A method for evaluating current-limiting effect of a PTC characteristic material

Abstract

The application provides a PTC characteristic material current limiting effect evaluation method, and belongs to the technical field of PTC characteristic materials, and comprises the following steps: a plurality of PTC material resistance samples are prepared according to orthogonal test principles, current limiting effect experiments are conducted on the samples, and relevant data are recorded; after data preprocessing and characteristic equation establishment, the data are expanded by using a fitting equation to obtain a training data set; finally, a PTC characteristic material current limiting effect evaluation model is constructed by using a generative adversarial neural network; and the proportion of 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, which comprehensively reflects the dynamic response characteristics of the PTC material. The application solves the technical problem that the current method cannot quickly evaluate the current limiting effect of the PTC characteristic material, and the current limiting effect of the PTC characteristic material is often obtained through experiments.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of PTC characteristic materials, and particularly relates to a PTC characteristic material current limiting effect evaluation method. BACKGROUND

[0002] Positive Temperature Coefficient (PTC) material is a functional material with special resistance-temperature characteristics, and its resistance will significantly increase with temperature rise, thereby generating self-limiting effect. This unique PTC characteristic makes PTC material widely used in power electronics, electrical protection, temperature sensing and many other fields. In power electronic systems, PTC material can be used as key devices such as overload protection, short circuit protection and thermal fuse, which can quickly cut off the current under accident or abnormal working conditions, effectively reducing the risk of equipment damage. In the electrical field, PTC material is widely used in temperature control of electric heating products such as electric kettles and hair dryers, to achieve safe and reliable temperature limitation. In addition, PTC material can also be used as a temperature sensing element, which is used in battery management systems, industrial automation and other application scenarios with strict requirements for temperature monitoring and control.

[0003] Although PTC material plays an important role in many applications, there are still some problems in the evaluation and prediction of its current limiting characteristics. First, the current limiting characteristics of PTC material are influenced by multiple factors such as material formula, process, temperature, etc., which have strong complexity and nonlinearity, making it difficult to fully evaluate its current limiting performance through simple experimental methods. Second, existing simulation analysis methods are mostly based on simplified thermal-electric coupling models, which cannot accurately predict the dynamic response and current limiting effect of PTC material under actual working conditions. In addition, for the development of new PTC materials, a large amount of experimental data is needed, but existing experimental methods are often inefficient and difficult to evaluate the current limiting characteristics of different material formulas with high throughput.

[0004] That is, the existing method often needs to obtain the current limiting effect of the PTC characteristic material through a large number of experiments, and there is a technical problem that the current limiting effect of the PTC characteristic material cannot be quickly evaluated. SUMMARY

[0005] Therefore, the application provides a PTC characteristic material current limiting effect evaluation method, which can solve the technical problem that the existing method often needs 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.

[0006] The application is implemented as follows:

[0007] The application provides a PTC characteristic material current limiting effect evaluation method, comprising the following steps:

[0008] S10, selecting different materials and proportions to prepare multiple groups of PTC material resistance samples based on orthogonal test principles;

[0009] S20, performing current limiting effect experiments on each group of PTC material resistance 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 according to the experimental data;

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

[0011] S40, establishing a PTC characteristic equation set using thermoelectric coupling theory, 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 thermal diffusion equation;

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

[0013] S60, using data augmentation technology to augment the first data set to obtain a second data set, using the fitted equation set to screen the second data set to obtain a third data set, recording each group 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 PTC characteristic material current limiting effect evaluation model, wherein the training input of the training data set is each item of metadata in the third data, and the training output is the current limiting effect evaluation curve corresponding to the metadata;

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

[0016] The current limiting effect experiment uses programmable direct current power supply, high-precision data acquisition system, constant temperature oven and other equipment, and 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 while recording the voltage and temperature changes;

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

[0021] 5) Hold maximum current for a period of time to observe steady state behavior;

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

[0023] Below are the specific formula expressions for each equation in the PTC characteristic equation set:

[0024] 1. Joule heating equation:

[0025] where Q is heat (unit J); t is time (unit s); I is current (unit A); R(T) is temperature dependent resistance function (unit Ω); T is temperature (unit K); x, y, z are spatial coordinates (unit m); α, β, γ are thermal diffusivity in each direction (unit m 2 / s); R(T) can be measured by experiment, I is known input, α, β, γ can be obtained by material property lookup.

[0026] 2. Heat conduction equation:

[0027] where ρ is material density (unit kg / m 3 ); c p is specific heat capacity (unit J / (kg·K)); k is thermal conductivity (unit W / (m·K)); is Laplace operator; q v is heat source per unit volume (unit W / m 3 ); μ is dynamic viscosity (unit Pa·s); Φ is viscous dissipation function; ρ, c p , k can be obtained by material property, q v can be calculated by Joule heating equation, μ and Φ can be neglected in most PTC applications.

[0028] 3. Temperature coefficient of resistance equation:

[0029]

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

[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); D is the electric displacement (unit C / m 2 ); E can be calculated from the voltage and geometry, which can be neglected 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 from the voltage measurement, which can be neglected in most PTC applications.

[0035] 6. Heat flux density equation:

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

[0037] 7. Specific heat capacity equation:

[0038] where c p0 is the specific heat capacity at constant temperature (unit J / (kg·K)); a1, a2, a3, a4 are fitting coefficients; c p0 , a1, a2, a3, a4 can be obtained from experimental measurements and data fitting.

[0039] 8. Thermal diffusivity equation:

[0040] where D is the thermal diffusivity (unit m 2 / s); Q v is the volumetric heat source (unit W / m 3 ); τ is the thermodynamic temperature coefficient; p is the pressure (unit Pa); Q v can be calculated from the Joule heat, τ needs to be obtained from experimental measurements, which can be neglected in most PTC applications.

[0041] These equations form a complex coupled system that describes the behavior of PTC materials in terms of current, temperature, and heat conduction. 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 experimental setup for obtaining the main experimental data involved in the PTC characteristic equations:

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

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

[0045] Experimental steps:

[0046] a) Place the PTC sample in the thermostat, connect the four-wire resistance measurement instrument and the temperature sensor.

[0047] b) Set the temperature range of the thermostat (such as -40℃ to 200℃), and increase the temperature in steps of 5℃.

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

[0049] d) Repeat the temperature increase-decrease cycle 3 times to ensure the repeatability of the data.

[0050] e) Use the least squares method to fit the data to 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℃).

[0053] 2. Specific heat capacity measurement experiment (for obtaining c p0 , α1, α2, α3, α4):

[0054] Experimental equipment:

[0055] Differential scanning calorimeter (DSC); high-purity reference sample (such as sapphire); precision balance;

[0056] Experimental steps:

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

[0058] b) Put the sample and reference into the sample cell and reference cell of the DSC.

