation window.

[0091] To identify the robust operating window for each acid system. Figure 7 The 75th percentiles of lithium leaching rate and EYR were calculated separately for each acid system, and candidate schemes that were not lower than both percentile thresholds were defined as the excellent performance region; this rule is not a uniform absolute lithium leaching rate threshold. The excellent region temperature ranges of the ten acid systems differed significantly, covering an overall range of 40.5–100.0℃; the recommended point temperatures in Table 3, selected based on the principle of maximizing lithium leaching rate within the excellent region, are concentrated in the range of 56.5–63.0℃, but this should not be used to interpret the complete excellent region of each system as a common window of 56–63℃.

[0092] The optimal range widths for each acid system reflect different operational sensitivities. For example, the optimal range temperatures are 60.5–62.0℃ for sulfuric acid, 59.0–62.0℃ for nitric acid, and 60.5–61.0℃ for potassium pyrosulfate; 44.0–97.0℃ for sodium dihydrogen phosphate, 40.5–71.0℃ for formic acid, 42.0–68.0℃ for ammonium sulfate, and 57.5–100.0℃ for ammonium persulfate. Table 3 lists the recommended parameter points determined based on the principle of maximizing lithium leaching rate within their respective upper quartile intersections, which can serve as candidate conditions for subsequent experimental verification and scale-up studies.

[0093] Table 4. Comparison of observed and predicted lithium leaching rates in independent model validation experiments.

[0094] Independent validation was performed using five experimental conditions not included in model training (Table 4). The absolute errors between observed and predicted values ​​ranged from 0.0879% to 0.7679%, with a mean absolute error of 0.3732% and a five-point coefficient of determination R0. 2 The value is 0.9757. This small-scale validation supports the model's predictive consistency under the tested extrinsic parameters, but does not constitute a basis for ruling out overfitting or proving industrial-scale generalization.

[0095] The observed lithium leaching rates from five independent validation experiments ranged from 84.389% to 92.183%, corresponding to predicted values ​​of 84.613% to 91.739%, indicating that the model was able to follow the trend within this range. These results, along with the test set metrics, support the SLEO framework for proposing candidate conditions for subsequent experiments, but further validation with more independent samples and scale-up experiments is still needed.

[0096] This embodiment establishes a Sustainable Leach Evaluation and Optimization (SLEO) framework for predicting, interpreting, calculating emergy, and screening candidate conditions for lithium recycling from spent LFP batteries. APIE achieves R on 1,128 reserved test samples. 2 The R-values ​​were 0.9934, RMSE was 1.2425%, and MAE was 0.7068%; the R-values ​​of the five independent validation experiments were... 2 The value is 0.9757, and the MAE is 0.3732%. The former is used to characterize the model performance on a unified test set, while the latter is used to characterize the prediction consistency under small-scale external experimental conditions.

[0097] Cross-system comparisons of ten acid leaching pathways showed that acid concentration and the H₂O₂ / Li molar ratio were the two features with the highest average absolute contributions in this SHAP analysis. The recommended temperature range for each acid system was 56.5–63.0℃, but the temperature range of the optimal region could be as wide as 40.5–100.0℃; therefore, clustering of recommended points does not equate to the existence of a uniform thermal window. The recommended EYRs for oxalic acid and citric acid were 0.08 and 0.01, respectively; the recommended lithium leaching rate for ammonium sulfate was 99.40%, with an EYR of 0.40 and a total energy consumption of 267.67 kJ, approximately 52% lower than the recommended energy consumption of 557.97 kJ for sulfuric acid. Within the optimal region, there may be points with higher EYRs but lower lithium leaching rates; engineering selection should be determined by considering both objectives and system boundaries.

[0098] While the scope of this study is limited by the inherent uncertainties in feedstock composition and conversion factors, this work provides a robust computational template for sustainable resource management. Future research should prioritize pilot-scale validation for continuous operations. In conclusion, the SLEO framework facilitates a paradigm shift in battery recycling, moving from narrow yield maximization to holistic optimization that considers system value and ecological balance.

