Electronic component accelerated test design optimization method considering uncertainty

Abstract

The invention discloses an electronic component accelerated test design optimization method considering uncertainty, and belongs to the technical field of electronic component reliability analysis. The problems that in an existing acceleration test design, stress condition selection is unreasonable, and degradation modeling deviation is large are solved. According to the method, a prediction framework based on the Bayesian neural network is constructed by taking test variables as input and the service life of an electronic component as output, approximate reasoning is performed on posterior distribution of model parameters by utilizing a variational inference method, so that the Bayesian neural network is constructed, a weak physical constraint term is introduced into a variational inference framework of a Bayesian neural network model, and the service life of the electronic component is predicted. Collaborative optimization of the model expression capability and the physical credibility is realized; a reward function is obtained based on the obtained Bayesian neural network, a reinforcement learning strategy function is adopted to guide generation of candidate test combinations, and a candidate test combination complete set is obtained; and based on a greedy incremental search mechanism, exploring an optimal subset scale in a combination number space to obtain an optimal combination number and an optimal test combination variable.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electronic component reliability analysis, and relates to an electronic component accelerated test design optimization method. BACKGROUND

[0002] With the wide application of electronic products, the reliability problem of electronic components is increasingly prominent. In order to accurately evaluate the performance degradation behavior of electronic components under long-term service conditions, accelerated life testing (ALT) has become a key means widely used in current engineering practice. Accelerated testing induces device degradation and failure in a short period of time by applying high stress conditions (such as high temperature, high pressure, high humidity, etc.), so as to infer the life indicators under normal use conditions. However, how to reasonably design the accelerated test conditions and sample allocation scheme to maximize the information acquisition efficiency under limited resources has always been a core problem in accelerated test design.

[0003] Traditional accelerated test design is mainly based on failure physical models, such as Arrhenius model, electric field stress model, etc., combined with statistical analysis methods to configure stress levels and sample sizes. However, such methods often rely on empirical parameter settings, and it is difficult to handle the nonlinear relationship between complex working conditions, multiple stress coupling and degradation processes, resulting in waste of test resources or large model bias. In recent years, with the development of artificial intelligence technology, neural networks have increasingly outstanding performance in complex nonlinear modeling problems, and have the ability to learn high-dimensional mapping relationships from limited samples. SUMMARY

[0004] The application is to solve the problems of unreasonable stress condition selection and large degradation modeling bias in existing accelerated test design.

[0005] An electronic component accelerated test design optimization method considering uncertainty, comprising the following steps:

[0006] Step one: build a prediction architecture based on Bayesian neural network with test variables as input and electronic component life as output, and use variational inference method to approximate the posterior distribution of model parameters for inference, so as to build a Bayesian neural network;

[0007] Step two: according to the Bayesian neural network built in step one, introduce a differentiable weak physical constraint term in the variational inference framework of the Bayesian neural network model, so as to realize the collaborative optimization of model expression ability and physical credibility;

[0008] Step three: based on the Bayesian neural network obtained in step two, get the reward function, and use the reinforcement learning strategy function to guide the generation of candidate test combinations to get the complete set of candidate test combinations;

[0009] Step four: based on the candidate combination set in step three, based on the greedy incremental search mechanism, explore the optimal subset size in the combination number space to obtain the optimal combination number K * and the optimal test combination variable.

[0010] Further, the specific implementation process of step one includes the following steps:

[0011] Let the test variable be d represents the dimension, that is, the test variable type; the output electronic component life is denoted as y, it is assumed that the logarithmic life log(y) of the electronic component is mapped by a set of test variables x via a Bayesian neural network f(·), and it is considered that the Bayesian neural network weight w satisfies the prior uncertainty distribution p(w), and the Bayesian neural network model prediction output is denoted as z represents the value of the model after logarithmic transformation on the output variable, and represents the prediction target; x represents the input variable, which is the combination of the test design variables, represents the observation data set, which is used to train the model; p(z|x,w) represents the prediction distribution of the model for the input x under the given network weight w; represents the posterior distribution of the network weight after the BNN model is trained; represents the observation data after the training of the BNN model, the overall prediction distribution of the input x;

[0012] For the posterior distribution Variable inference is used to approximate the true posterior distribution, and the Bayesian inference problem is converted into a variable optimization problem, and a joint variable distribution q φ (w) is constructed for all weights in the network, and q φ (w) and The KL divergence between q φ (w) is used to realize that q

[0013] Further, the Bayesian neural network f(·) is as follows:

[0014] z=log(y)=f(x;w), w~p(w) (1)

[0015] where z represents the logarithmic life of the real data, and a Gaussian likelihood modeling assumption is made for it, which is subject to It is indicated that there is a certain degree of unexplained error between the model prediction value f(x;w) and the real observation value log(y), that is, the observation value will not accurately fall on the BNN model prediction value; f(·) represents the BNN model mapping function, w represents the BNN model weight, and p(w) represents the prior uncertainty distribution.

