Thermistor particle preparation optimization method based on machine learning

Abstract

The invention belongs to the technical field of thermosensitive material preparation, and particularly relates to a thermistor particle preparation optimization method based on machine learning. According to the method, a data set containing preparation process parameters, performance indexes and physical and chemical mechanism knowledge of thermistor particles is constructed, the preparation process parameters comprise material components and preparation conditions, and a machine learning model is utilized to predict an optimal preparation condition; and multi-target collaborative optimization of the Curie temperature point and the resistance temperature coefficient of the thermistor particles is realized. Compared with a traditional trial and error method, the research and development cost can be reduced, and the target performance prediction error is smaller than 5%. By fusing the physical and chemical mechanism and the data driving model, the problem that multiple performance parameters are difficult to accurately regulate and control by a traditional method is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of thermosensitive material preparation, and specifically relates to an optimization method for preparing thermistor particles based on machine learning. Background Art

[0002] With the rapid development of emerging fields such as electric vehicles and wearable devices, the demand and scrapping volume of lithium batteries are increasing continuously. Lithium batteries contain a large amount of precious metals such as Li, Ni, Co, etc., and have high recycling value; at the same time, lithium batteries also contain toxic and harmful substances such as electrolytes and binders. The environmental problems and resource utilization technologies that may be caused by scrapped lithium batteries have long attracted wide attention.

[0003] The key to recycling scrapped lithium batteries lies in safe discharge pretreatment. The current commonly used unorganized chemical discharge mode of soaking in NaCl solution has low cost and good conductivity, but the outer shell of the battery positive electrode is easy to be damaged, causing harmful substances to leak, polluting the environment and endangering the health of personnel. After measuring the discharge wastewater, it is found that the solution contains a large amount of metal ions such as Fe, Al, Li, Mn, Ni, organic compounds and fluorides. After measuring the gas released during the discharge process, it is found that in addition to hydrogen and oxygen, there are also a large amount of hydrogen fluoride, Cl2 and organic pollutants. In contrast, placing the battery in solid conductive particles and converting electrical energy into particle heat energy has significant advantages in the physical discharge mode, which can reduce pollution leakage and is more environmentally friendly and safe. Among them, the performance of the solid conductive particles is crucial. To achieve safe and effective physical discharge, the solid conductive particles, that is, thermistor particles, must simultaneously meet the conditions of a lower Curie temperature point and a higher resistance temperature coefficient, which is convenient for realizing open circuit at low temperature and open circuit at high temperature, and solving the thermal runaway problem of physical discharge.

[0004] Existing thermistors are mostly used in temperature control sensors and heaters, with a higher Curie temperature point (Tc) or a lower resistance temperature coefficient (α), which cannot meet the technical requirements for safe physical discharge of lithium batteries. Chinese Patent Application (CN 114456312A) discloses a thermosensitive material with a low Curie temperature, but its resistance temperature coefficient only reaches 8% / °C, which is difficult to meet the physical discharge requirements. In the prior art, the non-linear relationship between doping element selection, sintering temperature control and multi-performance collaborative optimization has not been revealed, resulting in high experimental blindness and long R & D cycle. Chinese Patent Application (CN 117352101A) discloses a method for quickly predicting the electrical conductivity of thermoelectric materials based on machine learning. It is based on a single model of traditional random forest, relying on chemical formula analysis and statistical features, and only focuses on the prediction of a single performance (electrical conductivity) of thermoelectric materials, which cannot meet the requirements of complex application scenarios (such as safe discharge of lithium batteries).

[0005] The traditional R & D and preparation methods of thermosensitive materials mainly rely on experimental exploration, and the process conditions are complex. This process requires a large amount of experimental costs and time. Moreover, whenever the material combination or preparation conditions are adjusted, a series of cumbersome experiments need to be carried out again, with a long R & D cycle and high costs. At the same time, the generally adopted preparation methods of positive temperature coefficient thermistors often make it difficult to control multiple performance parameters simultaneously, greatly limiting the application of this kind of material.

[0006] The above background technology refers to the following publicly disclosed documents: [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. [2] Zhao Jiaojiao, Wang Bo, Zhang Boqi. Research on the preparation method of lead - free barium titanate - based positive temperature coefficient thermistor ceramic materials[J]. Paper Making Equipment & Materials, 2022, 51(12): 68 - 70. [3] A composite positive temperature coefficient thermistor material and its preparation method, Tianjin Ruiken New Material Technology Co., Ltd., Application No.: CN202210326315.X, Application Date: 2022 - 03 - 30. [4] Lead - free PTC thermistor ceramic materials with low room - temperature resistivity and high resistance - ratio and their preparation methods, Shanghai Institute of Materials Research, Application No.: CN202211569319.7, Application Date: 2022 - 12 - 08. Summary of the Invention

