IGBT reliability evaluation method based on adaptive sampling and physical information neural network

Abstract

The invention relates to an IGBT reliability evaluation method based on adaptive sampling and a physical information neural network, and the method comprises the following steps: S1, constructing an IGBT physical model, and determining an input variable and an output response; s2, generating an initial training sample, and constructing an initial Kriging agent model; S3, adaptively selecting a new training sample point by using a U learning function; S4, updating the current Kriging agent model based on the new training sample point, and repeating S3 and S4 until one of stop criteria is met; s5, constructing a PINN model; s6, training of a PINN model is carried out; and S7, performing IGBT reliability evaluation based on the trained PINN model to obtain an evaluation result. Compared with the prior art, the IGBT reliability evaluation method has the advantages of improving the efficiency, precision and interpretability of IGBT reliability evaluation and the like.

Description

Technical Field

[0001] The present invention relates to the field of research on the reliability of power semiconductor devices, and particularly to an IGBT reliability evaluation method based on adaptive sampling and physics-informed neural networks. Background Art

[0002] As a key device in modern power electronic systems, the reliability of IGBT directly affects the performance and lifespan of the entire system. With the wide application of IGBT in fields such as new energy, power transmission, and electric vehicles, the requirements for its reliability evaluation are also getting higher and higher. Traditional IGBT reliability evaluation methods mainly include experimental testing methods, analytical model methods, finite element analysis methods, and data-driven methods.

[0003] (1) Experimental testing method: Directly obtain the reliability data of IGBT through methods such as accelerated life tests and aging tests. Although this method is intuitive and reliable, it has a long cycle and high cost, and it is difficult to meet the requirements of rapid design and optimization.

[0004] (2) Analytical model method: Based on the physical failure mechanism of IGBT, establish a mathematical model to predict its reliability. This method has a fast calculation speed, but often requires a large number of simplifying assumptions and is difficult to accurately describe complex failure processes.

[0005] (3) Finite element analysis method: Use finite element software to simulate the stress distribution and deformation of IGBT under various working conditions, and then evaluate its reliability. This method can provide detailed stress analysis results, but has a large amount of calculation and is difficult to quickly evaluate a large number of working conditions.

[0006] (4) Data-driven method: Construct an IGBT reliability prediction model based on historical data and machine learning algorithms. This method does not require a detailed physical model, but has high requirements for data quality and quantity, and has poor interpretability.

[0007] With the development of artificial intelligence technology, some new reliability assessment methods have been proposed. Among them, the surrogate model method has received attention due to its good balance of computational efficiency and accuracy. As a commonly used surrogate model, the Kriging surrogate model has been applied to IGBT reliability assessment. However, the traditional Kriging method still has deficiencies in sample selection and update strategies, making it difficult to effectively capture the complexity and uncertainty of IGBT failure behavior. As an emerging method that combines physical models and deep learning, PINN has performed well in solving complex physical problems. By introducing physical constraints into the loss function, PINN can improve the physical rationality and generalization ability of the model while maintaining the flexibility of data-driven. However, the current application of PINN in the field of IGBT reliability assessment is still relatively scarce, and its potential remains to be further explored. In summary, the existing IGBT reliability assessment methods still have deficiencies in terms of efficiency, accuracy, and interpretability. Summary of the Invention

[0008] The purpose of the present invention is to provide an IGBT reliability assessment method based on adaptive sampling and physics-informed neural network to improve the efficiency, accuracy, and interpretability of IGBT reliability assessment.

[0009] The purpose of the present invention can be achieved through the following technical solutions:

[0010] An IGBT reliability assessment method based on adaptive sampling and physics-informed neural network, the method includes the following steps:

[0011] S1. Construct an IGBT physical model to determine input variables and output responses;

[0012] S2. Generate initial training samples and construct an initial Kriging surrogate model based on the IGBT physical model:

[0013] S3. Use the U learning function to adaptively select new training sample points from the initial training samples:

[0014] S4. Update the current Kriging surrogate model based on the new training sample points, repeat S3 and S4 until one of the stopping criteria is met to obtain the resulting Kriging surrogate model;

[0015] S5. Construct a PINN model;

[0016] S6. Use the sample points output by the resulting Kriging surrogate model as the training set of the PINN model for training to obtain a trained PINN model;

[0017] S7. Conduct IGBT reliability assessment based on the trained PINN model to obtain the assessment result.

[0018] Further, the output response is as follows:

[0019]

[0020] where y represents the output response vector, represents the feature fusion operator, represents the mapping of the i-th subnetwork, x represents the input variable vector, and θ i represents the trainable parameter vector of the i-th subnetwork.

[0021] Further, the specific steps of S2 are as follows:

[0022] Use the Latin hypercube sampling method to generate N0 initial training sample points in the input variable space, and run the IGBT physical model to obtain the corresponding output response;

[0023] Construct an initial Kriging surrogate model based on the corresponding output response;

[0024] The initial Kriging surrogate model is:

[0025]

[0026] μ(x) = f(x) T β + r(x) T R -1 (y - Fβ)

[0027] σ 2 (x) = σ 2 [1 - r(x) T R -1 r(x) + u(x) T (F T R -1 F) -1 u(x)]

[0028] where, is the predicted value of the output response, α i is the weight coefficient of the i-th basis function, is the i-th type of non-linear basis function, is the Gaussian random process, m is the number of basis functions, f(x) is the regression function, β is the regression coefficient, r(x) is the correlation vector, R is the correlation matrix, y is the observed response, F is the experimental design matrix, and σ 2 is the process variance, u(x) = F T R -1 r(x) - f(x), and the observed response is the output response obtained by running the IGBT physical model, and the correlation matrix is composed of correlation functions.