[0016] Furthermore, the joint variation distribution q φ (w) are as follows:

[0017]

[0018] Where q φ (w) is controlled by a set of trainable variational parameters φ, Represents the weight of the j-th neuron in the l-th layer of BNN connected to the i-th neuron; in the variational inference framework, in order to achieve the weight of each neural network Approximation of the posterior distribution, introducing a set of trainable variational parameters are used to characterize the mean and standard deviation of the weights respectively; σ ij Use Softplus function to calculate a free variable ρ ij Mapping, that is, σ ij =log(1+exp(ρ ij )).

[0019] Furthermore, by minimizing q φ (w) and The KL divergence between φ (w) approximates the true posterior distribution The process includes:

[0020] The approximate posterior distribution constructed based on the variational parameters is determined as follows:

[0021]

[0022] Where φ=(μ ij ,ρ ij ) represents the set of all variational parameters in the entire neural network, which is the main object that needs to be optimized during the training process;

[0023] Minimize the KL divergence, that is The equivalent deformation method in variational inference is introduced, that is, maximizing the evidence lower bound ELBO to indirectly minimize the KL divergence between the posterior distributions, and the variational objective function form is obtained To achieve q φ (w) approximates the true posterior distribution

[0024] Furthermore, the weak physical constraint term introduced in the variational inference framework of the Bayesian neural network model as follows:

[0025]

[0026] in, consistency loss function representing the consistency of the BNN model prediction behavior with the prior physical trend, consistency loss function representing the pseudo-label consistency; trend pseudo-label sample; target response trend function generated by the failed physical trend; operation for extracting trend indicators from the BNN model output, i.e., for extracting information that can be compared with the physical trend, D'(·,·) is a distance measure function for trend consistency; M is the total number of pseudo-label samples; numerical pseudo-label sample; M represents the number of pseudo-label samples, representing the average of all sampling values, representing the uncertainty regularization, i.e., the variance of all predicted values, representing the mean fitting.

[0027] Further, in the variational inference framework of the Bayesian neural network model, a differentiable weak physical constraint term is introduced, and the objective function for the collaborative optimization of model expression ability and physical credibility is as follows:

[0028]

[0029] Further, in the process of guiding the generation of candidate test combinations, a reinforcement learning strategy function is adopted, "state" s is the current test variable combination, "action" a represents the newly generated test combination, and the candidate test combination agent reward function is:

[0030]

[0031]

[0032] wherein z k represents the kth selected initialization test combination, representing the weighting coefficient of each loss, the negative sign indicating that the goal is to minimize the loss function term, thereby maximizing the reward; is an uncertainty driving term, representing the uncertainty of the test combination corresponding to the input data set, the variance of the Bayesian neural network prediction life output, f(x,ω k predicted output of the Bayesian neural network under input, σ 2 (·) is the variance of the predicted output; is a sample representativeness distance term, representing the distance between the sample distribution generated by the test combination and the known distribution, MMD represents the maximum mean difference, representing the simulated sample distribution generated by the combination p prior represents the empirical distribution, i.e., determined according to historical data; T phys (z k ) represents the response trend function reflecting how the lifetime evolves with time or stress, target (z k ) represents the target response trend function generated based on weak physical principles, d denotes the Spearman rank consistency distance measure function;

[0033] The function mapping from the environmental state to the action, the policy function z k = π θ (s k ), z k represents the kth generated trial combination, s k represents the input state; the policy function π θ (s k ) takes the current trial state feature as input and outputs the next step design variable combination s k ' = π θ (s k ); based on the policy function, the optimal parameters are found in all possible state spaces, so that the trial combination output by the policy can maximize the candidate trial combination set of the agent reward function.

[0034] Further, the response trend function reflecting how the lifetime evolves with time or stress is as follows:

[0035] T phys (z k ) = log(y) ~ α·ξ + β·logt + γ

[0036] where the stress variable ξ and the time variable t are the main physical driving factors, and α, β, γ are adjustable coefficients.