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

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

[0061] e) Calculate the specific heat capacity of the PTC sample at different temperatures using the reference with known specific heat capacity.

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

[0063]

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

[0065] Experimental equipment: Transient Plane Source (TPS) instrument; constant temperature oven;

[0066] Experimental steps:

[0067] a) Prepare two identical size PTC material samples (usually 30mm in diameter and 10mm in thickness).

[0068] b) Clamp the TPS sensor between the two samples.

[0069] c) Put the entire device into the constant temperature oven and set different temperature points (e.g. 25°C, 50°C, 75°C, 100°C, etc.).

[0070] d) At each temperature point, apply a constant power current pulse to the sensor for 10-80s through the TPS instrument.

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

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

[0073] 4. Thermoelectric coupling coefficient measurement experiment (for obtaining 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 long strip shape (e.g. 1cm x 0.5cm x 5cm).

[0077] b) Connect electrodes and temperature sensors 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 decay curve of voltage versus time.

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

[0083] h) Calculate the thermoelectric coupling coefficient L using the Onsager reciprocity relation 12 .

[0084] 5. Thermodynamic temperature coefficient measurement experiment (for obtaining τ):

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

[0086] Experimental steps:

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

[0088] b) Slowly increase the pressure at different temperatures (e.g. 25°C, 50°C, 75°C, 100°C).

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

[0090] d) Calculate the thermodynamic temperature coefficient using the formula , where S represents the constant entropy.

[0091] These experiments need to be carried out under strict control and repeated multiple times to ensure the accuracy and repeatability of the data. After processing the obtained data, it can be used for each parameter in the PTC characteristic equation set.

[0092] The current-limiting effect evaluation curve is a set of multi-dimensional curves describing the current-voltage relationship, temperature-time relationship, resistance-temperature relationship, and 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-dependent resistance function (unit: Ω); T(t) is the temperature function as a function of 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 a reference temperature (unit: Ω); B is a 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, H(x) = 1 when x ≥ 0, otherwise H(x) = 0.

[0102] 4. Current-limiting multiple-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 multi-dimensional curve set, denoted as:

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

[0107] where C(V, t) represents the current-limiting effect evaluation curve set under given voltage V and time t.

[0108] Further, in order to completely describe the current-limiting characteristics of PTC materials, the following additional functions also 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 (unit: W).

[0112] 6. Heat dissipation function:

[0113]

[0114] where Q(t) is the cumulative 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. Recovery characteristic function:

[0116]

[0117] where 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 current limiting effect evaluation curve set can be represented 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 set comprehensively describes the electrical, thermal, and time characteristics of PTC materials during the current limiting process, and can be used to evaluate and compare the current limiting effects of different PTC materials.

[0121] Wherein, the way of screening the second data set by using the fitting equation set is: by comparing the augmented data with the prediction of the fitting equation set, retaining the data points that meet the expected physical model, and eliminating or adjusting abnormal data.

[0122] The detailed description is as follows:

[0123] 1. First, input each data point in the second data set into the fitting equation set.

[0124] 2. For each data point, calculate its predicted value in the fitting equation set.

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

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

[0127] 5. For data points with errors less than the threshold, retain them in the dataset.

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

[0129] a. If the error is only slightly higher than the threshold, consider fine-tuning the data points to meet the predictions of the fitting equation set.

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

[0131] 7. For the removed data points, analyze their characteristics to determine whether they are outliers or reflect special circumstances. If the latter, consider establishing a separate model to handle these special circumstances.

[0132] 8. Repeat the above steps until all data points in the second dataset are processed.

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

[0134] 10. If the size of the screened dataset is significantly reduced, consider adjusting the error threshold or re-expanding the data to ensure there is enough data for subsequent model training.

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

[0136] The training target 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 dynamic balance of the adversarial process. The generator network tries to generate realistic flow limiting effect evaluation curves, while the discriminator network tries to distinguish between real curves and generated curves.

[0137] Further, the initial discrimination of the discriminator network is pre-trained using the PTC characteristic equation set and experimental data to obtain preliminary cognition of the characteristics of the real PTC material flow limiting effect curve. The specific process can be represented as follows:

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

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

[0140] 1. Confidence evaluation function C of PTC characteristic equation set PTC (x):

[0141]

[0142] wherein C i (x) respectively represent confidence evaluation functions based on current-voltage relationship, temperature-time relationship, resistance-temperature relationship, and current-limiting multiple-time relationship.

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

[0144]

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

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

[0147]

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

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

[0150] wherein y1 = C PTC (x), y2 = S exp (x); β is a weighting coefficient, 0≤β≤1.

[0151] Pre-training process:

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

[0153] 2. Construct training set wherein x iThe experimental data and the augmented data, y i For the label:

[0154]

[0155] 3. Optimize the objective function:

[0156]

[0157] 4. Update the parameters using gradient descent:

[0158]

[0159] where θ represents all trainable parameters in D init ; η is the learning rate.

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

[0161] Data that meets the PTC characteristic equation set has high reliability;

[0162] Data similar to existing experimental data is more likely to be real.

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

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

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

[0166] Further, the data augmentation technology further includes inferring more intermediate data from existing data points by interpolation and extrapolation methods.

[0167] Wherein, the fitting method adopts the least squares method.

[0168] Wherein, the ratio refers to the proportion of each component used to synthesize the PTC material.

[0169] Specifically, the step S10 comprises:

[0170] Step 101, according to the orthogonal test design principle, constructing a factor level table containing polymer matrix type, conductive filler type, filler content, dispersant type and amount, crosslinking agent type and amount;

[0171] Step 102, select a suitable orthogonal table design test scheme, randomly allocate each factor and level to the columns of the orthogonal table;

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

[0173] Step 104, melt blending is performed using a twin-screw extruder, the temperature is set to be 20-50 degrees Celsius higher than the melting point of the base polymer, and the screw rotating speed is 100-200 revolutions per minute;

[0174] Step 105, the extruded material is used to prepare a round piece or a long strip sample with a thickness of 2 millimeters using an injection molding machine or a tablet press, which is used for subsequent resistance testing.

[0175] The step S20 specifically comprises:

[0176] Step 201, build a current limiting effect experiment platform including a programmable direct current power supply, a high-precision data acquisition system and a thermostat;

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

[0178] Step 203, set the initial experimental parameters, set the thermostat 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, increase the current by 0.1 ampere every 10 seconds until the current reaches the preset maximum value or the temperature reaches the critical value;

[0180] Step 205, keep the maximum current or critical temperature for 10 minutes to observe the steady-state characteristics;

[0181] Step 206, perform a load reduction experiment, gradually reduce the current to the initial value 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 the current limiting effect evaluation curve.