[0099] This embodiment establishes a Sustainable Leach Evaluation and Optimization (SLEO) framework for predicting, interpreting, calculating emergy, and screening candidate conditions for lithium recycling from spent LFP batteries. APIE achieves R on 1,128 reserved test samples. 2 The R-values ​​were 0.9934, RMSE was 1.2425%, and MAE was 0.7068%; the R-values ​​of the five independent validation experiments were... 2 The value is 0.9757, and the MAE is 0.3732%. The former is used to characterize the model performance on a unified test set, while the latter is used to characterize the prediction consistency under small-scale external experimental conditions.

[0100] Cross-system comparisons of ten acid leaching pathways showed that acid concentration and the H₂O₂ / Li molar ratio were the two features with the highest average absolute contributions in this SHAP analysis. The recommended temperature range for each acid system was 56.5–63.0℃, but the temperature range of the optimal region could be as wide as 40.5–100.0℃; therefore, clustering of recommended points does not equate to the existence of a uniform thermal window. The recommended EYRs for oxalic acid and citric acid were 0.08 and 0.01, respectively; the recommended lithium leaching rate for ammonium sulfate was 99.40%, with an EYR of 0.40 and a total energy consumption of 267.67 kJ, approximately 52% lower than the recommended energy consumption of 557.97 kJ for sulfuric acid. Within the optimal region, there may be points with higher EYRs but lower lithium leaching rates; engineering selection should be determined by considering both objectives and system boundaries.

[0101] This invention also provides a sustainable lithium recycling optimization device for spent lithium iron phosphate batteries, used to implement the methods described in any of the above embodiments, such as... Figure 12 As shown, the device includes: The data preprocessing module 1201 is configured to acquire historical leaching experimental data, construct an association database including raw material parameters, process parameters and lithium leaching rate, and clean and normalize the data in the association database to obtain a standardized dataset. The model training module 1202 is configured to train an adaptive physical information ensemble model based on the standardized dataset, the adaptive physical information ensemble model including a physical information neural network, a CatBoost model and a K-nearest neighbor model; The lithium leaching rate prediction module 1203 is configured to input the process parameters to be optimized into the trained adaptive physical information ensemble model to obtain the predicted lithium leaching rate, including: inputting the process parameters to be optimized into the physical information neural network, the CatBoost model, and the K-nearest neighbor model respectively to obtain their respective basic prediction values; determining the adaptive weights of the physical information neural network, the CatBoost model, and the K-nearest neighbor model respectively based on the local neighborhood information of the process parameters to be optimized in the feature space; and performing a weighted summation of the basic prediction values ​​of the physical information neural network, the CatBoost model, and the K-nearest neighbor model according to their respective adaptive weights to obtain the predicted lithium leaching rate. The regrid output rate calculation module 1204 is configured to calculate the regrid output rate based on the predicted lithium leaching rate through the regrid accounting module, wherein the regrid output rate is the ratio of total regrid output to total regrid input. The optimal leaching scheme screening module 1205 is configured to generate candidate schemes for each acid system within the parameter feasible region using a Bayesian optimization algorithm with the objective of maximizing the lithium leaching rate. For each acid system, the upper quartile thresholds of the lithium leaching rate and energy yield of the candidate schemes are determined respectively. Candidate schemes that are not lower than both thresholds are constituted as an excellent performance candidate set, and the candidate scheme with the highest lithium leaching rate in the excellent performance candidate set is determined as the recommended optimal leaching scheme for the acid system.

[0102] This invention provides an electronic device. The electronic device may include a processor and a memory, wherein the processor and the memory can communicate; exemplarily, the processor and the memory communicate via a communication bus.

[0103] The processor executes computer execution instructions stored in memory, causing the processor to perform the scheme in the above embodiments. The processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0104] The communication bus can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The system bus can be divided into address bus, data bus, control bus, etc. Transceivers are used to enable communication between database access devices and other computers (e.g., clients, read-write libraries, and read-only libraries). Memory may include random access memory (RAM) and may also include non-volatile memory.