[0007] The object of the present invention is to overcome the deficiencies of the prior art and provide a method for preparing thermistor particles that meets multi-objective requirements and is optimized based on machine learning. The prepared thermistor particles simultaneously meet the conditions of a relatively low Curie temperature point and a relatively high resistance temperature coefficient. By means of machine learning, the development efficiency of thermistor particles is improved, and the effects of different reaction variables on the various properties of the product are comprehensively considered, so as to optimize the screening of reactants and the design of reaction conditions, and achieve precise control of the properties of thermistor particles. The present invention synergistically optimizes the multi-objective properties (Curie temperature point Tc and resistance temperature coefficient α) of thermistor particles, which better meets the requirements of complex application scenarios (such as safe discharge of lithium batteries); in the construction of the machine learning model, the topological relationship between material composition - process - performance is modeled through a graph convolutional neural network (GCN) to support the mining of complex non-linear relationships; at the same time, physical and chemical mechanisms (such as the constraint of the doping ion radius and lattice matching) are integrated, and the mechanism knowledge is transformed into quantifiable features or model constraint conditions, improving the prediction accuracy and interpretability.

[0008] The object of the present invention can be achieved by the following technical solutions.

[0009] The present invention provides an optimization method for preparing thermistor particles based on machine learning, which includes the following steps: S1: Construct a data set containing the preparation process parameters, performance indicators, and physical and chemical mechanism knowledge of thermistor particles, and perform preprocessing; the preparation process parameters include material composition and preparation conditions, and the performance indicators include the Curie temperature point and resistance temperature coefficient of thermistor particles; S2: Construct and optimize a machine learning model Integrate the physical and chemical mechanism knowledge 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; S3: Use the performance indicators of thermistor particles as target labels, and use the data set in S1 to train the optimized machine learning model constructed in S2; S4: Input the desired performance indicators of thermistor particles into the trained machine learning model, and the model outputs the most suitable combination of material composition and preparation conditions; S5: Prepare thermistor particles according to the combination of material composition and preparation conditions output by the model; S6: Test the performance indicators of the prepared thermistor particles. If the test data does not meet the target requirements, add the test data obtained to the data set in step S1 and retrain the model. When the test data meets the requirements, terminate the update and determine the optimal scheme for preparing thermistor particles.

[0010] 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 the high-temperature solid-phase method. The specific steps include: mixing the raw materials of the barium titanate matrix and the dopant element precursor, performing wet ball milling and then drying, pre-burning in an inert atmosphere first, adding the sintering aid AST and performing wet ball milling again and then drying, and finally sintering in an air atmosphere.

[0011] In the present invention, in step S1, in the data set, the material components include: the dosage of the barium titanate matrix, the type and dosage of the dopant element, and the dosage of the sintering aid AST. The preparation conditions include: the sintering temperature, the pre-burning time, the heat preservation time, the heating and cooling rate, and the ball milling time.

[0012] In the present invention, in step S1, when constructing the data set, the physical and chemical mechanism knowledge is transformed into quantifiable features or constraint conditions. The physical and chemical mechanism knowledge includes: the crystal structures of the barium titanate matrix and the thermistor particles, the atomic numbers, ionic radii, valence states, electronegativities of each element in the matrix and the doping material, and the matrix lattice distortion energy, oxygen vacancy concentration, grain size, and electron cloud overlap integral; among them: Lattice distortion energy Calculated by the difference in ionic radius between the doping ion and the barium titanate matrix ion Calculate: , Wherein, , And Are the radii of the doping atom and the host atom respectively; Oxygen vacancy concentration Calculated by the following formula: , Wherein, 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, with a value of 1.2 eV, Is the Boltzmann constant, Is the temperature; The grain size after sintering Predicted based on the Beck equation: , Where Is the grain size, Is the sintering time, Is the Boltzmann constant, Is the temperature; The electron cloud overlap integral of the doping ion and the barium titanate lattice The calculation method is as follows: , wherein, and are the radii of the doping atom and the host atom, respectively.

[0013] In the present invention, in step S1, in the dataset, the min-max scaling method is used to normalize the numerical parameters, mapping the numerical parameters to the interval [0,1] to avoid model bias caused by variable scale differences; the non-numerical parameters involved are encoded using one-hot encoding.

[0014] 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.

[0015] In the present invention, in step S2, the machine learning model is the graph neural network model GCN. During the forward propagation of the network, the influence degree of different parameters on the performance index is reflected through the calculation of attention weights. The construction of the graph structure is based on the perovskite crystal structure. Elements (such as Ba, Ti, O) are set as nodes, and the node features include physical parameters such as atomic number, ionic radius, valence state, lattice distortion energy, and the usage of each element. Then, edges are constructed according to the chemical bonds and doping substitution relationships between atoms: Ba and Ti are connected by O to form the perovskite skeleton. Elements such as Sr, La, Y, etc. are connected to the Ba node when substituting the Ba site, and elements such as Nb, Mn, etc. are connected to the Ti node when substituting the Ti site. The edge features describe the interactions between atoms through bond strength, distance, and type (chemical bond, substitution relationship, weak interaction, etc.), and finally form the graph data that maps the microstructure of the material.

