A thermistor particle preparation optimization method based on machine learning

Abstract

This invention belongs to the technical field of thermosensitive material preparation, specifically a method for optimizing the preparation of thermistor particles based on machine learning. This method constructs a dataset containing thermistor particle preparation process parameters, performance indicators, and knowledge of physicochemical mechanisms. The preparation process parameters include material composition and preparation conditions. A machine learning model is then used to predict the optimal preparation conditions, achieving multi-objective collaborative optimization of the Curie temperature and resistance temperature coefficient of thermistor particles. Compared with traditional trial-and-error methods, this invention can reduce R&D costs, with a target performance prediction error of less than 5%. By integrating physicochemical mechanisms with data-driven models, this invention solves the problem of traditional methods' difficulty in accurately controlling multiple performance parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of thermosensitive material preparation, and in particular to a method for optimizing the preparation of thermistor particles based on machine learning. Background Art

[0002] With the rapid development of emerging sectors such as electric vehicles and wearable devices, the demand for and waste volume of lithium batteries continues to grow. Lithium batteries contain large amounts of precious metals such as lithium, nickel, and cobalt, which have high recycling value. However, they also contain toxic and hazardous substances such as electrolytes and binders. The potential environmental impact of waste lithium batteries and the need for resource recovery technologies have long attracted widespread attention.

[0003] The key to recycling scrapped lithium batteries lies in safe discharge pretreatment. While the currently commonly used unstructured chemical discharge method, which involves immersion in a NaCl solution, is low-cost and offers excellent conductivity, it can easily damage the battery's positive electrode casing, allowing harmful substances to leak, polluting the environment and endangering human health. Testing of the discharge wastewater revealed that the solution contains significant amounts of metal ions such as Fe, Al, Li, Mn, and Ni, as well as organic compounds and fluorides. Testing of the gases released during discharge revealed significant amounts of hydrogen fluoride, Cl2, and organic pollutants, in addition to hydrogen and oxygen. In comparison, a physical discharge method, in which the battery is enclosed in solid conductive particles and the electrical energy is converted into particle heat, offers significant advantages, reducing pollution leakage and being more environmentally friendly and safe. The performance of the solid conductive particles is crucial. To achieve safe and effective physical discharge, the solid conductive particles, or thermistor particles, must simultaneously possess a low Curie temperature and a high temperature coefficient of resistance, facilitating both low-temperature open-circuit and high-temperature open-circuit disconnection, thus addressing the thermal runaway issue associated with physical discharge.

[0004] Existing thermistors, mostly used in temperature sensors and heaters, have high Curie temperatures (Tc) or low resistance temperature coefficients (α), failing to meet the technical requirements for safe physical discharge of lithium batteries. A Chinese patent application (CN 114456312A) discloses a low-Curie-temperature thermistor material, but its resistance temperature coefficient reaches only 8% / °C, making it difficult to meet physical discharge requirements. Prior art has yet to uncover the nonlinear relationship between doping element selection, sintering temperature control, and the coordinated optimization of multiple properties, leading to high experimental blindness and long R&D cycles. A Chinese patent application (CN 117352101A) discloses a machine learning-based method for rapidly predicting the electrical conductivity of thermoelectric materials. This method, based on a single traditional random forest model, relies on chemical formula analysis and statistical features, focusing solely on predicting a single thermoelectric material property (conductivity), failing to meet the requirements of complex application scenarios (such as safe lithium battery discharge).

[0005] Traditional R&D and preparation methods for thermosensitive materials rely primarily on experimental exploration, with complex process conditions. This process requires significant experimental costs and time. Furthermore, any adjustments to material combinations or preparation conditions require repeated, tedious experiments, resulting in a lengthy and costly R&D cycle. Furthermore, conventional methods for preparing positive temperature coefficient thermistors often make it difficult to simultaneously control multiple performance parameters, significantly limiting the application of this material.

[0006] The above background technology refers to the following published documents:

[0007] [1]Shimada T., Touji K., Katsuyama Y., et al. Lead free PTCR ceramics and its electrical properties[J]. Journal of the European Ceramic Society, 2007; 27(13-15): 3877-3882.

[0008] [2] Zhao Jiaojiao, Wang Bo, Zhang Boqi. Research on preparation method of lead-free barium titanate-based positive temperature coefficient thermistor ceramic materials[J]. Papermaking Equipment and Materials, 2022, 51(12): 68-70.

[0009] [3] A composite positive temperature coefficient thermistor material and preparation method, Tianjin Ruiken New Material Technology Co., Ltd., application number: CN202210326315.X, application date: 2022-03-30.

[0010] [4] Lead-free PTC thermistor ceramic material with low room temperature resistivity and high lift-to-resistance ratio and its preparation method, Shanghai Institute of Materials Co., Ltd., application number: CN202211569319.7, application date: 2022-12-08. Summary of the Invention

[0011] The present invention aims to overcome the shortcomings of existing technologies by providing a multi-objective method for preparing thermistor particles based on machine learning optimization. The prepared thermistor particles simultaneously meet the requirements of a low Curie temperature and a high temperature coefficient of resistance (TCR). This method utilizes machine learning to improve the development efficiency of thermistor particles. By comprehensively considering the impact of different reaction variables on various product properties, the method optimizes the selection of reactants and the design of reaction conditions, achieving precise control of thermistor particle performance. This method collaboratively optimizes the multi-objective performance of thermistor particles (Curie temperature Tc and TCR α), better meeting the requirements of complex application scenarios (such as safe discharge of lithium batteries). In constructing the machine learning model, a graph convolutional neural network (GCN) is used to model the topological relationships between material composition, process, and performance, enabling the mining of complex nonlinear relationships. Furthermore, the method integrates physical and chemical mechanisms (such as dopant ion radius and lattice matching constraints) to transform mechanistic knowledge into quantifiable features or model constraints, improving prediction accuracy and interpretability.