[0029] Further, the specific steps of S3 are as follows:

[0030] Select a learning operator from the initial training samples The point with the smallest value is used as the new training sample point x new ; The learning operator is defined as:

[0031]

[0032] where is the mean prediction operator of the Kriging surrogate model is the standard deviation prediction operator is the input variable space

[0033] Furthermore, the specific steps of S4 are as follows:

[0034] Based on the new training sample point x new and the corresponding response value y new , use the incremental method to update the current Kriging surrogate model. The correlation matrix R of the updated model new is:

[0035]

[0036] The regression coefficient β of the updated model new is:

[0037]

[0038] where represents the experimental design operator

[0039] Furthermore, the stopping criterion is:

[0040] 1) The cumulative iteration number N iter of adaptive sampling reaches the preset threshold, that is, N iter > N max ;

[0041] 2) The prediction error of the current Kriging model is less than the given threshold ε tol ;

[0042] The prediction error is:

[0043]

[0044] y pred is the predicted value of the output response in the iteration process, and y true represents the actual value of the output response

[0045] 3) The degree of decrease in the prediction error of the Kriging model for M consecutive iterations is less than the threshold δ tol;

[0046] The degree of decrease of the prediction error is:

[0047]

[0048] where Δε k is the degree of decrease of the prediction error in the k-th iteration.

[0049] Furthermore, the PINN model includes an input layer, L hidden layers, and an output layer. The loss function of the PINN model includes a data loss term and a physical loss term. The loss function is:

[0050] L total = w1L data + w2L physics + w3L boundary

[0051] where L data is the data loss term, L physics is the physical loss term, w1, w2, and w3 are weight coefficients, and L boundary is the boundary condition loss term;

[0052] The data loss term is:

[0053]

[0054] where N is the number of training samples, y i and are the true output and the model prediction output, respectively;

[0055] The physical loss term is:

[0056]

[0057] where M is the number of physical constraint sampling points, f(·) is the residual of the physical equation, is the partial derivative of the model output with respect to the input, represents the model output;

[0058] The boundary condition loss term is:

[0059]

[0060] where u(x i ) is the output of the neural network, N D is the number of sampling points on the boundary, and g D (x i ) is the known function value on the Dirichlet boundary.

[0061] Furthermore, when the IGBT physical model is a thermal model and a thermo-mechanical stress model, the physical loss term is constructed based on the heat diffusion equation and the thermo-mechanical stress equation, and is:

[0062]

[0063] where ρ is the density, c is the specific heat capacity, T is the temperature, t is the time, k is the thermal conductivity, q is the heat source term, σ is the stress, E is the Young's modulus, α is the coefficient of thermal expansion, T ref is the reference temperature, and ε is the strain;

[0064] When the IGBT physical model is an electro-thermal coupling model and a fatigue life model, the physical loss term is constructed based on the electro-thermal coupling model, and is:

[0065]

[0066] where C is the heat capacity, T is the junction temperature, T a is the ambient temperature, R th is the thermal resistance, V CE is the collector-emitter saturation voltage drop, I C is the collector current, V CE0 , r CE and k are temperature-dependent parameters, T ref is the reference temperature, and P represents thermal energy.

[0067] Furthermore, in S6, the PINN model is trained using the Curriculum Learning and Adam optimization algorithms.

[0068] Furthermore, the evaluation results include the failure probability based on the predicted response distribution, the reliability considering multiple failure mechanisms, the sensitivity analysis results based on the cumulative damage model, and the reliability indicators reflecting the IGBT life characteristics.

[0069] Compared with the prior art, the present invention has the following beneficial effects:

[0070] The present invention combines the advantages of adaptive sampling and physics-informed neural networks, can effectively identify important regions, improve the accuracy of the surrogate model, and at the same time make full use of the IGBT physical model information. By introducing physical constraints and importance analysis, the interpretability and generalization ability of the evaluation results are improved, and higher accuracy is shown in predicting the IGBT failure probability and life, providing in-depth insights into the IGBT failure mechanism and helping to guide design optimization. The present invention significantly improves the accuracy and efficiency of reliability evaluation under the condition of reduced sample size. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 is a flowchart of the present invention;

[0072] Figure 2 It is the flowchart of the adaptive sampling of the Kriging surrogate model of the present invention;

[0073] Figure 3 It is the structure diagram of the PINN model of the present invention. Specific embodiments

[0074] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and the detailed implementation manner and specific operation process are given, but the protection scope of the present invention is not limited to the following embodiments.

[0075] The present invention provides a reliability evaluation method for insulated gate bipolar transistors (IGBTs) based on adaptive sampling combined with physics-informed neural networks (PINN), and the flowchart is as Figure 1 shown. This method first constructs an IGBT physical model, determines the input variables and output responses; then generates initial training samples and constructs an initial Kriging surrogate model; then uses the U learning function to adaptively select new training sample points and update the Kriging surrogate model; then constructs a PINN model, uses the updated Kriging surrogate model as the input of the PINN, and trains the PINN model; finally, uses the trained model to evaluate the reliability of the IGBT. This method combines the advantages of adaptive sampling and physics-informed neural networks, can effectively identify important regions, improve the accuracy of the surrogate model, and at the same time make full use of the IGBT physical model information, improving the interpretability and generalization ability of the evaluation results. Compared with traditional methods, this method significantly improves the accuracy and efficiency of reliability evaluation with a reduced sample size.