[0016] In the present invention, 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: the dimension of the hidden layer ∈ [64,512], the number of convolutional layers ∈ [2,5], the 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: the lattice distortion energy weight α ∈ [0.1,0.5], the oxygen vacancy concentration weight β ∈ [0.05,0.3]; The optimization objective is to minimize the prediction error MSE and maximize the physical constraint satisfaction at the same time. The Gaussian process regression is used to construct the surrogate model during the optimization process.

[0017] In the present invention, in step S2, during the model construction process, mechanism knowledge is incorporated into the model architecture or training process in the form of prior information, the doping amount is restricted so that the lattice distortion energy ≤ 0.5 eV / atom, the doping concentration is controlled so that the oxygen vacancy concentration ≤ 0.05, the doping combinations with an electron cloud overlap integral ≥ 0.5 are screened, the sintering process is optimized so that the grain size is controlled in the range of 1 - 5 μm, a specific network layer structure or loss function adjustment method is designed, the graph convolution features and physical features are spliced and then the performance indicators are output through a fully connected layer, that is, the predicted values of the Curie temperature point and the resistance temperature coefficient of the prepared thermistor particles.

[0018] In the present invention, in step S2, in the constructed model, the attention mechanism is combined with GCN; in step S3, when training the model, the attention weights in the forward propagation process of the network model are used to quantify the contributions of different nodes and edges to the prediction.

[0019] In the present invention, in step S3, the training loss function adopts a multi-task joint loss: , where is the basic regression loss, , , are the losses constrained by the grain size, oxygen vacancy concentration, and doping amount respectively, , , are the weight parameters.

[0020] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. The present invention uses a machine learning method to assist in the preparation of thermistor particles, avoiding the waste of resources caused by the traditional experimental-intensive "trial and error" experiments, reducing the R & D cost, shortening the R & D cycle, and improving the predictability and repeatability of the R & D process.

[0021] 2. The present invention introduces a machine learning method, uses the attention weights in the forward propagation process of the network model to quantify the contributions of different nodes and edges to the prediction, can identify the influence degrees of different parameters in a large amount of complex experimental data, thereby quickly locating the key parameters, reducing the trial and error cost, and providing a "data-driven" regulation direction.

[0022] 3. Adopting a multi-objective optimization design method to simultaneously meet the conditions of a lower Curie temperature point and a higher resistance temperature coefficient of the material, and forming a closed-loop optimization process by feeding back the experimental data to update the model, which has good practical value.

[0023] 4. Innovatively integrate the physicochemical mechanism formed by the properties of thermistor particles into the machine learning prediction process, achieving the deep integration of mechanism and data, improving the reliability and interpretability of model prediction, and reducing the dependence of the model on data. Description of the Drawings

[0024] Figure 1 It is the logical framework diagram of the present invention.

[0025] Figure 2 It is the prediction performance evaluation diagram of the XGBoost model in Example 1, namely (a) Curie temperature point and (b) temperature coefficient of resistance.

[0026] Figure 3 It is the prediction performance evaluation diagram of the XGBoost model in Example 2, namely (a) Curie temperature point and (b) temperature coefficient of resistance.

[0027] Figure 4 It is the prediction performance evaluation diagram of the GCN model in Example 3, namely (a) Curie temperature point and (b) temperature coefficient of resistance.

[0028] Figure 5 It is the prediction performance evaluation diagram of the GCN model in Example 4, namely (a) Curie temperature point and (b) temperature coefficient of resistance. Detailed Embodiments

[0029] The present invention will be further elaborated and illustrated through examples below. The examples are only demonstrations of the present disclosure content and do not delimit the scope of limitation. Without conflict, the technical features of each embodiment in the present invention can be combined accordingly.

[0030] The present invention provides a method for preparing thermistor particles that meets multi-objective requirements based on machine learning optimization, including the following steps: S1: Obtain the preparation process parameters such as the material composition and preparation conditions of the thermistor particles and the corresponding electrical property test results as a data set, and divide the data set into a training set, a validation set, and a test set; S2: Select a machine learning model that can handle small data sets and nonlinear problems, and select a method for adjusting and optimizing the hyperparameters of the model; S3: Use the data set in S1 to train and test the machine learning model selected in S2, and evaluate the model performance; S4: According to the output result of the model after training and evaluation in S3, it is used as a preparation plan for the expected target performance; S5: Prepare thermistor particles by the high-temperature solid-phase method according to the expected preparation plan; S6: Test the target performance of the prepared thermistor particles. If the test data do not meet the target requirements, update the data set and the model.

[0031] Further, in S1, the preparation process parameters such as the material composition and preparation conditions of the thermistor particles, the corresponding electrical and physical property test results, and the relevant mechanism knowledge are obtained as a data set. Specifically: conduct literature research and experimental tests on various materials used in the preparation, and establish a data set including parameters such as material composition (such as the amount of barium titanate and the amount of doped elements), preparation conditions (such as sintering temperature and ball milling time), performance indicators (such as the Curie temperature point of the particles and the temperature coefficient of particle resistance), and mechanism knowledge (such as the Curie temperature point of undoped barium titanate, the ionic radius of each element, the ionic radius of each element, and the valence state of each element).

