Cobalt-nickel separation coefficient prediction method and system based on structural knowledge embedding

Abstract

The invention provides a cobalt-nickel separation coefficient prediction method and system based on structural knowledge embedding, and belongs to the field of cobalt-nickel resource recovery. The method comprises the following steps: constructing a cobalt-nickel separation coefficient original data set comprising leachate composition parameters, extractant structure information and operation condition parameters; performing data preprocessing and feature engineering processing on the original data set to obtain a feature data set meeting machine learning modeling requirements; respectively constructing a reference prediction model and a knowledge embedding prediction model in which domain knowledge features are introduced on the feature data set, performing model performance comparison, and determining a candidate prediction model; performing hyper-parameter optimization on the candidate prediction model based on a comprehensive evaluation loss function considering prediction precision and over-fitting suppression to obtain a target prediction model; and stable prediction of the cobalt-nickel separation coefficient under the unknown working condition is realized by using the target prediction model. The method can adapt to data distribution difference and stably predict the cobalt-nickel separation coefficient.

Description

Technical Field

[0001] This invention relates to the field of cobalt and nickel resource recycling technology, and in particular to a method and system for predicting the cobalt-nickel separation coefficient in waste lithium battery solutions based on structural knowledge embedding. Background Technology

[0002] Cobalt and nickel are common and valuable metal elements found in spent lithium-ion batteries, typically coexisting in solution during battery leaching. Due to the high similarity between cobalt and nickel ions in ionic radius, electronegativity, and coordination characteristics, their chemical behaviors in solution are highly similar, making efficient and selective separation during extraction difficult. The cobalt-nickel separation coefficient is a comprehensive indicator reflecting the characteristics of multi-metal interactions, and its prediction differs from modeling the efficiency of a single metal.

[0003] In existing technologies, cobalt-nickel separation typically relies on repeated experiments with extractant systems and operating conditions. This involves gradually optimizing the extraction process by changing the type and ratio of extractant, as well as reaction conditions, using single-factor or multi-factor experimental methods to achieve a high cobalt-nickel separation coefficient. However, these methods are primarily based on empirical trial and error, resulting in high experimental costs and long cycles. Furthermore, when faced with complex extraction systems with high parameter dimensions and a large combination space, they struggle to efficiently screen for high-performance extraction systems. The fundamental reason for this is the lack of a systematic understanding of the intrinsic relationship between extractant structure, reaction conditions, solvent composition, and the cobalt-nickel separation coefficient.

[0004] With the development of data-driven methods, machine learning technology, due to its ability to uncover potential correlations from large amounts of experimental data, has been increasingly applied to the fields of material performance prediction and process modeling. Currently, machine learning models have been applied in the screening and performance evaluation of metal-organic framework materials, membrane materials, and alloy materials, providing new technical approaches for modeling the relationship between parameters and performance in complex systems. However, applying machine learning methods to predict the cobalt-nickel separation coefficient in spent lithium-ion battery solutions still faces significant challenges. On the one hand, the composition of leachates from spent lithium-ion batteries from different sources varies significantly, resulting in complex sample distributions. On the other hand, the extractants and related components in the extraction system have diverse structural types, and significant nonlinear relationships exist between variables. Furthermore, the range of cobalt-nickel separation coefficients is large, often spanning multiple orders of magnitude, further increasing the difficulty of model construction and stable prediction.

[0005] Therefore, there is an urgent need for a method and system that can adapt to differences in data distribution and stably predict the cobalt-nickel separation coefficient, in order to rationally characterize the structural features of the extractant and combine them with experimental parameters under complex extraction system conditions. Summary of the Invention

[0006] The objective of this invention is to provide a method and system for predicting the cobalt-nickel separation coefficient based on structural knowledge embedding. This aims to solve the technical problem that cobalt and nickel have similar properties in existing waste lithium battery solutions, making selective separation difficult, and that traditional experimental methods relying on trial and error are difficult to efficiently and accurately obtain the cobalt-nickel separation coefficient in complex extraction systems.

[0007] To achieve the above objectives, in a first aspect, the present invention provides a method for predicting the cobalt-nickel separation coefficient based on structural knowledge embedding, the steps of which include:

[0008] S1. Based on literature database retrieval, construct an original dataset of cobalt-nickel separation coefficients, including leachate composition parameters, extractant structure information, and operating condition parameters;

[0009] S2. Perform data preprocessing and feature engineering on the original dataset to obtain a feature dataset that meets the requirements of machine learning modeling;

[0010] S3. Construct a baseline prediction model without domain knowledge features and a knowledge embedding prediction model with domain knowledge features on the feature dataset, respectively, and compare the model performance to determine the candidate prediction model.

[0011] S4. Based on a comprehensive evaluation loss function that balances prediction accuracy and overfit suppression, the candidate prediction model is optimized for hyperparameters to obtain the target prediction model.

[0012] S5. Using the target prediction model, predict and output the cobalt-nickel separation coefficient under unknown waste lithium battery solution conditions.