[0012] The purpose of the present invention can be achieved through the following technical solutions.

[0013] The present invention provides a method for optimizing the preparation of thermistor particles based on machine learning, which comprises the following steps:

[0014] S1: Construct a dataset containing thermistor particle preparation process parameters, performance indicators, and physical and chemical mechanism knowledge, and perform preprocessing. The preparation process parameters include material composition and preparation conditions, and the performance indicators include the Curie temperature and resistance temperature coefficient of thermistor particles.

[0015] S2: Build and optimize machine learning models

[0016] Incorporate knowledge of physical and chemical mechanisms into the model architecture or training process in the form of prior information, and design a specific network layer structure or loss function adjustment method;

[0017] S3: Using the performance indicators of thermistor particles as target labels, the optimized machine learning model constructed in S2 is trained using the dataset in S1.

[0018] S4: Input the desired performance indicators of thermistor particles into the trained machine learning model, and the model outputs the most suitable material composition and preparation conditions;

[0019] S5: Prepare thermistor particles according to the material composition and preparation conditions output by the model;

[0020] S6: The prepared thermistor particles are tested for performance indicators. If the test data does not meet the target requirements, the test data is added to the data set in step S1 and the model is retrained. When the test data meets the requirements, the update is terminated to determine the optimal solution for the preparation of the thermistor particles.

[0021] In the present invention, in step S1, the thermistor particles are barium titanate-based thermistor particles, and the preparation process of the thermistor particles is a high-temperature solid-phase method. The specific steps include: mixing the raw materials of the barium titanate matrix and the doping element precursor, wet ball milling and then drying, first pre-calcining under an inert atmosphere, then adding a sintering aid AST, wet ball milling and then drying, and finally sintering in an air atmosphere.

[0022] In the present invention, in step S1, the data is concentrated, the material composition includes: the amount of barium titanate matrix, the type and amount of doping elements, and the amount of sintering aid AST, and the preparation conditions include: sintering temperature, pre-firing time, holding time, heating and cooling rate and ball milling time.

[0023] In the present invention, in step S1, when constructing the data set, the physicochemical mechanism knowledge is converted into quantifiable features or constraints. The physicochemical mechanism knowledge includes: the crystal structure of the barium titanate matrix and thermistor particles, the atomic number, ionic radius, valence state, electronegativity of each element in the matrix and doping material, as well as the matrix lattice distortion energy, oxygen vacancy concentration, grain size, and electron cloud overlap integral; wherein:

[0024] Lattice distortion energy The difference in ionic radius between doped ions and barium titanate matrix calculate:

[0025] ,

[0026] in, , and are the radii of the dopant atom and the host atom, respectively;

[0027] Oxygen vacancy concentration Calculated by the following formula:

[0028] ,

[0029] in, is the concentration of the doping element, is the difference between the valence state of the doping element and the valence state of the replaced host ion, is the oxygen vacancy formation energy, which is 1.2 eV. is the Boltzmann constant, is temperature;

[0030] Grain size after sintering Prediction based on Beck equation:

[0031] ,

[0032] in is the grain size, is the sintering time, is the Boltzmann constant, is temperature;

[0033] Electron cloud overlap integral of dopant ions and barium titanate lattice The calculation method is as follows:

[0034] ,

[0035] in, and are the radii of the dopant atom and the host atom, respectively.

[0036] In the present invention, in step S1, the data set is normalized by using the minimum-maximum scaling method to map the numerical parameters to the interval [0, 1] to avoid model deviation caused by the scale difference of the dependent variable; the non-numeric parameters involved are encoded using one-hot encoding.

[0037] In the present invention, in step S2, the selected machine learning model is one of random forest, support vector machine, XGBoost, Adaboost or deep learning network.

[0038] In the present invention, in step S2, the machine learning model is a graph neural network model GCN. During the forward propagation of the network, the degree of influence of different parameters on the performance indicators is reflected by calculating the attention weight. The construction of the graph structure is based on the perovskite crystal structure, and elements (such as Ba, Ti, O) are set as nodes. The node characteristics include physical parameters such as atomic number, ionic radius, valence state, lattice distortion energy and the amount of each element. Then, the edges are constructed based on the interatomic chemical bonds and doping substitution relationships: Ba and Ti are connected through O to form a perovskite skeleton, and elements such as Sr, La, and Y are connected to the Ba node when replacing the Ba position, and Nb, Mn, etc. are connected to the Ti node when replacing the Ti position. The edge features describe the interatomic interaction through bond strength, distance and type (chemical bond, substitution relationship, weak interaction, etc.), and finally form graph data that maps the microstructure of the material.

[0039] In the present invention, in step S2, the Bayesian optimization algorithm is used to adjust the graph convolutional neural network (GCN) hyperparameters. The specific optimization parameters include:

[0040] (1) Network structure parameters: hidden layer dimension ∈ [64, 512], number of convolutional layers ∈ [2, 5], dropout rate ∈ [0.1, 0.5];

[0041] (2) Training process parameters: learning rate ∈ [0.0001, 0.1], weight decay ∈ [1e-5, 1e-3], batch size ∈ [16, 128];

[0042] (3) Physical constraint weights: lattice distortion energy weight α∈[0.1,0.5], oxygen vacancy concentration weight β∈[0.05,0.3];

[0043] The optimization goal is to minimize the prediction error MSE while maximizing the satisfaction of physical constraints. The optimization process uses Gaussian process regression to construct a surrogate model.

