Method for evaluating current limiting effect of PTC (Positive Temperature Coefficient) characteristic material

Abstract

The invention provides a PTC characteristic material current limiting effect evaluation method, and belongs to the technical field of PTC characteristic materials, and the method comprises the following steps: preparing a plurality of groups of PTC material resistance samples according to an orthogonal test principle, carrying out a current limiting effect experiment on the PTC material resistance samples, recording related data, carrying out data preprocessing and characteristic equation establishment, carrying out data expansion by using a fitting equation, and carrying out current limiting effect evaluation on the PTC material resistance samples. And obtaining a training data set. And finally, a generative adversarial neural network is adopted to construct a PTC characteristic material current limiting effect evaluation model. The proportion of the PTC material to be evaluated is input, and a predicted current limiting effect evaluation curve (including current-voltage characteristics, temperature-time characteristics, resistivity-temperature characteristics and current limiting multiple-time characteristics) is output to comprehensively reflect the dynamic response characteristics of the PTC material. According to the method, the technical problem that the current limiting effect of the PTC characteristic material cannot be rapidly evaluated due to the fact that the current limiting effect of the PTC characteristic material often needs to be obtained through an experiment mode in an existing method is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of PTC characteristic materials, and in particular, relates to a method for evaluating the current limiting effect of a PTC characteristic material. Background Art

[0002] Positive Temperature Coefficient (PTC) material is a functional material with special resistance-temperature characteristics. Its resistance increases significantly with the increase of temperature, thus producing a self-limiting current effect. This unique PTC characteristic makes PTC materials widely used in many fields such as power electronics, electrical protection, and temperature sensing. In power electronic systems, PTC materials can be used as key components such as overload protection, short circuit protection, and thermal fuses to quickly cut off current in accidents or abnormal conditions, effectively reducing the risk of equipment damage. In the field of electrical appliances, PTC materials are widely used in temperature control of electric heating products such as electric kettles and hair dryers to achieve safe and reliable temperature limits. In addition, PTC materials can also be used as temperature sensing elements and are used in battery management systems, industrial automation, and other application scenarios that have strict requirements for temperature monitoring and control.

[0003] Although PTC materials play an important role in many applications, there are still some problems in the evaluation and prediction of their current limiting characteristics. First, the current limiting characteristics of PTC materials are affected by multiple factors such as material formula, process, temperature, etc., and are highly complex and nonlinear, making it difficult to comprehensively evaluate their current limiting performance through simple experimental methods. Secondly, most of the existing simulation analysis methods are based on simplified thermoelectric coupling models, which cannot accurately predict the dynamic response and current limiting effect of PTC materials under actual working conditions. In addition, the development of new PTC materials requires a large amount of experimental data support, but the existing experimental methods are often inefficient and it is difficult to evaluate the current limiting characteristics of different material formulas in a high-throughput manner.

[0004] That is to say, existing methods often require a large number of experiments to obtain the current-limiting effect of PTC characteristic materials, and there is a technical problem that the current-limiting effect of PTC characteristic materials cannot be quickly evaluated. Summary of the invention

[0005] In view of this, the present invention provides a method for evaluating the current limiting effect of PTC characteristic materials, which can solve the technical problem that the existing methods often need to obtain the current limiting effect of PTC characteristic materials through experiments and cannot quickly evaluate the current limiting effect of PTC characteristic materials.

[0006] The present invention is achieved in that:

[0007] The present invention provides a method for evaluating the current limiting effect of a PTC characteristic material, comprising the following steps:

[0008] S10. Based on the orthogonal test principle, different materials and proportions are selected to prepare multiple groups of PTC material resistor samples;

[0009] S20, conducting a current limiting effect experiment on each group of PTC material resistor samples, recording experimental data, including voltage, temperature, time, current, resistivity, power, thermal conductivity and specific heat capacity, and generating a current limiting effect evaluation curve based on the experimental data;

[0010] S30, after preprocessing the experimental data including data cleaning and normalization operations, combining the proportions of the PTC material resistor samples to obtain a first data set;

[0011] S40, using thermoelectric coupling theory to establish a PTC characteristic equation group, including Joule heat equation, heat conduction equation, resistance temperature coefficient equation, current density equation, electric field strength equation, heat flux density equation, specific heat capacity equation and heat diffusion equation;

[0012] S50, fitting the PTC characteristic equation group using the first data set to obtain a fitted PTC characteristic equation group, recorded as a fitting equation group;

[0013] S60, using data augmentation technology to augment the first data set to obtain a second data set, using the fitting equation group to filter the second data set to obtain a third data set, recording each set of data in the third data set as metadata, and generating a current limiting effect evaluation curve according to the metadata;

[0014] S70, constructing a training data set using the third data set, and training a generative adversarial neural network using the training data set to obtain a current limiting effect evaluation model for PTC characteristic materials, wherein the training input of the training data set is each metadata in the third data, and the training output is a current limiting effect evaluation curve corresponding to the metadata;

[0015] S80, using the PTC characteristic material current limiting effect evaluation model, inputting the ratio of the PTC characteristic material to be evaluated, and outputting a predicted current limiting effect evaluation curve.

[0016] The current limiting effect experiment uses a programmable DC power supply, a high-precision data acquisition system, a constant temperature box and other equipment. The specific experimental steps include:

[0017] 1) Fix the PTC sample in the test fixture;

[0018] 2) Set the initial current and voltage;

[0019] 3) Gradually increase the current and record the voltage and temperature changes;

[0020] 4) Stop increasing when the current reaches the preset maximum value or the temperature reaches the critical value;

[0021] 5) Maintain the maximum current for a period of time and observe the steady-state characteristics;

[0022] 6) Reduce the current to the initial value and record the cooling process data.

[0023] The following is the specific formula expression of each equation in the PTC characteristic equation group:

[0024] 1. Joule heat equation:

[0025] Where Q is heat (unit J); t is time (unit s); I is current (unit A); R (T) is the temperature-dependent resistance function (unit Ω); T is temperature (unit K); x, y, z are spatial coordinates (unit m); α, β, γ are thermal diffusivities in each direction (unit m 2 / s); R(T) can be obtained through experimental measurement, I is a known input, and α, β, γ can be obtained through material property query.

[0026] 2. Heat conduction equation:

[0027] Where ρ is the material density (unit: kg / m 3 );c p is the specific heat capacity (unit J / (kg·K)); k is the thermal conductivity (unit W / (m·K)); is the Laplace operator; q v is the heat source per unit volume (unit W / m 3 ), μ is the dynamic viscosity (unit: Pa·s), Φ is the viscosity dissipation function, ρ, c p ,k can be obtained through material properties, q v Calculated by Joule's heat equation, μ and Φ can be ignored in most PTC applications.

[0028] 3. Temperature coefficient of resistance equation:

[0029]

[0030] Where R0 is the resistance at reference temperature T0 (unit: Ω); α1, α2, α3 are temperature coefficients (unit: K-1, K-2, K-3); E a is the activation energy (unit J); k B is the Boltzmann constant (unit: J / K); R0, T0, α1, α2, α3 can be obtained by experimental measurement, E a Can be determined by material properties.

[0031] 4. Current density equation:

[0032] Where J is the current density (unit A / m 2 ), σ(T) is the temperature-dependent conductivity (unit S / m), E is the electric field strength (unit V / m), and D is the electric displacement (unit C / m 2 ); E can be calculated from voltage and geometry, Can be ignored in most PTC applications.

[0033] 5. Electric field strength equation:

[0034] Where V is the electric potential (unit V); A is the magnetic vector potential (unit Wb / m); V can be obtained by voltage measurement, Can be ignored in most PTC applications.

[0035] 6. Heat flux equation:

[0036] Where q is the heat flux (unit: W / m 2 );L 12 is the thermoelectric coupling coefficient; μ e is the electronic chemical potential (unit J); e is the electronic charge (unit C); k can be obtained from the material properties, It can be calculated by temperature distribution, L 12 and μ e It needs to be obtained through complex quantum mechanical calculations or experimental measurements.

[0037] 7. Specific heat capacity equation:

[0038] In the formula, c p0 is the specific heat capacity at room temperature (unit: J / (kg·K)); a1, a2, a3, a4 are fitting coefficients; c p0 ,a1,a2,a3,a4 can be obtained through experimental measurement and data fitting.

[0039] 8. Heat diffusion equation:

[0040] Where D is the thermal diffusion coefficient (unit: m 2 / s); Q v is the heat source per unit volume (unit W / m 3 );τ is the thermodynamic temperature coefficient;p is the pressure (unit: Pa); Q v It can be calculated by Joule heat, and τ needs to be obtained through experimental measurement. Can be ignored in most PTC applications.

[0041] These equations form a complex coupled system that describes the behavior of the PTC material with respect to current, temperature, heat conduction, etc. Solving this system of equations usually requires the use of numerical methods such as finite element analysis or finite difference methods.

[0042] The following is a description of the experiment for obtaining the main experimental data involved in the PTC characteristic equation group:

[0043] 1. Resistance-temperature relationship experiment (used to obtain R(T), R0, T0, α1, α2, α3):

[0044] Experimental equipment: high-precision four-wire resistance measuring instrument; programmable constant temperature box; temperature sensor (such as platinum resistance or thermocouple); data acquisition system;

[0045] Experimental steps:

[0046] a) Place the PTC sample in a constant temperature box and connect it to a four-wire resistance meter and a temperature sensor.

[0047] b) Set the temperature range of the thermostat (e.g. -40°C to 200°C) and increase the temperature in steps of 5°C.

[0048] c) After each temperature point stabilizes, record the temperature and the corresponding resistance value.

[0049] d) Repeat the heating-cooling cycle 3 times to ensure the repeatability of the data.

[0050] e) Use the least squares method to fit the data and obtain the R(T) function:

[0051] R(T)=R0·(1+α1(T-T0)+α2(T-T0) 2 +α3(T-T0) 3 );

[0052] Where R0 is the resistance value at T0 (usually 25°C).

[0053] 2. Specific heat capacity measurement experiment (used to obtain c p0 ,a1,a2,a3,a4):

[0054] Experimental equipment:

[0055] Differential Scanning Calorimeter (DSC); High-purity reference sample (e.g., sapphire); Precision balance;

[0056] Experimental steps:

[0057] a) Prepare 10-50 mg of PTC material sample and weigh it accurately.

[0058] b) Place the sample and reference into the sample and reference cells of the DSC.

[0059] c) Set the temperature program, such as from -50°C to 250°C, with a heating rate of 10°C / min.

[0060] d) Record the difference in heat flow between the sample and the reference as a function of temperature.

[0061] e) Using a reference material with known specific heat capacity, calculate the specific heat capacity of the PTC sample at different temperatures.