[0032] Further, in S1, perform normalization processing on the variables. Using the maximum and minimum values of the variable data, scale data of different orders of magnitude to the same [0, 1] interval to ensure that the model will not deviate due to the scale of the variables; furthermore, a non-linear model can capture more complex dependence relationships, such as the product or high-order term relationships between variables, which is crucial for understanding more complex system dynamics and improving prediction accuracy; through normalization processing, that is, scaling all input variables to the same scale, it can prevent the model from assigning too much importance to some variables with larger scales during the training process, help improve the generalization ability of the model, and ensure the fairness and appropriate influence of each input variable in the model training.

[0033] Further, in S1, deeply study the physical and chemical mechanism of the formation of the thermistor particle performance, transform the relevant mechanism knowledge into quantifiable features or constraint conditions, and integrate them into the data set construction process. The specific mechanism knowledge includes lattice distortion energy, oxygen vacancy concentration, grain size, and electron cloud overlap integral; The lattice distortion energy is calculated by the difference in ionic radii between the doped ions and the barium titanate matrix ions ( ) to calculate the lattice distortion energy (eV / atom), where is the lattice distortion energy, and are the radii of the doped atom and the host atom respectively; the oxygen vacancy concentration is calculated by establishing an oxygen vacancy concentration model , where is the oxygen vacancy concentration, is the concentration of the doped element, is the difference between the valence state of the doped element and the valence state of the replaced host ion, is the oxygen vacancy formation energy, with a value of 1.2 eV, is the Boltzmann constant, is the temperature; The prediction of grain size is based on the Beck equation to predict the grain size after sintering, and the formula is , where is the grain size, is the sintering time, is the Boltzmann constant, is the temperature; Calculate the overlap integral of the electron cloud between the doped ions and the barium titanate lattice , where is the overlap integral of the electron cloud, and are the radii of the doped atom and the host atom respectively; The above mechanism parameters are normalized and then incorporated into the dataset construction as independent features or constraints.

[0034] Furthermore, in S1, one-hot encoding is performed on non-numerical parameters such as crystal structure and doping type to distinguish different crystal structures and doping type parameters.

[0035] Furthermore, in S1, the splitting of the dataset into a training set, a validation set, and a test set is specifically as follows: During the training process, the dataset is randomly divided into a training set, a validation set, and a test set according to the ratio of 8:1:1.

[0036] 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.

[0037] 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: (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 objective is to minimize the prediction error MSE while maximizing the physical constraint satisfaction degree. The Gaussian process regression is used to construct a surrogate model during the optimization process.

[0038] Further, in S2, during the model construction process, weight analysis based on the attention mechanism is used. During the forward propagation of the network, attention weights are obtained through training and learning, representing the importance of different parameters.

[0039] Further, in S2, during the model construction process, mechanism knowledge is incorporated into the model architecture or training process in the form of prior information. The doping amount is restricted so that the lattice distortion energy ≤ 0.5 eV / atom, the doping concentration is controlled so that the oxygen vacancy concentration ≤ 0.05, doping combinations with an electron cloud overlap integral ≥ 0.5 are screened, the sintering process is optimized so that the grain size is controlled within the range of 1 - 5 μm, a specific network layer structure or loss function adjustment method is designed to splice the graph convolution features and physical features and then output the dual-target prediction value through a fully connected layer. The loss function adopts a multi-task joint loss: , where is the basic regression loss, , , are the losses constrained by the grain size, oxygen vacancy concentration, and doping amount respectively, , , are the weight parameters; the core tasks of the model are to simultaneously predict the Curie temperature point (Tc) and the resistance temperature coefficient (α) of the thermistor particles through the mean square error (MSE), ensuring the model's accurate prediction ability for key performance parameters; through the relative error penalty term of the grain size, the influence of the sintering process on the material microstructure is constrained, preventing the model from sacrificing the material structure stability in pursuit of the accuracy of Tc and α; through the mean square error penalty term of the oxygen vacancy concentration, the material conductance mechanism is controlled, balancing conductivity and thermal stability, and avoiding failures caused by extreme doping; through the mean square error penalty term of the number of active doping ions, the doping ratio is optimized, preventing structural distortion or deterioration of electrical properties caused by excessive doping; through hyperparameter adjustment, the prediction accuracy and physical feasibility are balanced, avoiding a single target dominating the model training.

[0040] Further, in S3, the evaluation metrics adopt the mean square error MSE and the coefficient of determination R 2 , and the formula is: ; ; where, 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 prediction results.

[0041] Further, in S4, according to the output result of the model after training and evaluation in S3, it is used as the preparation plan expected to achieve the target performance. Specifically: input the desired Curie temperature point of the particles and the temperature coefficient of resistance, and the most suitable material composition and preparation conditions matched according to the model output are used as the preparation plan.

[0042] Further, in S6, the target performance of the prepared thermistor particles is tested. Specifically: the two-wire method is used to measure the target performance of the thermistor particles, and the main performances studied are the Curie temperature point and the temperature coefficient of resistance.