[0044] In the present invention, in step S2, during the model construction process, the mechanism knowledge is integrated into the model architecture or training process in the form of prior information, the doping amount is limited so that the lattice distortion energy is ≤0.5eV / atom, the doping concentration is controlled so that the oxygen vacancy concentration is ≤0.05, the doping combination with the electron cloud overlap integral ≥0.5 is screened, the sintering process is optimized so that the grain size is controlled within the range of 1-5μm, a specific network layer structure or loss function adjustment method is designed, and the graph convolution features and physical features are spliced ​​together to output the performance indicators through the fully connected layer, i.e., the predicted values ​​of the Curie temperature point and the resistance temperature coefficient of the prepared thermistor particles.

[0045] In the present invention, in step S2, the attention mechanism and GCN are combined in the constructed model; in step S3, when training the model, the attention weights in the forward propagation process of the network model are used to quantify the contribution of different nodes and edges to the prediction.

[0046] In the present invention, in step S3, the loss function of training adopts multi-task joint loss:

[0047] ,

[0048] in is the basic regression loss, 、 、 are the losses due to grain size, oxygen vacancy concentration and doping amount constraints, 、 、 is the weight parameter.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] 1. The present invention uses machine learning methods to assist in the preparation of thermistor particles, avoiding the waste of resources caused by traditional experimental-intensive "trial and error" experiments, reducing R&D costs, shortening the R&D cycle, and improving the predictability and repeatability of the R&D process.

[0051] 2. This invention introduces machine learning methods and utilizes the attention weights in the forward propagation process of the network model to quantify the contribution of different nodes and edges to the prediction. It can identify the degree of influence of different parameters in a large amount of complex experimental data, thereby quickly locating key parameters, reducing trial and error costs, and providing a "data-driven" regulation direction.

[0052] 3. The multi-objective optimization design method is used to simultaneously meet the conditions of low material Curie temperature and high resistance temperature coefficient. The model is updated by feeding back experimental data to form a closed-loop optimization process with good practical value.

[0053] 4. The physicochemical mechanism of thermistor particle performance formation is innovatively integrated into the machine learning prediction process, achieving a deep fusion of mechanism and data, improving the reliability and interpretability of model predictions, and reducing the model's dependence on data. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a logical framework diagram of the present invention.

[0055] Figure 2 Graphs showing the prediction performance evaluation of the XGBoost model in Example 1, showing (a) Curie temperature and (b) resistance temperature coefficient.

[0056] Figure 3 Graphs showing the prediction performance evaluation of the XGBoost model in Example 2, showing (a) Curie temperature and (b) resistance temperature coefficient.

[0057] Figure 4 Graphs showing the prediction performance evaluation of the GCN model in Example 3, showing (a) Curie temperature and (b) resistance temperature coefficient.

[0058] Figure 5 Graphs showing the prediction performance evaluation of the GCN model in Example 4, showing (a) Curie temperature and (b) resistance temperature coefficient. DETAILED DESCRIPTION

[0059] The present invention will be further described and illustrated by the following examples. The examples are merely illustrative of the present disclosure and do not limit its scope. The technical features of the various embodiments of the present invention may be combined accordingly, provided that there is no conflict between them.

[0060] The present invention provides a method for preparing thermistor particles based on machine learning optimization that meets multiple objectives, comprising the following steps:

[0061] S1: Obtain the material composition, preparation conditions and other preparation process parameters of thermistor particles and the corresponding electrical performance test results as a data set, and split the data set into a training set, a validation set and a test set;

[0062] S2: Select a machine learning model that can handle small datasets and nonlinear problems, and choose a method to adjust and optimize the model's hyperparameters;

[0063] S3: Use the dataset in S1 to train and test the machine learning model selected in S2 and evaluate the model performance;

[0064] S4: Based on the output of the model after training and evaluation in S3, a preparation plan is prepared as expected to achieve the target performance;

[0065] S5: Prepare thermistor particles using a high-temperature solid-phase method according to the expected preparation plan;

[0066] S6: Test the target performance of the prepared thermistor particles. If the test data does not meet the target requirements, update the data set and model.

[0067] Furthermore, in S1, the material composition, preparation conditions and other preparation process parameters of the thermistor particles and the corresponding electrical and physical performance test results and related mechanism knowledge are obtained as a data set. Specifically, literature research and experimental testing are conducted on various materials used in the preparation to establish a data set including parameters such as material composition (such as barium titanate dosage, doping element dosage), preparation conditions (such as sintering temperature, ball milling time), performance indicators (such as particle Curie temperature, particle resistance temperature coefficient) and mechanism knowledge (such as undoped barium titanate Curie temperature, ionic radius of each element, ionic radius of each element, ionic valence state of each element).

[0068] Furthermore, in S1, the variables are normalized, and the maximum and minimum values ​​of the variable data are used to scale data of different orders of magnitude to the interval [0,1] to ensure that the model will not be biased by the scale of the variables; further, nonlinear models can capture more complex dependencies, such as the product or high-order term relationship between variables, which is crucial for understanding more complex system dynamics and improving prediction accuracy; through normalization, that is, scaling all input variables to the same scale, the model can be prevented from assigning too much importance to certain variables due to their large scale during training, which helps to improve the generalization ability of the model and ensure the fairness and appropriate influence of each input variable in model training.