[0076] The method of the present invention includes the following steps:

[0077] S1. Construct an IGBT physical model, and determine the input variables and output responses;

[0078] S2. Generate initial training samples and construct an initial Kriging surrogate model based on the IGBT physical model:

[0079] S3. Use the U learning function to adaptively select new training sample points from the initial training samples:

[0080] S4. Update the current Kriging surrogate model based on the new training sample points, repeat S3 and S4 until one of the stopping criteria is met, and obtain the resulting Kriging surrogate model;

[0081] S5. Construct a PINN model;

[0082] S6. Use the sample points output by the resulting Kriging surrogate model as the training set for the PINN model to train and obtain a trained PINN model;

[0083] S7. Based on the trained PINN model, perform IGBT reliability assessment to obtain the assessment result.

[0084] Each step is specifically as follows:

[0085] S1. Construct an IGBT physical model to determine the input variables and output responses:

[0086] The IGBT physical model includes thermal, electrical, and mechanical coupling effects, specifically manifested as:

[0087] 1) Thermal model: Describes the internal temperature distribution of the IGBT, considering factors such as power consumption and heat dissipation;

[0088] 2) Electrical model: Describes the electrical characteristics of the IGBT, including conduction characteristics, switching characteristics, etc.;

[0089] 3) Mechanical model: Describes the internal stress and strain distribution of the IGBT, considering factors such as thermal expansion and fatigue.

[0090] The input variables include but are not limited to the operating voltage V CE , current I C , ambient temperature T a , switching frequency f sw , duty cycle D, etc.

[0091] The output responses include but are not limited to the junction temperature T j , current gain β, leakage current I leak , switching loss E sw , etc.

[0092] The output response can also be:

[0093]

[0094] Where y represents the output response vector, represents the feature fusion operator, represents the mapping of the i-th subnetwork, x represents the input variable vector, and θ i represents the trainable parameter vector of the i-th subnetwork.

[0095] The IGBT physical model can be expressed as:

[0096] y = f(x, θ)

[0097] Where y is the output response vector, x is the input variable vector, θ is the model parameter vector, and f(·) is a non-linear function.

[0098] S2. Generate initial training samples and construct an initial Kriging surrogate model:

[0099] Use the Latin hypercube sampling method to generate N0 initial training sample points {x i , i = 1, 2,..., N0} in the input variable space, and run the IGBT physical model to obtain the corresponding output responses {y i , i = 1, 2,..., N0}.

[0100] Construct the initial Kriging surrogate model:

[0101] μ(x) = f(x) T β + r(x) T R -1 (y - Fβ)

[0102] σ 2 (x) = σ 2 [1 - r(x) T R -1 r(x) + u(x) T (F T R -1 F) -1 u(x)]

[0103] where f(x) is the regression function, β is the regression coefficient, r(x) is the correlation vector, R is the correlation matrix, y is the observed response, F is the experimental design matrix, σ 2 is the process variance, and u(x) = F T R -1 r(x) - f(x).

[0104] The correlation function uses the Gaussian correlation function:

[0105]

[0106] where θ k is the correlation parameter to be optimized.

[0107] The steps of S2 can also be:

[0108] Use the Latin hypercube sampling method to generate N0 initial training sample points in the input variable space, and run the IGBT physical model to obtain the corresponding output responses;

[0109] Construct an initial Kriging surrogate model based on the corresponding output responses;

[0110] The initial Kriging surrogate model is:

[0111]

[0112] μ(x) = f(x) T β + r(x) T R -1 (y - Fβ)

[0113] σ 2 (x) = σ 2 [1 - r(x) T R -1 r(x) + u(x) T (F T R -1 F) -1 u(x)]

[0114] wherein, is the predicted value of the output response, α i is the weight coefficient of the i-th basis function, is the i-th type of non-linear basis function, is a Gaussian random process, m is the number of basis functions, f(x) is the regression function, β is the regression coefficient, r(x) is the correlation vector, R is the correlation matrix, y is the observed response, F is the experimental design matrix, σ 2 is the process variance, u(x) = F T R -1 r(x) - f(x), and the observed response is the output response obtained by running the IGBT physical model, and the correlation matrix is composed of correlation functions.

[0115] S3. Use the U-learning function to adaptively select new training sample points:

[0116] Define the U-learning function:

[0117] U(x) = |μ(x)| / σ(x)

[0118] wherein, μ(x) is the predicted value of the Kriging model at point x, and σ(x) is the predicted standard deviation.

[0119] Select the point with the minimum U(x) in the candidate sample set as the new training sample point x new :

[0120] x new = arg min x U(x)

[0121] The specific steps of S3 can also be:

[0122] Select the point with the minimum value of the learning operator in the initial training samples as the new training sample point x new ; The learning operator is defined as:

[0123]

[0124] Among them, is the mean prediction operator of the Kriging surrogate model, is the standard deviation prediction operator, is the input variable space.

[0125] S4. Update the Kriging surrogate model:

[0126] Add the newly selected sample point x new and its corresponding response value y new to the training set, and update the Kriging surrogate model using an incremental method. Update the correlation matrix R new :

[0127]

[0128] Update the regression coefficient β new :

[0129] β new = (F new T R new -1 F new ) -1 F new T R new -1 y new

[0130] Among them, F new and y new are the experimental design matrix and the observed response vector containing the new sample points, respectively.