[0043] Further, in S6, if the test data does not meet the target requirements, the test data obtained will be added to the data set and the model will be retrained. When the test data meets the requirements, the update will be terminated and the optimal plan for preparing the thermistor particles will be determined.

[0044] The following are specific examples.

[0045] Example 1

[0046] In this example, for step S1, an exact method for constructing and preprocessing the data set will be given as follows: Collect literature data and experimental data, covering the following parameters: 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%); Preparation conditions: sintering temperature (1150 - 1350 °C), ball milling time (12 - 36 h), pre - sintering time (0.5 - 2 h); performance indicators: Curie temperature point (Tc, target range: 45 - 55 °C), temperature coefficient of resistance (α, target value: ≥12% / °C).

[0047] Perform binary processing on non - numerical parameters (such as encoding doping element Y as [1,0,0]).

[0048] Adopt the Min - Max method to map each parameter to the [0,1] interval. The formula is: , where represents the normalized value, that is, the result after mapping to the [0,1] interval, represents a certain parameter value in the original data, represents the minimum value of all original data of this parameter, represents the maximum value of all original data of this parameter; for example, sintering temperature 1150 °C → 0, 1350 °C → 1.

[0049] Randomly divided into a training set, a validation set, and a test set in a ratio of 8:1:1.

[0050] In this embodiment, for step S2, an exact model construction and optimization method will be given as follows: Select the XGBoost regression model because it has strong adaptability to small data sets and non-linear relationships.

[0051] When performing hyperparameter tuning, determine the optimal parameter combination through Bayesian optimization. Specifically: control the tree complexity max_depth = 5, learning rate learning_rate = 0.1, number of trees n_estimators = 200, subsample ratio subsample = 0.8.

[0052] In this embodiment, for step S3, an exact model training and validation method will be given as follows: During the training process, the input features include 10 parameters such as the content of barium titanate matrix, Y doping amount, sintering temperature, etc., and the output target is the dual-target prediction of Tc and α.

[0053] The loss function is selected as the weighted mean squared error (MSE), and the weights are Tc:α = 6:4.

[0054] Evaluate the model performance on the test set and pay attention to the reliability of the model prediction. The evaluation metrics include the mean squared error (MSE): Coefficient of determination (R 2 )

[0055] Training evaluation results: Training set MSE = 0.04, R 2 = 0.94; Test set MSE = 0.07, R 2 = 0.89.

[0056] Feature importance ranking: Sintering temperature (35%), Y doping amount (28%), flux ratio (20%).

[0057] In this embodiment, for step S4, an exact expected preparation plan will be given as follows: According to the input target performance: Tc = 55 °C, α = 13% / °C. Model recommended parameters: Material composition: BaTiO3 = 81.8 mol%, doped element Sr (16.0 mol%), Y = 2.2 mol%, AST = 3.5 wt%; Preparation conditions: Sintering temperature = 1180 °C, ball milling time = 24 h, pre-sintering time = 1 h.

[0058] In this embodiment, for the operation of preparing the thermistor particles by the high-temperature solid-phase method in step S5, the steps are as follows: Weigh BaCO3 (99.9%), TiO2 (99.8%), SrCO3 (99.99%), and Y2O3 (99.99%), and mix them according to the stoichiometric ratio. Add zirconia balls (diameter 3 mm, ball-to-material ratio 3:1) and anhydrous ethanol (volume ratio 1:1.5), and perform planetary ball milling for 24 h (rotation speed 300 rpm). After the ball-milled slurry is vacuum-dried at 80 °C for 8 h, it is sieved through a 200-mesh sieve. Pre-sinter at 1150 °C for 1 h with a heating rate of 5 °C / min. Add the AST sintering aid and perform wet ball milling for 24 h. After the ball milling is completed, put it into a vacuum drying oven for drying. Add a 5% PVA solution according to a mass ratio of 1:20, and grind thoroughly for 1 h. After grinding, dry for 0.5 h. Press the sample powder into a Φ10 mm × 2 mm wafer. Heat it to 1180 °C at a rate of 5 °C / min in an air atmosphere, hold for 2 h, and then cool it to room temperature with the furnace.

[0059] For the thermistor particles prepared according to the above implementation steps, perform a resistance-temperature characteristic test. Measure the impedance-temperature curve through an impedance analyzer (Agilent 4294A), and the inflection point corresponds to Tc. Calculate the resistivity change rate in the range of 25 - 100 °C. The formula is: ... The test result is Tc = 58 °C, α = 13.2% / °C. Add the experimental data of this time to the data set. After retraining, the test set R 2 is increased to 0.91. As Figure 2 shown, the prediction error of the XGBoost model for Tc is concentrated within ±3 °C, indicating that the model has high reliability.

[0060] Example 2 In order to compare and verify the influence of different element-doped barium titanate on the performance of the thermistor particles, in this embodiment, the data set of step S1 is adjusted, replacing Y with La (ionic radius 1.06 Å), and literature data and experimental data are collected.