[0183] The step S30 specifically comprises:

[0184] Step 301, use the 3 standard deviation criterion, the box plot method and the density-based clustering algorithm to clean the experimental data, and eliminate 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 using the min-max normalization method;

[0186] Step 303, organize the experimental data of each set of positive temperature coefficient material resistance samples into a structured data table, including sample identification, material formula information, and normalized data of each physical quantity;

[0187] Step 304, combine all sample data tables into a large data set, with each row representing a complete set of measurement data at a time point;

[0188] Step 305, use 5-fold cross-validation method for data quality evaluation, construct a multiple linear regression model to predict key parameters, and if the relative error of the average prediction error is less than 10%, the data set is considered to be of good quality.

[0189] Among them, the step S40 specifically includes:

[0190] Step 401, based on the thermoelectric coupling theory, establish a positive temperature coefficient material electro-thermal coupling model including Joule heat equation, heat conduction equation, resistance temperature coefficient equation, current density equation, electric field intensity equation, heat flux density equation, specific heat capacity equation, and thermal diffusion equation;

[0191] Step 402, determine the boundary conditions and initial conditions of the equation set, including voltage or current conditions at the electrode contact surface, heat exchange conditions at 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 set, and divide the material sample into grids with a size controlled within 0.1 to 1 millimeters;

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

[0194] Step 405, use the Newton-Raphson iterative method to solve the nonlinear equation set, with the relative error less than 0.000001 as the iteration convergence criterion;

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

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

[0197] The step S50 specifically comprises:

[0198] Step 501, selecting Levenberg-Marquardt algorithm for nonlinear least squares fitting;

[0199] Step 502, defining the objective function as the weighted sum of squared errors between experimental data and theoretical model predictions, and setting weight factors according to the importance and measurement accuracy of each physical quantity;

[0200] Step 503, setting initial values and value ranges for each fitting parameter according to physical significance and empirical values;

[0201] Step 504, performing iterative optimization, calculating Jacobian matrix and residual vector, solving incremental equation, updating parameters until convergence conditions are met or maximum iteration times are reached;

[0202] Step 505, performing parameter sensitivity analysis, perturbing each fitting parameter by plus and minus 10%, observing changes in model output, and calculating sensitivity coefficients;

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

[0204] The step S60 specifically comprises:

[0205] Step 601, using Gaussian noise injection method, cubic spline interpolation method, synthetic minority over-sampling technique, and data generation method based on physical model guidance to augment the first data set, with an augmentation ratio of 5 to 10 times the original data volume;

[0206] Step 602, inputting the augmented data into the fitting equation set obtained in step S50 to calculate theoretical predictions;

[0207] Step 603, comparing the deviation between the predictions and the augmented data, setting the screening criteria as relative deviation not exceeding 3 times the standard deviation of the original data, absolute deviation not exceeding 5% of the physical quantity measurement range, and data points satisfying basic physical constraints;

[0208] Step 604, combining the augmented data that passes the screening with the original first data set to form a third data set;

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

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

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

[0212] The step S70 specifically comprises:

[0213] Step 701, design a generative adversarial neural network structure, both the generator network and the discriminator network adopt a multi-layer perceptron structure, including an input layer, 3-4 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, and the loss function of the discriminator adopts binary cross-entropy, and the optimization algorithm selects Adam optimizer;

[0215] Step 703, randomly divide the third data set into a training set and a validation set in a ratio of 8:2, 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, training the generator, etc.;

[0217] Step 705, evaluate the model performance on the validation set every 100 batches, and if the performance on the validation set does not improve for 5 consecutive evaluations, reduce the learning rate;

[0218] Step 706, repeat the training process until the 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 sample quality, diversity, and model stability, and select the best-performing model as the final current-limiting effect evaluation model for positive temperature coefficient characteristic materials;

[0220] Step 708, fine-tune the model using a small amount of high-quality experimental data, and implement a post-processing module for converting the model output back to actual physical quantities, generating visual current-limiting effect evaluation curves.

[0221] The step S80 specifically comprises:

[0222] Step 801, receive the formula information of the positive temperature coefficient characteristic material to be evaluated input by the user, including the type of polymer matrix, the type of conductive filler, the content of filler, the type and amount of dispersing agent, the type and amount of crosslinking agent;

[0223] Step 802, convert the input formula information into a standardized input vector consistent with the training data format;

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

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

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

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

[0228] Step 807, calculate 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 a chart.

[0230] Optionally, the step S20 further includes:

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

[0232] Step 209, measure the thermal conductivity of the positive temperature coefficient material sample using the transient plane heat source method, at temperature points of 25 degrees Celsius, 50 degrees Celsius, 75 degrees Celsius, 100 degrees Celsius, etc.

[0233] Step 210, measure the thermoelectric coupling coefficient of the positive temperature coefficient material sample using a Harman device, with the sample made into a long strip shape of 1 centimeter by 0.5 centimeters by 5 centimeters, and measured under vacuum conditions;

[0234] Step 211, measure the thermodynamic temperature coefficient of the positive temperature coefficient material sample using an autoclave, slowly increasing the pressure at different temperatures, and recording 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, introduce a physical constraint term into the loss function to ensure that the generated current limiting effect evaluation curve satisfies the basic physical laws such as the Joule heat law and the Ohm law;

[0237] Step 710, an adaptive learning rate adjustment mechanism is implemented to dynamically adjust the learning rates of the generator and discriminator based on the trends of their loss changes, 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 fitting ability to high-quality data;

[0239] Step 712, a model integration mechanism is implemented to train multiple generative adversarial neural network models with different initializations or structures, and their outputs are weighted and averaged to improve the stability and accuracy of the prediction.

[0240] Compared with the prior art, the PTC characteristic material current limiting effect evaluation method provided by the application has the following advantages:

[0241] Firstly, the method combines orthogonal experimental design, physical model and machine learning technology to establish a comprehensive and efficient PTC material current limiting effect evaluation system. Compared with traditional methods, the method greatly reduces the number of experiments required, while improving the accuracy and efficiency of evaluation. For example, when evaluating the current limiting performance of a new type of PTC material, traditional methods may require hundreds of experiments and take several weeks; while using the method, only a few dozen key experiments are needed, and reliable evaluation results can be obtained within a few hours.

[0242] Secondly, the PTC characteristic equation system established by the method fully considers the thermoelectric coupling effect, material nonlinear characteristics and other complex factors, and compared with existing simplified models, it can more accurately describe the behavior of PTC materials under actual working conditions. This model based on physical mechanism not only improves the accuracy of prediction, but also enhances the interpretability of results. For example, by analyzing the changes of each parameter in the equation system, the influence mechanism of material composition and structure on its current limiting performance can be understood in depth, providing theoretical guidance for material optimization.

[0243] Furthermore, the method innovatively introduces data augmentation technology and generative adversarial neural network, effectively overcoming 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, the method can predict its current limiting performance under various extreme conditions through data augmentation and GAN model.