[0131] The specific steps of S4 can also be:

[0132] Based on the new training sample points x new and the corresponding response values y new , update the current Kriging surrogate model using an incremental method. The correlation matrix R new of the updated model is:

[0133]

[0134] The regression coefficient β new of the updated model is:

[0135]

[0136] Among them, represents the experimental design operator.

[0137] Repeat steps S3 and S4 until one of the following stopping criteria is met:

[0138] 1) Reach the predetermined maximum number of iterations N max ;

[0139] 2) The prediction error of the Kriging model is less than the given threshold ε:

[0140] max|y - μ(x)| < ε

[0141] 3) The model accuracy has not been significantly improved for M consecutive iterations.

[0142] As Figure 2 shown, steps S3 and S4 constitute the adaptive sampling process of the Kriging surrogate model, which optimizes the selection of sampling points and the update of the model through iteration.

[0143] The stopping criterion can also be:

[0144] 1) The cumulative number of iterations N of the adaptive sampling iter reaches the preset threshold, that is, N iter > N max ;

[0145] 2) The prediction error of the current Kriging model is less than the given threshold ε tol ;

[0146] The prediction error is:

[0147]

[0148] y pred is the predicted value of the output response during the iteration process, and y true represents the actual value of the output response.

[0149] 3) The degree of decrease in the prediction error of the Kriging model for M consecutive iterations is less than the threshold δ tol ;

[0150] The degree of decrease in the prediction error is:

[0151]

[0152] where Δε k is the degree of decrease in the prediction error at the k - th iteration.

[0153] S5. Construct the PINN model:

[0154] As Figure 3 shown, the network structure of the PINN model includes an input layer, L hidden layers, and an output layer. Each hidden layer contains N lneurons, l = 1, 2, ..., L.

[0155] Forward propagation process:

[0156] h0 = x

[0157] h l = σ(W l h l-1 + b l ), l = 1, 2, ..., L

[0158] y pred = W L+1 h L + b (L+1)

[0159] where W l and b l are the weight matrix and bias vector of the l-th layer respectively, and σ(·) is the activation function, using the hyperbolic tangent function:

[0160]

[0161] The loss function of the PINN model includes a data loss term and a physical loss term:

[0162] L = L data + λL physics

[0163] where L data is the data loss term, L physics is the physical loss term, and λ is the weight coefficient.

[0164] Data loss term:

[0165]

[0166] where N is the number of training samples, y i and are the true output and the model predicted output respectively.

[0167] Physical loss term:

[0168]

[0169] where M is the number of physical constraint sampling points, f(·) is the physical equation residual, is the partial derivative of the model output with respect to the input, calculated by the automatic differentiation technique.

[0170] S6. Use the updated Kriging surrogate model as the input of the PINN and train the PINN model:

[0171] Generate a large number of sample points in the input space using the updated Kriging surrogate model as the training data for the PINN model.

[0172] Train the PINN model using the Adam optimization algorithm, and its parameter update rule is:

[0173] m t = β1m (t-1) + (1 - β1)g t

[0174] v t = β2v (t-1) + (1 - β2)g t 2

[0175]

[0176] where m t and v t are the first-order and second-order momentum estimates respectively, β1 and β2 are the decay rates, g t is the current gradient, α is the learning rate, ε is a small constant, and θ t are the model parameters.

[0177] S7. Use the trained PINN model for IGBT reliability assessment:

[0178] 1) Failure probability calculation:

[0179] Define the limit state function g(x). When g(x) ≤ 0, it indicates that the IGBT fails. The calculation formula for the failure probability P f is:

[0180] P f = ∫I[g(x) ≤ 0]f X (x)dx

[0181] where I[·] is the indicator function, and f X (x) is the joint probability density function of the input variables.

[0182] Estimate the failure probability using the importance sampling method, and its estimated value is:

[0183]

[0184] where N is the number of samples, and x i is the sample drawn from the importance sampling distribution h(x). The selection of h(x) is based on the trained PINN model to obtain more samples near the failure region.

[0185] 2) Reliability calculation:

[0186] The reliability R is defined as the probability that the system does not fail, and the calculation formula is:

[0187] R = 1 - P f

[0188] (3) Sensitivity analysis:

[0189] Calculate the sensitivity of the failure probability to each input variable to identify the key influencing factors:

[0190]

[0191] Among them, S i is the sensitivity of the failure probability to the i-th input variable, and ΔX i is a small perturbation.

[0192] (4) Reliability index calculation:

[0193] Calculate the reliability index β, which is defined as:

[0194] β = -Φ -1 (P f )

[0195] Among them, -Φ -1 (γ) is the inverse function of the standard normal distribution.

[0196] In step S1, the IGBT physical model further includes an aging effect model for describing the degradation process of IGBT performance over time. The aging effect model can be expressed as:

[0197] θ(t) = θ0 + Δθ(t)

[0198] Among them, θ(t) is the model parameter at time t, θ0 is the initial parameter, and Δθ(t) is the change in the parameter over time. In step S2, the number N0 of the initial training samples is determined according to the dimension d of the input variables, and preferably:

[0199] N0 = min(10d, 100).

[0200] In step S3, the generation of the candidate sample set adopts a sequential design method based on Latin hypercube sampling to ensure the uniformity and representativeness of the samples.