[0037] Further, based on the greedy incremental search mechanism, the process of exploring the optimal subset size in the combination number space includes:

[0038] The normalized comprehensive score function is determined as:

[0039]

[0040] where is the normalized result of ; w represents the adaptive weight coefficient, represents the normalized probability value of the ith combination on the jth index; represents the information entropy of the jth index; ε represents a small constant to prevent numerical abnormalities; is the upper limit of the total entropy, l represents the total number of scoring indicators;

[0041] In order to maximize the trial utility score, the optimal trial combination subset is selected from the entire set of candidate trial combinations generated by the policy function based on a greedy incremental search mechanism, while satisfying the resource budget constraint and representative coverage requirements. The formal optimization goal is as follows:

[0042]

[0043] st∑Cost(c i′ )≤B,RepCov(S)≥R min

[0044] Among them, Cost(c i′ ) represents the resource consumption of the i'th experimental combination, RepCov(S) represents the representative coverage of the subset S in the original input variable space; S represents the final selected experimental combination subset, B represents the experimental cost constraint, K * represents the optimal number of experimental combinations, c i′ ∈S indicates that the final subset of experimental combinations is selected, R min Minimum representativeness threshold.

[0045] Beneficial effects:

[0046] By introducing virtual samples and weak physical constraints, the present invention effectively alleviates the impact of scarce training data on the generalization performance of the model; at the same time, it takes into account physical interpretability and uncertainty expression capabilities, significantly improving the prediction accuracy and boundary robustness of the Bayesian model in small sample scenarios; at the same time, this also ensures the reasonable selection of stress conditions and can effectively solve the problem of large deviation in degradation modeling.

[0047] The strategy generation and scoring mechanism proposed in this invention can automatically screen representative and physically reasonable experimental combinations, saving experimental costs while ensuring prediction credibility, and can effectively solve the problem of inefficient sample allocation.

[0048] The present invention has strong versatility and is applicable to the accelerated degradation modeling and test optimization of various electronic devices, including IGBTs, MOSFETs, capacitors, resistors, and other electronic devices. The model structure and input variables can be flexibly adjusted according to the different failure mechanisms of the devices; therefore, the present invention has good engineering practical value and promotion potential. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flow chart of the optimization method for accelerated test design of electronic components considering uncertainty. DETAILED DESCRIPTION

[0050] To solve the problems in the background art, the present application provides an electronic component accelerated test design optimization method considering uncertainty. Firstly, the variational inference method is used to approximately infer the posterior distribution of the model parameters to quantify the prediction uncertainty. At the same time, the generalized weak physical constraint mechanism is introduced to embed the structural information of the basic failure physical model into the Bayesian loss function in the form of soft constraint, thereby improving the generalization ability of the model in the physical boundary region. Secondly, the virtual sample points are introduced based on the existing test data through the sample expansion strategy to enhance the input space coverage and the learning ability of the model to the boundary behavior. Further, to improve the credibility and generalization of the Bayesian modeling in the actual engineering scene, the unlabeled samples and weak physical information are jointly embedded into the test optimization function, and on this basis, the simulation test strategy method based on the strategy generation mechanism is proposed, and the reinforcement learning strategy function is used to guide the construction and selection of the candidate test combination. Finally, the comprehensive score function integrating the uncertainty measure, physical consistency and sample representativeness is constructed, and the greedy incremental search mechanism is used to determine the optimal test subset size in the combination number space.

[0051] The present application comprehensively considers the physical prior and data-driven modeling capability, which can significantly improve the scientificity of the accelerated test design and the degradation modeling accuracy, and is suitable for reliability evaluation and life prediction tasks of various electronic components such as IGBT, MOSFET, capacitor, resistor, etc. The following will be described in combination with specific embodiments.

[0052] Specific embodiment one: in combination with Figure 1 It is explained that the present embodiment,

[0053] The present embodiment is an electronic component accelerated test design optimization method considering uncertainty, comprising the following steps:

[0054] Step one: construct a prediction architecture based on Bayesian neural network, and use variational inference method to approximately infer the posterior distribution of model parameters.