[0013] As a further improvement to the above scheme, the cobalt-nickel separation coefficient is a ratio characterizing the distribution behavior of cobalt and nickel under the same extraction system and operating conditions.

[0014] As a further improvement to the above scheme, the data preprocessing and feature engineering processing in step S2 includes:

[0015] Perform duplicate value consolidation and outlier removal on continuous variables in the dataset;

[0016] The categorical variables are coded, and the categorical variables include at least solution type, solvent type, and extractant type.

[0017] Furthermore, molecular fingerprint characterization is introduced for the types of extractants, converting the molecular structure information of the extractants into structural feature vectors;

[0018] Meanwhile, correlation analysis is performed on the processed features for use in subsequent model construction.

[0019] As a further improvement to the above scheme, the molecular fingerprint includes one or more of MACCS molecular fingerprint, Morgan molecular fingerprint, or count-type Morgan molecular fingerprint.

[0020] As a further improvement to the above scheme, step S3 includes: under the same training data conditions, constructing a benchmark prediction model without extractant structural features and a knowledge embedding prediction model with extractant structural features, and selecting candidate models for predicting cobalt-nickel separation coefficients by comparing the prediction performance of the models.

[0021] As a further improvement to the above scheme, the model comparison in step S3 includes:

[0022] On the dataset processed in step S2, prediction models with and without MACCS molecular fingerprint features are constructed based on a variety of preset machine learning model categories.

[0023] By cross-validating different models on randomly partitioned training and test sets, and comparing and analyzing the model performance based on evaluation results including at least mean absolute error, root mean square error, coefficient of determination, and overall accuracy, the preferred model categories and corresponding dataset combinations for predicting cobalt-nickel separation coefficients are obtained.

[0024] As a further improvement to the above scheme, the machine learning model category includes one or more of the following: lightweight gradient boosting machine, category feature gradient boosting machine, extreme gradient boosting model, or histogram gradient boosting model.

[0025] As a further improvement to the above scheme, in the model performance comparison process in step S3, the overall accuracy index is used as the basis for model evaluation. The overall accuracy index comprehensively reflects the prediction error index and the goodness of fit index, and is used to compare the performance of the prediction model that introduces molecular fingerprint features and the prediction model that does not introduce molecular fingerprint features.

[0026] As a further improvement to the above scheme, in step S4, when optimizing the hyperparameters of the candidate prediction model, a comprehensive evaluation loss function that simultaneously reflects the model prediction error and the degree of overfitting is used as the optimization objective to obtain a target model for predicting the cobalt-nickel separation coefficient.

[0027] As a further improvement to the above scheme, the comprehensive evaluation loss function in step S4 includes both the prediction error index and the overfitting constraint index.

[0028] The overfitting constraint index is characterized by the relationship between the prediction error of the validation set and the prediction error of the training set.

[0029] As a further improvement to the above scheme, the calculation formula for the comprehensive evaluation loss function is as follows:

[0030] ;

[0031] in, The average RMSE performance on the validation set; The average RMSE performance of the training set; For the average validation set R 2 .

[0032] Secondly, the present invention also provides a system for predicting the cobalt-nickel separation coefficient in waste lithium battery solutions, comprising:

[0033] The data construction module is used to build a dataset of cobalt-nickel separation coefficients;

[0034] The feature processing module is used for data preprocessing and structural knowledge feature construction.

[0035] The knowledge embedding modeling module is used to introduce the molecular structure features of the extractant to build a predictive model;

[0036] The model comparison module is used to compare the performance of models that incorporate structural knowledge features and those that do not.

[0037] The prediction output module is used to output the prediction results of the cobalt-nickel separation coefficient.

[0038] Because the present invention adopts the above technical solutions, the beneficial effects of this application are as follows:

[0039] This invention provides a method for predicting the cobalt-nickel separation coefficient based on structural knowledge embedding. This invention uses the cobalt-nickel separation coefficient as the prediction object and simultaneously incorporates leachate composition parameters, extractant structural information, and operating condition parameters into the dataset. This enables the prediction model to characterize the relative separation behavior of cobalt and nickel in the same extraction system. Through the combination of these technical features, this invention avoids modeling only the extraction efficiency of a single metal, better aligning with the actual process requirements for selective separation under conditions where cobalt and nickel have similar properties, and helps to improve the analytical focus of the cobalt-nickel separation process.

[0040] By introducing a molecular fingerprint-based extraction agent structure characterization method into the machine learning modeling process and comparing it with benchmark models that do not incorporate structural information, the model can comprehensively consider the impact of extractant structural differences on cobalt-nickel separation behavior. This technical feature enables the machine learning model to not only rely on experimental condition parameters during training but also reflect the correlation between extractant molecular structure characteristics and separation coefficients. This allows for more reasonable prediction results under complex and diverse extraction system conditions, providing structural support for the analysis of cobalt-nickel separation systems.

[0041] By optimizing the hyperparameters of the model using a comprehensive evaluation loss function that balances prediction accuracy and overfit suppression, the stability and applicability of the prediction model under complex data conditions are improved. At the same time, the feasibility of combining machine learning models with molecular structure characterization methods for solution separation problems is verified.