[0062] f) Use polynomial fitting to obtain the specific heat capacity equation:

[0063]

[0064] 3. Thermal conductivity measurement experiment (for obtaining k):

[0065] Experimental equipment: transient plane heat source method (TPS) instrument; constant temperature box;

[0066] Experimental steps:

[0067] a) Prepare two PTC material samples of the same size (usually discs with a diameter of 30 mm and a thickness of 10 mm).

[0068] b) The TPS sensor is sandwiched between two samples.

[0069] c) Place the entire device in a constant temperature box and set different temperature points (such as 25℃, 50℃, 75℃, 100℃, etc.).

[0070] d) At each temperature point, a constant power current pulse (usually lasting 10-80s) is applied to the sensor by the TPS instrument.

[0071] e) Record the temperature change curve of the sensor over time.

[0072] f) Use the analysis software provided by the TPS instrument to calculate the thermal conductivity based on the temperature change curve.

[0073] 4. Thermoelectric coupling coefficient measurement experiment (used to obtain L 12 ):

[0074] Experimental equipment: Harman device; high-precision voltmeter; constant current source; temperature control system;

[0075] Experimental steps:

[0076] a) Make the PTC sample into a suitable strip shape (e.g. 1 cm×0.5 cm×5 cm).

[0077] b) Connect electrodes and a temperature sensor to both ends of the sample.

[0078] c) Place the sample in a temperature-controlled vacuum chamber.

[0079] d) Apply a small current (e.g. 100 mA) to the sample through a constant current source.

[0080] e) Quickly cut off the current and immediately measure the voltage across the sample.

[0081] f) Record the voltage decay curve over time.

[0082] g) Calculate the Seebeck coefficient and conductivity by analyzing the voltage decay curve.

[0083] h) Using the Onsager reciprocity relationship, calculate the thermoelectric coupling coefficient L 12 .

[0084] 5. Thermodynamic temperature coefficient measurement experiment (used to obtain τ):

[0085] Experimental equipment: autoclave; high-precision temperature and pressure sensors; data acquisition system;

[0086] Experimental steps:

[0087] a) Place the PTC sample in an autoclave and fill it with inert gas (such as nitrogen).

[0088] b) Slowly increase the pressure at different temperatures (such as 25℃, 50℃, 75℃, 100℃).

[0089] c) Record the pressure and the corresponding temperature change.

[0090] d) Using the formula Calculate the thermodynamic temperature coefficient, where S indicates that entropy remains constant.

[0091] These experiments need to be carried out under strictly controlled conditions and repeated many times to ensure the accuracy and repeatability of the data. After processing, the obtained data can be used for each parameter in the PTC characteristic equation group.

[0092] The current limiting effect evaluation curve is a multidimensional curve set describing the current-voltage relationship, the temperature-time relationship, the resistance-temperature relationship, and the current limiting multiple-time relationship. The current limiting effect evaluation curve can be described by the following mathematical expression:

[0093] 1. Current-voltage relationship:

[0094]

[0095] Where I is the current (unit A); V is the voltage (unit V); t is the time (unit s); R(T) is the temperature-related resistance function (unit Ω); T(t) is the temperature change function with time (unit K); τ1 is the current response time constant (unit s).

[0096] 2. Temperature-time relationship:

[0097]

[0098] Where T0 is the initial temperature (unit K); ΔT max is the maximum temperature rise (unit K); τ2 is the temperature response time constant (unit s).

[0099] 3. Resistance-temperature relationship:

[0100]

[0101] Where R0 is the resistance at the reference temperature (unit Ω); B is the material characteristic constant (unit K); α is the PTC effect coefficient; T c is the Curie temperature (unit K); n is the PTC effect index; H(x) is the Heaviside step function, when x≥0, H(x)=1, otherwise H(x)=0.

[0102] 4. Current limiting multiples-time relationship:

[0103]

[0104] Where, M(t) is the current limiting multiple; I max is the maximum allowable current (unit A); I(t) is the current at time t (unit A); I0 is the initial current (unit A); β is the current limiting coefficient; τ3 is the current limiting response time constant (unit s);

[0105] These relationships can be combined into a set of multidimensional curves, represented as:

[0106] C(V,t)={I(V,t),T(t),R(T(t)),M(t)};

[0107] Where C(V,t) represents a set of current limiting effect evaluation curves at a given voltage V and time t.

[0108] Furthermore, in order to fully describe the current limiting characteristics of PTC materials, the following additional functions need to be considered:

[0109] 5. Power dissipation function:

[0110] P(t)=V·I(V,t);

[0111] Where P(t) is the power dissipation at time t (in W).

[0112] 6. Heat dissipation function:

[0113]

[0114] Where Q(t) is the accumulated heat at time t (unit J); h is the heat transfer coefficient (unit W / (m 2 ·K)); A is the surface area of ​​the PTC element (unit: m 2 );T amb is the ambient temperature (unit K).

[0115] 7.Restore characteristic function:

[0116]

[0117] In the formula, R rec (t) is the resistance value during the recovery process (unit: Ω); R max is the resistance value when the maximum temperature is reached (unit Ω); τ4 is the recovery time constant (unit s);

[0118] In summary, the complete set of current limiting effect evaluation curves can be expressed as:

[0119] C full (V,t)={I(V,t),T(t),R(T(t)),M(t),P(t),Q(t),R rec (t)};

[0120] This multi-dimensional curve collection comprehensively describes the electrical, thermal and time characteristics of the PTC material during the current limiting process and can be used to evaluate and compare the current limiting effects of different PTC materials.

[0121] The method of using the fitting equation group to screen the second data set is specifically: by comparing the augmented data with the prediction of the fitting equation group, retaining the data points that meet the expectations of the physical model, and eliminating or adjusting the abnormal data.

[0122] The detailed description is as follows:

[0123] 1. First, each data point in the second data set is input into the fitting system of equations.

[0124] 2. For each data point, calculate its predicted value in the fitted system of equations.

[0125] 3. Compare the error between the predicted value and the actual value. You can use indicators such as mean square error (MSE) or mean absolute error (MAE).

[0126] 4. Set an acceptable error threshold, which can be determined based on actual needs and data characteristics.

[0127] 5. For data points with an error less than the threshold, keep them in the dataset.

[0128] 6. For data points with errors greater than the threshold, further analysis is performed:

[0129] a. If the error is only slightly above the threshold, consider fine-tuning the data point to make it consistent with the predictions of the fitted system of equations.

[0130] b. If the error is significantly higher than the threshold, the data point is removed from the data set.

[0131] 7. For the excluded data points, analyze their characteristics to determine whether they are outliers or reflect some special circumstances. If it is the latter, you can consider building a separate model to handle these special circumstances.

[0132] 8. Repeat the above steps until all data points in the second data set have been processed.

[0133] 9. Perform statistical analysis on the filtered data set to ensure that the data distribution still represents the characteristics of the original data.

[0134] 10. If the size of the dataset is significantly reduced after screening, you can consider adjusting the error threshold or re-augmenting the data to ensure that there is enough data for subsequent model training.

[0135] The generative adversarial neural network includes a generator network and a discriminator network, and the generator network is used to generate a corresponding current limiting effect evaluation curve according to the input metadata.

[0136] The training goal of the generative adversarial neural network is to minimize the loss function of the generator and maximize the loss function of the discriminator, forming a dynamically balanced adversarial process. The generator network attempts to generate a realistic current limiting effect evaluation curve, while the discriminator network strives to distinguish between the real curve and the generated curve.

[0137] Furthermore, the initial discrimination of the discriminator network is pre-trained using the PTC characteristic equation group and experimental data to obtain a preliminary understanding of the characteristics of the current limiting effect curve of the real PTC material. The specific process can be expressed as follows:

[0138] D init (x) = f(C PTC (x),S exp (x)

[0139] Where D init(x) is the initial discriminant function; x is the input data (including voltage, temperature, time, current, resistivity, power, thermal conductivity and specific heat capacity); C PTC (x) is the confidence evaluation function based on the PTC characteristic equation group; S exp (x) is the similarity evaluation function based on experimental data; f is the combination function.

[0140] 1. PTC characteristic equation group confidence evaluation function C PTC (x):

[0141]

[0142] In the formula, C i (x) represents the confidence evaluation function based on the current-voltage relationship, temperature-time relationship, resistance-temperature relationship and current limiting multiple-time relationship respectively.

[0143] Each confidence evaluation function can be expressed as:

[0144]

[0145] Where N is the number of sampling points; x ij is the actual value of the input data at the jth sampling point; is the theoretical value calculated according to the PTC characteristic equation group; σ i is the allowable error range.

[0146] 2. Similarity evaluation function S based on experimental data exp (x):

[0147]

[0148] Where K is the number of samples in the experimental data set; x k is the kth experimental data sample; σ is the bandwidth parameter of the Gaussian kernel function.

[0149] 3. Combination function f: f(y1,y2)=βy1+(1-β)y2;

[0150] In the formula, y1=C PTC (x), y2 = S exp (x); β is the trade-off coefficient, 0≤β≤1.

[0151] Pre-training process:

[0152] 1. Collect the experimental data set of the current limiting effect evaluation curve of real PTC materials

[0153] 2. Construct training set where x iIncluding the real experimental data and augmented data, y i For tags:

[0154]

[0155] 3. Optimize the objective function:

[0156]

[0157] 4. Update parameters using gradient descent:

[0158]

[0159] In the formula, θ represents D init All trainable parameters in ; η is the learning rate.

[0160] Through this pre-training method, the discriminator network can learn:

[0161] The data that conforms to the PTC characteristic equation group has a higher credibility;

[0162] Data that are similar to existing experimental data are more likely to be true.

[0163] This method enables the discriminator to gain a preliminary understanding of the characteristics of the current limiting effect curve of the real PTC material, which helps to better distinguish between real data and generated data in subsequent GAN training, and improve the training effect of the model and the reliability of the generated results.

[0164] Wherein, the normalization adopts the maximum-minimum normalization method.

[0165] The data augmentation technology is to generate more random sample data within the distribution range of the first data set using a Monte Carlo simulation method.

[0166] Furthermore, the data augmentation technology also includes inferring more intermediate data based on existing data points through interpolation and extrapolation methods.

[0167] The fitting method adopts the least square method.

[0168] The ratio refers to each component and its ratio used to synthesize the PTC material.