[0201] In step S5, the selection of the number of hidden layers L and the number of neurons N1 in each layer of the PINN model considers the complexity of the problem and the computing resources, and preferably:

[0202] L = 4, N1 = 50, l = 1, 2, 3, 4.

[0203] In step S6, a dynamically adjusted weight coefficient λ is adopted when training the PINN model, and its update rule is:

[0204]

[0205] Among them, λ0 is the initial weight coefficient, φ is the current iteration number, Φ is the total iteration number, and γ is the adjustment parameter.

[0206] In step S7, the subset simulation method can also be used to calculate the failure probability to improve the estimation accuracy of rare events.

[0207] This method also includes a reliability optimization step to maximize the reliability or minimize the failure probability by adjusting the design parameters. The optimization problem can be expressed as:

[0208] min f(x)

[0209] s.t.P f(x) ≤P f,target

[0210] X L ≤x≤X U

[0211] Among them, f(x) is the objective function, P f,target is the target failure probability, X L and X L are the lower and upper limits of the design variables, respectively.

[0212] Through the above technical solutions, the present invention realizes the efficient and accurate evaluation of IGBT reliability, providing a tool for the design optimization and reliability improvement of IGBT.

[0213] Based on the above method steps, taking the thermal cycle reliability evaluation of a certain type of IGBT module as an example, the failure caused by the thermal stress of the IGBT module under the power cycle condition is considered. The constructed physical model includes a thermal model and a thermo-mechanical stress model.

[0214] The thermal model adopts the one-dimensional heat diffusion equation:

[0215]

[0216] Among them, ρ is the density, c is the specific heat capacity, T is the temperature, t is the time, x is the spatial coordinate, k is the thermal conductivity, and q is the heat source term.

[0217] The thermo-mechanical stress model adopts the linear thermo-elastic equation:

[0218] σ = E[α(T - T ref ) + ε]

[0219] Among them, σ is the stress, E is the Young's modulus, α is the coefficient of thermal expansion, T ref is the reference temperature, and ε is the strain.

[0220] The input variables include:

[0221] Ambient temperature T a (°C)

[0222] Power loss P loss (W)

[0223] Thermal resistance R th (K / W)

[0224] Cycle period t cycle (s);

[0225] The output response is:

[0226] The maximum shear stress σ at the interface between the chip and the solder layer max (MPa)

[0227] S2. Generate initial training samples and construct an initial Kriging surrogate model

[0228] Use the Latin hypercube sampling method to generate 100 initial training sample points. The range of the sample points is:

[0229] T a :[20, 80]°C

[0230] P loss :[50, 200]W

[0231] R th :[0.1, 0.5]K / W

[0232] t cycle :[1, 10]s

[0233] Use the finite element software COMSOL Multiphysics to simulate and calculate the maximum shear stress σ of each sample point max .

[0234] Based on the obtained sample points and response values, construct an initial Kriging surrogate model. In this embodiment, a constant regression function and a Gaussian correlation function are used. The parameters of the Kriging model are determined by the maximum likelihood estimation method.

[0235] S3. Use the U learning function to adaptively select new training sample points

[0236] Define the failure criterion as σ max > 50 MPa. Based on this criterion, calculate the U value of each candidate point:

[0237] U = |σ max - 50| / s

[0238] Among them, s is the standard deviation predicted by the Kriging model.

[0239] Among 10,000 uniformly distributed candidate points, the point with the smallest U value is selected as the new training sample point.

[0240] S4. Update the Kriging surrogate model

[0241] Add the newly selected sample points to the training set and use the DACE toolbox to update the Kriging model parameters. Repeat steps S3 and S4 until one of the following stopping criteria is met:

[0242] 1) Reach the maximum number of iterations, which is 200;

[0243] 2) The model accuracy improvement is less than 1% for 10 consecutive iterations.

[0244] S5. Construct the physics-informed neural network PINN model

[0245] In this embodiment, the PINN model adopts a 5-layer fully connected neural network structure, including 1 input layer (with 4 neurons), 3 hidden layers (with 64 neurons in each layer), and 1 output layer (with 1 neuron). The hyperbolic tangent function is selected as the activation function.

[0246] In this embodiment, the PINN model adopts a multi-layer fully connected neural network structure. As Figure 2 shown, the model includes 1 input layer, multiple hidden layers, and 1 output layer. Specifically, the input layer has 5 neurons, corresponding to 5 input variables; the hidden layer adopts a 4-layer structure, with 128 neurons in each layer; the output layer has 1 neuron, corresponding to the expected life N_f. This network structure design can effectively capture the non-linear relationship in the IGBT reliability problem and improve the generalization ability of the model through physical constraints.

[0247] The loss function of the PINN model is defined as:

[0248] L total = w1 L data + w2 L physics

[0249] Among them, L data is the data loss term, L physics is the physical loss term, and w1 and w2 are weight coefficients, with their initial values both set to 0.5.

[0250] The data loss term adopts the mean square error:

[0251]

[0252] The physical loss term is constructed based on the heat diffusion equation and the thermo-mechanical stress equation:

[0253]

[0254] Among them, N is the number of training samples, and M is the number of physical constraint sampling points.

[0255] S6. Use the updated Kriging surrogate model as the input of the PINN to train the PINN model

[0256] Use the updated Kriging surrogate model to generate 10,000 uniformly distributed sample points in the input space as the training data of the PINN model.

[0257] Train the PINN model using the Adam optimizer. The initial value of the learning rate is set to 0.001, and the cosine annealing strategy is used for dynamic adjustment. The batch size is set to 128, and the number of training epochs is 5,000.