[0042] This invention reduces the model's dependence on specific training data while ensuring that the prediction error is within a reasonable range, making the obtained model more suitable for application scenarios with large differences in leachate composition, and providing a reference technical path for the application of machine learning methods in the metal solution separation process. Attached Figure Description

[0043] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0044] Figure 1 This is a flowchart illustrating a method for predicting the cobalt-nickel separation coefficient based on structural knowledge embedding disclosed in this invention.

[0045] Figure 2 A heatmap of Pearson correlation coefficients for features in the dataset disclosed in this invention;

[0046] Figure 3 This is a schematic diagram showing the performance comparison of models with and without MACCS fingerprints as disclosed in this invention.

[0047] Figure 4 This is a schematic diagram of the Optuna hyperparameter optimization of the CatBoost model disclosed in this invention;

[0048] Figure 5 This is a schematic diagram illustrating the fitting effect of the optimal CatBoost model disclosed in this invention.

[0049] The realization of the objective, functional characteristics and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0052] Example 1

[0053] See Figures 1-5 This invention provides a method for predicting the cobalt-nickel separation coefficient based on structural knowledge embedding, the steps of which include:

[0054] S1. Constructing the original dataset of cobalt-nickel separation coefficients:

[0055] Experimental data related to cobalt-nickel separation in leachate from waste lithium batteries were collected by searching and screening publicly available literature databases. The data included at least leachate composition parameters, extractant structure information, and extraction process operating condition parameters. The original dataset was constructed using the cobalt-nickel separation coefficient as the prediction target.

[0056] Specifically, in literature databases such as Web of Science, CNKI, and Google Scholar, the titles and abstracts of relevant documents were searched using keywords related to the cobalt-nickel separation process. Specifically, search keywords could include "spent lithium ion battery," "cobalt nickel separation," "recovery," and "extraction."

[0057] After obtaining the search results, literature irrelevant to the cobalt-nickel separation process or with incomplete experimental conditions was manually screened out. The experimental data from the retained literature were then organized, and continuous and categorical parameters were extracted to form the original dataset. The continuous features in the original dataset include initial cobalt and nickel concentrations, extractant concentrations, O / A ratio, initial pH, equilibrium pH, temperature, time, extraction rate, and partition ratio; categorical variables include the types of anions in the solution, extractant types, co-extractant types, and organic solvent types; and the predictive variable y is the cobalt-nickel separation coefficient.

[0058] By simultaneously incorporating cobalt and nickel information at the data level, the dataset can reflect the relative separation relationship between the two in the same extraction system, thus avoiding modeling only the efficiency of a single metal from the outset. This is beneficial for subsequent models to characterize the selective separation behavior of cobalt and nickel.

[0059] S2. Data preprocessing and feature engineering:

[0060] The raw dataset obtained in step S1 is preprocessed, including outlier handling, missing value handling, and normalization of categorical and continuous variables. Based on this, features are constructed from the leachate composition parameters, operating condition parameters, and extractant structure information to form a feature dataset that meets the requirements of machine learning modeling.

[0061] By unifying the data scale and feature representation, the differences between experimental data from different sources are reduced, providing a stable data foundation for subsequent model training, which helps to improve the training efficiency and consistency of the model.

[0062] S3. Construct and compare the baseline prediction model with the knowledge embedding prediction model:

[0063] On the aforementioned feature dataset, a baseline prediction model without extractant structure information and a knowledge embedding prediction model incorporating extractant structure-related features are constructed respectively. The prediction performance of the two types of models is compared through methods such as cross-validation, and a candidate prediction model with better overall performance is selected.

[0064] Through the above comparison process, the role of structural knowledge features in predicting the cobalt-nickel separation coefficient can be verified. This allows the model to further reflect the influence of extractant structural differences on separation behavior while considering experimental condition parameters, thereby improving the model's ability to express the differences in complex extraction systems.

[0065] S4. Model optimization based on comprehensive evaluation loss function:

[0066] For the candidate prediction models obtained in step S3, a comprehensive evaluation loss function that takes into account both prediction error and overfit suppression is set, and the model hyperparameters are optimized accordingly to obtain the target prediction model.

[0067] By simultaneously constraining prediction accuracy and model generalization ability during the optimization process, the dependence of the model on specific training samples can be reduced, enabling the obtained model to maintain relatively stable prediction performance even under conditions of large range of separation coefficient values ​​and uneven data distribution.

[0068] S5, Cobalt-Nickel Separation Coefficient Prediction Output:

[0069] The target prediction model inputs the leachate composition parameters, extractant structure information, and operating condition parameters under unknown waste lithium battery solution conditions, and outputs the predicted cobalt-nickel separation coefficient under the corresponding conditions. This method allows for quantitative evaluation of different extraction systems before experimentation, providing a reference for the screening and optimization of cobalt-nickel separation systems, thereby reducing the experimental process reliant on trial and error and lowering experimental costs.