[0069] Furthermore, in S1, we conducted in-depth research on the physical and chemical mechanisms of thermistor particle performance formation, converted the relevant mechanism knowledge into quantifiable features or constraints, and integrated them into the dataset construction process. The specific mechanism knowledge includes lattice distortion energy, oxygen vacancy concentration, grain size, and electron cloud overlap integral.

[0070] The lattice distortion energy is calculated by the difference in ionic radius between the doped ions and the barium titanate matrix ( ) Calculate the lattice distortion energy (eV / atom), where is the lattice distortion energy, and are the radii of the dopant atom and the host atom respectively; the oxygen vacancy concentration is calculated by establishing an oxygen vacancy concentration model Calculate, where is the oxygen vacancy concentration, is the concentration of the doping element, is the difference between the valence state of the doping element and the valence state of the replaced host ion, is the oxygen vacancy formation energy, which is 1.2 eV. is the Boltzmann constant, is temperature;

[0071] Grain size prediction is based on Beck equation to predict the grain size after sintering. The formula is: ,in is the grain size, is the sintering time, is the Boltzmann constant, is temperature;

[0072] Calculation of the electron cloud overlap integral between dopant ions and the barium titanate lattice ,in is the electron cloud overlap integral, and are the radii of the dopant atom and the host atom, respectively;

[0073] The above mechanism parameters are normalized and then integrated into the data set as independent features or constraints.

[0074] Furthermore, in S1, non-numeric parameters such as crystal structure and doping type are one-hot encoded to distinguish parameters such as different crystal structures and doping types.

[0075] Furthermore, in S1, the data set is divided into a training set, a validation set and a test set. Specifically, during the training process, the data set is randomly divided into a training set, a validation set and a test set in a ratio of 8:1:1.

[0076] Furthermore, in S2, the selected machine learning model is one of random forest, support vector machine, XGBoost, Adaboost, and deep learning network; preferably, the machine learning model is a graph convolutional neural network (GCN) deep learning network model.

[0077] Furthermore, in S2, the Bayesian optimization method is used to adjust the hyperparameters of the machine learning model, and the cross-validation method is used to evaluate the performance of the model under different hyperparameters. The specific optimization parameters include:

[0078] (1) Network structure parameters: hidden layer dimension ∈ [64, 512], number of convolutional layers ∈ [2, 5], dropout rate ∈ [0.1, 0.5];

[0079] (2) Training process parameters: learning rate ∈ [0.0001, 0.1], weight decay ∈ [1e-5, 1e-3], batch size ∈ [16, 128];

[0080] (3) Physical constraint weights: lattice distortion energy weight α∈[0.1,0.5], oxygen vacancy concentration weight β∈[0.05,0.3];

[0081] The optimization goal is to minimize the prediction error MSE while maximizing the satisfaction of physical constraints. The optimization process uses Gaussian process regression to construct a surrogate model.

[0082] Furthermore, in S2, during the model construction process, a weight analysis based on the attention mechanism is used. During the forward propagation of the network, attention weights are obtained through training and learning to indicate the importance of different parameters.

[0083] Furthermore, in S2, during the model construction process, the mechanism knowledge is integrated into the model architecture or training process in the form of prior information. The doping amount is limited to make the lattice distortion energy ≤0.5eV / atom, the doping concentration is controlled to make the oxygen vacancy concentration ≤0.05, the doping combination with the electron cloud overlap integral ≥0.5 is screened, the sintering process is optimized to control the grain size in the range of 1-5μm, and a specific network layer structure or loss function adjustment method is designed to splice the graph convolution features with the physical features and output the dual-target prediction value through the fully connected layer. The loss function adopts a multi-task joint loss: ,in is the basic regression loss, 、 、 are the losses due to grain size, oxygen vacancy concentration and doping amount constraints, 、 、 is a weight parameter; the core task of the model is to simultaneously predict the Curie temperature (Tc) and temperature coefficient of resistance (α) of thermistor particles through the mean square error (MSE) to ensure the model's ability to accurately predict key performance parameters; the relative error penalty term of grain size is used to constrain the influence of the sintering process on the material microstructure, preventing the model from sacrificing the stability of the material structure in pursuit of Tc and α accuracy; the mean square error penalty term of oxygen vacancy concentration is used to control the material conductivity mechanism, balance conductivity and thermal stability, and avoid failure caused by extreme doping; the mean square error penalty term of the number of active doping ions is used to optimize the doping ratio to prevent structural distortion or electrical performance degradation caused by excessive doping; through hyperparameter adjustment, the prediction accuracy and physical feasibility are balanced to avoid a single goal dominating the model training.

[0084] Furthermore, in S3, the evaluation index adopts mean square error MSE and determination coefficient R 2 , the formula is: ; ;in, is the total number of samples, is the actual result of the test set, is the result predicted by the machine learning model, is the mean of the predicted results.

[0085] Furthermore, in S4, based on the output results of the model after training and evaluation in S3, a preparation plan is used as the expected performance target, specifically: the expected Curie temperature point and resistance temperature coefficient of the particles are input, and the most suitable material composition and preparation conditions output by the model are matched as the preparation plan.

[0086] Furthermore, in S6, the target performance of the prepared thermistor particles is tested, specifically: the target performance of the thermistor particles is measured using a two-wire method, and the main performances studied are the Curie temperature and the temperature coefficient of resistance.

[0087] Furthermore, in S6, if the test data does not meet the target requirements, the test data is added to the data set and the model is retrained. When the test data meets the requirements, the update is terminated to determine the optimal solution for the preparation of thermistor particles.

[0088] The following are specific examples.