[0105] The electronic device provided in this embodiment of the invention can be the terminal device described in the above embodiments.

[0106] This invention also provides a computer-readable storage medium storing computer instructions. When these computer instructions are executed on a computer, the computer performs the technical solution of the optimized method for sustainable lithium recycling of waste lithium iron phosphate batteries described in the above embodiments.

[0107] This invention also provides a computer program product, which includes a computer program stored in a computer-readable storage medium. At least one processor can read the computer program from the computer-readable storage medium. When the at least one processor executes the computer program, it can implement the technical solution of the optimized method for sustainable lithium recycling of waste lithium iron phosphate batteries described in the above embodiments.

[0108] In the several embodiments provided by this invention, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or modules, and may be electrical, mechanical, or other forms.

[0109] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to implement the solution of this embodiment according to actual needs.

[0110] Furthermore, the functional modules in the various embodiments of the present invention can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The unit composed of the above modules can be implemented in hardware or in the form of hardware plus software functional units.

[0111] The integrated modules described above, implemented as software functional modules, can be stored in a computer-readable storage medium. These software functional modules, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute certain steps of the methods of the various embodiments of the present invention.

[0112] It should be understood that the aforementioned processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. A general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly manifested as execution by a hardware processor, or execution by a combination of hardware and software modules within the processor.

[0113] The memory may include high-speed RAM, and may also include non-volatile storage (NVM), such as at least one disk storage device, and may also be a USB flash drive, external hard drive, read-only memory, disk or optical disc, etc.

[0114] Buses can be Industry Standard Architecture (ISA) buses, Peripheral Component Interconnect (PCI) buses, or Extended Industry Standard Architecture (EISA) buses, etc. Buses can be categorized into address buses, data buses, control buses, etc.

[0115] The aforementioned storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The storage medium can be any available medium that can be accessed by a general-purpose or special-purpose computer.

[0116] An exemplary storage medium is coupled to a processor, enabling the processor to read information from and write information to the storage medium. Alternatively, the storage medium can be an integral part of the processor. The processor and storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and storage medium can exist as discrete components in an electronic control unit or main control device.

[0117] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0118] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention 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; and these 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 the present invention.

Claims

1. An optimized method for sustainable lithium recycling from spent lithium iron phosphate batteries, characterized in that, The method includes: Historical leaching experiment data were obtained, and a correlation database including raw material parameters, process parameters and lithium leaching rate was constructed. The data in the correlation database were then cleaned and normalized to obtain a standardized dataset. Based on the standardized dataset, an adaptive physical information ensemble model is trained, which includes a physical information neural network, a CatBoost model, and a K-nearest neighbor model. The process parameters to be optimized are input into the trained adaptive physical information ensemble model to obtain the predicted lithium leaching rate. This includes: inputting the process parameters to be optimized into the physical information neural network, the CatBoost model, and the K-nearest neighbor model respectively to obtain their respective basic predicted values; determining the adaptive weights of the physical information neural network, the CatBoost model, and the K-nearest neighbor model based on the local neighborhood information of the process parameters to be optimized in the feature space; and weighting and summing the basic predicted values ​​of the physical information neural network, the CatBoost model, and the K-nearest neighbor model according to their respective adaptive weights to obtain the predicted lithium leaching rate. Based on the predicted lithium leaching rate, the energy value output rate is calculated by the energy value accounting module. The energy value output rate is the ratio of total energy value output to total energy value input. With the goal of maximizing the lithium leaching rate, a Bayesian optimization algorithm is used to generate candidate solutions for each acid system within the parameter feasible region. For each acid system, the upper quartile thresholds of the lithium leaching rate and energy yield of the candidate solutions are determined. Candidate solutions that are not lower than both thresholds are formed into a set of excellent performance candidates. The candidate solution with the highest lithium leaching rate in the set of excellent performance candidates is determined as the recommended optimal leaching solution for the acid system.