[0070] This invention enables the prediction of cobalt-nickel separation coefficients using a machine learning model embedded with structural knowledge under complex extraction system conditions. The prediction process considers both experimental parameters and the structural characteristics of the extractant, thus improving the rationality and stability of the prediction results. Furthermore, this method provides a feasible path for applying machine learning techniques to the selective separation of metal solutions.

[0071] In a preferred embodiment, the cobalt-nickel separation coefficient is defined as the ratio of the distribution behavior of cobalt and nickel under the same extraction system and operating conditions. Specifically, under the same leachate composition, the same extractant system, and the same operating parameters, the distribution results of cobalt and nickel between the two phases are obtained, and the ratio of their distribution behavior is used as the characterization index of the cobalt-nickel separation coefficient.

[0072] By adopting the above-described method for defining the separation coefficient, the prediction target can directly reflect the relative separation characteristics of cobalt and nickel in the same system, rather than describing the extraction efficiency of a single metal. Since cobalt and nickel ions are chemically highly similar, their separation effect is usually influenced by the same extractant structure and operating conditions. Characterizing their distribution behavior as a ratio helps eliminate the interference of changes in overall system conditions on the prediction results for a single metal. In this invention, the cobalt-nickel separation coefficient is used as the prediction output of the machine learning model. This allows the model to focus on the relative changes between cobalt and nickel during training and prediction, thus better reflecting the practical technical problem of selective separation. This improves the model's ability to characterize the selective separation behavior of cobalt and nickel, making the prediction results more applicable to applications such as extraction system screening and process scheme comparison.

[0073] In a preferred embodiment, the data preprocessing and feature engineering process in step S2 specifically includes the following:

[0074] First, the continuous variables in the dataset are processed by consolidating records with consistent sources and duplicate values, and removing outliers that significantly deviate from the overall distribution range. This reduces the interference of duplicate samples and outliers on the model training process, allowing the model to focus more on the effective correlation between the cobalt-nickel separation coefficient and key experimental parameters, thus improving the stability of the modeling process.

[0075] Specifically, for example, to remove outlier data in a dataset where the x variable is the same but the y variable is different, the interquartile range method can be used to remove data outside the lower and upper limits.

[0076] Secondly, the categorical variables in the dataset are encoded, including at least solution type, solvent type, and extractant type. Preferably, the solution type, extractant type, and co-extractant type are all encoded using unique thermal encoding. By transforming different categories of information into a unified numerical feature form, the model can handle different extraction system conditions within the same computational framework, thereby enhancing the model's adaptability to diverse experimental conditions.

[0077] Furthermore, based on the aforementioned categorical variable encoding, a molecular fingerprinting method is introduced for extractant types, converting the molecular structure information of the extractant into a structural feature vector. Specifically, MACCS encoding is used for organic solvents to determine the content ratios of cycloalkanes, alkanes, and aromatics. This processing enables the model to perceive the impact of differences in the molecular structure of different extractants on the cobalt-nickel separation behavior during training, thus allowing for a more reasonable response to changes in the separation coefficient under similar experimental conditions but with different extractant structures.

[0078] Finally, correlation analysis is performed on the processed feature data to check for linear or monotonic correlations among the features, providing a reference for subsequent model construction and parameter optimization. This analysis helps identify the degree of correlation between features, avoids redundant features from causing unnecessary impact on model training, and thus improves the overall expressive efficiency of the model.

[0079] Specifically, in this embodiment, the Pearson correlation coefficient is used to detect feature correlation. The Pearson correlation coefficient measures the degree of linear correlation between two continuous feature variables, and its calculation formula is shown below:

[0080] ;

[0081] Where n is the number of samples. and Let be the values ​​of the two feature variables in the i-th sample, respectively. and These are the sample means of the corresponding feature variables.

[0082] like Figure 2 The heatmap features show the correlation matrix between various feature variables in the dataset. Its vertical and horizontal axes list the exact same variable names, covering key physicochemical parameters affecting the cobalt-nickel separation coefficient. These include continuous or coded features such as feed composition, extractant parameters, and reaction conditions. It covers feature variables such as initial cobalt / nickel concentration (Cobalt / Nickel g / L), extractant concentration, saponification rate, solvent ratio, temperature, contact time, A / O (comparative), and initial / equilibrium pH.

[0083] In the graph, the color of each grid cell reflects the Pearson correlation coefficient (ranging from -1 to 1) between the corresponding features on the horizontal and vertical axes. The shade of color indicates the strength of the linear correlation. The core information reflected in the chart is the correlation coefficient value: each square in the graph represents the correlation coefficient between two variables, such as the Pearson correlation coefficient.

[0084] This graph is used to check for severe linear correlations (collinearity) between features to ensure that the features input to the model are independent. For example... Figure 2 As shown, the highest Pearson correlation coefficient (r) among features is 0.76, indicating a strong positive linear correlation between some features. For example, the relationship between extractant concentration and partition ratio may appear as dark patches. This heatmap allows researchers to identify highly collinear features, thereby optimizing model input, ensuring the model is not biased due to feature redundancy, and ensuring that subsequent machine learning models can more accurately predict the cobalt-nickel separation coefficient.