[0089] Example 1

[0090] In this embodiment, for step S1, an example of a specific data set construction and preprocessing method is given as follows:

[0091] Collect literature data and experimental data, covering the following parameters:

[0092] Material composition: barium titanate matrix (81.0~83.5 mol%), doping element Sr (16.0 mol%), doping element Y (0.5~3.0 mol%), sintering aid AST (Al2O3-SiO2-TiO2, 2~5 wt%);

[0093] Preparation conditions: sintering temperature (1150-1350°C), ball milling time (12-36 h), pre-firing time (0.5-2 h); performance indicators: Curie temperature (Tc, target range: 45-55°C), temperature coefficient of resistance (α, target value: ≥12% / °C).

[0094] Non-numeric parameters (such as the doping element Y coded as [1,0,0]) are processed in binary format.

[0095] Using the Min-Max method, each parameter is mapped to the interval [0,1], and the formula is: , where Represents the normalized value, that is, the result after mapping to the [0,1] interval, Represents a parameter value in the original data, Indicates the minimum value of all original data of the parameter. Indicates the maximum value of all raw data of this parameter; for example, sintering temperature 1150℃→0, 1350℃→1.

[0096] The dataset was randomly divided into training set, validation set, and test set in a ratio of 8:1:1.

[0097] In this embodiment, for step S2, an example of a specific model construction and optimization method is given as follows:

[0098] The XGBoost regression model is selected because of its strong adaptability to small data sets and nonlinear relationships.

[0099] When performing hyperparameter tuning, the optimal parameter combination is determined through Bayesian optimization, specifically: controlling the tree complexity max_depth=5, learning_rate=0.1, the number of trees n_estimators=200, and the subsample ratio subsample=0.8.

[0100] In this embodiment, for step S3, an example of a specific model training and verification method is given as follows:

[0101] During the training process, the input features include 10 parameters such as barium titanate matrix content, Y doping amount, and sintering temperature, and the output target is the dual-target prediction of Tc and α.

[0102] The loss function is weighted mean square error (MSE) with a weight of Tc:α=6:4.

[0103] Evaluate model performance on the test set, focusing on the reliability of model predictions. Evaluation metrics include mean squared error (MSE):

[0104] Coefficient of determination (R 2 ).

[0105] Training evaluation results: training set MSE=0.04, R 2 =0.94; test set MSE=0.07, R 2 =0.89.

[0106] Feature importance ranking: sintering temperature (35%), Y doping amount (28%), and sintering aid ratio (20%).

[0107] In this embodiment, for step S4, an exact expected preparation scheme is given as follows:

[0108] According to the input target performance: Tc=55℃, α=13% / ℃. Model recommended parameters:

[0109] Material composition: BaTiO3 = 81.8 mol%, doped element Sr (16.0 mol%), Y = 2.2 mol%, AST = 3.5wt%;

[0110] Preparation conditions: sintering temperature = 1180 °C, ball milling time = 24 h, pre-sintering time = 1 h.

[0111] In this embodiment, the steps for preparing thermistor particles by using a high-temperature solid-phase method in step S5 are as follows:

[0112] BaCO₃ (99.9%), TiO₂ (99.8%), SrCO₃ (99.99%), and Y₂O₃ (99.99%) were weighed and mixed in a stoichiometric ratio. Zirconia balls (3 mm diameter, ball-to-material ratio 3:1) and anhydrous ethanol (volume ratio 1:1.5) were added, and the mixture was subjected to planetary ball milling for 24 h at 300 rpm. The milled slurry was vacuum dried at 80°C for 8 h and then passed through a 200-mesh sieve. It was pre-calcined at 1150°C for 1 h at a heating rate of 5°C / min. AST sintering aid was added and wet ball milling was performed for 24 h. After ball milling, the mixture was dried in a vacuum oven. A 5% (mass fraction) PVA solution was added at a mass ratio of 1:20, and the mixture was thoroughly milled for 1 h. After milling, the mixture was dried for 0.5 h. The sample powder was pressed into 10 mm × 2 mm discs. The mixture was heated to 1180°C at 5°C / min in air, held for 2 h, and then cooled to room temperature.

[0113] Thermistor particles prepared according to the above steps were tested for resistance-temperature characteristics. The impedance-temperature curve was measured using an impedance analyzer (Agilent 4294A). The inflection point corresponds to Tc. The resistivity change rate in the range of 25-100°C was calculated using the formula: The test results are Tc=58℃,α=13.2% / ℃. Add the experimental data to the dataset and retrain the test set R 2 Improved to 0.91. Figure 2 As shown in the figure, the prediction error of the XGBoost model for Tc is concentrated within ±3°C, indicating that the model has high reliability.

[0114] Example 2

[0115] In order to compare and verify the effects of different element-doped barium titanate on the performance of thermistor particles, in this embodiment, the data set of step S1 was adjusted by replacing Y with La (ionic radius 1.06 Å), and literature data and experimental data were collected.

[0116] In this embodiment, for the construction and training of the model in step S2-3, the same XGBoost parameters are used, the test set MSE=0.08, R 2 =0.87, indicating that La has a weak effect on reducing Tc.

[0117] In this embodiment, for the output of the optimization solution in step S4, the model recommends La=2.8 mol%, sintering temperature=1220° C., and AST=4.0 wt%.

[0118] In this embodiment, the measured Tc=67°C and α=11.5% / °C in step S5 are significantly different from the target performance, and the La doping amount needs to be increased to 3.2 mol% and the experiment needs to be repeated.