[0061] In this embodiment, for the construction and training of the model in steps 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.

[0062] In this embodiment, for the output of the optimization scheme in step S4, the model recommends the scheme of La = 2.8 mol%, sintering temperature = 1220 °C, and AST = 4.0 wt%.

[0063] In this embodiment, for step S5, the measured Tc = 67°C and α = 11.5% / °C, which deviate significantly from the target performance. It is necessary to increase the La doping amount to 3.2 mol% and conduct experiments again.

[0064] Example 3 In this embodiment, the data set in step S1 of Example 1 is expanded, and new co-doping data of Nb (0.5 - 1.5 mol%) and Y are added. The introduction of Nb 5+ ionic radius (0.64 Å) and lattice distortion energy (calculated by DFT) are used as new features.

[0065] In this embodiment, for step S2, a specific model construction and optimization method will be given as follows: After in-depth research and comparative analysis of various machine learning models, considering the complex associations and graph structure characteristics of the data, the graph convolutional neural network (GCN) model is selected. GCN can effectively process graph data. Through the message passing mechanism between nodes, it learns the potential representations of node features and discovers the hidden relationships between samples, making it suitable for predicting the performance of thermistors.

[0066] In terms of the model architecture, the graph structure is constructed based on the perovskite crystal structure. Elements (such as Ba, Ti, O) are set as nodes, and the node features include physical parameters such as atomic number, ionic radius, valence state, lattice distortion energy, and the usage amounts of each element. Then, edges are constructed according to the chemical bonds and doping substitution relationships between atoms: Ba and Ti are connected by O to form the perovskite framework. When elements such as Sr, La, Y replace the Ba site, they are connected to the Ba node, and when Nb, Mn, etc. replace the Ti site, they are connected to the Ti node. The edge features describe the interactions between atoms 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. In the graph neural network model, the input layer is used to input the constructed graph structure data; the convolutional layer includes 2 layers of graph convolutional layers, with the number of neurons being 128 and 64 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 convolutional layers to reduce the dimensionality 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, and the graph convolutional features and physical features are concatenated and then the dual-target prediction values are output through the fully connected layer.

[0067] When performing hyperparameter tuning, the optimizer AdamW is selected. It adds a weight decay mechanism to the Adam optimizer, which helps prevent model overfitting. The learning rate is set to 0.005, and the weight decay is 1e-4; the number of training epochs is 100, and the early stopping method (patience = 20) is adopted.

[0068] 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 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 objective is to minimize the prediction error MSE and maximize the physical constraint satisfaction at the same time. The Gaussian process regression is used to construct a surrogate model in the optimization process.

[0069] The loss function uses a custom loss where is the basic regression loss, , , , are the losses for the constraints of grain size, oxygen vacancy concentration, and doping amount respectively, , , , , , are the weight parameters; The core task of the model is to predict the Curie temperature point (Tc) and the resistance temperature coefficient (α) of the thermistor particles through the mean square error (MSE), ensuring the model's accurate prediction ability for key performance parameters; Through the relative error penalty term of the grain size, the influence of the sintering process on the material microstructure is constrained, preventing the model from sacrificing the material structure stability in pursuit of the accuracy of Tc and α; Through the mean square error penalty term of the oxygen vacancy concentration, the material conductivity mechanism is controlled, balancing conductivity and thermal stability, and avoiding failures caused by extreme doping; Through the mean square error penalty term of the number of active doping ions, the doping ratio is optimized, preventing structural distortion or electrical property deterioration caused by excessive doping; Take 0.1 to weaken the constraint intensity of the grain size, because it can be compensated by process adjustment, Take 0.2 to moderately strengthen the control of the oxygen vacancy concentration, because it is sensitive to electrical properties, Take 0.3 to focus on constraining the doping amount, because it directly affects the material stability and reliability. Through hyperparameter adjustment, the prediction accuracy and physical feasibility are balanced, and avoiding a single target from dominating the model training.

[0070] In this embodiment, for step S3, a specific model training and verification method will be given as follows: 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 the validation loss. In each round of training, the graph data is input into the model, the predicted values are calculated through forward propagation, then the loss value is calculated according to the loss function, and the model parameters are updated through backpropagation. To prevent overfitting, an early stopping strategy is adopted. When the MSE of the validation set does not decrease for 50 consecutive rounds of training, the training is stopped. The evaluation results are: MSE of the training set = 0.03, R 2 = 0.96; MSE of the test set = 0.05, R 2 = 0.93; The contribution degrees of key features are obtained based on the attention weights: sintering temperature (38%), Y doping amount (30%), Nb doping amount (18%).

[0071] In this embodiment, for step S4, a specific expected preparation scheme will be given as follows: According to the input target performance: Tc = 50°C, α = 14% / °C. The model-recommended parameters are: Material composition: Y = 2.0 mol%, Nb = 0.5 mol%, AST = 3.8 wt%.

[0072] Preparation conditions: sintering temperature = 1175°C, ball milling time = 30 h, pre-sintering time = 1.5 h.