[0085] Through the above data preprocessing and feature engineering, the resulting feature dataset maintains the integrity of the original experimental information while possessing clear structure and computable features, providing a stable data foundation for the subsequent cobalt-nickel separation coefficient prediction model based on structural knowledge embedding.

[0086] As a preferred embodiment, the molecular fingerprint used to characterize the molecular structure of the extractant includes one or more of MACCS molecular fingerprint, Morgan molecular fingerprint, or counting Morgan molecular fingerprint.

[0087] In practical implementation, depending on the complexity of the extractant molecule structure and modeling requirements, one molecular fingerprint can be selected as the structural feature, or multiple molecular fingerprints can be combined to describe the key structural units and local connectivity relationships in the extractant molecule. By adopting the above molecular fingerprint characterization method, molecular structure information can participate in model training in a unified and computable form, which is beneficial for the model to distinguish the influence of different extractant structures on the cobalt-nickel separation behavior under the same experimental conditions.

[0088] Employing different types of molecular fingerprints helps reflect the compositional characteristics and local structural differences of extractant molecules at different structural levels. This allows the prediction model to obtain more comprehensive structural information when facing extractant systems with diverse structural types, thereby improving its ability to characterize the changing trends of the cobalt-nickel separation coefficient. Furthermore, it enhances the model's adaptability to complex extraction systems without increasing experimental variables.

[0089] In a preferred embodiment, step S3 includes constructing and comparing different types of prediction models under the same training data conditions to determine candidate models for predicting the cobalt-nickel separation coefficient.

[0090] Specifically, based on the feature dataset obtained in step S2, a baseline prediction model without extractant structural features is first constructed. The baseline prediction model only uses the leachate composition parameters and operating condition parameters for modeling. At the same time, under the same data partitioning and training conditions, a knowledge embedding prediction model with extractant structural features is constructed, so that while learning the influence of experimental conditions, the model can further consider the role of extractant structural differences in cobalt-nickel separation behavior.

[0091] Subsequently, the predictive performance of the two types of models was compared and analyzed, and candidate models for predicting the cobalt-nickel separation coefficient were selected accordingly. By constructing and comparing models under the same training data conditions, the influence of data differences on model evaluation results can be effectively eliminated, making the model selection process more objective and facilitating the assessment of the actual role of introducing extractant structural features in predicting the cobalt-nickel separation coefficient.

[0092] Through the above steps, the obtained candidate model, while taking into account experimental conditions, further reflects the influence of extractant structure on the selective separation of cobalt and nickel, thus better meeting the separation prediction needs under conditions where cobalt and nickel have similar properties, and providing a reliable foundation for subsequent model optimization and separation system screening.

[0093] In a preferred embodiment, the model comparison in step S3 is performed based on the feature dataset processed in step S2, and specifically includes the following process:

[0094] First, based on multiple pre-defined machine learning model categories, prediction models were constructed under the same data conditions: one without MACCS molecular fingerprint features and the other with MACCS molecular fingerprint features. By comparing different models under two scenarios—relying solely on experimental condition parameters and considering extractant structural information—with or without incorporating MACCS molecular fingerprint features during model construction, a foundation was provided for analyzing the impact of structural features on the prediction of cobalt-nickel separation coefficients.

[0095] Subsequently, cross-validation was performed on the different models using randomly partitioned training and test sets, and performance was evaluated based on the prediction results during the validation process. The evaluation metrics included at least mean absolute error, root mean square error, coefficient of determination, and overall accuracy. This multi-metric comprehensive evaluation approach allowed for a comparative analysis of the predictive performance of different models. By employing multi-dimensional evaluation metrics, biases in judging model merits based on a single metric can be avoided, resulting in a more comprehensive and robust model selection.

[0096] In the above model comparison process, the machine learning models used included one or more of the following: lightweight gradient boosting machine, categorical feature gradient boosting machine, extreme gradient boosting model, or histogram gradient boosting model. All of these models possess strong nonlinear modeling capabilities and adaptability to complex data distributions, making them suitable for prediction scenarios with a large range of cobalt-nickel separation coefficient values ​​and complex feature relationships.

[0097] By employing the model comparison method described above, the impact of different model categories and the inclusion of MACCS molecular fingerprint features on prediction performance can be objectively compared under the same data conditions. This allows for the identification of the optimal model category and corresponding dataset combination for predicting cobalt-nickel separation coefficients. This process helps to screen out prediction models that are more suitable for describing the relative separation behavior of cobalt and nickel in the same extraction system, providing a reliable foundation for subsequent model optimization and separation system analysis.

[0098] In a preferred embodiment, during the model performance comparison process in step S3, the overall accuracy index is used as the basis for model evaluation to comprehensively assess the performance of different prediction models.

[0099] Specifically, the default hyperparameters are first used to evaluate each of the above model classes.

[0100] Multiple random partitioning validation: To eliminate the randomness bias caused by a single data partition, multiple random seeds (e.g., 100) are set to repeatedly partition the dataset randomly. At the same time, two different extractant encoding methods are compared: one-hot encoding and MACCS molecular fingerprinting. Five-fold cross-validation is performed on the training set with different partitions in four different function spaces. The average OAI of the validation set is used for evaluation. By comparing the average performance of different models on the validation set, the machine learning model category with the best prediction performance is selected.