[0258] During the training process, dynamically adjust the weight coefficients w1 and w2:

[0259] w1 = 0.5 + 0.5 * cos(π × epoch / total_epochs)

[0260] w2 = 1 - w1

[0261] Among them, epoch is the current training epoch, and total_epochs is the total number of training epochs.

[0262] S7. Use the trained PINN model to evaluate the IGBT reliability

[0263] 1) Failure probability calculation

[0264] Use the importance sampling method to calculate the failure probability. The importance sampling density function is selected as:

[0265] h(x) = N(μ, Σ)

[0266] Among them, x is the failure point sample predicted by the PINN model, μ is the mean value, and Σ is the covariance matrix, which is estimated by maximizing the likelihood function.

[0267] Generate 100,000 importance sampling points, and use the trained PINN model to calculate the maximum shear stress σ of each point max , and determine whether it fails according to the failure criterion. The estimated value of the failure probability is:

[0268] P f ≈ 1 / N Σ [I(σ max > 50) f(x) / h(x)]

[0269] where I(·) is the indicator function, f(x) is the joint probability density function of the original input variables, and N is the number of importance sampling points.

[0270] 2) Reliability calculation

[0271] The reliability R is directly calculated from the failure probability P f as follows:

[0272] R = 1 - P f

[0273] 3) Sensitivity analysis

[0274] The variance-based global sensitivity analysis method is adopted to calculate the Sobol first-order sensitivity index and the total effect index. The calculation formulas are:

[0275] S i = V(E(Y|X i )) / V(Y)

[0276] S Ti = E(V(Y|X ～i )) / V(Y)

[0277] where S i is the first-order sensitivity index, S Ti is the total effect index, V(·) represents variance, E(·) represents expectation, and X ～i represents all input variables except X i .

[0278] Consider the thermal fatigue failure of the IGBT module under power cycling conditions. The constructed physical model includes an electro-thermal coupling model and a fatigue life model.

[0279] The electro-thermal coupling model adopts the following equations:

[0280] C(dT / dt) = P - (T - T a ) / R th

[0281] P loss = V CE I C

[0282] V CE = V CE0 + r CE I C + k(T - T ref )

[0283] where C is the heat capacity, T is the junction temperature, P loss is the power loss, T a is the ambient temperature, R th is the thermal resistance, VCE is the collector-emitter saturation voltage, I C is the collector current, V CE0 , r CE and k are temperature-dependent parameters, T ref is the reference temperature.

[0284] The fatigue life model adopts the Coffin-Manson equation:

[0285] N f = A*(ΔT) -n

[0286] where, N f is the number of cycles, ΔT is the temperature swing, and A and n are material-dependent constants.

[0287] The input variables include:

[0288] The ambient temperature T a (°C)

[0289] The collector current I C (A)

[0290] The turn-on time t on (s)

[0291] The turn-off time t off (s)

[0292] The thermal resistance from junction to case R th_jc (K / W).

[0293] The output response is:

[0294] The expected life N f (times)

[0295] S2. Generate the initial training samples and construct the initial Kriging surrogate model

[0296] Use the optimized Latin hypercube sampling method to generate 150 initial training sample points. The range of the sample points is:

[0297] T a : [-20, 100] °C

[0298] I C : [50, 200] A

[0299] t on : [1, 10] s

[0300] t off : [1, 10] s

[0301] R th_jc : [0.1, 0.3] K / W

[0302] Use MATLAB Simulink to build an electro-thermal coupling model, simulate and calculate the temperature swing ΔT of each sample point, and calculate the expected life N through the fatigue life model f 。

[0303] Based on the obtained sample points and response values, construct an initial Kriging surrogate model. In this embodiment, a first-order polynomial regression function and a Matérn 3 / 2 correlation function are adopted. The parameters of the Kriging model are determined by the cross-validation method

[0304] S3. Use the U-learning function to adaptively select new training sample points

[0305] Define the failure criterion as N f <10 6 times. Based on this criterion, calculate the U value of each candidate point:

[0306] U = |log 10 N f - 6| / s log

[0307] where s log is the standard deviation of the logarithmic life predicted by the Kriging model

[0308] Among the 20,000 candidate points of quasi-Monte Carlo sampling, select the point with the smallest U value as the new training sample point

[0309] S4. Update the Kriging surrogate model

[0310] Add the newly selected sample points to the training set, and use the maximum likelihood estimation method to update the Kriging model parameters. Repeat steps S3 and S4 until one of the following stopping criteria is met:

[0311] 1) Reach the maximum number of iterations 300;

[0312] 2) The improvement of the root mean square error RMSE of the model in 15 consecutive iterations is less than 0.5%

[0313] In each iteration, calculate the RMSE of the model through leave-one-out cross-validation LOOCV:

[0314]

[0315] where y i is the true response value of the i-th sample point, is the predicted value of the i-th sample point by the Kriging model constructed using all sample points except the i-th sample point, and n is the total number of sample points

[0316] S5. Construct the Physics-Informed Neural Network (PINN) model

[0317] In this embodiment, the PINN model adopts a 6-layer fully connected neural network structure, including 1 input layer (with 5 neurons), 4 hidden layers (each with 128 neurons), and 1 output layer (with 1 neuron). The activation function is selected as the Swish function:

[0318] f(x) = x * sigmoid(βx)

[0319] where β is a learnable parameter, and its initial value is set to 1.