[0169] Specifically, step S10 includes:

[0170] Step 101, according to the orthogonal experimental design principle, construct a factor level table including polymer matrix type, conductive filler type, filler content, dispersant type and dosage, cross-linking agent type and dosage;

[0171] Step 102, select a suitable orthogonal array design test plan, and randomly assign each factor and level to the columns of the orthogonal array;

[0172] Step 103, prepare materials according to the test plan and mix them, use a high-speed mixer to mix the components according to the set ratio, the mixing time is 30 minutes, and the speed is 2000 revolutions per minute;

[0173] Step 104, using a twin-screw extruder for melt blending, the temperature is set to 20 degrees Celsius to 50 degrees Celsius above the melting point of the matrix polymer, and the screw speed is 100 to 200 revolutions per minute;

[0174] Step 105 : Use an injection molding machine or a tablet press to prepare a disc or strip sample with a thickness of 2 mm from the extruded material for subsequent resistance testing.

[0175] Wherein, the step S20 specifically includes:

[0176] Step 201, building a current limiting effect experimental platform including a programmable DC power supply, a high-precision data acquisition system, and a constant temperature box;

[0177] Step 202, fix the positive temperature coefficient material sample in a test fixture consisting of two silver-plated copper electrodes, and fix a thermocouple at the center of the sample surface;

[0178] Step 203, setting initial experimental parameters, setting the constant temperature box temperature to 25 degrees Celsius, the initial current to 0.1 ampere, and the initial voltage to 0.1 volt;

[0179] Step 204: Perform a step loading experiment, increasing the current by 0.1 ampere every 10 seconds until the current reaches a preset maximum value or the temperature reaches a critical value;

[0180] Step 205, maintaining the maximum current or critical temperature for 10 minutes and observing the steady-state characteristics;

[0181] Step 206, perform a load reduction experiment, gradually reduce the current to the initial value, reduce it by 0.1 ampere every 10 seconds, and record the cooling process data;

[0182] Step 207: Calculate the resistivity, power, thermal conductivity and specific heat capacity according to the recorded data, and draw a current limiting effect evaluation curve.

[0183] Wherein, the step S30 specifically includes:

[0184] Step 301: Use the 3-times standard deviation criterion, box plot method and density-based clustering algorithm to clean the experimental data and remove obviously abnormal data points;

[0185] Step 302: normalize all physical quantities such as voltage, temperature, time, current, resistivity, power, thermal conductivity and specific heat capacity by using the minimum and maximum normalization method;

[0186] Step 303: organize the experimental data of each group of positive temperature coefficient material resistor samples into a structured data table, including sample identification, material formula information and normalized data of various physical quantities;

[0187] Step 304: merge the data tables of all samples into a large data set, where each row represents a complete set of measurement data at a time point;

[0188] Step 305: Use the 5-fold cross-validation method to evaluate data quality and build a multivariate linear regression model to predict key parameters. If the relative error of the average prediction error is less than 10%, the data set is considered to have good quality.

[0189] Wherein, the step S40 specifically includes:

[0190] Step 401: Based on the thermoelectric coupling theory, a positive temperature coefficient material electrothermal coupling model including the Joule heat equation, the heat conduction equation, the resistance temperature coefficient equation, the current density equation, the electric field strength equation, the heat flux density equation, the specific heat capacity equation and the heat diffusion equation is established;

[0191] Step 402, determining boundary conditions and initial conditions of the equation group, including voltage or current conditions of the electrode contact surface, heat exchange conditions on the sample surface, initial temperature distribution and initial voltage distribution;

[0192] Step 403, select the finite element method to solve the positive temperature coefficient characteristic equation group, mesh the material sample, and control the mesh size within the range of 0.1 mm to 1 mm;

[0193] Step 404: Use the Galerkin weighted residual method to perform spatial discretization, and use the implicit Euler method for time discretization;

[0194] Step 405, using the Newton-Raphson iteration method to solve the nonlinear equations, and setting the iteration convergence criterion to a relative error less than 0.000001;

[0195] Step 406: Use an adaptive time step strategy, set the initial time step to 0.000001 seconds, and dynamically adjust the time step according to the rate of change of the solution;

[0196] Step 407: perform numerical stability and convergence analysis, use different grid sizes and time steps to perform calculations, compare the temperature and current values ​​of key nodes, and ensure the stability of the numerical solution.

[0197] Wherein, the step S50 specifically includes:

[0198] Step 501, select the Levenberg-Marquardt algorithm to perform nonlinear least squares fitting;

[0199] Step 502: define the objective function as the weighted square error between the experimental data and the predicted value of the theoretical model, and set the weight factor according to the importance and measurement accuracy of each physical quantity;

[0200] Step 503, setting an initial value and a value range for each parameter to be fitted according to physical meaning and empirical value;

[0201] Step 504, perform iterative optimization, calculate the Jacobian matrix and the residual vector, solve the incremental equation, and update the parameters until the convergence condition is met or the maximum number of iterations is reached;

[0202] Step 505: perform parameter sensitivity analysis, perturb each fitting parameter by plus or minus 10%, observe the change of model output, and calculate the sensitivity coefficient;

[0203] Step 506: Use indicators such as determination coefficient, root mean square error and mean absolute percentage error to evaluate the fitting quality. The determination coefficient should be greater than 0.95, the root mean square error should be less than 10% of the standard deviation of the experimental data, and the mean absolute percentage error should be less than 5%.

[0204] Wherein, the step S60 specifically includes:

[0205] Step 601: The first data set is augmented by using a Gaussian noise injection method, a cubic spline interpolation method, a synthetic minority class oversampling technique, and a data generation method guided by a physical model, and the augmentation ratio is set to 5 to 10 times the original data volume;

[0206] Step 602: input the augmented data into the fitting equations obtained in step S50 to calculate the theoretical prediction value;

[0207] Step 603: compare the deviation between the predicted value and the augmented data, and set the screening criteria as the relative deviation does not exceed 3 times the standard deviation of the original data, the absolute deviation does not exceed 5% of the measurement range of the physical quantity, and the data points should meet basic physical constraints;

[0208] Step 604: merge the screened augmented data with the original first data set to form a third data set;

[0209] Step 605: Perform statistical analysis on the third data set to ensure that its distribution characteristics are similar to those of the original data set, calculate the mean, standard deviation, skewness and kurtosis of each physical quantity, and compare them with the original data set. The difference should be within 10%;

[0210] Step 606: Use cubic spline interpolation to generate high-resolution data points for each set of data in the third data set, and apply a Savitzky-Golay filter to perform smoothing processing;

[0211] Step 607: plot the processed data into a multi-dimensional curve set, including a current-voltage curve, a temperature-time curve, a resistance-temperature curve, and a current-limiting multiple-time curve.

[0212] Wherein, the step S70 specifically includes:

[0213] Step 701, designing a generative adversarial neural network structure, where both the generator network and the discriminator network adopt a multi-layer perceptron structure, including an input layer, 3 to 4 hidden layers and an output layer;

[0214] Step 702: define the loss function of the generator as a combination of mean square error and adversarial loss, the loss function of the discriminator adopts binary cross entropy, and the optimization algorithm uses Adam optimizer;

[0215] Step 703: randomly divide the third data set into a training set and a validation set in a ratio of 8 to 2, and perform standardization processing on the input data and the output data respectively;

[0216] Step 704: Execute the model training process, adopt an alternating training strategy, and each iteration includes the steps of randomly extracting data from the training set, generating fake samples, training the discriminator, and training the generator;

[0217] Step 705: Evaluate the model performance on the validation set every 100 batches. If the performance on the validation set does not improve after 5 consecutive evaluations, reduce the learning rate.

[0218] Step 706: Repeat the training process until a preset number of training rounds is reached or the performance of the validation set no longer improves;

[0219] Step 707: Evaluate the model performance using indicators such as the quality, diversity, and model stability of the generated samples, and select the model with the best performance as the final current limiting effect evaluation model for the positive temperature coefficient characteristic material;

[0220] Step 708: Use a small amount of high-quality experimental data to fine-tune the model, and implement a post-processing module to convert the model output back into actual physical quantities and generate a visualized current limiting effect evaluation curve.

[0221] Wherein, the step S80 specifically includes:

[0222] Step 801, receiving formula information of a positive temperature coefficient characteristic material to be evaluated input by a user, including polymer matrix type, conductive filler type, filler content, dispersant type and amount, cross-linking agent type and amount;

[0223] Step 802: Convert the input recipe information into a standardized input vector consistent with the training data format;

[0224] Step 803: input the normalized input vector into the generative adversarial neural network model trained in step S70;

[0225] Step 804: Obtain standardized current limiting effect evaluation curve data output by the model;

[0226] Step 805: Use a post-processing module to convert the standardized output data into actual physical quantities;

[0227] Step 806, generating a multi-dimensional current limiting effect evaluation curve set including a current-voltage curve, a temperature-time curve, a resistance-temperature curve, and a current limiting multiple-time curve;

[0228] Step 807, calculating key performance indicators, such as maximum current limiting multiple, response time, steady-state temperature, etc.;

[0229] Step 808: Output the generated current limiting effect evaluation curve and key performance indicators to the user in the form of charts.

[0230] Optionally, the step S20 further includes:

[0231] Step 208, using a differential scanning calorimeter to measure the specific heat capacity of the positive temperature coefficient material sample, the temperature range is -50 degrees Celsius to 250 degrees Celsius, and the heating rate is 10 degrees Celsius per minute;

[0232] Step 209, using a transient plane heat source method to measure the thermal conductivity of the positive temperature coefficient material sample, measuring at temperature points such as 25 degrees Celsius, 50 degrees Celsius, 75 degrees Celsius, and 100 degrees Celsius;

[0233] Step 210, using a Harman device to measure the thermoelectric coupling coefficient of a positive temperature coefficient material sample, the sample is made into a strip of 1 cm x 0.5 cm x 5 cm, and the measurement is performed under vacuum conditions;

[0234] Step 211: Use an autoclave to measure the thermodynamic temperature coefficient of a positive temperature coefficient material sample, slowly increase the pressure at different temperatures, and record the pressure and corresponding temperature changes.

[0235] Optionally, the step S70 further includes:

[0236] Step 709: In the training process of the generative adversarial neural network, a physical constraint term is introduced into the loss function to ensure that the generated current limiting effect evaluation curve satisfies basic physical laws, such as Joule's heat law and Ohm's law;

[0237] Step 710: Implement an adaptive learning rate adjustment mechanism to dynamically adjust the learning rates of the generator and discriminator according to the change trend of the loss to maintain the stability of the training process;

[0238] Step 711: In the later stage of model training, gradually increase the proportion of real data in the training batch to improve the model's ability to fit high-quality data;

[0239] Step 712: Implement a model integration mechanism to train multiple generative adversarial neural network models with different initializations or structures, and perform weighted averaging of their outputs to improve the stability and accuracy of predictions.