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

[0245] In summary, the present application solves the technical problem that the existing method often needs to obtain the current limiting effect of the PTC characteristic material through experimental means and cannot quickly evaluate the current limiting effect of the PTC characteristic material. BRIEF DESCRIPTION OF DRAWINGS

[0246] Figure 1 The flowchart of the method provided by the present application. DETAILED DESCRIPTION

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

[0248] As Figure 1 shown is a PTC characteristic material current limiting effect evaluation method flowchart provided by the present application, the method comprises the following steps:

[0249] S10, based on the principle of orthogonal test, a plurality of PTC material resistance samples are prepared by selecting different materials and proportions;

[0250] S20, current limiting effect experiments are performed on each group of PTC material resistance samples, experimental data are recorded, including voltage, temperature, time, current, resistivity, power, thermal conductivity and specific heat capacity, and current limiting effect evaluation curves are generated according to the experimental data;

[0251] S30, after the experimental data are preprocessed including data cleaning and normalization operation, the proportions of the PTC material resistance samples are combined to obtain a first data set;

[0252] S40, a PTC characteristic equation set is established by using thermoelectric coupling theory, including Joule heat equation, heat conduction equation, resistance temperature coefficient equation, current density equation, electric field intensity equation, heat flow density equation, specific heat capacity equation and thermal diffusion equation;

[0253] S50, the PTC characteristic equation set is fitted by using the first data set to obtain a fitted PTC characteristic equation set, denoted as fitted equation set;

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

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

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

[0257] The specific implementation of the above steps is described in detail as follows:

[0258] The specific implementation of step S10 is as follows: first, a factor level table is constructed according to the orthogonal test design principle. In the present application, the following factors are mainly considered: polymer matrix type (such as polyethylene, polypropylene, polystyrene, etc.), conductive filler type (such as carbon black, carbon nanotube, graphene, etc.), filler content (mass percentage), dispersant type and amount, crosslinking agent type and amount. Each factor selects 3 to 5 levels. 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 nanotube, graphene, and carbon fiber; and the filler content can be selected from 10%, 20%, 30%, 40%, and 50% levels. Second, an orthogonal table is used to design the test scheme. 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 test scheme. Then, the materials are prepared and mixed according to the test scheme. The polymer matrix, conductive filler, dispersant, and crosslinking agent are mixed at the set ratio using a high-speed mixer, with a mixing time of 30 minutes and a rotation speed of 2000 revolutions per minute. The mixed materials are melt blended using a twin-screw extruder, with a temperature set to 20-50°C above the melting point of the matrix polymer and a screw rotation speed of 100-200 revolutions per minute. Finally, the extruded materials are made into standard test samples. An injection molding machine or a tablet press is used to prepare circular or long strip-shaped samples with a thickness of 2 millimeters for subsequent resistance testing. The sample size can be set to a circular piece with a diameter of 30 millimeters or a long strip with a size of 100 millimeters x 10 millimeters x 2 millimeters. During the preparation process, the injection molding temperature is set to 10-30°C above the melting point of the matrix polymer, and the mold temperature is room temperature to 80°C. Three parallel samples are prepared for each formula 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 the orthogonal test method, providing a comprehensive experimental data basis for subsequent current limiting effect evaluation. The orthogonal test method can investigate the influence of multiple factors on the performance of PTC materials in fewer test times, effectively improving the test efficiency and reducing the cost.

[0259] The specific implementation of step S20 is as follows: 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 kilohertz, voltage measurement accuracy better than 0.1%, temperature measurement accuracy better than 0.5°C), a constant temperature oven (temperature range -40°C to 200°C, temperature uniformity better than ±0.5°C). Second, fix the PTC sample in the test fixture. The test fixture consists of two copper electrodes, the electrode surface is plated with silver 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 oven 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 while recording the voltage and temperature changes. Stop increasing when the current reaches the preset maximum value (such as 10 amperes) or the temperature reaches the critical value (such as 150°C). Hold at the maximum current or critical temperature for 10 minutes to observe the steady-state characteristics. Finally, perform a load reduction experiment. Gradually reduce the current to the initial value by 0.1 amperes every 10 seconds, record the cooling process data, and stop until the sample temperature drops to the initial temperature. Throughout the experiment, the high-precision data acquisition system records voltage, current, temperature, and time data in real time. The sampling rate is set to 100 hertz to capture rapid changes in 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 sample cross-sectional area, and l is the sample length. 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 source method, and the specific heat capacity is determined by differential scanning calorimetry. Based on the obtained experimental data, draw current-voltage curves, temperature-time curves, resistance-temperature curves, and current limiting multiple-time curves. The current-voltage curve reflects the non-linear characteristics of the material, the temperature-time curve shows the thermal response speed of the material, the resistance-temperature curve reflects the strength of the PTC effect, and the current limiting multiple-time curve directly represents the current limiting performance of the material. The current limiting multiple is defined as the ratio of the maximum allowed 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 reflecting the performance of the materials. These data provide a solid experimental foundation for subsequent data analysis and model construction.

[0260] The specific implementation of step S30 is as follows: First, clean the experimental data. Remove obviously abnormal data points, such as outliers caused by equipment failure or human operation errors. The specific method includes: 1) Calculate the mean and standard deviation of each group of data using the 3σ criterion, and mark the data points deviating from the mean by more than 3 times the standard deviation as outliers. 2) Use the box plot method to consider data points outside the interval of 1.5 times the interquartile range as outliers. 3) Use clustering algorithms such as DBSCAN (Density-Based Spatial Clustering of Applications with Noise) to identify data points not belonging to the main cluster as outliers. Second, perform data normalization. In order to eliminate the dimensional differences between different physical quantities, the minimum-maximum normalization method is used. 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. Normalize all physical quantities such as voltage, temperature, time, current, resistivity, power, thermal conductivity, and specific heat capacity. Then, construct a unified data format. Organize the experimental data of each PTC material resistance sample into a structured data table, including the following fields: sample ID, polymer matrix type, conductive filler type, filler content, dispersant type and amount, crosslinking agent type and amount, 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, with each row representing a complete set of measurement data at a time point, including material formulation information and the values of various physical quantities. Finally, evaluate the data quality. Use the cross-validation method to randomly divide the data set into 5 parts, use 4 parts as the training set and 1 part as the validation set each time, and build a simple regression model (such as multiple linear regression) to predict key parameters (such as maximum current limiting multiple). If the average prediction error of the 5 cross-validation is within an acceptable range (such as a relative error of less than 10%), the data set is considered to be of good quality. Otherwise, the data cleaning and normalization process needs to be rechecked, and additional experimental data may be added if necessary. The purpose of this step is to integrate experimental data from different PTC material samples into a unified, high-quality data set. Data cleaning ensures data reliability, normalization allows different physical quantities to be compared and analyzed on the same scale, and data merging provides a rich sample for subsequent model training. This preprocessing process is a key foundation for building an accurate PTC characteristic material current limiting effect evaluation model.