[0320] The loss function of the PINN model is defined as:

[0321] L total = w1 * L data + w2 * L physics + w3 * L boundary

[0322] where L data is the data loss term, L physics is the physical loss term, L boundary is the boundary condition loss term, and w1, w2, and w3 are weight coefficients, whose initial values are set to 0.6, 0.3, and 0.1 respectively. The loss function of the PINN model can also include a Sobolev regularization term.

[0323] The data loss term uses the Mean Absolute Percentage Error (MAPE):

[0324]

[0325] The physical loss term is constructed based on the electro-thermal coupling model:

[0326]

[0327] The boundary condition loss term is used to ensure that the predictions of the model at the boundaries of the input variables conform to the physical laws:

[0328]

[0329] where α, β, γ, and δ are positive constants, which are used to ensure that the lifespan decreases as the corresponding variables increase.

[0330] S6. Use the updated Kriging surrogate model as the input of the PINN and train the PINN model

[0331] Generate 50,000 quasi-Monte Carlo sampling points in the input space using the updated Kriging surrogate model as the training data of the PINN model.

[0332] The PINN model is trained using the AdaBelief optimizer with an initial learning rate of 0.001, and a cosine annealing strategy is adopted for dynamic adjustment. The batch size is set to 256, and the number of training epochs is 10,000.

[0333] During the training process, the weight coefficients w1, w2, and w3 are dynamically adjusted:

[0334] w1 = 0.6 + 0.2sin(πepoch / total_epochs)

[0335] w2 = 0.3 - 0.1sin(πepoch / total_epochs)

[0336] w3 = 0.1 - 0.1sin(πepoch / total_epochs)

[0337] where epoch is the current training epoch and total_epochs is the total number of training epochs.

[0338] To prevent overfitting, early stopping and L2 regularization are adopted. The validation set ratio is 20%, and patience is set to 100 epochs. The L2 regularization coefficient is set to 0.0001.

[0339] S7. Use the trained PINN model for IGBT reliability assessment

[0340] 1) Failure probability calculation

[0341] The subset simulation method is used to calculate the failure probability. The parameter settings for subset simulation are as follows:

[0342] Conditional probability p0 = 0.1

[0343] Markov chain length N = 1000

[0344] Number of samples N for each subset s = 10000

[0345] The estimated value of the failure probability is:

[0346] P f ≈ p0 m * (1 / N s ) × ΣI(Y < Y m )

[0347] where m is the number of subsets, Y m is the threshold of the last subset, and I(·) is the indicator function.

[0348] 2) Reliability function calculation

[0349] Calculate the reliability function R(t) at different time points t:

[0350]

[0351] where is the cumulative distribution function of the lifetime N f obtained by the kernel density estimation method.

[0352] 3) Importance measure analysis

[0353] Adopt the importance measure method based on variance to calculate the contribution of each input variable to the lifetime prediction. The importance measure indicators include:

[0354] Main effect index S i = V(E(Y|X i )) / V(Y)

[0355] Total effect index S Ti = 1–V(E(Y|X ～i )) / V(Y)

[0356] where V(·) represents variance, E(·) represents expectation, and X ～i represents all input variables except X i .

[0357] Through the above steps, this embodiment realizes the efficient and accurate reliability assessment of the IGBT module under power cycling conditions, providing technical support for the design optimization and lifetime prediction of IGBTs.

[0358] The beneficial effects of the present invention are as follows:

[0359] By combining adaptive sampling and physics-informed neural networks, this method significantly reduces the number of simulations required. Compared with traditional methods, the computational efficiency is increased by 3 - 5 times, which is particularly suitable for the reliability assessment of complex IGBT systems.

[0360] Due to the introduction of physical constraints and adaptive sampling strategies, this method shows high accuracy in predicting the IGBT failure probability and lifetime. In the test cases, the prediction error is reduced by 20 - 30%. The introduction of physics-informed neural networks enables the model to have better generalization ability and can make reasonable predictions outside the range of training data, which is particularly important for evaluating the reliability of IGBTs under extreme conditions.

[0361] This method is applicable to various IGBT failure modes and operating conditions, and can conveniently integrate different physical models and failure criteria. By introducing physical constraints and importance analysis, this method provides in-depth insights into the IGBT failure mechanism, which helps to guide design optimization. This method not only gives point estimates, but also can provide confidence intervals of reliability indices, providing more comprehensive information for decision-making. Compared with full-scale finite element analysis, this method greatly reduces the computational resource requirements, making it possible to perform reliability assessment of complex IGBT systems on ordinary workstations, providing an efficient, accurate and flexible new method for IGBT reliability assessment, and is expected to play a role in the fields of IGBT design, life prediction and reliability management.

[0362] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative efforts. Therefore, all technical solutions that can be obtained by those skilled in the art in this technical field based on the concept of the present invention through logical analysis, reasoning or limited experiments on the basis of the prior art should fall within the protection scope determined by the claims.

Claims

1. An IGBT reliability evaluation method based on adaptive sampling and physics-informed neural network, characterized in that, The method includes the following steps: S1. Construct an IGBT physical model and determine the input variables and output responses; S2. Generate initial training samples and construct an initial Kriging surrogate model based on the IGBT physical model: S3. Use the U learning function to adaptively select new training sample points from the initial training samples: S4. Update the current Kriging surrogate model based on the new training sample points, and repeat S3 and S4 until one of the stopping criteria is met to obtain the resulting Kriging surrogate model; S5. Construct a PINN model, and the loss function of the PINN model includes a data loss term, a physical loss term, and a boundary condition loss term; S6. Use the sample points output by the resulting Kriging surrogate model as the training set of the PINN model for training to obtain a trained PINN model; S7. Conduct IGBT reliability assessment based on the trained PINN model to obtain an assessment result.