[0240] Compared with the prior art, the method for evaluating the current limiting effect of a PTC characteristic material provided by the present invention has the following beneficial effects:

[0241] First, this method establishes a comprehensive and efficient PTC material current limiting effect evaluation system by combining orthogonal experimental design, physical models and machine learning technology. Compared with traditional methods, this method greatly reduces the number of experiments required, while improving the accuracy and efficiency of the evaluation. For example, when evaluating the current limiting performance of a new PTC material, traditional methods may require hundreds of experiments and take weeks; using this method, only dozens of key experiments are required to obtain reliable evaluation results within a few hours.

[0242] Secondly, the PTC characteristic equations established by this method fully consider complex factors such as thermoelectric coupling effects and material nonlinear characteristics. Compared with the existing simplified models, they can more accurately describe the behavior of PTC materials under actual working conditions. This model based on physical mechanisms not only improves the accuracy of predictions, but also enhances the interpretability of the results. For example, by analyzing the changes in the parameters in the equations, we can gain an in-depth understanding of the influence of material composition and structure on its current limiting performance, providing theoretical guidance for material optimization.

[0243] Furthermore, this method innovatively introduces data augmentation technology and generative adversarial neural networks to effectively overcome the problem of insufficient experimental data. This method not only improves the generalization ability of the model, but also generates high-quality virtual data, greatly expanding the range of material formulations that can be evaluated. For example, for a newly developed PTC composite material, even if there is only limited experimental data, this method can predict its current limiting performance under various extreme conditions through data augmentation and GAN models.

[0244] In addition, the current limiting effect evaluation curves output by this method (including current-voltage characteristics, temperature-time characteristics, resistivity-temperature characteristics, and current limiting multiple-time characteristics) fully reflect the dynamic response characteristics of PTC materials. These curves can not only help researchers to deeply understand the working mechanism of the material, but also provide important references for engineering applications. For example, by analyzing the current limiting multiple-time characteristic curve, the response speed and stability of the material can be accurately evaluated, providing a basis for selecting the most suitable PTC material for different application scenarios.

[0245] In summary, the present invention solves the technical problem that the existing methods often need to obtain the current limiting effect of the PTC characteristic material through experiments, and cannot quickly evaluate the current limiting effect of the PTC characteristic material. BRIEF DESCRIPTION OF THE DRAWINGS

[0246] Figure 1 A flow chart of the method provided by the present invention. DETAILED DESCRIPTION

[0247] In order to make the purpose, technical solution and advantages of the embodiments of the present invention more clear, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0248] like Figure 1 FIG. 1 is a flow chart of a method for evaluating the current limiting effect of a PTC characteristic material provided by the present invention. The method comprises the following steps:

[0249] S10. Based on the orthogonal test principle, different materials and proportions are selected to prepare multiple groups of PTC material resistor samples;

[0250] S20, conducting a current limiting effect experiment on each group of PTC material resistor samples, recording experimental data, including voltage, temperature, time, current, resistivity, power, thermal conductivity and specific heat capacity, and generating a current limiting effect evaluation curve based on the experimental data;

[0251] S30, after preprocessing the experimental data including data cleaning and normalization operations, combining the proportions of the PTC material resistor samples to obtain a first data set;

[0252] S40, using thermoelectric coupling theory to establish a PTC characteristic equation group, including Joule heat equation, heat conduction equation, resistance temperature coefficient equation, current density equation, electric field strength equation, heat flux density equation, specific heat capacity equation and heat diffusion equation;

[0253] S50, fitting the PTC characteristic equation group using the first data set to obtain a fitted PTC characteristic equation group, which is recorded as a fitting equation group;

[0254] S60, using data augmentation technology to augment the first data set to obtain a second data set, using a fitting equation group to filter the second data set to obtain a third data set, recording each set of data in the third data set as metadata, and generating a current limiting effect evaluation curve according to the metadata;

[0255] S70, constructing a training data set using the third data set, and training a generative adversarial neural network using the training data set to obtain a current limiting effect evaluation model for PTC characteristic materials, wherein the training input of the training data set is each metadata in the third data, and the training output is a current limiting effect evaluation curve corresponding to the metadata;

[0256] S80, using a PTC characteristic material current limiting effect evaluation model, inputting a ratio of the PTC characteristic material to be evaluated, and outputting a predicted current limiting effect evaluation curve.

[0257] The specific implementation methods of the above steps are described in detail below:

[0258] The specific implementation of step S10 is: first, according to the principle of orthogonal experimental design, a factor level table is constructed. In the present invention, the following factors are mainly considered: polymer matrix type (such as polyethylene, polypropylene, polystyrene, etc.), conductive filler type (such as carbon black, carbon nanotubes, graphene, etc.), filler content (mass percentage), dispersant type and dosage, cross-linking agent type and dosage. Select 3 to 5 levels for each factor. For example, the polymer matrix type can be selected from polyethylene, polypropylene, and polystyrene; the conductive filler type can be selected from carbon black, carbon nanotubes, graphene, and carbon fiber; the filler content can be selected from 10%, 20%, 30%, 40%, and 50% 5 levels. Secondly, the orthogonal table is used to design the experimental plan. According to the number of factors and the number of levels, a suitable orthogonal table is selected, such as L16 (45) or L25 (56). Each factor and level is randomly assigned to the columns of the orthogonal table to form a complete experimental plan. Then, the materials are prepared and mixed according to the experimental plan. The polymer matrix, conductive filler, dispersant and cross-linking agent were mixed in a set ratio using a high-speed mixer, with a mixing time of 30 minutes and a speed of 2000 rpm. The mixed materials were melt-blended using a twin-screw extruder, with the temperature set to 20°C to 50°C above the melting point of the matrix polymer and the screw speed set to 100 rpm to 200 rpm. Finally, the extruded material was made into a standard specimen. A 2 mm thick disc or strip sample was prepared using an injection molding machine or a tablet press for subsequent resistance testing. The sample size can be set to a 30 mm diameter disc or a 100 mm × 10 mm × 2 mm strip. During the preparation process, the injection molding temperature was set to 10°C to 30°C above the melting point of the matrix polymer, and the mold temperature was room temperature to 80°C. Three parallel samples were prepared for each formulation to ensure the reliability of the data. The purpose of this step is to systematically design and prepare PTC material samples with different material compositions and ratios through an orthogonal test method, so as to provide a comprehensive experimental data basis for the subsequent current limiting effect evaluation. The orthogonal test method can examine the impact of multiple factors on the performance of PTC materials within a smaller number of tests, effectively improving test efficiency and reducing costs.

[0259] The specific implementation method of step S20 is: first, build a current limiting effect experimental platform. The experimental platform includes a programmable DC power supply (rated voltage 0 to 100 volts, rated current 0 to 50 amperes), a high-precision data acquisition system (sampling rate not less than 1 kHz, voltage measurement accuracy better than 0.1%, temperature measurement accuracy better than 0.5°C), and a constant temperature box (temperature range -40°C to 200°C, temperature uniformity better than ±0.5°C). Secondly, fix the PTC sample in a test fixture. The test fixture consists of two copper electrodes, and the electrode surface is silver-plated to reduce the contact resistance. Apply thermal conductive silicone grease between the sample and the electrode to ensure good electrical and thermal contact. A thermocouple is fixed at the center of the sample surface to measure the sample temperature. Then, set the initial experimental parameters. Set the constant temperature box temperature to 25°C and start the experiment after the temperature stabilizes. Set the initial current to 0.1 amperes and the initial voltage to 0.1 volts. Next, perform a step loading experiment. Increase the current by 0.1 amperes every 10 seconds, and record the voltage and temperature changes at the same time. Stop increasing when the current reaches the preset maximum value (such as 10 amperes) or the temperature reaches a critical value (such as 150°C). Maintain the maximum current or critical temperature for 10 minutes and observe the steady-state characteristics. Finally, perform a load reduction experiment. Gradually reduce the current to the initial value, reducing it by 0.1 amperes every 10 seconds, and record the cooling process data until the sample temperature drops to the initial temperature. During the entire experiment, the high-precision data acquisition system records voltage, current, temperature, and time data in real time. The sampling rate is set to 100 Hz to capture rapidly changing electrical characteristics. Based on the recorded data, calculate the resistivity, power, thermal conductivity, and specific heat capacity. The resistivity calculation formula is: Where R is the measured resistance, A is the cross-sectional area of ​​the sample, and l is the length of the sample. The power calculation formula is P=UI, where U is the voltage and I is the current. The thermal conductivity is measured according to the transient plane heat source method, and the specific heat capacity is determined by differential scanning calorimetry. Based on the experimental data obtained, a current limiting effect evaluation curve is drawn. These curves include current-voltage curves, temperature-time curves, resistance-temperature curves, and current limiting multiples-time curves. The current-voltage curve reflects the nonlinear characteristics of the material, the temperature-time curve shows the thermal response speed of the material, the resistance-temperature curve reflects the intensity of the PTC effect, and the current limiting multiples-time curve intuitively represents the current limiting performance of the material. The current limiting multiple is defined as the ratio of the maximum allowable current to the actual current, and the calculation formula is M=I max / I actual The purpose of this step is to comprehensively evaluate the current limiting effect of PTC materials through systematic experimental methods and obtain key curves and parameters that reflect material performance. These data provide a solid experimental basis for subsequent data analysis and model building.

[0260] The specific implementation method of step S30 is: first, clean the experimental data. Eliminate obviously abnormal data points, such as outliers caused by equipment failure or human error. The specific method includes: 1) Using the 3σ criterion, calculate the mean and standard deviation of each group of data, and mark the data points that deviate from the mean by more than 3 times the standard deviation as outliers. 2) Using the box plot method, data points that are more than 1.5 times the upper and lower quartile range are regarded as outliers. 3) Using a clustering algorithm such as DBSCAN (density-based clustering algorithm), data points that do not belong to the main cluster are identified as outliers. Secondly, perform data normalization. In order to eliminate the dimensional differences between different physical quantities, the minimum-maximum normalization method is adopted. The normalization formula is Where x is the original data, x min and x max are the minimum and maximum values ​​of the physical quantity, respectively. All physical quantities such as voltage, temperature, time, current, resistivity, power, thermal conductivity and specific heat capacity are normalized. Then, a unified data format is constructed. The experimental data of each group of PTC material resistor samples are organized into a structured data table, including the following fields: sample ID, polymer matrix type, conductive filler type, filler content, dispersant type and dosage, cross-linking agent type and dosage, normalized voltage, temperature, time, current, resistivity, power, thermal conductivity, and specific heat capacity data. Next, merge the data sets. Merge the data tables of all samples into a large data set, and each row represents a complete set of measurement data at a time point, including material formula information and the values ​​of each physical quantity. Finally, perform data quality assessment. Using the cross-validation method, the data set is randomly divided into 5 parts, 4 parts are used as training sets and 1 part is used as a validation set each time, and a simple regression model (such as multivariate linear regression) is constructed to predict key parameters (such as the maximum current limiting multiple). If the average prediction error of 5 cross-validations is within an acceptable range (such as a relative error of less than 10%), the data set quality is considered to be good. Otherwise, it is necessary to recheck the data cleaning and normalization process and supplement the experimental data if necessary. The purpose of this step is to integrate the experimental data from different PTC material samples into a unified, high-quality data set. Data cleaning ensures the reliability of the data, normalization allows different physical quantities to be compared and analyzed on the same scale, and data merging provides rich samples for subsequent model training. This preprocessing process is the key basis for building an accurate PTC characteristic material current limiting effect evaluation model.