[0261] The specific implementation of step S40 is as follows: First, based on the theory of thermoelectric coupling, establish an electro-thermal coupling model of PTC materials. The model includes the following key equations: 1) Joule heat equation: describes the heat generated when current passes through PTC materials. The formula is where Q is heat, t is time, I is current, R(T) is temperature-dependent resistance function, T is temperature, x, y, z are spatial coordinates, a, b, g are thermal diffusivity coefficients in respective directions.2) Heat conduction equation: describes heat transfer inside PTC material. Formula is where p is material density, c p is specific heat capacity, k is thermal conductivity, is Laplace operator, q v is heat source per unit volume, m is dynamic viscosity, F is viscous dissipation function.3) Temperature coefficient of resistance equation: describes the relationship between PTC material resistance and temperature. Formula is where R0 is resistance at reference temperature T0, a1, a2, a3 are temperature coefficients, E a is activation energy, k B is Boltzmann constant.4) Current density equation: describes current distribution in PTC material. Formula is where J is current density, s(T) is temperature-dependent conductivity, E is electric field strength, D is electric displacement.5) Electric field strength equation: describes electric field distribution in PTC material. Formula is where V is electric potential, A is magnetic vector potential.6) Heat flux density equation: describes heat flow distribution in PTC material. Formula is where q is heat flux density, L 12 is thermoelectric coupling coefficient, m e is electronic chemical potential, e is electronic charge.7) Specific heat capacity equation: describes the change of PTC material specific heat capacity with temperature. Formula is where c p0 is specific heat capacity at constant temperature, a1, a2, a3, a4 are fitting coefficients.8) Thermal diffusion equation: describes heat diffusion process in PTC material. Formula is where D is thermal diffusion coefficient, Q v is heat source per unit volume, T is thermodynamic temperature coefficient, p is pressure.

[0262] Next, determine the boundary conditions and initial conditions in the equation set. Boundary conditions include:1) Voltage or current conditions at electrode contact surface, which can be expressed as V = V0 or J · n = J0, where n is surface normal vector.2) Heat exchange conditions at sample surface, which can be expressed as where h is convective heat transfer coefficient, T amb is ambient temperature. 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 chosen to solve the PTC characteristic equations. Due to the complexity and strong coupling of the equations, the finite element method (FEM) is employed for the solution. The specific steps are as follows: 1) The PTC material sample is meshed, and the mesh size is determined according to the sample geometric characteristics and the required calculation accuracy, generally controlled within the range of 0.1 to 1 millimeter. 2) The continuous partial differential equations are discretized into 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 iterative method is used to solve the nonlinear equations. The relative error is set as the convergence criterion, and the relative error is less than 1x10-6. 4) The adaptive time step strategy is adopted, and the initial time step is set to 1x10-6 seconds. The time step is dynamically adjusted according to the solution change rate to balance the calculation efficiency and accuracy. Finally, the numerical stability and convergence are analyzed. Different mesh sizes and time steps are used for calculation, and the temperature and current values of the key nodes are compared to ensure the stability of the numerical solution. At the same time, the energy balance is calculated to verify the physical reasonableness of the numerical solution. The purpose of this step is to establish a comprehensive PTC characteristic equation set that can accurately describe the electro-thermal coupling behavior of PTC materials during the current limiting process. By solving this equation set, 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, a suitable fitting algorithm is selected. Considering the complexity and nonlinearity of the PTC characteristic equation set, the nonlinear least squares method is used for fitting. Specifically, the Levenberg-Marquardt algorithm is used, which combines the advantages of gradient descent and Gauss-Newton methods and is suitable for parameter estimation of complex nonlinear systems. Second, the objective function is defined. The objective function is the weighted sum of the squared errors between the experimental data and the theoretical model prediction values, expressed as 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, and w i is the weight factor. The weight factor is set according to the importance and measurement accuracy of each physical quantity, for example, the current and temperature can be given higher weights (such as 1.5), the resistivity and thermal conductivity can be given medium weights (such as 1.0), and other parameters can be given lower weights (such as 0.5). Then, the parameters are initialized. According to the physical meaning and empirical value, the initial value and value range of each parameter to be fitted are set. For example, the initial value of the resistance temperature coefficient α1 can be set to 1x10 -3 K -1 , and the value range is 1x10 -4 K -1 to 1x10-2 K -1 The initial value of thermal conductivity k can be set to 0.5 W / (m·K), with a range of 0.1 W / (m·K) to 2 W / (m·K). Next, iterative optimization is performed. Parameter optimization is performed using the Levenberg-Marquardt algorithm, and the iterative process is as follows: 1) Calculate the Jacobian matrix J and the residual vector r. 2) Solve the increment equation (J T J+λdiag(J T J))Δβ=-J T r. 3) Update the parameter β new =β old +Δβ. 4) Calculate the new objective function value, if it decreases, accept the update and decrease 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 to a relative change in parameters less than 1×10-6 or a relative change in objective function value less than 1×10-8. The maximum number of iterations is set to 1000. Then, parameter sensitivity analysis is performed. A ±10% perturbation is applied to each fitting parameter, and the change in model output is observed. The sensitivity coefficient is calculated, where y is the model output and β i is the i-th parameter. Parameters with a sensitivity coefficient greater than 0.1 are considered sensitive parameters and require special attention to their fitting accuracy. Finally, the fitting results are evaluated. The coefficient of determination R 2 , root mean square error (RMSE), and mean absolute percentage error (MAPE) are used to evaluate the quality of the fitting. The R 2 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, the experimental data needs to be rechecked, the initial parameters need to be adjusted, or the model structure needs to be modified. The purpose of this step is to optimize the parameters in the PTC characteristic equation set through data fitting, so that the theoretical model can accurately reflect the experimental observations. The fitted equation set provides a reliable theoretical basis for subsequent data screening and model training.