[0055] Let the test variable be d represents the dimension, i.e. the test variable type (such as stress level, sample number, sampling time, etc., which is determined according to the actual design needs), and the output electronic component life is denoted as Assume that the logarithmic life log(y) of the electronic component can be mapped by a set of test variables x via the Bayesian neural network f(·), and the specific form is as follows:

[0056] z = log(y) = f(x; w), w ~ p(w) (1)

[0057] Where z represents the true data logarithmic life, and the Gaussian likelihood modeling assumption is made for it, which is subject to There is a certain degree of unexplained error between the model predicted value f(x; w) and the true observation value log(y), that is, the observation value does not accurately fall on the BNN model predicted value. f(·) represents the BNN model mapping function, w represents the BNN learnable network weight, and p(w) represents the prior uncertainty distribution, that is, the subjective uncertainty of the model parameters before training. The present application adopts an independent Gaussian distribution (other distributions can also be assumed according to actual conditions), and the specific expression form is as follows:

[0058]

[0059] Formula (2) represents that all connection weights of each layer l of the BNN model are subject to a Gaussian distribution with zero mean and variance β -1 , and the Bayesian neural network model prediction output is as shown in formula (3):

[0060]

[0061] Wherein, z represents the value of the model after logarithmic transformation of the output variable, representing the prediction target; x represents the input variable, which is the combination of the test design variables, represents the observation data set, which is used to train the model; p(z|x,w) represents the prediction distribution of the model for the input x under the given network weight w; represents the posterior distribution of the network weight after training of the BNN model; represents the overall prediction distribution of the input x after observing the data , and the formula is the core expression of the BNN model for prediction and uncertainty evaluation;

[0062] However, the above posterior distribution is difficult to be analyzed in high-dimensional space, and the variational inference is used to approximate the real posterior distribution, so that the Bayesian inference problem is converted into a variational optimization problem, and the specific expression form is as follows:

[0063]

[0064] In the formula, q φ (w) is a joint variational distribution constructed for all learnable weights in the network, which is used to approximate the real posterior distribution in high-dimensional space. The distribution is controlled by a set of trainable variational parameters φ, represents the weight of the jth neuron of the lth layer of the BNN connected to the ith neuron. In the variational inference framework, in order to realize the approximation of the posterior distribution of each neural network weight , a set of trainable variational parameters respectively, are used to characterize the mean and standard deviation of the learnable weights. Considering that the standard deviation must be strictly positive, the present invention does not directly optimize σ ij but instead maps a free variable ρ ij using a Softplus function, i.e.,

[0065] σ ij = log(1 + exp(ρ ij )) (5)

[0066] where ρ ij is not a network variable directly involved in the computation of the BNN model, but a free variable that parameterizes the structure of the posterior distribution of the learnable weights. Specifically, ρ ij is mapped to the standard deviation parameter σ ij by a softplus function, thus controlling the range of uncertainty of the learnable weights in the approximate posterior distribution.

[0067] The approximate posterior distribution constructed based on the above variational parameters can be further expressed as:

[0068]

[0069] where φ = (μ ij , ρ ij ) represents the set of all variational parameters in the entire neural network, which is the main object to be optimized in the training process. The goal of formula (5) is to make it as close as possible to the true posterior, i.e., to minimize the KL divergence between them:

[0070]

[0071] However, since the true posterior cannot be analytically solved, formula (7) cannot be directly calculated. The present invention introduces an equivalent transformation method in variational inference, i.e., maximizing the Evidence Lower Bound (ELBO), to indirectly minimize the KL divergence between the posterior distributions. Specifically, first, the basic expression of variational inference is given:

[0072]

[0073] where logp(x) represents the log marginal likelihood of the observed data, represents the variational lower bound, and KL(·) represents the KL divergence between the variational distribution and the true posterior. Since is a constant, minimizing the KL divergence is equivalent to maximizing the ELBO:

[0074]

[0075] ​According to the assumptions in formula (9), It can be represented by the following formula:

[0076]

[0077] Substituting the specific form into the form, we can finally get the variational objective function form:

[0078]

[0079] in, represents the log-life Gaussian likelihood model, KL(q φ (w)||p(w)) represents the KL divergence between multi-dimensional Gaussians and has a closed analytical expression.

[0080] Step 2: Based on the basic framework of the BNN network established in step 1, to further improve the credibility and scalability of the model in engineering application scenarios, it is necessary to embed existing physical common sense into the modeling process in the form of constraints. This paper proposes a generalized weak physical constraint modeling mechanism. By introducing differentiable weak physical constraints into the variational inference framework of the BNN model, it achieves the coordinated optimization of model expressiveness and physical credibility:

[0081] According to the BNN model, the modeling target is logarithmic life span z = log(y), and the input is the experimental variable Define the predicted output as f(x;w); parameters w~q φ (w) is the weight sampling under the variational distribution. Determine the consistency loss between the prediction behavior of the BNN model under weak physical knowledge and the prior physical trend:

[0082]

[0083] in, Represents trend pseudo-label samples; represents the target response trend function generated by the failure physics trend; represents the operation of extracting trend indicators from the BNN model output, that is, extracting information comparable to physical trends. D′(·,·) is a distance metric for trend consistency, and M is the total number of pseudo-labeled samples. The key advantage of this constraint is that it does not rely on the explicit form of the physical equations, but instead relies on physical trend relationships, such as the monotonicity of "lifespan decreases with increasing stress" or the robustness of lifespan to sampling frequency.

