A method for predicting activity coefficient of rare earth electrolyte solution based on machine learning

Abstract

This invention discloses a machine learning-based method for predicting the activity coefficient of rare earth electrolyte solutions, belonging to the field of rare earth electrolyte technology. The method involves acquiring historical electrolyte solution data of the target rare earth element, performing preprocessing operations, and dividing the data into training and test sets according to a preset ratio. A Debye-Hückel term is constructed from the obtained training set. Higher-order interaction terms from the Pitzer model are introduced into the Debye-Hückel term, and based on the training electrolyte solution dataset, an input term for a thermodynamic parameter prediction model is constructed. After the input term is input into the thermodynamic parameter prediction model, the activity coefficient of the target rare earth element is output from the model output layer through a nonlinear transformation. The trained model is then validated and adjusted based on test electrolyte solution data. This invention is faster than experimental measurement methods; more accurate than existing machine algorithms; and shortens the time required to acquire thermodynamic parameters, reducing acquisition costs.

Description

Technical Field

[0001] This invention relates to the field of rare earth electrolyte technology, and in particular to a method for predicting the activity coefficient of rare earth electrolyte solutions based on machine learning. Background Technology

[0002] Rare earth electrolytes have wide applications in numerous fields, such as rare earth metallurgy and fuel cells. Accurately understanding the thermodynamic parameters of rare earth electrolytes is crucial for optimizing their performance, improving production efficiency, and reducing costs. Among these thermodynamic parameters, the activity coefficient is the most important. Current technologies for obtaining the thermodynamic parameters of rare earth electrolytes primarily rely on experimental measurement methods.

[0003] However, experimental measurement methods are often costly, time-consuming, and complex. Furthermore, with the continuous emergence of novel rare-earth electrolyte materials, traditional methods cannot quickly, efficiently, and accurately obtain their thermodynamic parameters, thus slowing down the material development process. Therefore, there is an urgent need to provide a machine learning-based method for predicting the thermodynamic parameters of rare-earth electrolytes. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a machine learning-based method for predicting the activity coefficient of rare earth electrolyte solutions.

[0005] To achieve the above technology, the specific steps are as follows:

[0006] S1. Obtain historical electrolyte solution data of the target rare earth through open source data, and perform preprocessing operations on the obtained data; divide the preprocessed data into training electrolyte solution dataset and test electrolyte solution dataset according to a preset ratio;

[0007] Historical electrolyte solution data for the target rare earth element includes: element types, content, temperature, and pressure of the target rare earth solution;

[0008] Preprocessing removes outliers; Z-score normalization is applied to the concentration and temperature of the solution; one-heat encoding is used to convert each rare earth element into a binary vector, where only the corresponding element's position is 1 and the rest are 0, which facilitates the processing and differentiation of different rare earth element types and helps in the subsequent accurate prediction of thermodynamic parameters; missing value processing is performed by using KNN interpolation on the sparse data of solution concentration.

[0009] S2. Construct Debye-Hückel terms from the obtained training electrolyte solution dataset for analysis of low-concentration electrolyte solutions;

[0010] The Debye-Hückel term expression is as follows:

[0011]

[0012] In the formula, I represents the ionic strength of the solution; B represents a constant related to the solvent dielectric constant and temperature; and a represents the radius of the ion.

[0013] S3. Introduce higher-order interaction terms from the Pitzer model into the Debye-Hückel term and construct the input terms of the thermodynamic parameter prediction model input layer based on the training electrolyte solution dataset;

[0014] Higher-order interaction terms in the Pitzer model are used to enhance the model's generalization ability to high-concentration, multi-component systems; these higher-order interaction terms include the two-body interaction parameter β. (0) and concentration-dependent correction parameter β (1) ;

[0015] The elements of the target rare earth solution in the training electrolyte dataset are selected, and the radius of the elements is obtained based on the elements; the temperature of the target rare earth electrolyte solution is also selected.

[0016] XGBoost was selected as the thermodynamic parameter prediction model.

[0017] The inputs to the thermodynamic parameter prediction model include: Debye-Hückel terms and higher-order interaction terms (β) from the Pitzer model. (0) and β (1) The elemental radius, elemental concentration, and electrolyte temperature of the target rare earth element are also considered.

[0018] S4. Input Items: After inputting thermodynamic parameters into the prediction model, the activity coefficient of the target rare earth element is output from the model output layer through nonlinear transformation to complete model training.

[0019] The expression for the nonlinear transformation is as follows:

[0020]

[0021] In the formula, A represents a constant related to the solvent and temperature; z + z - α represents the charge number of the positive and negative ions, respectively; I represents the ionic strength of the solution; B represents a constant related to the solvent dielectric constant and temperature; a represents the radius of the ion; β represents the ionic radius. (0) Represents the two-body interaction parameter; β (1) Indicates the concentration-dependent correction parameter; γ ± Indicates the activity coefficient;

[0022] The hidden layer inputs its output to the output layer via the ReLU function; the activation function uses the ReLU function to avoid the gradient vanishing problem and improve the performance of the thermodynamic parameter prediction model.