[0264] The specific implementation of step S60 is as follows: First, select appropriate data augmentation techniques. Considering the complexity and nonlinearity of PTC material characteristics, the following methods are combined: 1) Gaussian noise injection: Add Gaussian noise with mean 0 and standard deviation 0.5% to 2% of the original data standard deviation 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 Over-sampling Technique): For some material formulations with fewer samples, use the SMOTE algorithm to generate new synthetic samples. 4) Physics model guided data generation: Based on the PTC characteristic equation set fitted in step S50, generate new theoretical data points by changing boundary conditions and initial conditions. Second, perform the data augmentation process. For each set of data in the first data set, apply the above augmentation techniques. The augmentation ratio is set to 5 to 10 times the original data amount, and the specific ratio is determined according to the sparsity and quality of the original data. For material formulations with fewer samples, the augmentation ratio can be appropriately increased. The generated new data points should cover the original data range and moderately extend to the uncovered area to improve the generalization ability of the model. Then, filter the augmented data using the fitted equation set. Input the augmented data into the fitted equation set obtained in step S50 to calculate the theoretical prediction value. Compare the deviation between the prediction value and the augmented data, and set the filtering criteria as follows: 1) The relative deviation does not exceed 3 times the original data standard deviation. 2) The absolute deviation does not exceed 5% of the physical quantity measurement range. 3) The data points should satisfy basic physical constraints, such as constant positive resistivity, temperature not exceeding the material melting point, etc. Data points that do not meet these criteria will be removed. Next, construct the third data set. Combine the filtered augmented data with the original first data set to form the third data set. 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%. If the difference is too large, adjust the augmentation parameters or filtering criteria and re-execute the augmentation and filtering process. Finally, generate the current limiting effect evaluation curve. For each set of data (called meta-data) in the third data set, use interpolation and smoothing techniques to generate a continuous current limiting effect evaluation curve. The specific steps include: 1) Use cubic spline interpolation on current-voltage, temperature-time, resistance-temperature and current limiting multiple-time data to generate high-resolution data points. 2) Apply Savitzky-Golay filter to smooth the interpolated data to remove possible noise and jitter. 3) Plot the processed data into a set of multi-dimensional curves, including current-voltage curve, temperature-time curve, resistance-temperature curve and current limiting multiple-time curve. The purpose of this step is to expand the original data set and generate more abundant and diverse training samples.Through the guidance and screening of the theoretical model, the physical rationality of the data expansion is ensured, and sufficient and high-quality data support is provided for subsequent machine learning model training.

[0265] The specific implementation of step S70 is as follows: first, the structure of a generative adversarial neural network (GAN) is designed. 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 of the input layer is the same as the dimension of the metadata, the hidden layers use LeakyReLU activation functions, 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 of the output layer is equal to the number of sampling points of the flow limiting effect evaluation curve, and a tanh activation function is used. The discriminator network also adopts an MLP structure, but in the opposite direction, and the number of nodes increases layer by layer from the input layer to the hidden layers, such as 64, 128, 256, and 512. The output layer of the discriminator has one node, and a sigmoid activation function is used. Second, the loss function and optimization algorithm are defined. The loss function of the generator adopts a combination of mean square error (MSE) and adversarial loss, expressed as L G =αMSE(G(z),y)+βlog(1-D(G(z))), where G(z) is the output of the generator, y is the real curve, D(G(z)) is the score of the generated sample by the discriminator, and α and β are weighting coefficients, which can be initially set to 0.7 and 0.3. The loss function of the discriminator adopts binary cross-entropy, expressed as The optimization algorithm selects the Adam optimizer, with an initial learning rate of 0.0002, and β1 and β2 set to 0.5 and 0.999, respectively. Then, prepare the training data. Randomly divide the third data set into a training set (80%) and a validation set (20%). Standardize the input data (metadata) and output data (current-limiting effect evaluation curve) to have a mean of 0 and a standard deviation of 1. Next, perform the model training process. The training process uses an alternating training strategy, with each iteration including the following steps: 1) randomly select a batch of data (batch size set to 64) from the training set. 2) use the generator to generate fake samples. 3) train the discriminator, alternating between real samples and generated fake samples. 4) train the generator while fixing the discriminator parameters. 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 does not improve for 5 consecutive evaluations, reduce the learning rate (by a factor of 0.9). 8) repeat steps 1) to 7) until the pre-set number of training rounds (e.g., 1000 rounds) is reached or the performance on the validation set no longer improves. Then, perform model evaluation and selection. Evaluate the model performance using the following indicators: 1) the quality of generated samples: calculate the mean squared error of generated samples and real samples in various key features (such as maximum current-limiting multiple, response time, etc.). 2) the diversity of generated samples: use the Fréchet Inception Distance (FID) to evaluate the similarity of the distribution of generated samples and real samples. 3) the stability of the model: observe the trend of the generator and discriminator losses during training to ensure that both reach a dynamic balance. According to these indicators, select the best-performing model as the final PTC characteristic material current-limiting effect evaluation model. Finally, fine-tune and post-process the selected model. Fine-tune the model using a small amount of high-quality experimental data 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 visual current-limiting effect evaluation curves. 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, enabling it to output predicted current-limiting effect evaluation curves for input PTC characteristic materials to be evaluated.

[0266] Step S80 is implemented 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 relationship curve

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

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

[0273] Specifically, the principles of the present application are:

[0274] 1. Orthogonal test design principle: This method uses orthogonal test design to select the formula and preparation process parameters of PTC materials. Orthogonal test is a high-efficiency multi-factor experimental design method, which can obtain the maximum amount of information in the least number of experiments. By reasonably arranging experimental factors and levels, the influence of each factor on the current limiting performance of PTC materials can be systematically studied, while the number of experiments is significantly reduced. This not only improves the experimental efficiency, but also ensures that the obtained data has good representativeness and balance, 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 equation set established by this method fully considers the physical mechanisms such as Joule heating effect, heat conduction, and resistance temperature effect, and describes 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 limitations of simplified models that 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 the cost and time constraints of experiments, it is often difficult to obtain a large amount of high-quality experimental data. This method innovatively introduces data augmentation techniques such as adding Gaussian noise, interpolation method and SMOTE algorithm. These techniques can generate a large number of virtual data points while maintaining the statistical properties of the original data, effectively expanding the size 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 composed of two mutually adversarial neural networks, generator and discriminator. In this method, GAN is used to learn the distribution characteristics of PTC material current limiting effect evaluation curves. The generator is responsible for generating realistic current limiting effect evaluation curves according to the input material parameters, while the discriminator is responsible for distinguishing between real curves and generated curves. Through this adversarial learning process, the model can capture complex nonlinear relationships and potential data patterns, 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 comprehensively consider the relationship between material composition, microstructure, and macroscopic performance, improving the accuracy and interpretability of the model. For example, by analyzing the parameters in the PTC characteristic equation set, the influence of the material microstructure can be traced back, providing guidance for material design.

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

[0280] S10, based on the orthogonal test principle, select different materials and proportions to prepare multiple groups of PTC material resistance samples:

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

[0282] Suppose there are n influencing factors, each factor has k i levels (i = 1, 2,..., n), then an orthogonal table L m (q s ) can be constructed, where:

[0283] m: number of experiments

[0284] q: number of levels of factors (assuming the number of levels of all factors is the same)

[0285] s: number of factors

[0286] The selection of the orthogonal table needs to meet:

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

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

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

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

[0291] 4. x4: Crosslinking agent type

[0292] 5. x5: Crosslinking agent content (mass percentage)

[0293] Assuming there are 3 levels for each factor, we can choose L 27 (3 5 ) orthogonal table.