[0119] Example 3

[0120] In this example, the data set of step S1 in Example 1 is expanded to include data on Nb (0.5-1.5 mol%) co-doping with Y. 5+ Ionic radius (0.64 Å) and lattice distortion energy (calculated by DFT) are added as new features.

[0121] In this embodiment, for step S2, an example of a specific model construction and optimization method is given as follows:

[0122] After in-depth research and comparative analysis of various machine learning models, and considering the complex data associations and graph structure, we selected the Graph Convolutional Neural Network (GCN) model. GCN effectively processes graph data. Through inter-node message passing, it learns the latent representations of node features and explores hidden relationships between samples, making it suitable for predicting thermistor performance.

[0123] In terms of model architecture, the graph structure is constructed based on the perovskite crystal structure, with elements (such as Ba, Ti, and O) set as nodes. The node characteristics include physical parameters such as atomic number, ionic radius, valence state, lattice distortion energy, and the amount of each element. Edges are then constructed based on the interatomic chemical bonds and doping substitution relationships: Ba and Ti are connected through O to form the perovskite skeleton, and elements such as Sr, La, and Y are connected to the Ba node when replacing the Ba position, and Nb, Mn, etc. are connected to the Ti node when replacing the Ti position. The edge characteristics describe the interatomic interactions through bond strength, distance, and type (chemical bond, substitution relationship, weak interaction, etc.), and ultimately form graph data that maps the microstructure of the material. The input layer in the graph neural network model is used to input the constructed graph structure data; the convolution layer includes two graph convolution layers, with 128 and 64 neurons respectively. By aggregating the feature information of adjacent nodes, the feature representation of the current node is updated. The activation function uses the ReLU function to increase the nonlinear ability of the network, and the Dropout rate is 0.3; a global average pooling layer is added between the two convolution layers to reduce the dimension of the node features, reduce the number of parameters, and improve the computational efficiency of the model; the output layer is a fully connected layer, which splices the graph convolution features with the physical features and outputs the dual-target prediction values ​​through the fully connected layer.

[0124] When performing hyperparameter tuning, the optimizer selected is AdamW, which adds a weight decay mechanism to the Adam optimizer to help prevent model overfitting. The learning rate is set to 0.005 and the weight decay is set to 1e-4. The training round is 100 epochs, and the early stopping method (patience = 20) is used.

[0125] The Bayesian optimization algorithm is used to adjust the hyperparameters of the graph convolutional neural network. The specific optimization parameters include: (1) network structure parameters: hidden layer dimension ∈ [64, 512], number of convolution layers ∈ [2, 5], dropout rate ∈ [0.1, 0.5]; (2) training process parameters: learning rate ∈ [0.0001, 0.1], weight decay ∈ [1e-5, 1e-3], batch size ∈ [16, 128]; (3) physical constraint weight: lattice distortion energy weight α ∈ [0.1, 0.5], oxygen vacancy concentration weight β ∈ [0.05, 0.3]; the optimization goal is to minimize the prediction error MSE while maximizing the physical constraint satisfaction. The optimization process uses Gaussian process regression to construct a surrogate model.

[0126] The loss function uses custom loss ,in is the basic regression loss, , 、 、 are the losses due to grain size, oxygen vacancy concentration and doping amount constraints, , , , 、 、 The core task of the model is to simultaneously predict the Curie temperature (Tc) and temperature coefficient of resistance (α) of thermistor particles through the mean square error (MSE), ensuring the model's ability to accurately predict key performance parameters. The relative error penalty term of grain size is used to constrain the influence of the sintering process on the material microstructure, preventing the model from sacrificing material structural stability in pursuit of Tc and α accuracy. The mean square error penalty term of oxygen vacancy concentration is used to control the material conductivity mechanism, balance conductivity and thermal stability, and avoid failure caused by extreme doping. The mean square error penalty term of the number of active doping ions is used to optimize the doping ratio to prevent structural distortion or electrical performance degradation caused by excessive doping. Taking 0.1, the constraint strength of grain size is weakened, because it can be compensated by process adjustment. Take 0.2 to moderately strengthen the control of oxygen vacancy concentration, because it is sensitive to electrical properties. Take 0.3 and focus on constraining the doping amount, because it directly affects the stability and reliability of the material. Through hyperparameter adjustment, balance the prediction accuracy and physical feasibility to avoid a single goal dominating the model training.

[0127] In this embodiment, for step S3, an example of a specific model training and verification method is given as follows:

[0128] During the training process, the optimized GCN model is trained using the training set. The input data is loaded in the form of a graph structure, and the node features and adjacency matrix are processed through the PyTorch Geometric framework. The validation set is used to monitor model overfitting, and the best model is saved at the lowest point of validation loss. In each round of training, the graph data is input into the model, the prediction value is calculated through forward propagation, and then the loss value is calculated according to the loss function, and then the model parameters are updated through back propagation. In order to prevent overfitting, an early stopping strategy is adopted. When the MSE of the validation set no longer decreases in 50 consecutive rounds of training, the training is stopped. The evaluation results are MSE=0.03 for the training set and R 2 =0.96; test set MSE=0.05, R 2 =0.93; the key feature contributions based on the attention weights are: sintering temperature (38%), Y doping amount (30%), and Nb doping amount (18%).

[0129] In this embodiment, a specific expected preparation scheme for step S4 is given as follows:

[0130] According to the input target performance: Tc=50℃, α=14% / ℃. Model recommended parameters:

[0131] Material composition: Y=2.0 mol%, Nb=0.5 mol%, AST=3.8 wt%.

[0132] Preparation conditions: sintering temperature = 1175 °C, ball milling time = 30 h, pre-sintering time = 1.5 h.