[0023] The thermodynamic parameter prediction model uses mean square error (MSE) as a loss function to measure the difference between the activity coefficient and historical thermodynamic parameters;

[0024] The thermodynamic parameter prediction model uses the stochastic gradient descent algorithm to adjust the parameters of the machine learning model until the training error reaches its minimum.

[0025] S5. Validate and adjust the trained model based on the test electrolyte solution data;

[0026] Validation includes: using 5-fold cross-validation to ensure model generalization;

[0027] The adjustment methods are as follows: use L2 regularization to prevent overfitting; interpret feature importance through SHAP analysis; calculate the model error on the test data until MSE≤0.08 is achieved.

[0028] The beneficial effects of this invention are:

[0029] This invention introduces the Debye-Hückel term for the analysis of low-concentration electrolyte solutions, while also incorporating higher-order interaction terms from the Pitzer model to correct the effects of ion pairs and complexes at high concentrations. Through a thermodynamic parameter prediction model, the thermodynamic parameters of rare-earth electrolytes can be predicted quickly and accurately, thereby significantly shortening the time and cost of obtaining these parameters.

[0030] The method of this invention is not limited by experimental conditions and can predict the thermodynamic parameters of rare earth electrolytes under various complex conditions, providing strong support for the application of rare earth electrolytes in different scenarios. Furthermore, the system of this invention has good scalability; with continuous data accumulation and updates, the thermodynamic parameter prediction model can be further optimized, improving the accuracy and reliability of the model predictions. Attached Figure Description

[0031] Figure 1 This is a flowchart of the steps of the present invention. Detailed Implementation

[0032] The present invention will be further described in detail below with reference to specific embodiments.

[0033] like Figure 1 As shown, a machine learning-based method for predicting the activity coefficient of rare earth electrolyte solutions is presented, predicting the activity coefficient of LaCl3 at 298 K and a concentration of 2.5 mol / L. The steps are as follows:

[0034] S1. Obtain historical electrolyte solution data of the target rare earth through open source data, and perform preprocessing operations on the obtained data; divide the preprocessed data into training electrolyte solution dataset and test electrolyte solution dataset according to a preset ratio;

[0035] In this embodiment, the open-source data includes: historical experimental records, research reports, and experimental databases (such as NIST and ICDD); the preset ratio is 8:2.

[0036] Historical electrolyte solution data for the target rare earth element includes: element types, content, temperature, and pressure of the target rare earth solution;

[0037] Preprocessing operations include: removing outliers; Z-score normalization of solution concentration and temperature; converting each rare earth element type into a binary vector using one-heat encoding, where only the corresponding element's position is 1 and the rest are 0, thus facilitating the processing and differentiation of different rare earth element types and aiding in accurate subsequent thermodynamic parameter prediction; and handling missing values, i.e., using KNN interpolation to process sparse solution concentration data.

[0038] S2. Construct Debye-Hückel terms from the obtained training electrolyte solution dataset for analysis of low-concentration electrolyte solutions;

[0039] The Debye-Hückel term expression is as follows:

[0040]

[0041] In the formula, I represents the ionic strength of the solution; B represents a constant related to the solvent dielectric constant and temperature; and a represents the radius of the ion.

[0042] In this embodiment, the prediction target is LaCl3 solution, and I = 3 × 2.0 = 6.0.

[0043] S3. Introduce higher-order interaction terms from the Pitzer model into the Debye-Hückel term and construct the input terms of the thermodynamic parameter prediction model input layer based on the training electrolyte solution dataset;

[0044] The number of neurons in the input layer is the same as the number of input items to ensure that the data enters the input layer completely and accurately;

[0045] Higher-order interaction terms in the Pitzer model are used to enhance the model's generalization ability to high-concentration, multi-component systems; these higher-order interaction terms include the two-body interaction parameter β and the concentration-dependent correction parameter β. 1 ;

[0046] The elements of the target rare earth solution in the training electrolyte dataset are selected, and the radius of the elements is obtained based on the elements; the temperature of the target rare earth electrolyte solution is also selected.

[0047] In this embodiment, La 3 + radius is Cl - radius is The target rare earth electrolyte solution temperature is 298K;

[0048] XGBoost was selected as the thermodynamic parameter prediction model.

[0049] The inputs to the thermodynamic parameter prediction model include: Debye-Hückel terms and higher-order interaction terms (β) from the Pitzer model. (0) and β (1) The elemental radius, elemental concentration, and electrolyte temperature of the target rare earth element are also considered.

[0050] S4. Input Items: After inputting thermodynamic parameters into the prediction model, the activity coefficient of the target rare earth element is output from the model output layer through nonlinear transformation to complete model training.