[0261] The specific implementation of step S40 is: first, based on the thermoelectric coupling theory, an electrothermal coupling model of the PTC material is established. The model includes the following key equations: 1) Joule heat equation: describes the heat generated when current passes through the PTC material. The formula is Where Q is heat, t is time, I is current, R(T) is the temperature-related resistance function, T is temperature, x, y, z are spatial coordinates, α, β, γ are thermal diffusion coefficients in each direction. 2) Heat conduction equation: describes the heat transfer inside the PTC material. The formula is Where ρ is the material density, c p is the specific heat capacity, k is the thermal conductivity, is the Laplace operator, q v is the heat source per unit volume, μ is the dynamic viscosity, and Φ is the viscous dissipation function. 3) Resistance temperature coefficient equation: describes the relationship between the resistance of the PTC material and the temperature. The formula is Where R0 is the resistance at reference temperature T0, α1, α2, α3 are temperature coefficients, E a is the activation energy, k B is the Boltzmann constant. 4) Current density equation: describes the current distribution in the PTC material. The formula is Where J is the current density, σ(T) is the temperature-dependent conductivity, E is the electric field strength, and D is the electric displacement. 5) Electric field strength equation: describes the electric field distribution in the PTC material. The formula is Where V is the electric potential and A is the magnetic vector potential. 6) Heat flux density equation: describes the heat flux distribution in the PTC material. The formula is Where q is the heat flux, L 12 is the thermoelectric coupling coefficient, μ e is the electronic chemical potential, and e is the electronic charge. 7) Specific heat capacity equation: describes the change of specific heat capacity of PTC materials with temperature. The formula is where c p0 is the specific heat capacity at room temperature, a1, a2, a3, a4 are fitting coefficients. 8) Heat diffusion equation: describes the heat diffusion process in PTC materials. The formula is Where D is the thermal diffusion coefficient, Q v is the heat source per unit volume, τ is the thermodynamic temperature coefficient, and p is the pressure.

[0262] Next, determine the boundary conditions and initial conditions in the equations. The boundary conditions include: 1) the voltage or current condition at the electrode contact surface, which can be expressed as V = V0 or J·n = J0, where n is the surface normal vector. 2) the heat exchange condition on the sample surface, which can be expressed as Where h is the convective heat transfer coefficient, T amb is the ambient temperature. The initial conditions include: 1) Initial temperature distribution T(x,y,z,0) = T init (x,y,z). 2) Initial voltage distribution V(x,y,z,0) = V init(x, y, z). Then, a suitable numerical method is selected to solve the PTC characteristic equations. Due to the complexity and strong coupling of the equations, the finite element method (FEM) is used to solve them. The specific steps are as follows: 1) The PTC material sample is meshed, and the mesh size is determined according to the sample geometry and the calculation accuracy requirements, and is generally controlled in the range of 0.1 mm to 1 mm. 2) The continuous partial differential equations are discretized into a set of algebraic equations. The Galerkin weighted residual method is used for spatial discretization, and the implicit Euler method is used for time discretization. 3) The Newton-Raphson iteration method is used to solve the nonlinear equations. The iterative convergence criterion is set to a relative error of less than 1×10-6. 4) An adaptive time step strategy is adopted, and the initial time step is set to 1×10-6 seconds. The time step is dynamically adjusted according to the rate of change of the solution to balance the calculation efficiency and accuracy. Finally, numerical stability and convergence analysis are performed. Calculations are performed using different mesh sizes and time steps, and the temperature and current values ​​of key nodes are compared to ensure the stability of the numerical solution. At the same time, the physical rationality of the numerical solution is verified by calculating the energy balance. The purpose of this step is to establish a comprehensive set of PTC characteristic equations that can accurately describe the electrothermal coupling behavior of PTC materials during current limiting. By solving this set of equations, the performance of PTC materials under different working conditions can be predicted, providing a theoretical basis for subsequent data analysis and model optimization.

[0263] The specific implementation of step S50 is as follows: First, select a suitable fitting algorithm. Considering the complexity and nonlinear characteristics of the PTC characteristic equation group, the nonlinear least squares method is used for fitting. Specifically, the Levenberg-Marquardt algorithm is used, which combines the advantages of the gradient descent method and the Gauss-Newton method and is suitable for parameter estimation of complex nonlinear systems. Secondly, define the objective function. The objective function is the weighted square error sum between the experimental data and the theoretical model prediction value, and the expression is Where β is the parameter vector to be estimated, y i is the experimental observation value, f(x i ,β) is the model prediction value, w i is the weight factor. The weight factor is set according to the importance of each physical quantity and the measurement accuracy. For example, a higher weight (such as 1.5) can be given to current and temperature, a medium weight (such as 1.0) can be given to resistivity and thermal conductivity, and a lower weight (such as 0.5) can be given to other parameters. Then, initialize the parameters. Set the initial value and value range for each parameter to be fitted according to the physical meaning and empirical value. For example, the initial value of the resistance temperature coefficient α1 can be set to 1×10 -3 K -1 , the value range is 1×10 -4 K -1 Up to 1×10-2 K -1 ; The initial value of thermal conductivity k can be set to 0.5W / (m·K), and the value range is 0.1W / (m·K) to 2W / (m·K). Next, perform iterative optimization. The Levenberg-Marquardt algorithm is used for parameter optimization. The iterative process is as follows: 1) Calculate the Jacobian matrix J and the residual vector r. 2) Solve the incremental equation (J T J+λdiag(J T J))Δβ=-J T r. 3) Update parameter β new =β old +Δβ. 4) Calculate the new objective function value. If it decreases, accept the update and reduce λ; otherwise, reject the update and increase λ. 5) Repeat steps 1) to 4) until the convergence condition is met or the maximum number of iterations is reached. The convergence condition is set as the relative change of the parameter is less than 1×10-6 or the relative change of the objective function value is less than 1×10-8. The maximum number of iterations is set to 1000. Then, perform parameter sensitivity analysis. Perform a ±10% perturbation on each fitting parameter and observe the changes in the model output. Calculate the sensitivity coefficient Where y is the model output, β i is the i-th parameter. Parameters with a sensitivity coefficient greater than 0.1 are considered sensitive parameters and their fitting accuracy needs to be focused on. Finally, the fitting results are evaluated. The determination coefficient R 2 , root mean square error (RMSE) and mean absolute percentage error (MAPE) to evaluate the quality of the fit. 2 The value should be greater than 0.95, the RMSE should be less than 10% of the standard deviation of the experimental data, and the MAPE should be less than 5%. If the fitting results do not meet these standards, it is necessary to recheck the experimental data, adjust the initial parameters, or consider modifying the model structure. The purpose of this step is to optimize the parameters in the PTC characteristic equation group through data fitting so that the theoretical model can accurately reflect the experimental observation results. The fitted equation group provides a reliable theoretical basis for subsequent data screening and model training.

[0264] The specific implementation of step S60 is: first, select a suitable data augmentation technology. Considering the complexity and nonlinearity of PTC material properties, a strategy combining the following methods is adopted: 1) Gaussian noise injection method: add Gaussian noise with a mean of 0 and a standard deviation of 0.5% to 2% of the standard deviation of the original data to each dimension of the original data. 2) Interpolation method: use cubic spline interpolation to generate new data points between existing data points. 3) SMOTE (Synthetic Minority Oversampling Technology): for certain material formulas with a small number of samples, use the SMOTE algorithm to generate new synthetic samples. 4) Physical model-guided data generation: based on the PTC characteristic equation group fitted in step S50, new theoretical data points are generated by changing the boundary conditions and initial conditions. Secondly, perform the data augmentation process. For each set of data in the first data set, apply the above augmentation technology. The augmentation ratio is set to 5 to 10 times the amount of the original data, and the specific ratio is determined according to the sparsity and quality of the original data. For material formulas with a small number of samples, the augmentation ratio can be appropriately increased. The generated new data points should cover the range of the original data and be appropriately extended to the uncovered areas to improve the generalization ability of the model. Then, the augmented data is screened using the fitting equation group. The augmented data is input into the fitting equation group obtained in step S50 to calculate the theoretical prediction value. Compare the deviation between the predicted value and the augmented data, and set the screening criteria as follows: 1) The relative deviation does not exceed 3 times the standard deviation of the original data. 2) The absolute deviation does not exceed 5% of the measurement range of the physical quantity. 3) The data points should meet basic physical constraints, such as resistivity is always positive, the temperature does not exceed the melting point of the material, etc. Data points that do not meet these standards will be eliminated. Next, a third data set is constructed. The augmented data that has passed the screening is merged with the original first data set to form a third data set. The third data set is statistically analyzed to ensure that its distribution characteristics are similar to those of the original data set. The mean, standard deviation, skewness and kurtosis of each physical quantity are calculated, and the difference should be within 10% compared with the original data set. If the difference is too large, it is necessary to adjust the augmentation parameters or screening criteria, and re-execute the augmentation and screening process. Finally, a current limiting effect evaluation curve is generated. For each set of data in the third data set (called metadata), interpolation and smoothing techniques are used to generate a continuous current limiting effect evaluation curve. The specific steps include: 1) Using cubic spline interpolation for current-voltage, temperature-time, resistance-temperature and current limiting multiple-time data to generate high-resolution data points. 2) Applying a Savitzky-Golay filter to smooth the interpolated data to remove possible noise and jitter. 3) Plotting the processed data into a set of multidimensional curves, including current-voltage curves, temperature-time curves, resistance-temperature curves and current limiting multiple-time curves. The purpose of this step is to expand the original data set and generate richer and more diverse training samples.Through the guidance and screening of theoretical models, the physical rationality of the augmented data is ensured, providing sufficient and high-quality data support for subsequent machine learning model training.