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

[0295]

[0296] where x ij represents the level of the jth factor in the ith experiment.

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

[0298] S20, conduct current limiting effect experiments on each group of PTC material resistance samples, record experimental data, including voltage, temperature, time, current, resistivity, power, thermal conductivity and specific heat capacity, and generate current limiting effect evaluation curves according to the experimental data:

[0299] In this step, current limiting effect experiments need to be conducted on each group of PTC material samples, and relevant data need to be recorded. Assuming that measurements are taken at t time points, for each sample, the following data matrix can be obtained:

[0300]

[0301] where:

[0302] V ij : Voltage of the ith sample at the jth time point (unit: V)

[0303] T ij : Temperature of the ith sample at the jth time point (unit: K)

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

[0305] I ij : Current of the ith sample at the jth time point (unit: A)

[0306] ρ ij : Resistivity of the ith sample at the jth time point (unit: Ω·m)

[0307] Pij : 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. Mainly including the following several kinds of 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: p = f3(T)

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

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

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

[0317] Where a0, a1,..., a n are fitting coefficients, which can be solved by least squares method:

[0318]

[0319] S30, after preprocessing the experimental data including data cleaning, normalization, merging the material and ratio of the PTC material resistance sample to obtain the first data set:

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

[0321] 1. Data cleaning:

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

[0323]

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

[0325] Handling missing values: Interpolation methods can be used, such as linear interpolation:

[0326]

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

[0328] 2. Normalization operation:

[0329] Using the Min-Max normalization method, all variables are scaled to the interval [0, 1]:

[0330]

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

[0332] 3. Merge data:

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

[0334] S40, establish a PTC characteristic equation set using thermoelectric coupling theory, including a Joule heat equation, a heat conduction equation, a temperature coefficient of resistance equation, a current density equation, an electric field strength equation, a heat flux density equation, a specific heat capacity equation, and a thermal diffusion equation:

[0335] The PTC characteristic equation set is 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 heat (J), t is time (s), I is current (A), R(T) is a temperature-dependent resistance function (Ω), k is thermal conductivity (W / (m·K)), T is temperature (K), is the gradient operator.

[0338] 2. Heat conduction equation:

[0339]

[0340] Where ρ is density (kg / m³) 3 ), c p It is the specific heat capacity (J / (kg·K)), q v It is a heat source per unit volume (W / m 3 ).

[0341] 3. Equation for the temperature coefficient of resistance:

[0342] R(T)=R0[1+α(T-T0)+β(T-T0) 2 ];

[0343] Where R0 is the resistance (Ω) at the 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 ), where 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 density equation:

[0351]

[0352] Where q is the heat flux density (W / m³) 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. Thermal diffusion equation:

[0357]

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

[0359] These equations form a coupled partial differential equation system that describes the behavior of the PTC material under the influence of electric field and temperature gradient. Solving this system usually requires numerical methods such as finite element method or finite difference method.

[0360] S50, fitting the PTC characteristic equation set with the first data set to obtain a fitted PTC characteristic equation set, denoted as fitted equation set:

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

[0362] Define the objective function:

[0363]

[0364] Where θ is the parameter vector to be fitted, N is the number of samples, M is the number of observed variables, 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). Gradient descent method or more advanced optimization algorithms (such as Levenberg-Marquardt algorithm) can be used to solve it.

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

[0367] 1. Joule heat equation: k;

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

[0369] 3. Temperature coefficient of resistance equation: R0, α, β, T0;

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

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

[0372] 6. Heat flux density equation: k;

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

[0374] 8. Thermal diffusivity equation: α;

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

[0376] The initial fitting process can be represented 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 the parameters:

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

[0383] 3. Repeat step 2 until convergence or 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 fitted equations are obtained:

[0388] 1. Fitted Joule heating equation:

[0389] 2. Fitted heat conduction equation:

[0390] 3. Fitted temperature coefficient of resistance equation:

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

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

[0393] 6. Fitted heat flux equation:

[0394] 7. Fitted specific heat capacity equation:

[0395] 8. The fitted heat diffusion equation:

[0396] where the parameters with asterisks represent the optimal values obtained by fitting.

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

[0398] 1. Data augmentation:

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

[0400] a) Add Gaussian noise:

[0401] x new = x + ∈, ∈ ~ N(0, σ 2 );

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

[0403] b) Interpolation method:

[0404] For time series data, linear interpolation or spline interpolation can be used to generate new data points.

[0405] Linear interpolation:

[0406] where (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] where x i is the selected sample, x j is one of the k-nearest neighbors of x i , and λ ∈ [0, 1] is a random number.

[0411] Suppose the data set is expanded to m times the original size, obtaining a second data set D2.

[0412] 2. Data screening:

[0413] The second data set is screened using the fitted equation set. For each data point, its error with the fitted equation set prediction is calculated:

[0414]

[0415] where y ij is the jth observed variable of the ith data point, is the fitted equation set prediction, σ j is the standard deviation of the jth variable.

[0416] A threshold τ is set, if e i < τ, the data point is kept, otherwise it is discarded. This results in a third data set D3.

[0417] 3. Generating current-limiting effect evaluation curves:

[0418] For each set of metadata in the third data set, the following current-limiting effect evaluation curves 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: p = 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 fitting can be used:

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

[0425] The coefficients a0, a1,..., a n can be solved by least squares method.

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

[0427] 1. Constructing a training data set:

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

[0429] 2. Generate a 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, represented as:

[0432] where z is the input noise, θ g is the generator parameter.

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

[0434] where y is the real or generated curve data, θ d is the discriminator parameter.

[0435] The training steps can use the general training steps of the generative adversarial neural network.

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

[0437] After training, 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, input the ratio of the PTC characteristic material to be evaluated, and output the predicted current-limiting effect evaluation curve:

[0439] 1. Input data preprocessing:

[0440] The ratio of the PTC characteristic material to be evaluated is represented as a vector x test , and normalized processing is performed:

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

[0442] 2. Generate a predicted curve:

[0443] Generate predicted current-limiting effect evaluation curve using trained generator G:

[0444] 3. Post-processing:

[0445] De-normalize generated curve data to get current-limiting effect evaluation curve in actual scale:

[0446]

[0447] where 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 expressed as continuous functions through interpolation or fitting. For example, for the current-voltage characteristic curve, a polynomial fitting can be used:

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

[0456] where coefficients a0, a1,..., a n are solved by least squares method.