[0073] In this embodiment, for the operation of preparing thermistor particles by the high-temperature solid-phase method in step S5, the steps are as follows: Weigh BaCO3, TiO2, SrCO3, Y2O3, Nb2O5 (purity ≥ 99.9%) and mix them according to the stoichiometric ratio. Add zirconia balls (diameter 3 mm, ball-to-material ratio 3:1) and anhydrous ethanol (volume ratio 1:1.5), and perform planetary ball milling for 30 h (rotation speed 300 rpm). After the ball-milled slurry is vacuum dried at 80°C for 8 h, it is sieved through a 200-mesh sieve. Pre-sinter at 1150°C for 1 h with a heating rate of 5°C / min. Add the AST sintering aid and perform wet ball milling for 30 h. After ball milling is completed, place it in a vacuum drying oven for drying. Add a 5% PVA solution according to a mass ratio of 1:20, grind thoroughly for 1 h, and dry for 0.5 h after grinding. Press the sample powder into a Φ10 mm × 2 mm disc. Heat it to 1175°C at a rate of 5°C / min in an air atmosphere, hold for 2.5 h, and then cool it to room temperature with the furnace.

[0074] Test results: Tc = 52°C, α = 14.0% / °C.

[0075] Example 4 In this embodiment, the same dataset as in Embodiment 3 is used for the dataset in step S1.

[0076] To compare and verify the effectiveness of the custom loss function set in the mechanism integration network in Embodiment 3, for the construction of the model in step S2 in this embodiment, the mean squared error (MSE) is used as the loss function in this embodiment, and the remaining network structures, hyperparameter settings, etc. are the same as those in Embodiment 3.

[0077] In this embodiment, for the training of the model in step S3, the same method as in Embodiment 3 is used, and the test set MSE = 0.07, R 2 = 0.87, indicating that the effect of training the model using the custom loss function in Embodiment 3 is better than that of training using the mean squared error (MSE) as the loss function.

[0078] In this embodiment, for the output of the optimization scheme in step S4, the model-recommended scheme is Y = 1.8 mol%, Nb = 0.7 mol%, AST = 4.0 wt%, sintering temperature = 1250 °C, ball milling time = 30 h, and pre-sintering time = 1 h.

[0079] In this embodiment, for step S5, the measured Tc = 61 °C and α = 13.2% / °C. Compared with Embodiment 3, the gap between the measured performance and the target performance of the particles prepared according to the model-recommended scheme in this embodiment is relatively large, indicating the effectiveness of the custom loss function in Embodiment 3.

[0080] Embodiments 1-4 verify the universality and efficiency of the method of the present invention. The embodiments show that the present invention can reduce the number of experiments by 70%, and the target performance prediction error is less than 5%. In Embodiment 3, by introducing a graph convolutional neural network (GCN) and integrating physical and chemical mechanisms with data, an efficient modeling of the complex topological relationship between material composition - process - performance is achieved, and its test set R 2 reaches 0.93, which is significantly better than traditional models. In addition, the co-doping synergistic effect of 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.

[0081] In summary, the present invention introduces advanced machine learning techniques to assist in the preparation process of thermistor particles, abandoning the traditional "trial and error" mode 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 unnecessary experimental times, thus 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 and effectively improve the R & D efficiency. The machine learning method adopted by the present invention has powerful data processing capabilities and can accurately identify the influence degree of different parameters on the performance of thermistor particles in a large amount of 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 limitation that traditional preparation methods are difficult to precisely control performance. The present invention adopts the concept of multi-objective optimization design and is committed to making the prepared thermistor particles meet the dual conditions of a relatively low Curie temperature point and a relatively high resistance temperature coefficient at the same time. This design method effectively solves the performance deficiency problem of traditional thermistors in specific application scenarios (such as the physical discharge safety of lithium batteries), greatly expanding the application range of thermistors and having significant practical value and market competitiveness. The present invention innovatively integrates the physical and chemical mechanism of the formation of thermistor particle performance into the machine learning prediction process, realizing the deep integration of mechanism and data. This integration method not only utilizes the powerful prediction ability of the data-driven machine learning model but also gives full play to the guiding and constraining role of mechanism 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 prediction, and at the same time reducing the model's dependence on data.

[0082] The above embodiments only represent alternative embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these modifications and improvements also belong to the protection scope of the present invention.

Claims

1. An optimization method for preparing thermistor particles based on machine learning, characterized in that, It includes the following steps: S1: Construct a dataset containing the preparation process parameters, performance indicators, and known physical and chemical mechanism knowledge of thermistor particles, and perform preprocessing; The preparation process parameters include material composition and preparation conditions, and the performance indicators include the Curie temperature point and the resistance temperature coefficient of the thermistor particles; S2: Construct and optimize a machine learning model Integrate the physical and chemical mechanism knowledge 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: Use the performance indicators of the thermistor particles as the target labels, and use the dataset in S1 to train the optimized machine learning model constructed in S2; S4: Input the expected performance indicators of the thermistor particles into the trained machine learning model, and the model outputs the most suitable combination of material composition and preparation conditions; S5: Prepare thermistor particles according to the combination of material composition and preparation conditions output by the model; S6: Test the performance indicators of the prepared thermistor particles. If the test data does not meet the target requirements, add the test data obtained to the dataset in step S1 and retrain the model. When the test data meets the requirements, terminate the update and determine the optimal scheme for preparing the thermistor particles.