[0265] The specific implementation method of step S70 is: first, design the structure of the generative adversarial neural network (GAN). The generator network adopts a multi-layer perceptron (MLP) structure, including an input layer, 3-4 hidden layers and an output layer. The number of nodes in the input layer is the same as the metadata dimension, the hidden layer uses the LeakyReLU activation function, and the number of nodes decreases layer by layer from the input layer to the output layer, such as 512, 256, 128, and 64. The number of nodes in the output layer is equal to the number of sampling points of the current limiting effect evaluation curve, and the tanh activation function is used. The discriminator network also adopts the MLP structure, but in the opposite direction. The number of nodes increases layer by layer from the input layer to the hidden layer, such as 64, 128, 256, and 512. The output layer of the discriminator is one node, and the sigmoid activation function is used. Secondly, define the loss function and optimization algorithm. The loss function of the generator adopts a combination of mean square error (MSE) and adversarial loss, and the expression is L G =αMSE(G(z),y)+βlog(1-D(G(z))), where G(z) is the output of the generator, y is the true curve, D(G(z)) is the score of the discriminator on the generated sample, α and β are weight coefficients, and the initial values ​​can be set to 0.7 and 0.3. The loss function of the discriminator uses binary cross entropy, which is expressed as The optimization algorithm uses the Adam optimizer, the learning rate is initially set to 0.0002, and β1 and β2 are set to 0.5 and 0.999 respectively. Then, prepare the training data. The third data set is randomly divided into a training set (80%) and a validation set (20%). The input data (metadata) and the output data (current limiting effect evaluation curve) are standardized so that their mean is 0 and their standard deviation is 1. Next, the model training process is performed. The training process adopts an alternating training strategy, and each iteration includes the following steps: 1) Randomly extract a batch of data from the training set (batch size is set to 64). 2) Use the generator to generate fake samples. 3) Train the discriminator, alternating between real samples and generated fake samples. 4) Fix the discriminator parameters and train the generator. 5) Calculate and record the losses of the generator and discriminator. 6) Evaluate the model performance on the validation set every 100 batches. 7) If the performance on the validation set has not improved for 5 consecutive evaluations, reduce the learning rate (multiply by 0.9). 8) Repeat steps 1) to 7) until the preset number of training rounds (such as 1000 rounds) is reached or the performance of the validation set is no longer improved. Then, perform model evaluation and selection. Use the following indicators to evaluate model performance: 1) Quality of generated samples: Calculate the mean square error between generated samples and real samples on various key features (such as maximum current limiting multiples, response time, etc.). 2) Diversity of generated samples: Use Fréchet Inception Distance (FID) to evaluate the similarity between the distribution of generated samples and real samples. 3) Stability of the model: Observe the changing trend of the generator and discriminator losses during training to ensure that the two reach a dynamic balance. Based on these indicators, select the model with the best performance as the final PTC characteristic material current limiting effect evaluation model. Finally, fine-tune and post-process the selected model. Use a small amount of high-quality experimental data to fine-tune the model to improve its accuracy under specific materials or working conditions. Implement a post-processing module to convert the standardized data output by the model back to actual physical quantities and generate a visual current limiting effect evaluation curve. The purpose of this step is to build a generative model that can accurately predict the current limiting effect of PTC materials. Through the adversarial training mechanism of GAN, the model not only learns the statistical characteristics of the data, but also captures the underlying physical laws, so that it can output the predicted current limiting effect evaluation curve for the input PTC characteristic material to be evaluated.

[0266] The specific implementation process of step S80 is as follows:

[0267] 1. Input the ratio of the PTC material to be evaluated into the PTC characteristic material current limiting effect evaluation model, and output a set of comprehensive evaluation curves describing the current limiting effect of the PTC material, including:

[0268] (1) Current-voltage relationship curve

[0269] (2) Temperature-time relationship curve

[0270] (3) Resistance-temperature curve

[0271] (4) Current limiting multiple-time relationship curve

[0272] In addition, related additional functions can also be calculated and output, such as power dissipation function, heat dissipation function and recovery characteristic function, etc. Through these multi-dimensional curve sets, the electrical, thermal and time characteristics of the PTC material to be evaluated during the current limiting process can be fully described, providing users with comprehensive current limiting effect evaluation results.

[0273] Specifically, the principle of the present invention is:

[0274] 1. Principle of orthogonal experimental design: This method uses orthogonal experimental design to select the formula and preparation process parameters of PTC materials. Orthogonal experiment is an efficient multi-factor experimental design method that can obtain the maximum amount of information with the least number of experiments. By reasonably arranging the experimental factors and levels, the influence of various factors on the current limiting performance of PTC materials can be systematically studied, while significantly reducing the number of experiments. This not only improves the experimental efficiency, but also ensures that the data obtained are well representative and balanced, laying a solid foundation for subsequent model establishment and data analysis.

[0275] 2. Thermoelectric coupling theory: The current limiting effect of PTC materials is essentially a complex thermoelectric coupling process. The PTC characteristic equations established by this method fully consider physical mechanisms such as Joule heating effect, heat conduction, and resistance temperature effect, and describe the interaction of these processes through partial differential equations. This model based on physical mechanisms can accurately capture the dynamic behavior of PTC materials under different working conditions, overcoming the limitation that simplified models cannot accurately describe complex working conditions.

[0276] 3. Data augmentation technology: The quantity and quality of experimental data directly affect the performance of the model. However, due to experimental costs and time constraints, it is usually difficult to obtain a large amount of high-quality experimental data. This method innovatively introduces data augmentation techniques, such as adding Gaussian noise, interpolation, and SMOTE algorithms. These techniques can generate a large number of virtual data points while maintaining the statistical characteristics of the original data, effectively expanding the scale and diversity of the training data set and improving the generalization ability of the model.

[0277] 4. Generative Adversarial Network (GAN) Principle: GAN is a powerful generative model consisting of two adversarial neural networks, a generator and a discriminator. In this method, GAN is used to learn the distribution characteristics of the current limiting effect evaluation curve of PTC materials. The generator is responsible for generating realistic current limiting effect evaluation curves based on the input material parameters, while the discriminator is responsible for distinguishing between the real curve and the generated curve. Through this adversarial learning process, the model is able to capture complex nonlinear relationships and potential data patterns, thereby generating high-quality evaluation curves.

[0278] 5. Multi-scale modeling principle: This method combines macroscopic experimental data, mesoscopic physical models and microscopic material parameters to achieve multi-scale PTC material modeling. This multi-scale modeling method can fully consider the relationship between material composition, microstructure and macroscopic performance, and improve the accuracy and interpretability of the model. For example, by analyzing the parameters in the PTC characteristic equation group, the influence of the material microstructure can be traced back to provide guidance for material design.

[0279] In order to better understand and implement the present invention, a specific embodiment 1 of the present invention is provided below. The specific steps of this embodiment 1 are described in detail as follows:

[0280] S10. Based on the orthogonal test principle, different materials and proportions are selected to prepare multiple groups of PTC material resistor samples:

[0281] In this step, an orthogonal test design method is used to prepare different PTC material resistor samples. The orthogonal test method can effectively reduce the number of experiments while ensuring the reliability of the test results.

[0282] Assume there are n influencing factors, each with k i levels (i=1,2,...,n), then we can construct an orthogonal table L m (q s ),in:

[0283] m: number of experiments

[0284] q: the number of levels of the factor (assuming that all factors have the same number of levels)

[0285] s: number of factors

[0286] The selection of orthogonal array must satisfy:

[0287] For PTC materials, the following factors may be considered:

[0288] 1.x1: Conductive filler type (such as carbon black, graphite, carbon nanotubes, etc.)

[0289] 2.x2: Conductive filler content (mass percentage)

[0290] 3.x3: Polymer matrix type (such as polyethylene, polypropylene, etc.)

[0291] 4.x4: Cross-linking agent type

[0292] 5.x5: Cross-linking agent content (mass percentage)

[0293] Assuming each factor has 3 levels, you can choose L 27 (3 5 )Orthogonal array.

[0294] The experimental design matrix can be expressed as:

[0295]

[0296] Among them, x ij represents the level of the jth factor in the ith experiment.

[0297] Based on this experimental design, 27 groups of different PTC material resistor samples can be prepared.

[0298] S20, conduct a current limiting effect experiment on each group of PTC material resistor samples, record the experimental data, including voltage, temperature, time, current, resistivity, power, thermal conductivity and specific heat capacity, and generate a current limiting effect evaluation curve based on the experimental data:

[0299] In this step, it is necessary to conduct a current limiting effect experiment on each group of PTC material samples and record the relevant data. Assuming that the measurement is performed at t time points, the following data matrix can be obtained for each sample:

[0300]

[0301] in:

[0302] V ij : The voltage of the i-th sample at the j-th time point (unit: V)

[0303] T ij : The temperature of the i-th sample at the j-th time point (unit: K)

[0304] t j : jth time point (unit: s)

[0305] I ij : The current of the i-th sample at the j-th time point (unit: A)

[0306] ρ ij : The resistivity of the i-th sample at the j-th time point (unit: Ω·m)

[0307] Pij : The power of the i-th sample at the j-th time point (unit: W)

[0308] k ij : Thermal conductivity of the i-th sample at the j-th time point (unit: W / (m·K))

[0309] c pij : Specific heat capacity of the i-th sample at the j-th time point (unit: J / (kg·K))

[0310] Based on these data, a current limiting effect evaluation curve can be generated, which mainly includes the following relationship curves:

[0311] 1. Current-voltage relationship curve: I = f1 (V)

[0312] 2. Temperature-time relationship curve: T = f2(t)

[0313] 3. Resistivity-temperature relationship curve: ρ=f3(T)

[0314] 4. Current limiting factor-time relationship curve: M = f4(t), where the current limiting factor M = I max / I(t)

[0315] These curves can be obtained by fitting the data. For example, for the current-voltage relationship, a polynomial fit can be used:

[0316] I=a0+a1V+a2V 2 +...+a n V n

[0317] Among them, a0, a1, ..., a n is the fitting coefficient, which can be solved by the least squares method:

[0318]

[0319] S30, after preprocessing the experimental data including data cleaning and normalization operations, the materials and proportions of the PTC material resistor samples are combined to obtain a first data set:

[0320] Data preprocessing is a key step to ensure the accuracy of subsequent analysis. It mainly includes the following operations:

[0321] 1. Data cleaning:

[0322] Remove outliers: Use the Z-score method. For each variable x, calculate:

[0323]

[0324] Among them, μ is the mean value of the variable and σ is the standard deviation. If |z|>3, the data point is considered to be an outlier and needs to be deleted or corrected.

[0325] To handle missing values: you can use interpolation methods, such as linear interpolation:

[0326]

[0327] Among them, x i is the missing data point, x i-1 and x i+1 is the adjacent known data point, t i ,t i-1 and t i+1 is the corresponding time point.