[0457] 5. Evaluation indicators:

[0458] To quantify the evaluation of PTC characteristic material current-limiting effect, the following indicators can be calculated:

[0459] a) Maximum current-limiting multiple:

[0460] b) Response time:

[0461] c) Stable 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] Summary:

[0466] This embodiment 1 establishes an efficient PTC characteristic material current limiting effect evaluation method by combining experimental data, physical models and machine learning techniques. The main advantages of this method include:

[0467] 1. Utilizing orthogonal experimental design, the number of experiments is reduced, and the efficiency is improved.

[0468] 2. By establishing PTC characteristic equation set, the physical principle is integrated, and the model interpretability is enhanced.

[0469] 3. Using data augmentation technology and generative adversarial network, the problem of data deficiency is overcome, and the model generalization ability is improved.

[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 invention, the following provides an embodiment 2 of a specific application scenario of the invention: a certain power equipment production and research and development team needs a PTC material with superior performance as an overcurrent protection element. The PTC material needs to quickly respond in the case of short circuit or overcharge, limiting the current within a safe range, while having good durability and stability. The research and development team decides to use the PTC characteristic material current limiting effect evaluation method of the invention to accelerate the development and optimization process of the material. The implementation steps are as follows:

[0472] 1. Material selection and orthogonal experimental design

[0473] The research and development team first determines the main factors affecting the performance of PTC materials:

[0474] Conductive filler type (A): Carbon black (A1), Carbon nanotube (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); Crosslinking agent type (D): Diisopropylbenzene peroxide (D1), Dicumyl peroxide (D2), Diisopropylbenzene peroxide (D3); Crosslinking agent content (E): 1wt% (E1), 2wt% (E2), 3wt% (E3); Based on these factors, the team designed an L27(35) orthogonal test table, with a total of 27 experimental formulations.

[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 square sheet of 25mm x 25mm x 2mm. Subsequently, the R&D team used the following equipment to conduct the current limiting effect experiment: 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 place it in the constant temperature box.

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

[0480] c) Gradually increase the current at a rate of 1A / s, while recording the voltage and temperature changes.

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

[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 to obtain the characteristic parameters of each sample.

[0486] Here are some fitting results for one of the 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 = 1850 J / (kg·K)

[0490] 4. Data augmentation and selection

[0491] To augment the dataset, the development team used the following data augmentation techniques:

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

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

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

[0495] Through these techniques, the development team augmented the original 27 sets of data to 1000 sets. Subsequently, the 1000 sets of data were filtered using the fitted PTC characteristic equations, resulting in 800 valid data sets.

[0496] 5. GAN model training

[0497] The development team constructed a Generative Adversarial Network (GAN) to learn the current-limiting effect characteristics of PTC materials. Both the generator and the discriminator used 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 development team trained the model using the Adam optimizer for 10,000 epochs with a learning rate of 0.0002.

[0509] 6. Model evaluation and optimization

[0510] After training, the development team evaluated the model using the hold-out method. The development team divided the 800 sets of data into a training set (640 sets) and a test set (160 sets). On the test set, the model's average relative error 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 development team used the trained model to evaluate a new formula (A2B2C1D2E2, carbon nanotubes 25wt%, high-density polyethylene, dicumyl peroxide 2wt%). The model's predicted current-limiting effect evaluation curve is shown in Table 1:

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

[0514] Time (s) Current (A) Voltage (V) Temperature (°C) Resistance (Ω) Current limiting factor 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. Actual verification and performance evaluation

[0516] Based on the model's prediction results, the development 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 development team also calculated the following key performance indicators:

[0518] - Maximum current-limiting factor: 1.82

[0519] - Response time (reaching 90% of the maximum current-limiting factor): 7.2 seconds

[0520] - Stability time: 12.5 seconds

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

[0522] - Average power consumption: 523.6W

[0523] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical scope disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A method for evaluating the current-limiting effect of PTC characteristic materials, characterized in that, Includes the following steps: S10. Based on the principle of orthogonal experiment, multiple groups of PTC material resistance samples were prepared by selecting different materials and ratios; S20. Conduct current limiting effect experiments on each group of PTC material resistance samples, record experimental data, including voltage, temperature, time, current, resistivity, power, thermal conductivity and specific heat capacity, and generate current limiting effect evaluation curves based on the experimental data. S30. After preprocessing the experimental data, including data cleaning and normalization, the ratios of the PTC material resistance samples are combined to obtain the first dataset. S40. Establish a set of PTC characteristic equations using thermoelectric coupling theory, including Joule's equation, heat conduction equation, temperature coefficient of resistance equation, current density equation, electric field strength equation, heat flux density equation, specific heat capacity equation, and heat diffusion equation. S50. The PTC characteristic equation set is fitted using the first dataset to obtain the fitted PTC characteristic equation set, which is denoted as the fitted equation set. S60. Using data augmentation technology, the first dataset is augmented to obtain a second dataset. The second dataset is then filtered using the fitted equation system to obtain a third dataset. Each set of data in the third dataset is recorded as metadata, and a rate limiting effect evaluation curve is generated based on the metadata. S70. Construct a training dataset using the third dataset, and train a generative adversarial neural network using the training dataset to obtain a PTC characteristic material current limiting effect evaluation model. The training input of the training dataset is each metadata item in the third dataset, and the training output is the current limiting effect evaluation curve corresponding to the metadata. S80. Using the PTC characteristic material current limiting effect evaluation model, input the ratio of the PTC characteristic material to be evaluated, and output the predicted current limiting effect evaluation curve.

2. The method for evaluating the current-limiting effect of PTC characteristic materials according to claim 1, characterized in that, The current limiting effect evaluation curve is specifically a set of multi-dimensional curves describing the current-voltage relationship, temperature-time relationship, resistance-temperature relationship, and current limiting factor-time relationship.

3. The method for evaluating the current-limiting effect of PTC characteristic materials according to claim 1, characterized in that, The specific method for filtering the second dataset using the fitted equation system is as follows: by comparing the augmented data with the predictions of the fitted equation system, data points that conform to the expectations of the physical model are retained, and outlier data is removed or adjusted.

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

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

6. The method for evaluating the current-limiting effect of PTC characteristic materials according to claim 1, characterized in that, The normalization method used is the max-min normalization method.

7. The method for evaluating the current-limiting effect of PTC characteristic materials according to claim 1, characterized in that, The data augmentation technique involves using Monte Carlo simulation to generate more random sample data within the distribution range of the first dataset.

8. The method for evaluating the current-limiting effect of PTC characteristic materials according to claim 7, characterized in that, The data augmentation technology also includes using interpolation and extrapolation methods to infer more intermediate data based on existing data points.

9. The method for evaluating the current-limiting effect of PTC characteristic materials according to claim 1, characterized in that, The least squares method was used for fitting.

10. The method for evaluating the current-limiting effect of PTC characteristic materials according to claim 1, characterized in that, The ratio refers to each component used in the synthesis of the PTC material and its proportion.

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