[0101] By cross-validating and comparing multiple mainstream algorithms, the predictive performance of the two types of models is compared, and a candidate predictive model with superior overall performance is selected. Specifically, for example... Figure 3 This figure compares model performance with and without MACCS fingerprints, demonstrating the necessity of embedding domain knowledge (molecular fingerprints) into machine learning algorithms to improve prediction accuracy. The horizontal axis (model type) represents four pre-selected machine learning algorithm classes, from left to right: CatBoost, Lightweight Gradient Boosting (LGBoost), Histogram Gradient Boosting (HGBoost), and Extreme Gradient Boosting (XGBoost). The vertical axis represents the total accuracy (OAI) metric, a key performance indicator for model performance.

[0102] The specific formula for calculating OAI is as follows:

[0103] ;

[0104] The full accuracy index incorporates the coefficient of determination (R²). 2 The mean absolute error (MAE) and root mean square error (RMSE) are the three main parameters. Higher values ​​indicate better overall prediction accuracy of the model.

[0105] The red boxes represent those using MACCS molecular fingerprinting (described by 166 structural fragments), while the blue boxes represent those using only traditional one-hot encoding. Figure 3 It can be seen that, in all algorithms, the red boxes are generally higher than the blue boxes, indicating that molecular fingerprints can characterize the structural features of organic extractants at a deeper level.

[0106] A direct comparison reveals that the MACCS fingerprint dataset under the CatBoost model achieved a maximum average OAI of 3.71 across 100 partitions. The 38 random partitions showed the closest performance to the average OAI, thus earning it the designation as a candidate prediction model. This demonstrates that the MACCS fingerprint, by embedding knowledge of the extractant's substructure, significantly enhances the model's predictive ability for the cobalt-nickel separation coefficient.

[0107] Different models respond to structural knowledge to varying degrees. Tree models (such as CatBoost) are better able to utilize the structural information provided by molecular fingerprints due to their powerful nonlinear processing capabilities, while other models may offer limited improvement.

[0108] Specifically, when comparing the performance of prediction models that incorporate molecular fingerprint features with those that do not, the evaluation considers not only the prediction error on the validation data but also the model's ability to fit the changing trend of the cobalt-nickel separation coefficient. The overall accuracy index comprehensively reflects both prediction error and goodness-of-fit indices, ensuring that the model evaluation results simultaneously reflect both the magnitude of the prediction deviation and the overall fitting effect.

[0109] By adopting the above evaluation method, we can avoid making one-sided judgments on model performance based solely on a single error index, making the comparison of model performance more comprehensive and objective. This is beneficial for reasonably distinguishing the actual effects of the prediction model under different scenarios where structural features are not introduced. The model selected in this way is more suitable for describing the relative separation behavior of cobalt and nickel under conditions of similar properties, providing a stable model foundation for predicting the cobalt-nickel separation coefficient.

[0110] In a preferred embodiment, the comprehensive evaluation loss function used for model hyperparameter optimization in step S4 includes both prediction error index and overfitting constraint index, so as to balance prediction accuracy and generalization ability during the model optimization process.

[0111] Specifically, the prediction error metric reflects the overall prediction bias of the model on the validation data, while the overfitting constraint metric is characterized by the relationship between the prediction error on the validation set and the prediction error on the training set. When the model's prediction error on the training set is significantly lower than that on the validation set, it indicates that the model may be overfitting the training data. Introducing the aforementioned overfitting constraint metric helps to suppress this situation during the optimization process.

[0112] In one specific embodiment, the comprehensive evaluation loss function can be calculated according to the following formula:

[0113] ;

[0114] in, This represents the average root mean square error of the model on the validation set. This represents the average root mean square error of the model on the training set. This represents the average coefficient of determination of the model on the validation set.

[0115] By constructing a comprehensive evaluation loss function using the above formula, the model optimization objective is related not only to the prediction error on the validation set but also to the consistency of the model's error between the training and validation sets. This guides the model to achieve a balance between prediction accuracy and overfitting suppression during the hyperparameter search process. This approach is particularly suitable for modeling scenarios with a large range of cobalt-nickel separation coefficient values ​​and uneven sample distribution, and helps to obtain prediction models with good stability under unknown waste lithium battery solution conditions.

[0116] It should be noted that the specific form of the above comprehensive evaluation loss function can be adjusted according to the actual modeling needs. The purpose is to improve the applicability of the model in the cobalt-nickel separation coefficient prediction task by simultaneously introducing prediction error terms and overfitting constraint terms.

[0117] Specifically, in step S4, Optuna automatic optimization is used to automatically optimize the hyperparameters of the CaBoost model. The aim is to further enhance the model's prediction accuracy and strictly control the risk of overfitting through fine-tuning. The specific implementation process is as follows:

[0118] Optimize environment configuration: Select the data partition corresponding to the random seed (e.g., random seed 38) that best matches the average performance index in the initial comparison as the optimization benchmark.