[0133] In this embodiment, the steps for preparing thermistor particles by using a high-temperature solid-phase method in step S5 are as follows:

[0134] BaCO₃, TiO₂, SrCO₃, Y₂O₃, and Nb₂O₅ (purity ≥99.9%) were weighed and mixed in a stoichiometric ratio. Zirconia balls (3 mm diameter, ball-to-material ratio 3:1) and anhydrous ethanol (volume ratio 1:1.5) were added, and the mixture was subjected to planetary ball milling at 300 rpm for 30 h. The milled slurry was vacuum dried at 80°C for 8 h and then passed through a 200-mesh sieve. Pre-calcination was performed at 1150°C for 1 h at a heating rate of 5°C / min. AST sintering aid was added and wet ball milling was performed for 30 h. After ball milling, the mixture was dried in a vacuum oven. A 5% (mass fraction) PVA solution was added at a mass ratio of 1:20, and the mixture was thoroughly milled for 1 h. After milling, the mixture was dried for 0.5 h. The sample powder was pressed into 10 mm × 2 mm discs. The mixture was heated at 5°C / min to 1175°C in air, held at that temperature for 2.5 h, and then cooled to room temperature.

[0135] Test results: Tc=52℃, α=14.0% / ℃.

[0136] Example 4

[0137] In this embodiment, the data set in step S1 is the same as that in embodiment 3.

[0138] In order to compare and verify the effectiveness of the custom loss function that integrates the mechanism into the network settings in Example 3, for the construction of the step S2 model in this embodiment, the loss function part adopts the mean square error (MSE) as the loss function of this embodiment, and the rest of the network structure, hyperparameter settings, etc. are consistent with Example 3.

[0139] In this embodiment, the training of the model in step S3 is carried out using the same method as in embodiment 3, with a test set MSE of 0.07 and R 2=0.87, indicating that the model trained using the custom loss function in Example 3 is better than the model trained using the mean square error (MSE) as the loss function.

[0140] In this embodiment, for the output of the optimization solution of step S4, the model recommends Y=1.8 mol%, Nb=0.7 mol%, AST=4.0 wt%, sintering temperature=1250°C, ball milling time=30h, and pre-firing time=1h.

[0141] In this embodiment, for step S5, the measured Tc=61°C and α=13.2% / °C. Compared with Example 3, the measured performance of the particles prepared according to the model recommendation scheme in this embodiment is significantly different from the target performance, which illustrates the effectiveness of the customized loss function in Example 3.

[0142] Examples 1-4 verify the universality and efficiency of the method of the present invention. The examples show that the present invention can reduce the number of experiments by 70% and the target performance prediction error is less than 5%. Example 3 introduces a graph convolutional neural network (GCN) to integrate physical and chemical mechanisms and data to achieve efficient modeling of the complex topological relationship between material composition, process and performance. The test set R 2 The synergistic effect of co-doping Y and Nb increases α to 14.0% / °C, breaking through the performance bottleneck of traditional single-doping systems and providing an innovative solution for the precise design of thermistor particles.

[0143] As described above, the present invention introduces advanced machine learning technology to assist the thermistor particle preparation process, abandoning the traditional "trial and error" model that relies on a large number of repeated experiments. Through in-depth mining and analysis of experimental data by machine learning algorithms, key influencing factors can be quickly screened out, reducing the number of unnecessary experiments, thereby significantly reducing R&D costs and shortening the R&D cycle. At the same time, the repeatability and stability of the machine learning model make the R&D process more predictable, effectively improving R&D efficiency. The machine learning method used in the present invention has powerful data processing capabilities and can accurately identify the degree of influence of different parameters on the performance of thermistor particles in massive and complex experimental data. Based on this, precise control of the performance of thermistor particles can be achieved, and the material composition and preparation conditions can be flexibly adjusted according to actual needs to prepare thermistor particles that meet specific performance requirements, breaking through the limitations of traditional preparation methods that are difficult to accurately control performance. The present invention adopts a multi-objective optimization design concept and is committed to ensuring that the prepared thermistor particles simultaneously meet the dual conditions of a low Curie temperature and a high temperature coefficient of resistance. This design approach effectively addresses the performance deficiencies of traditional thermistors in specific application scenarios (such as the safe physical discharge of lithium batteries), greatly expanding their application range and demonstrating significant practical value and market competitiveness. The present invention innovatively integrates the physical and chemical mechanisms underlying thermistor particle performance into the machine learning prediction process, achieving a deep fusion of mechanism and data. This fusion approach not only leverages the powerful predictive capabilities of data-driven machine learning models but also fully leverages the guiding and constraining role of mechanistic knowledge on the model, enabling the model to more accurately capture the complex relationship between material composition, preparation conditions, and particle performance, improving the reliability and interpretability of model predictions while reducing the model's reliance on data.

[0144] The embodiments described above merely represent optional implementations of the present invention. It should be noted that a person skilled in the art may make several modifications and improvements without departing from the scope of the present invention, and these modifications and improvements also fall within the scope of protection of the present invention.