[0084] In order to fully explore the unobserved areas in the experimental design space, numerical pseudo-label samples are introduced Consistency constraint mechanism. By sampling points in high uncertainty regions in the input space The distribution mean predicted by the BNN model and a plurality of Monte Carlo samples constitute a pseudo-label prediction result set (Use the model parameter ω (s) Predicted The numerical pseudo-label consistency constraint term can be expressed as:

[0085]

[0086] Wherein, M represents the number of pseudo-label samples, Indicates the pseudo-label consistency loss function, Indicates the average value of all sampling values, Indicates the uncertainty regularization, that is, the variance of all predicted values, Indicates the mean fitting;

[0087] In combination with the above weak physical trend consistency term Construct how the joint weak constraint objective function of pseudo-label and physical knowledge:

[0088]

[0089] In the complete modeling optimization process, the weak physical constraint as a differentiable regularization term can be naturally embedded in the optimization objective of variational inference, and the final constructed generalized objective function is as follows:

[0090]

[0091] The objective function can be optimized end-to-end with the support of reparameterization techniques and Monte Carlo estimation, and the neural network structure that meets the data fitting, prior distribution consistency and weak physical trend consistency at the same time can be learned, thereby improving the model generalization ability and physical credibility.

[0092] Step three: according to the Bayesian neural network obtained in step two, a simulation test strategy method based on strategy generation mechanism is proposed, and a reinforcement learning strategy function is used to guide the candidate test combination generation.

[0093] The reinforcement learning usually relies on a state-action reward model R(s, a) when searching the trial space. In this study, the state s can be understood as the current combination of trial variables, and the action a represents a newly generated trial combination. Since the reinforcement learning reward function relies too much on the true Bayesian model evaluation and the complex physical consistency term, directly using it to train the policy network will face the high cost of calculation and dead loop. Therefore, a small-scale initial trial variable combination is generated using the initial policy, and an approximate proxy reward function is constructed based on the BNN model prediction results. Based on the policy function, high-value candidate combinations are sampled in the trial variable space. At the same time, the BNN prediction, uncertainty, trend consistency and representativeness are used as the proxy reward function, in order to realize efficient search in the trial variable space, reduce the dependence on the true label and complex physical model in the early stage of reinforcement learning, and quickly train the policy function and explore high-potential trial combinations. The proxy reward function of the candidate trial combination is defined as:

[0094]

[0095] where z k represents the kth selected initial trial combination, represents the weighted coefficient of each loss term, and the negative sign indicates that the goal is to minimize the loss function term, thereby maximizing the reward.

[0096] is the uncertainty driving term, which represents the variance of the Bayesian neural network prediction output on the corresponding input data set (i.e., the prediction uncertainty of the Bayesian neural network):

[0097]

[0098] where f(x, ω k ) is the prediction output of the Bayesian neural network under the input, and σ 2 (·) is the variance of the prediction output.

[0099] is the sample representativeness distance term, which represents the distance between the sample distribution generated by the trial combination and the known distribution:

[0100]

[0101] where MMD represents the maximum mean difference, which is a measure method for the difference between the trial variable sample distributions, represents the simulated sample distribution generated by the combination , and p prior represents the empirical distribution, which is determined according to the historical data.

[0102] ​ reflecting the difference between the neural network output under the candidate test combination and the actual failure physical knowledge:

[0103]

[0104] where T phys (z k ) represents the life trend response vector (or function value) predicted by the current Bayesian neural network model, that is, the response trend function reflecting how the life evolves with time or stress, T target (z k ) represents the target response trend function generated based on weak physical principles, and ‖·‖ d represents the Spearman rank consistency distance measure function. A semi-empirical construction method based on dominant stress variables and time variables is introduced to establish a target response function with reasonable physical trend characteristics. The construction result is as formula (19):

[0105] T phys (z k ) = log(y) ~ alpha * xi + beta * logt + gamma (18)

[0106] where the stress variable xi and the time variable t are the main physical driving factors, alpha, beta, and gamma are adjustable coefficients, respectively, for flexibly expressing the trend slope, time dependence, and baseline offset in different scenarios.