[0328] 2. Normalization operation:

[0329] Use the Min-Max normalization method to scale all variables to the [0,1] interval:

[0330]

[0331] Among them, x min and x max are the minimum and maximum values ​​of the variable, respectively.

[0332] 3. Merge data:

[0333] The cleaned and normalized data are combined with the material ratio information to obtain the first data set D1:

[0334] S40. Use the thermoelectric coupling theory to establish the PTC characteristic equation group, including the Joule heat equation, the heat conduction equation, the resistance temperature coefficient equation, the current density equation, the electric field strength equation, the heat flux density equation, the specific heat capacity equation and the heat diffusion equation:

[0335] The PTC characteristic equations are the core of describing the thermoelectric behavior of PTC materials. The following is a detailed description of each equation:

[0336] 1. Joule heat equation:

[0337] Where Q is the amount of heat (J), t is the time (s), I is the current (A), R(T) is the temperature-dependent resistance function (Ω), k is the thermal conductivity (W / (m·K)), and T is the temperature (K). is the gradient operator.

[0338] 2. Heat conduction equation:

[0339]

[0340] Where ρ is the density (kg / m 3 ), c p is the specific heat capacity (J / (kg·K)), q v is the heat source per unit volume (W / m 3 ).

[0341] 3. Temperature coefficient of resistance equation:

[0342] R(T)=R0[1+α(T-T0)+β(T-T0) 2 ];

[0343] Where R0 is the resistance (Ω) at reference temperature T0, α is the first-order temperature coefficient (K-1), and β is the second-order temperature coefficient (K-2).

[0344] 4. Current density equation:

[0345] J = σ(T)E;

[0346] Where J is the current density (A / m 2 ), σ(T) is the temperature-dependent conductivity (S / m), and E is the electric field strength (V / m).

[0347] 5. Electric field strength equation:

[0348]

[0349] Where V is the electric potential (V).

[0350] 6. Heat flux equation:

[0351]

[0352] Where q is the heat flux (W / m 2 ).

[0353] 7. Specific heat capacity equation:

[0354] c p (T) = c p0 +aT+bT 2 ;

[0355] Among them, c p0 , a and b are material-related constants.

[0356] 8. Heat diffusion equation:

[0357]

[0358] in, is the thermal diffusion coefficient (m 2 / s), is the Laplace operator.

[0359] These equations form a coupled set of partial differential equations that describe the behavior of the PTC material under the action of electric fields and temperature gradients. Solving this system of equations usually requires the use of numerical methods such as the finite element method or the finite difference method.

[0360] S50, fitting the PTC characteristic equation group using the first data set to obtain a fitted PTC characteristic equation group, which is recorded as a fitting equation group:

[0361] In this step, the first data set is needed to fit the unknown parameters in the PTC characteristic equation group. This is a complex nonlinear optimization problem that can be solved using the least squares method combined with a numerical optimization algorithm.

[0362] Define the objective function:

[0363]

[0364] Among them, θ is the parameter vector to be fitted, N is the number of samples, M is the number of observed variables, and y ij is the actual observed value, is the model prediction value.

[0365] The goal is to find the value of θ that minimizes F(θ). This can be solved using gradient descent or more advanced optimization algorithms such as the Levenberg-Marquardt algorithm.

[0366] For each equation, the parameters that need to be fitted are as follows:

[0367] 1. Joule heat equation: k;

[0368] 2. Heat conduction equation: ρ,c p ,k;

[0369] 3. Resistance temperature coefficient equation: R0, α, β, T0;

[0370] 4. Current density equation: parameters of σ(T);

[0371] 5. Electric field strength equation: no need to fit parameters;

[0372] 6. Heat flux equation: k;

[0373] 7. Specific heat capacity equation: c p0 ,a,b;

[0374] 8. Heat diffusion equation: α;

[0375] The fitting process can be expressed as the following iterative algorithm:

[0376] The initial fitting process can be expressed as the following iterative algorithm:

[0377] 1. Initialize parameter vector θ (0) ;

[0378] 2. For each iteration k:

[0379] a. Calculate the objective function value: F(θ (k) );

[0380] b. Calculate the gradient of the objective function:

[0381] c. Update parameters:

[0382] Where η is the learning rate (step size);

[0383] 3. Repeat step 2 until convergence or the maximum number of iterations is reached

[0384] For the Levenberg-Marquardt algorithm, the parameter update formula is:

[0385] θ (k+1) =θ (k) -(J T J+λI) -1 J T r;

[0386] Where J is the Jacobian matrix, r is the residual vector, λ is the damping factor, and I is the identity matrix.

[0387] After the fitting is completed, the fitting equation group is obtained:

[0388] 1. Joule heat equation after fitting:

[0389] 2. Heat conduction equation after fitting:

[0390] 3. The fitted resistance temperature coefficient equation:

[0391] 4. The current density equation after fitting: J = σ * (T)E;

[0392] 5. Electric field strength equation (remains unchanged):

[0393] 6. Heat flux density equation after fitting:

[0394] 7. Specific heat capacity equation after fitting:

[0395] 8. Heat diffusion equation after fitting:

[0396] The parameters marked with an asterisk represent the optimal values ​​obtained by fitting.

[0397] S60, using data augmentation technology to augment the first data set to obtain a second data set, using the fitting equation group to filter the second data set to obtain a third data set, recording each set of data in the third data set as metadata, and generating a current limiting effect evaluation curve according to the metadata:

[0398] 1. Data augmentation:

[0399] The first dataset can be augmented using the following methods:

[0400] a) Add Gaussian noise:

[0401] x new =x+∈,∈~N(0,σ 2 );

[0402] Here, x is the original data point and σ is the noise intensity.

[0403] b) Interpolation method:

[0404] For time series data, new data points can be generated using linear interpolation or spline interpolation.

[0405] Linear interpolation:

[0406] Among them, (x1, y1) and (x2, y2) are known data points, and (x, y) is the interpolation point.

[0407] c)SMOTE (Synthetic Minority Over-sampling Technique) algorithm:

[0408] For minority class samples, the SMOTE algorithm can be used to generate new samples:

[0409] x new =x i +λ(x j -x i );

[0410] Among them, x i is the selected sample, x j is x i is one of the k nearest neighbors of , and λ∈[0,1] is a random number.

[0411] Assume that the data set is expanded to m times of the original size to obtain a second data set D2.

[0412] 2. Data screening:

[0413] Use the fitted equations to filter the second data set. For each data point, calculate the error between the value predicted by the fitted equations:

[0414]

[0415] Among them, y ij is the jth observed variable of the ith data point, is the predicted value of the fitted equation system, σ j is the standard deviation of the j-th variable.

[0416] Set the threshold τ, if e i <τ, then the data point is retained, otherwise it is removed. In this way, the third data set D3 is obtained.

[0417] 3. Generate a current limiting effect evaluation curve:

[0418] For each set of metadata in the third data set, the following current limiting effect evaluation curve can be generated:

[0419] a) Current-voltage characteristic curve: I = f1 (V);

[0420] b) Temperature-time characteristic curve: T = f2(t);

[0421] c) Resistivity-temperature characteristic curve: ρ = f3 (T);

[0422] d) Current limiting multiple-time characteristic curve: M=f4(t);

[0423] These curves can be obtained by polynomial fitting or spline interpolation. For example, for the current-voltage characteristic curve, an n-order polynomial fit can be used:

[0424] I=a0+a1V+a2V 2 +...+a n V n

[0425] Coefficients a0, a1, ..., a n It can be solved by the least squares method.

[0426] S70, constructing a training data set using the third data set, and training a generative adversarial neural network using the training data set to obtain a current limiting effect evaluation model for PTC characteristic materials, wherein the training input of the training data set is each metadata in the third data, and the training output is a current limiting effect evaluation curve corresponding to the metadata:

[0427] 1. Build a training dataset:

[0428] Training Dataset where x i is metadata (including material ratio, experimental conditions, etc.), i is the corresponding current limiting effect evaluation curve (which can be expressed as a discrete point set or function parameter).

[0429] 2. Generative Adversarial Neural Network (GAN) Structure:

[0430] GAN consists of a generator G and a discriminator D.

[0431] Generator G: input layer->fully connected layer->LeakyReLU->fully connected layer->LeakyReLU->...->output layer, expressed as:

[0432] Where z is the input noise, θ g are the generator parameters.

[0433] Discriminator D: input layer->fully connected layer->LeakyReLU->fully connected layer->LeakyReLU->...->Sigmoid; expressed as: D(y; θ d ):y→[0,1];

[0434] Where y is the real or generated curve data, θ d are the discriminator parameters.

[0435] The training steps can be the general training steps of generating adversarial neural networks.

[0436] 4. PTC characteristic material current limiting effect evaluation model:

[0437] After training is completed, the generator G is the PTC characteristic material current limiting effect evaluation model. Given the input metadata x, the corresponding current limiting effect evaluation curve can be generated:

[0438] S80, using the PTC characteristic material current limiting effect evaluation model, inputting the ratio of the PTC characteristic material to be evaluated, and outputting a predicted current limiting effect evaluation curve:

[0439] 1. Input data preprocessing:

[0440] The PTC characteristic material ratio to be evaluated is represented as a vector x test , and normalize it:

[0441] Here, μ and σ are the mean and standard deviation of the training data.

[0442] 2. Generate prediction curve:

[0443] Use the trained generator G to generate the predicted current limiting effect evaluation curve:

[0444] 3. Post-processing:

[0445] The generated curve data is denormalized to obtain the actual scale current limiting effect evaluation curve:

[0446]

[0447] Among them, σ y and μ y are the standard deviation and mean of the current limiting effect evaluation curve in the training data.

[0448] 4. Output results:

[0449] The final output includes the following curves:

[0450] a) Predicted current-voltage characteristic curve: I = f1 (V);

[0451] b) Predicted temperature-time characteristic curve: T = f2(t);

[0452] c) Predicted resistivity-temperature characteristic curve: ρ = f3(T);

[0453] d) Predicted current limiting multiple-time characteristic curve: M = f4(t);

[0454] These curves can be interpolated or fitted to obtain continuous function expressions. For example, for the current-voltage characteristic curve, a polynomial fit can be used:

[0455] I=a0+a1V+a2V 2 +...+a n V n ;

[0456] Among them, the coefficients a0, a1, ..., a n Solved by least squares method.

[0457] 5. Evaluation indicators:

[0458] In order to quantitatively evaluate the current limiting effect of PTC characteristic materials, the following indicators can be calculated:

[0459] a) Maximum current limiting multiple:

[0460] b) Response time:

[0461] c) Stabilization time:

[0462] d) Temperature coefficient:

[0463] e) Power consumption:

[0464] These indicators can help comprehensively evaluate the current limiting performance of PTC characteristic materials.