[0119] Hyperparameter search space settings: Define the search range for the core parameters that affect generalization performance in the XGBoost model:

[0120] Regularization terms: Set the values ​​for L1 regularization and L2 regularization to be between 0 and 50.

[0121] Tree structure parameters: Set the maximum depth of the tree to 2 to 10 levels.

[0122] Sampling and Feature Ratios: The range of values ​​for sample subsampling ratio, feature ratio per layer, feature ratio per split point, and feature ratio per tree are all uniformly set to 0.1 to 1.

[0123] Custom Loss Function Guidance: In Optuna's iterative optimization process, instead of using a traditional single error function, a Comprehensive Evaluation Loss (CEI) is introduced as the objective function. This approach aims to achieve higher performance. While improving prediction accuracy, a penalty is imposed on the error offset between the training set and the validation set.

[0124] For details, see Figure 4 This diagram illustrates the Optuna hyperparameter optimization of the CatBoost model. The horizontal axis (Trial / Number of Trials) represents the number of iterations performed by the Optuna automatic optimization algorithm. As shown in the diagram, the system conducted approximately 200 trials, with each iteration representing an attempt at a different combination of hyperparameters. The vertical axis (Objective Value / Objective Function Value) is composed of the RMSE deviation between the validation and training sets and R0. 2 The system is designed to balance generalization ability and suppress overfitting. Lower values ​​indicate a more ideal overall performance for the model under that set of hyperparameters, achieving both high accuracy and low overfitting. The blue scatter dots in the graph represent the scores of each attempt, and the red step line represents the best (lowest) target value found so far. Through 200 iterations, the model locked in the optimal parameter combination: L2 regularization 44.19, tree depth 8, sampling ratio 0.12, learning rate 0.12, and number of decision trees. Applying the training set data to the above hyperparameter combination yielded the final target prediction model, significantly reducing the model's overfitting index and substantially improving generalization performance. This automated hyperparameter tuning process replaced traditional manual trial and error, ensuring excellent robustness of the model in the face of complex cobalt-nickel separation data.

[0125] Figure 5 The diagram illustrates the regression fit of the optimal CatBoost model. The horizontal axis (Actual separation coefficient (%) / actual separation coefficient) represents the experimentally measured cobalt-nickel separation coefficient.

[0126] The vertical axis (Predicted separation Efficiency (%)) represents the cobalt-nickel separation coefficient predicted by the optimized machine learning model based on the input parameters.

[0127] The data points (blue circles represent the training set, and yellow squares represent the test set) are closely arranged around the reference line (dashed line) of y=x. The closer the scatter points are to the dashed line, the closer the predicted value is to the true value, and the higher the model accuracy.

[0128] As shown in the graph, the distribution trends of the test set (blue dots) and the training set (yellow squares) are highly consistent, both closely surrounding the reference line. This demonstrates that after optimization with a custom loss function, the model not only possesses high prediction accuracy but also... 2 The model achieved a score of 0.73, an RMSE of 0.61, and a MAE of 0.39. Compared to the default hyperparameters, the final target prediction model demonstrated excellent generalization performance and prediction accuracy.

[0129] Example 2

[0130] This invention also provides a system for predicting the cobalt-nickel separation coefficient in waste lithium battery solutions, used to implement the aforementioned cobalt-nickel separation coefficient prediction method based on structural knowledge embedding. This system can be deployed on general-purpose computing devices and implemented through software modularization. The modules communicate with each other via data interfaces. Its structure and functions are as follows.

[0131] The data construction module is used to build a dataset of cobalt-nickel separation coefficients.

[0132] This module organizes publicly available literature data or experimental data to obtain data related to the separation of cobalt and nickel in waste lithium battery solutions. This data includes at least leachate composition parameters, extractant information, and operating condition parameters, with the cobalt-nickel separation coefficient serving as the corresponding target data. This module enables the system to simultaneously reflect the relative separation behavior of cobalt and nickel in the same extraction system at the data level, providing fundamental data support for subsequent predictive modeling.

[0133] The feature processing module is used to perform data preprocessing and structural knowledge feature construction on the dataset.

[0134] This module preprocesses the raw data, including operations such as organizing continuous variables and encoding categorical variables, and performs structured characterization of extractant-related information to form feature data that meets the requirements of machine learning modeling. This module reduces the impact of different data sources and experimental conditions on model training, giving the feature data a unified and computable form, which helps improve the stability of the system.

[0135] The knowledge embedding modeling module is used to introduce the molecular structure features of the extractant to build a predictive model.

[0136] Based on the data output by the feature processing module, this module incorporates the molecular structural features of the extractant as structural knowledge into the construction process of the prediction model. This allows the model to consider the effect of extractant structural differences on cobalt-nickel separation behavior while learning the influence of experimental conditions and parameters. This module helps improve the model's ability to express differences in complex extraction systems, making the prediction results more closely aligned with the selective separation problem of cobalt and nickel under conditions of similar properties.