Claims

1. A method for optimizing thermistor particle preparation based on machine learning, characterized in that: It includes the following steps: S1: Construct a data set containing thermistor particle preparation process parameters, performance indicators, and known physical and chemical mechanism knowledge, and perform preprocessing; Preparation process parameters include material composition and preparation conditions, and performance indicators include the Curie temperature and resistance temperature coefficient of thermistor particles; S2: Build and optimize machine learning models Incorporate knowledge of physical and chemical mechanisms into the model architecture or training process in the form of prior information, and design a specific network layer structure or loss function adjustment method to optimize the network model; S3: Using the performance indicators of thermistor particles as target labels, the optimized machine learning model constructed in S2 is trained using the dataset in S1. S4: Input the desired performance indicators of thermistor particles into the trained machine learning model, and the model outputs the most suitable material composition and preparation conditions; S5: Prepare thermistor particles according to the material composition and preparation conditions output by the model; S6: Testing the performance indicators of the prepared thermistor particles. If the test data does not meet the target requirements, the test data is added to the data set of step S1 and the model is retrained. When the test data meets the requirements, the update is terminated to determine the optimal solution for the preparation of the thermistor particles; wherein: In step S1, the thermistor particles are barium titanate-based thermistor particles. When constructing the dataset, the physicochemical mechanism knowledge is converted into quantifiable features or constraints. The physicochemical mechanism knowledge includes: the crystal structure of the barium titanate matrix and thermistor particles, the atomic number, ionic radius, valence state, electronegativity of each element in the matrix and dopant material, as well as the matrix lattice distortion energy, oxygen vacancy concentration, grain size, and electron cloud overlap integral. In step S2, the machine learning model is a graph neural network model (GCN). During the network's forward propagation, the influence of different parameters on performance indicators is reflected by calculating attention weights. The construction of the graph structure is based on the perovskite crystal structure, with elements set as nodes. Node features include atomic number, ionic radius, valence state, lattice distortion energy, and the amount of each element. Edges are then constructed based on interatomic chemical bonds and doping substitution relationships: Ba and Ti are connected through O to form the perovskite skeleton. When Sr, La, and Y elements replace Ba, they are connected to the Ba node. When Nb and Mn replace Ti, they are connected to the Ti node. Edge features describe the interatomic interactions through bond strength, distance, and type, ultimately forming graph data that maps the material's microstructure. In step S3, the training loss function adopts multi-task joint loss: ， in is the basic regression loss, 、 、 are the losses due to grain size, oxygen vacancy concentration and doping amount constraints, 、 、 is the weight parameter.

2. The method for optimizing thermistor particle preparation based on machine learning according to claim 1, characterized in that: In step S1, the preparation process of thermistor particles is a high-temperature solid-phase method, and the specific steps include: mixing the raw materials of the barium titanate matrix and the doping element precursor, wet ball milling and then drying, first pre-calcining under an inert atmosphere, then adding a sintering aid AST, wet ball milling and then drying, and finally sintering in an air atmosphere.

3. The method for optimizing thermistor particle preparation based on machine learning according to claim 2, characterized in that: In step S1, the data set is concentrated, and the material composition includes: the amount of barium titanate matrix, the type and amount of doping elements, and the amount of sintering aid AST. The preparation conditions include sintering temperature, pre-firing time, holding time, heating and cooling rate, and ball milling time.

4. The method for optimizing thermistor particle preparation based on machine learning according to claim 2, characterized in that: In step S1, the lattice distortion energy The difference in ionic radius between doped ions and barium titanate matrix calculate: ， in, , and are the radii of the dopant atom and the host atom, respectively; Oxygen vacancy concentration Calculated by the following formula: ， in, is the concentration of the doping element, is the difference between the valence state of the doping element and the valence state of the replaced host ion, is the oxygen vacancy formation energy, which is 1.2 eV. is the Boltzmann constant, is temperature; Grain size after sintering Prediction based on Beck equation: ， in is the grain size, is the sintering time, is the Boltzmann constant, is temperature; Electron cloud overlap integral of dopant ions and barium titanate lattice The calculation method is as follows: ， in, and are the radii of the dopant atom and the host atom, respectively.

5. The method for optimizing thermistor particle preparation based on machine learning according to claim 2, characterized in that: In step S1, the data set is normalized by using the minimum-maximum scaling method to map the numerical parameters to the interval [0,1] to avoid model bias caused by the scale difference of the dependent variable; the non-numeric parameters involved are encoded using one-hot encoding.

6. The method for optimizing thermistor particle preparation based on machine learning according to claim 1, characterized in that: In step S2, the Bayesian optimization algorithm is used to adjust the hyperparameters of the graph convolutional neural network (GCN). The specific optimization parameters include: (1) Network structure parameters: hidden layer dimension ∈ [64, 512], number of convolutional layers ∈ [2, 5], dropout rate ∈ [0.1, 0.5]; (2) Training process parameters: learning rate ∈ [0.0001, 0.1], weight decay ∈ [1e-5, 1e-3], batch size ∈ [16, 128]; (3) Physical constraint weights: lattice distortion energy weight α∈[0.1,0.5], oxygen vacancy concentration weight β∈[0.05,0.3]; The optimization goal is to minimize the prediction error MSE while maximizing the satisfaction of physical constraints. The optimization process uses Gaussian process regression to construct a surrogate model.

7. The method for optimizing thermistor particle preparation based on machine learning according to claim 1, characterized in that: In step S2, during the model construction process, the mechanism knowledge is integrated into the model architecture or training process in the form of prior information, the doping amount is limited so that the lattice distortion energy is ≤0.5eV / atom, the doping concentration is controlled so that the oxygen vacancy concentration is ≤0.05, the doping combination with the electron cloud overlap integral ≥0.5 is screened, the sintering process is optimized so that the grain size is controlled in the range of 1-5μm, the network layer structure or the loss function adjustment method is designed, and the graph convolution features and physical features are spliced ​​together to output the performance indicators through the fully connected layer, that is, the predicted values ​​of the Curie temperature point and the resistance temperature coefficient of the prepared thermistor particles.

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