[0051] The nonlinear transformation process is completed in the hidden layer of the thermodynamic parameter prediction model;

[0052] The expression for the nonlinear transformation is as follows:

[0053]

[0054] In the formula, A represents a constant related to the solvent and temperature; z + z - They represent positive ions (La) 3 +) and negative ions (Cl) - The charge number of the ion; I represents the ionic strength of the solution; B represents a constant related to the solvent dielectric constant and temperature; a represents the radius of the ion; β (0) β represents the two-body interaction parameter. (0) The range in rare earth electrolytes is generally 0.10-0.35 (high charge leads to enhanced electrostatic interaction), and in this embodiment, it is taken as 0.2; β (1) This represents the concentration-dependent correction parameter, β. (1) Range: typically -1.2 to 0.8, in this embodiment -0.05; γ ± Indicates the activity coefficient;

[0055] The hidden layer inputs its output to the output layer via the ReLU function; the activation function uses the ReLU function to avoid the gradient vanishing problem and improve the performance of the thermodynamic parameter prediction model.

[0056] The number of neurons in the output layer is the same as the number of output terms; in this invention, the output term is the activity coefficient.

[0057] The thermodynamic parameter prediction model uses mean square error (MSE) as a loss function to measure the difference between the activity coefficient and historical thermodynamic parameters;

[0058] The thermodynamic parameter prediction model uses the stochastic gradient descent algorithm to adjust the parameters of the machine learning model until the training error reaches its minimum.

[0059] S5. Validate and adjust the trained model based on the test electrolyte solution data;

[0060] Validation includes: using 5-fold cross-validation to ensure model generalization;

[0061] The adjustment methods are as follows: use L2 regularization to prevent overfitting; interpret feature importance through SHAP analysis; calculate the model error on the test data until MSE≤0.08 is achieved.

[0062] In this embodiment, XGBoost predicts the activity coefficient γ. ± =0.67, experimental value is 0.68 (error 2.9%); compared with the Pitzer model predicting the activity coefficient γ ± =0.62 (error 10.1%), demonstrating the advantages of this invention. At high concentrations (>1 mol / L), the root mean square error (RMSE) of this invention is reduced by 56% compared to the Pitzer model's root mean square error (RMSE), and the coefficient of determination (R²) is... 2 It improves upon the previous model by 12% and is 60 times faster than the Pitzer model.

[0063] In summary, this invention utilizes a thermodynamic parameter prediction model to rapidly and accurately predict the thermodynamic parameters of rare earth electrolytes, thereby significantly reducing the time and cost of acquiring these parameters. The method is not limited by experimental conditions and can predict the thermodynamic parameters of rare earth electrolytes under various complex conditions, providing strong support for their application in different scenarios. Furthermore, the system exhibits good scalability; with continuous data accumulation and updates, the thermodynamic parameter prediction model can be further optimized, improving its accuracy and reliability.

Claims

1. A method for predicting activity coefficients of rare earth electrolyte solutions based on machine learning, characterized by, Includes the following steps: S1. Obtain historical electrolyte solution data of the target rare earth through open source data, and perform preprocessing operations on the obtained data; Historical electrolyte solution data for the target rare earth element includes: element types, content, temperature, and pressure of the target rare earth solution; The preprocessed data is divided into a training electrolyte solution dataset and a test electrolyte solution dataset according to a preset ratio. S2. Construct Debye-Hückel terms from the obtained training electrolyte solution dataset for analysis of low-concentration electrolyte solutions; The expression for constructing the Debye-Hückel term is as follows: ； where I represents the ionic strength of the solution; B represents a constant related to the dielectric constant of the solvent and temperature; represents the radius of the ion; S3. Introduce higher-order interaction terms from the Pitzer model into the Debye-Hückel term and construct input terms for the input layer of the thermodynamic parameter prediction model based on the training electrolyte solution dataset. The higher-order interaction terms in the Pitzer model include: two-body interaction parameters. and concentration-dependent correction parameters ; The inputs include: the concentration of the target rare earth solution, the temperature of the target rare earth solution, the Debye-Hückel term, and the two-body interaction parameters. Concentration-dependent correction parameters and the ionic radius in the target rare earth solution; S4. Input Items: After inputting thermodynamic parameters into the prediction model, the activity coefficient of the target rare earth element is output from the model output layer through nonlinear transformation to complete model training. The expression for the nonlinear transformation is as follows: ； In the formula, This represents a constant related to the solvent and temperature; These represent the charge numbers of positive and negative ions, respectively. Indicates the activity coefficient; S5. Validate and adjust the trained model based on the test electrolyte solution data.

2. The method for predicting the activity coefficient of rare earth electrolyte solutions based on machine learning according to claim 1, characterized in that: The process of acquiring historical electrolyte solution data of the target rare earth element through open source data and performing preprocessing operations on the acquired data includes: removing outliers; performing Z-score normalization on the concentration and temperature of the solution; encoding each rare earth element using one-heat encoding; and performing KNN interpolation on the sparse concentration data of the solution.

3. The method of claim 1, wherein the method is based on machine learning. The validation methods for verifying and adjusting the trained model based on test electrolyte solution data include: using 5-fold cross-validation to ensure model generalization; the adjustment methods include: using L2 regularization to prevent overfitting; interpreting feature importance through SHAP analysis; and calculating the model error on the test electrolyte solution data until the mean squared error is ≤0.08.

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