2. The optimized method for sustainable lithium recycling from spent lithium iron phosphate batteries according to claim 1, characterized in that, The training process of the physical information neural network includes: The semi-empirical kinetic model is embedded in the loss function of the physical information neural network. The semi-empirical kinetic model defines the rate of change of lithium leaching rate based on the reaction rate constant, reaction time, and reaction order. (1) in, It is the lithium leaching rate. It is the reaction time. It is the reaction order. , where is the reaction rate constant, T is the reaction temperature in °C, Cacid is the acid concentration in mol / L, and Cox is the molar ratio of oxidant to lithium, which in this example is the molar ratio of H2O2 / Li. Calculate the reaction rate constant using the following formula: (2) Where A is the pre-exponential factor, and exp is the natural exponential function. Let R be the apparent activation energy, and R be the molar gas constant. a The reaction order is determined by the acid concentration. b The reaction order is the molar ratio of the oxidant to lithium. The total loss function for constructing the physical information neural network is expressed as follows: (3) in, Let E be the total loss function, E be the expectation operator (averaged across samples during batch training), and λ be the weighting coefficient between the data loss and the physical residual loss. For the predicted lithium leaching rate, For physical residuals, ; Based on the standardized dataset, the training of the physical information neural network is completed by minimizing the total loss function and simultaneously optimizing the network weights and the learnable physical parameters in the semi-empirical dynamics model.

3. The optimized method for sustainable lithium recycling of spent lithium iron phosphate batteries according to claim 1, characterized in that, Based on the local neighborhood information of the process parameters to be optimized in the feature space, the adaptive weights of the physical information neural network, the CatBoost model, and the K-nearest neighbor model are determined respectively, including: For the target prediction point corresponding to the process parameter to be optimized, its K nearest neighbor samples are identified in the feature space, and the local determination coefficients of each base model in the physical information neural network, the CatBoost model, and the K nearest neighbor model on the nearest neighbor samples are calculated; the formula for calculating the local determination coefficients is: (4) in, It is the basic model The local coefficient of determination, It is the target prediction point. It is the set of K nearest neighbor samples. It is the true value of the sample. It is the basic model The predicted value, It is the average of the true values ​​within the set. Based on the local determination coefficients, calculate the adaptive weights for each base model; (5) in, Basic Model Adaptive weights, Indicates the index of the base model. This indicates taking the maximum value. Representation of the basic model The local coefficient of determination.

4. The optimized method for sustainable lithium recycling of spent lithium iron phosphate batteries according to claim 1, characterized in that, It also includes a model interpretation step, which is used to quantify the impact of various process parameters on the lithium leaching rate, specifically including: The global importance of each process parameter is quantified based on normalized importance; the formula for calculating the global importance is as follows: (6) in, and It is a parameter and Importance metrics This is the total number of parameters; Based on the SHapley additive interpretation method, the marginal contribution value of each process parameter to a single predicted sample is calculated, and a summary attribution plot is generated to visualize the positive and negative influence direction of each process parameter on the lithium leaching rate. Based on the partial dependency graph analysis, the average response of the lithium leaching rate is simulated when a single process parameter changes, and the single-factor response curves of each process parameter are compared to identify the nonlinear influence of each process parameter.

5. The optimized method for sustainable lithium recycling of spent lithium iron phosphate batteries according to claim 1, characterized in that, The energy value calculation module calculates the energy value output rate using the following formula. : (7) in, For output energy value, Energy input; The formula for calculating the energy output value is as follows: (8) in, It is the lithium mass fraction in the black powder. This is the predicted lithium leaching rate. and These are the molar masses of lithium carbonate and lithium, respectively. It is the energy value per unit of production of primary lithium carbonate, g is the mass unit gram, 1 g means that 1 g of black powder is used as the accounting basis; The formula for calculating the input energy value is as follows: (9) in, This is the operating energy consumption value. It is the energy value of chemical reagent production. It is the environmental remediation cost energy value, which is calculated differently based on the characteristic pollutants of the acid leaching path.