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

3. The optimization method for preparing thermistor particles based on machine learning according to claim 2, wherein In step S1, in the dataset, the material composition includes: the amount of barium titanate matrix, the type and amount of dopant elements, and the amount of sintering aid AST, and the preparation conditions include sintering temperature, pre-burning time, heat preservation time, heating and cooling rate, and ball milling time.

4. The optimization method for preparing thermistor particles based on machine learning according to claim 2, wherein In step S1, when constructing the dataset, convert the physical and chemical mechanism knowledge into quantifiable features or constraint conditions. The physical and chemical mechanism knowledge includes: the crystal structures of the barium titanate matrix and the thermistor particles, the atomic numbers, ionic radii, valence states, electronegativities of each element in the matrix and the dopant material, as well as the matrix lattice distortion energy, oxygen vacancy concentration, grain size, and electron cloud overlap integral; among them: Lattice distortion energy Calculated by the difference in ionic radii between the doped ions and the barium titanate matrix ions Calculation: ， Among them, , and are the radii of the dopant atom and the host atom, respectively; Oxygen vacancy concentration Calculated by the following formula: ， Among them, is the concentration of the doping element, is the difference between the valence state of the doping element and the valence state of the substituted host ion, is the oxygen vacancy formation energy, with a value of 1.2 eV, is the Boltzmann constant, is the temperature; Grain size after sintering Predicted based on the Beck equation: ， wherein is the grain size, is the sintering time, is the Boltzmann constant, is the temperature; Overlap integral of the electron cloud between the doped ions and the barium titanate lattice The calculation method is as follows: ， wherein, and are the radii of the dopant atom and the host atom, respectively.

5. The optimization method for preparing thermistor particles based on machine learning according to claim 2, characterized in that, In step S1, in the dataset, the min-max scaling method is used to normalize the numerical parameters, and the numerical parameters are mapped to the [0,1] interval to avoid model bias caused by variable scale differences; the non-numeric parameters involved are encoded using one-hot encoding.

6. The optimization method for preparing thermistor particles based on machine learning according to claim 2, characterized in that, In step S2, the machine learning model selects one of random forest, support vector machine, XGBoost, Adaboost, or a deep learning network.

7. The optimization method for preparing thermistor particles based on machine learning according to claim 6, wherein In step S2, the machine learning model is a graph neural network model GCN. During the forward propagation of the network, the influence degree of different parameters on the performance index is reflected by calculating the attention weights. The graph structure is constructed based on the perovskite crystal structure, with elements set as nodes. The node features include atomic number, ionic radius, valence state, lattice distortion energy, and the dosage of each element. Then, edges are constructed according to the chemical bonds and doping substitution relationships between atoms: Ba and Ti are connected by O to form the perovskite framework. When Sr, La, and Y elements substitute the Ba site, they are connected to the Ba node. When Nb and Mn substitute the Ti site, they are connected to the Ti node. The edge features describe the interaction between atoms through bond strength, distance, and type, and finally form the graph data that maps the microstructure of the material.

8. The optimization method for preparing thermistor particles based on machine learning according to claim 7, wherein 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: the hidden layer dimension ∈ [64, 512], the number of convolutional layers ∈ [2, 5], and the Dropout rate ∈ [0.1, 0.5]; (2) Training process parameters: the learning rate ∈ [0.0001, 0.1], the weight decay ∈ [1e-5, 1e-3], and the batch size ∈ [16, 128]; (3) Physical constraint weights: the lattice distortion energy weight α ∈ [0.1, 0.5], and the oxygen vacancy concentration weight β ∈ [0.05, 0.3]; The optimization objective is to minimize the prediction error MSE while maximizing the physical constraint satisfaction degree. The Gaussian process regression is used to construct a surrogate model during the optimization process.

9. The optimization method for preparing thermistor particles based on machine learning according to claim 7, wherein, In step S2, during the model construction process, the mechanism knowledge is incorporated into the model architecture or training process in the form of prior information. The doping amount is restricted so that the lattice distortion energy ≤ 0.5 eV / atom, the doping concentration is controlled so that the oxygen vacancy concentration ≤ 0.05, the doping combinations with the electron cloud overlap integral ≥ 0.5 are screened, the sintering process is optimized so that the grain size is controlled in the range of 1 - 5 μm, the network layer structure or the loss function adjustment method is designed, and the graph convolutional features and physical features are concatenated and then output the performance index 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.

10. The optimization method for preparing thermistor particles based on machine learning according to claim 7, characterized in that, In step S3, the loss function for training adopts a multi-task joint loss: ， wherein is the basic regression loss, , , are the losses constrained by grain size, oxygen vacancy concentration, and doping amount respectively, , , are weight parameters.

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