[0137] The model comparison module is used to compare the performance of models that incorporate structural knowledge features and those that do not.

[0138] This module compares the performance of prediction models built solely based on experimental parameters with those built incorporating structural knowledge features under identical data conditions, and uses this comparison to select candidate models for predicting the cobalt-nickel separation coefficient. This comparison method makes the model selection process more objective and helps to determine the actual role of structural knowledge in the prediction task.

[0139] The prediction output module is used to output the prediction results of the cobalt-nickel separation coefficient.

[0140] This module inputs relevant parameters under unknown waste lithium battery solution conditions into a screened and optimized prediction model, and outputs the predicted cobalt-nickel separation coefficient under the corresponding conditions. This prediction output provides a reference for the screening and optimization of cobalt-nickel separation systems, thereby reducing the experimental process that relies on trial and error and lowering experimental costs.

[0141] Through the above-described system implementation method, the modules work together to achieve predictive modeling of the cobalt-nickel separation coefficient. This enables the system to simultaneously consider experimental parameters and extractant structure information under complex extraction system conditions, providing an achievable technical tool for the selective separation and analysis of cobalt and nickel in waste lithium battery solutions.

[0142] The above are merely preferred embodiments of the present invention and do not limit the patent scope of the present invention. All equivalent structural transformations made using the contents of the present invention specification and drawings under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A method for predicting the cobalt-nickel separation coefficient based on structural knowledge embedding, characterized in that, The steps include: S1. Based on literature database retrieval, construct an original dataset of cobalt-nickel separation coefficients, including leachate composition parameters, extractant structure information, and operating condition parameters; S2. Perform data preprocessing and feature engineering on the original dataset to obtain a feature dataset that meets the requirements of machine learning modeling; S3. Construct a baseline prediction model without domain knowledge features and a knowledge embedding prediction model with domain knowledge features on the feature dataset, respectively, and compare the model performance to determine the candidate prediction model. S4. Based on a comprehensive evaluation loss function that balances prediction accuracy and overfit suppression, the candidate prediction model is optimized for hyperparameters to obtain the target prediction model. S5. Using the target prediction model, predict and output the cobalt-nickel separation coefficient under unknown waste lithium battery solution conditions.

2. The method for predicting the cobalt-nickel separation coefficient based on structural knowledge embedding according to claim 1, characterized in that, The cobalt-nickel separation coefficient is a ratio representing the distribution behavior of cobalt and nickel under the same extraction system and operating conditions.

3. The method for predicting the cobalt-nickel separation coefficient based on structural knowledge embedding according to claim 1 or 2, characterized in that, The feature dataset construction in step S2 includes outlier removal for continuous variables and encoding for categorical variables.

4. A method for predicting the cobalt-nickel separation coefficient based on structural knowledge embedding according to claim 1 or 2, characterized in that, The domain knowledge features described in step S3 are introduced in the form of molecular fingerprints to characterize the influence of differences in extractant molecular structure on the selective separation behavior of cobalt and nickel.

5. The method for predicting the cobalt-nickel separation coefficient based on structural knowledge embedding according to claim 4, characterized in that, The molecular fingerprint includes one or more of MACCS molecular fingerprint, Morgan molecular fingerprint, or count-type Morgan molecular fingerprint.

6. A method for predicting the cobalt-nickel separation coefficient based on structural knowledge embedding according to claim 1 or 2, characterized in that, The prediction model constructed in step S3 is a gradient boosting regression model that can handle nonlinear feature relationships; The gradient boosting regression model includes one or more of the following: lightweight gradient boosting machine, categorical feature gradient boosting machine, extreme gradient boosting model, or histogram gradient boosting model.

7. A method for predicting the cobalt-nickel separation coefficient based on structural knowledge embedding according to claim 1 or 2, characterized in that, In step S4, an automated hyperparameter optimization algorithm is used to optimize the parameters of the prediction model; the optimization objective of the prediction model is to improve the generalization ability of the cobalt-nickel separation coefficient prediction.

8. A method for predicting the cobalt-nickel separation coefficient based on structural knowledge embedding according to claim 1 or 2, characterized in that, The comprehensive evaluation loss function described in step S4 includes both the prediction error index and the overfitting constraint index. The overfitting constraint index is characterized by the relationship between the prediction error of the validation set and the prediction error of the training set.

9. The method for predicting the cobalt-nickel separation coefficient based on structural knowledge embedding according to claim 8, characterized in that, The formula for calculating the comprehensive evaluation loss function is as follows: ； in, The average RMSE performance on the validation set; The average RMSE performance of the training set; For the average validation set R 2 .

10. A system for predicting the cobalt-nickel separation coefficient in waste lithium battery solutions, characterized in that, include: The data construction module is used to build a dataset of cobalt-nickel separation coefficients; The feature processing module is used for data preprocessing and structural knowledge feature construction. The knowledge embedding modeling module is used to introduce the molecular structure features of the extractant to build a predictive model; The model comparison module is used to compare the performance of models that incorporate structural knowledge features and those that do not. The prediction output module is used to output the prediction results of the cobalt-nickel separation coefficient.

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