6. The optimized method for sustainable lithium recycling of spent lithium iron phosphate batteries according to claim 1, characterized in that, To maximize the lithium leaching rate, a Bayesian optimization algorithm is used to iteratively optimize within the feasible region of the parameters, including: Using the trained adaptive physical information ensemble model as an alternative objective function for Bayesian optimization, the optimization problem is defined according to the following formula: (10) in, It is an input vector that includes eight process parameters. It is the feasible region of the parameters. It is the predicted lithium leaching rate output by the adaptive physical information integration model; A probabilistic proxy model is constructed with a Gaussian process as the objective function, and the sampling function is improved by maximizing the expectation. The next sampling point is iteratively selected within the feasible region of the parameters to approximate the global optimal solution that maximizes the lithium leaching rate.

7. The optimized method for sustainable lithium recycling of spent lithium iron phosphate batteries according to claim 1, characterized in that, Based on the lithium leaching rate and energy yield, the recommended optimal leaching scheme is selected from the candidate scheme set according to the acid system, including: Multiple candidate process parameter combinations are generated for each acid system using a Bayesian optimization algorithm, forming a candidate scheme set for the corresponding acid system; Call the energy value calculation module to calculate the energy value output rate corresponding to each scheme in the candidate scheme set of each acid system; For each acid system, the upper quartile thresholds of lithium leaching rate and energy yield of candidate schemes are calculated. Candidate schemes that are not lower than both thresholds are formed into a set of excellent performance candidates. The candidate scheme with the highest lithium leaching rate in the set of excellent performance candidates is taken as the recommended optimal leaching scheme for the acid system.

8. A sustainable lithium recycling optimization device for waste lithium iron phosphate batteries, characterized in that, The device includes: The data preprocessing module is configured to acquire historical leaching experiment data, construct a correlation database including raw material parameters, process parameters and lithium leaching rate, and clean and normalize the data in the correlation database to obtain a standardized dataset. The model training module is configured to train an adaptive physical information ensemble model based on the standardized dataset, the adaptive physical information ensemble model including a physical information neural network, a CatBoost model and a K-nearest neighbor model; The lithium leaching rate prediction module is configured to input the process parameters to be optimized into the trained adaptive physical information ensemble model to obtain the predicted lithium leaching rate. This includes: inputting the process parameters to be optimized into the physical information neural network, the CatBoost model, and the K-nearest neighbor model respectively to obtain their respective basic prediction values; determining the adaptive weights of the physical information neural network, the CatBoost model, and the K-nearest neighbor model based on the local neighborhood information of the process parameters to be optimized in the feature space; and performing a weighted summation of the basic prediction values ​​of the physical information neural network, the CatBoost model, and the K-nearest neighbor model based on their respective adaptive weights to obtain the predicted lithium leaching rate. The regrid output rate calculation module is configured to calculate the regrid output rate based on the predicted lithium leaching rate through the regrid accounting module, wherein the regrid output rate is the ratio of total regrid output to total regrid input. The optimal leaching scheme screening module is configured to generate candidate schemes for each acid system within the parameter feasible region using a Bayesian optimization algorithm with the objective of maximizing the lithium leaching rate. For each acid system, the upper quartile thresholds of the lithium leaching rate and energy yield of the candidate schemes are determined. Candidate schemes that are not lower than both thresholds are formed into an excellent performance candidate set, and the candidate scheme with the highest lithium leaching rate in the excellent performance candidate set is determined as the recommended optimal leaching scheme for the acid system.

9. An electronic device, characterized in that, include: A processor, and a memory communicatively connected to the processor; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory to implement the optimized method for sustainable lithium recycling of waste lithium iron phosphate batteries as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the optimized method for sustainable lithium recycling of spent lithium iron phosphate batteries as described in any one of claims 1-7.

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