[0465] Summarize:

[0466] This Example 1 combines experimental data, physical models and machine learning technology to establish an efficient method for evaluating the current limiting effect of PTC characteristic materials. The main advantages of this method include:

[0467] 1. Using orthogonal experimental design can reduce the number of experiments and improve efficiency.

[0468] 2. By establishing the PTC characteristic equation group, the physical principles are integrated and the interpretability of the model is enhanced.

[0469] 3. The use of data augmentation technology and generative adversarial networks overcomes the problem of insufficient data and improves the generalization ability of the model.

[0470] 4. The final evaluation model can quickly predict the current limiting effect of new materials, greatly shortening the material development cycle.

[0471] In order to further better understand and implement the present invention, the following is an example 2 of a specific application scenario of the present invention: A power equipment production R&D team needs a PTC material with superior performance as an overcurrent protection element. The PTC material needs to respond quickly in the case of a short circuit or overcharge, limit the current to a safe range, and have good durability and stability. The R&D team decided to use the current limiting effect evaluation method of the PTC characteristic material of the present invention to accelerate the material development and optimization process. The implementation steps are as follows:

[0472] 1. Material selection and orthogonal experimental design

[0473] The R&D team first identified the main factors that affect the performance of PTC materials:

[0474] Conductive filler type (A): carbon black (A1), carbon nanotubes (A2), graphite (A3); conductive filler content (B): 20wt% (B1), 25wt% (B2), 30wt% (B3); polymer matrix type (C): high-density polyethylene (C1), polypropylene (C2), polyvinylidene fluoride (C3); cross-linker type (D): diisopropylbenzene peroxide (D1), dicumyl peroxide (D2), diisopropylbenzene peroxide (D3); cross-linker content (E): 1wt% (E1), 2wt% (E2), 3wt% (E3); Based on these factors, the team designed an L27 (35) orthogonal experimental table, with a total of 27 groups of experimental formulas.

[0475] 2. Sample preparation and current limiting effect experiment

[0476] According to the orthogonal test table, the R&D team prepared 27 groups of PTC material samples, each group of samples was made into a 25mm×25mm×2mm square piece. Subsequently, the R&D team used the following equipment to conduct current limiting effect experiments: programmable DC power supply (0-100V, 0-100A); high-precision data acquisition system (sampling rate 1kHz); constant temperature box (-40℃ to 150℃);

[0477] The experimental steps are as follows:

[0478] a) Fix the PTC sample in the test fixture and put it into a constant temperature box.

[0479] b) Set the initial voltage to 12V (simulating the voltage of electrical equipment) and the initial current to 1A.

[0480] c) Increase the current gradually at a rate of 1 A / s, and record the voltage and temperature changes at the same time.

[0481] d) Stop increasing when the current reaches 50A or the temperature reaches 130°C.

[0482] e) Maintain the maximum current for 10 minutes and observe the steady-state characteristics.

[0483] f) Reduce the current to the initial value and record the cooling process data.

[0484] 3. Data processing and PTC characteristic equation fitting

[0485] After the experiment is completed, the R&D team cleans and normalizes the collected data, and then fits the PTC characteristic equation group to obtain the characteristic parameters of each group of samples.

[0486] The following are some fitting results for one set of samples (A2B2C1D2E2):

[0487] -Resistance temperature coefficient: α=0.0215K -1

[0488] - Thermal conductivity: k = 0.42 W / (m·K)

[0489] -Specific heat capacity: c p =1850J / (kg·K)

[0490] 4. Data augmentation and screening

[0491] To expand the dataset, the R&D team used the following data augmentation techniques:

[0492] -Add Gaussian noise (mean 0, standard deviation 5% of the original data)

[0493] - Linear interpolation (insert 4 new data points between every two experimental data points)

[0494] -SMOTE algorithm (oversampling of minority class samples)

[0495] Through these technologies, the R&D team expanded the original 27 sets of data to 1000 sets. Subsequently, the 1000 sets of data were screened using the fitted PTC characteristic equations, and 800 sets of valid data were finally obtained.

[0496] 5. GAN model training

[0497] The R&D team built a generative adversarial neural network (GAN) to learn the current limiting effect characteristics of PTC materials. Both the generator and the discriminator use a multi-layer perceptron (MLP) structure.

[0498] Generator structure:

[0499] - Input layer: 128 neurons (random noise)

[0500] - Hidden layer 1: 256 neurons, LeakyReLU activation

[0501] - Hidden layer 2: 512 neurons, LeakyReLU activation

[0502] -Output layer: 200 neurons (representing discrete points of the current limiting effect evaluation curve)

[0503] Discriminator structure:

[0504] - Input layer: 200 neurons

[0505] - Hidden layer 1: 512 neurons, LeakyReLU activation

[0506] - Hidden layer 2: 256 neurons, LeakyReLU activation

[0507] -Output layer: 1 neuron, Sigmoid activation

[0508] The R&D team used the Adam optimizer and trained for 10,000 epochs at a learning rate of 0.0002.

[0509] 6. Model evaluation and optimization

[0510] After the training was completed, the R&D team evaluated the model using the holdout method. The R&D team divided the 800 sets of data into a training set (640 sets) and a test set (160 sets). On the test set, the average relative error of the model was 3.2%, and the maximum relative error was 7.5%, meeting the set evaluation accuracy requirements (average relative error <5%, maximum relative error <10%).

[0511] 7. New material evaluation

[0512] The R&D team used the trained model to evaluate a new formula (A2B2C1D2E2, 25wt% carbon nanotubes, high-density polyethylene, 2wt% dicumyl peroxide). The current limiting effect evaluation curve predicted by the model is shown in Table 1:

[0513] Table 1 Current limiting effect evaluation curve data table

[0514] Time(s) Current (A) Voltage (V) Temperature(℃) Resistance(Ω) Current limiting multiple 0 1.00 12.00 25.0 12.00 1.00 5 6.00 12.05 26.2 2.01 1.00 10 11.00 12.15 29.8 1.10 1.00 15 16.00 12.32 36.5 0.77 1.00 20 21.00 12.60 48.2 0.60 1.00 25 26.00 13.26 67.9 0.51 1.00 30 31.00 15.50 95.6 0.50 1.00 35 35.42 24.80 121.3 0.70 1.13 40 33.75 33.75 128.7 1.00 1.48 45 30.00 42.00 130.2 1.40 1.67 50 27.50 46.75 130.5 1.70 1.82

[0515] 8. Practical verification and performance evaluation

[0516] Based on the model's predictions, the R&D team prepared actual samples and conducted verification experiments. The experimental results were highly consistent with the model's predictions, with an average relative error of 4.3%.

[0517] The R&D team also calculated the following key performance indicators:

[0518] -Maximum current limit multiple: 1.82

[0519] -Response time (reaching 90% of maximum current limit multiple): 7.2 seconds

[0520] - Stabilization time: 12.5 seconds

[0521] -PTC effect strength (maximum resistance / minimum resistance): 3.4

[0522] -Average power consumption: 523.6W

[0523] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for evaluating the current limiting effect of a PTC characteristic material, characterized in that: The following steps are involved: S10. Based on the orthogonal test principle, different materials and proportions are selected to prepare multiple groups of PTC material resistor samples; S20, conducting a current limiting effect experiment on each group of PTC material resistor samples, recording experimental data, including voltage, temperature, time, current, resistivity, power, thermal conductivity and specific heat capacity, and generating a current limiting effect evaluation curve based on the experimental data; S30, after preprocessing the experimental data including data cleaning and normalization operations, combining the proportions of the PTC material resistor samples to obtain a first data set; S40, using thermoelectric coupling theory to establish a PTC characteristic equation group, including Joule heat equation, heat conduction equation, resistance temperature coefficient equation, current density equation, electric field strength equation, heat flux density equation, specific heat capacity equation and heat diffusion equation; S50, fitting the PTC characteristic equation group using the first data set to obtain a fitted PTC characteristic equation group, recorded as a fitting equation group; S60, using data augmentation technology to augment the first data set to obtain a second data set, using the fitting equation group to filter the second data set to obtain a third data set, recording each set of data in the third data set as metadata, and generating a current limiting effect evaluation curve according to the metadata; S70, constructing a training data set using the third data set, and training a generative adversarial neural network using the training data set to obtain a current limiting effect evaluation model for PTC characteristic materials, wherein the training input of the training data set is each metadata in the third data, and the training output is a current limiting effect evaluation curve corresponding to the metadata; S80, using the PTC characteristic material current limiting effect evaluation model, inputting the ratio of the PTC characteristic material to be evaluated, and outputting a predicted current limiting effect evaluation curve.

2. A method for evaluating the current limiting effect of a PTC characteristic material according to claim 1, characterized in that: The current limiting effect evaluation curve is specifically a set of multidimensional curves that describe the current-voltage relationship, the temperature-time relationship, the resistance-temperature relationship, and the current limiting multiple-time relationship.

3. A method for evaluating the current limiting effect of a PTC characteristic material according to claim 1, characterized in that: The method of using the fitting equation group to screen the second data set is specifically: by comparing the augmented data with the predictions of the fitting equation group, retaining the data points that meet the expectations of the physical model, and eliminating or adjusting abnormal data.

4. A method for evaluating the current limiting effect of a PTC characteristic material according to claim 1, characterized in that: The generative adversarial neural network includes a generator network and a discriminator network, and the generator network is used to generate a corresponding current limiting effect evaluation curve according to the input metadata.

5. A method for evaluating the current limiting effect of a PTC characteristic material according to claim 4, characterized in that: The initial discrimination of the discriminator network is pre-trained using the PTC characteristic equation group and experimental data.

6. A method for evaluating the current limiting effect of a PTC characteristic material according to claim 1, characterized in that: The normalization adopts the maximum-minimum normalization method.

7. A method for evaluating the current limiting effect of a PTC characteristic material according to claim 1, characterized in that: The data augmentation technology uses a Monte Carlo simulation method to generate more random sample data within the distribution range of the first data set.

8. A method for evaluating the current limiting effect of a PTC characteristic material according to claim 7, characterized in that: The data augmentation technology also includes inferring more intermediate data based on existing data points through interpolation and extrapolation methods.

9. A method for evaluating the current limiting effect of a PTC characteristic material according to claim 1, characterized in that: The fitting method adopts the least square method.

10. A method for evaluating the current limiting effect of a PTC characteristic material according to claim 1, characterized in that: The ratio refers to each component and its ratio used to synthesize the PTC material.

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