2. The IGBT reliability evaluation method based on adaptive sampling and physics-informed neural network according to claim 1, wherein The output response is: where y represents the output response vector, represents the feature fusion operator, represents the mapping of the i-th subnetwork, x represents the input variable vector, and θ i represents the trainable parameter vector of the i-th subnetwork.

3. The IGBT reliability evaluation method based on adaptive sampling and physics-informed neural network according to claim 2, wherein The specific steps of S2 are: Use the Latin hypercube sampling method to generate N0 initial training sample points in the input variable space, and run the IGBT physical model to obtain the corresponding output responses; Construct an initial Kriging surrogate model based on the corresponding output responses; The initial Kriging surrogate model is: μ(x) = f(x) T β + r(x) T R -1 (y - Fβ) σ 2 (x) = σ 2 [1 - r(x) T R -1 r(x) + u(x) T (F T R -1 F) -1 u(x)] Among them, is the predicted value of the output response, and α i is the weight coefficient of the i-th basis function, is the i-th type of non-linear basis function, is the Gaussian random process, m is the number of basis functions, f(x) is the regression function, β is the regression coefficient, r(x) is the correlation vector, R is the correlation matrix, y is the observed response, F is the experimental design matrix, and σ 2 is the process variance, u(x) = F T R -1 r(x) - f(x), the observed response is the output response obtained by running the IGBT physical model, and the correlation matrix is composed of correlation functions.

4. The IGBT reliability evaluation method based on adaptive sampling and physics-informed neural network according to claim 1, wherein The specific steps of S3 are: Select a learning operator from the initial training samples The point with the smallest value is used as the new training sample point x new ; The learning operator is defined as: Among them, is the mean prediction operator of the Kriging surrogate model, is the standard deviation prediction operator, is the input variable space.

5. A reliability evaluation method for IGBT based on adaptive sampling and physics-informed neural network according to claim 1, characterized in that, The specific steps of S4 are: Based on the new training sample point x new and the corresponding response value y new , an incremental method is used to update the current Kriging surrogate model, and the correlation matrix R of the updated model new is as follows: The regression coefficient β of the updated model new is as follows: Among them, represents the experimental design operator.

6. The IGBT reliability evaluation method based on adaptive sampling and physics-informed neural network according to claim 1, characterized in that The stopping criteria are: 1) The cumulative iteration count N of adaptive sampling iter Reaches a preset threshold, which is N iter > N max ; 2) The prediction error of the current Kriging model is less than the given threshold ε tol ; The prediction error is: y pred is the predicted value of the output response during the iterative process, y true represents the actual value of the output response. 3) The degree of decrease in the prediction error of the Kriging model for M consecutive iterations is less than the threshold δ tol ; The degree of decrease in the prediction error is: where Δε k is the degree of decrease in the prediction error for the k-th iteration.

7. A reliability evaluation method for IGBT based on adaptive sampling and physics-informed neural network according to claim 1, characterized in that, The PINN model includes an input layer, L hidden layers, and an output layer. The loss function of the PINN model includes a data loss term and a physical loss term. The loss function is: L total = w1L data + w2L physics + w3L boundary Among them, L data is the data loss term, L physics is the physical loss term, w1, w2, and w3 are weight coefficients, and L boundary is the boundary condition loss term; The data loss term is: where N is the number of training samples, and y i and are the true output and the model predicted output, respectively; The physical loss term is: where M is the number of physically constrained sampling points, and f(·) is the residual of the physical equation, is the partial derivative of the model output with respect to the input, represents the model output; The boundary condition loss term is: where \(u(x i )\) is the output of the neural network, \(N D \) is the number of sampling points on the boundary, and \(g D (x i )\) is the known function value on the Dirichlet boundary.

8. A method for evaluating the reliability of IGBT based on adaptive sampling and physics-informed neural network according to claim 7, characterized in that, When the IGBT physical model is a thermal model and a thermo-mechanical stress model, the physical loss term is constructed based on the heat diffusion equation and the thermo-mechanical stress equation, and is: where ρ is the density, c is the specific heat capacity, T is the temperature, t is the time, k is the thermal conductivity, q is the heat source term, σ is the stress, E is the Young's modulus, α is the coefficient of thermal expansion, T ref is the reference temperature, and ε is the strain; When the IGBT physical model is an electro-thermal coupling model and a fatigue life model, the physical loss term is constructed based on the electro-thermal coupling model, and is: Among them, C is the heat capacity, T is the junction temperature, T a is the ambient temperature, R th is the thermal resistance, V CE is the collector-emitter saturation voltage drop, I C is the collector current, V CE0 , r CE and k are temperature-related parameters, T ref is the reference temperature, and P represents thermal energy.

9. The IGBT reliability evaluation method based on adaptive sampling and physics-informed neural network according to claim 1, wherein In S6, use Curriculum Learning and the Adam optimization algorithm to train the PINN model.

10. The IGBT reliability evaluation method based on adaptive sampling and physics-informed neural network according to claim 1, wherein The assessment result includes the failure probability based on the predicted response distribution, the reliability considering multiple failure mechanisms, the sensitivity analysis result based on the cumulative damage model, and the reliability index reflecting the IGBT life characteristics.

Images