[0107] The deterministic deep neural network strategy function is a deep network method that directly maps the state to a deterministic test action (combination), does not rely on sampling, is suitable for test design optimization of continuous variables, and has the advantages of high computational efficiency and simple implementation in strategy training. The present application adopts the deterministic deep neural network strategy function pi θ (s k ) to avoid the evaluation variance caused by random strategy, strengthen the fitting ability of strategy to efficient search direction, and serve as the core structure of strategy generation. The goal of the strategy function is to construct a function that maps from the environment state to the action (i.e., test combination variable):

[0108] z k = pi θ (s k ) (19)

[0109] where z k represents the kth generated test combination, s k represents the input state, including low-dimensional encoding of comprehensive information such as initialization sample space distribution characteristics, prediction uncertainty distribution, and physical trend response, and theta represents the set of trainable parameters of the strategy neural network.

[0110] The strategy function piθ (s k ) with the current trial state feature as input, output the next step design variable combination s k ' = π θ (s k ). Suppose that the strategy network contains L layers, and the activation function of each layer is φ L , then the overall mapping is represented as:

[0111] π θ (s k ) = W (L) φ L-1 (…φ1(W (1) s k +b (1) )…)+b (L) (20)

[0112] where W (L) , b (L) represent the weight matrix and bias of the Lth layer.

[0113] The learning goal of the strategy function is to find the optimal parameters in all possible state spaces, so that the trial combination output by the strategy can maximize the expected value of the agent's reward function:

[0114]

[0115] where represents the experience state distribution, i.e. the initial sample space distribution, π θ (s k ) represents the strategy function, and R(·) represents the agent's reward function. The strategy network uses the standard deep learning training mechanism, uses the back propagation algorithm to calculate the parameter gradient, and uses the Adam optimizer to update the parameters:

[0116]

[0117] where η represents the learning rate, represents the gradient term calculated by the back propagation algorithm. After training, the strategy network parameters θ * are fixed, and the forward propagation is used to generate a candidate trial combination set . The present application selects 30 samples as candidate trial combinations:

[0118]

[0119] where represents the candidate trial combination set generated based on the strategy function. After the strategy network generates a large-scale candidate trial combination set

[0120] Step four: Based on the candidate combination set in step three, construct a comprehensive score function, and based on a greedy incremental search mechanism, explore the optimal subset size in the combination number space.

[0121] To comprehensively evaluate the effectiveness of each test combination, a score function is defined based on the agent reward function, and the indicators are unified and optimized. The normalized comprehensive score function is defined as:

[0122]

[0123] wherein, represents the normalized score result of different indicators, The specific formula expression is the same as that in the agent reward function, and finally represented in normalized form; ω1-ω3 represents the adaptive weight coefficient, which improves the sensitivity and adaptability of the score function, and adopts an entropy-aware weight adjustment mechanism, defined as follows:

[0124] Calculate the probability distribution of the j'th indicator normalized score result in the full candidate test combination

[0125]

[0126] wherein, is the total number of candidate combinations.

[0127] Calculate the entropy value for the j'th indicator:

[0128]

[0129] wherein, H j′ represents the information entropy of the j'th indicator; p i′j′ represents the normalized probability value of the i'th combination on the j'th indicator; ε represents a small constant to prevent numerical anomalies;

[0130] Finally, the normalized entropy value is used to calculate the adaptive weight:

[0131]

[0132] wherein, is the upper limit of the total entropy, l represents the total score indicator number, H j′ represents the information entropy of the j'th indicator, which dynamically gives higher weight to the dimension with higher discriminability, reflecting the intelligence of multi-source score fusion.

[0133] In order to select the optimal test combination subset from the candidate test combination set generated by the policy function, to maximize the test utility score, while meeting the resource budget constraint and representative coverage requirement. The formal optimization objective is as follows: ​

[0134]

[0135] in, represents the comprehensive score function value of the i′th test combination, Cost(c i′ ) represents the resource consumption of the i′th experimental combination, RepCov(S) represents the representative coverage of the subset S in the original input variable space. S represents the final selected experimental combination subset, B represents the experimental cost constraint, K * represents the optimal number of experimental combinations, c i′ ∈S indicates that the final subset of experimental combinations is selected, R min The minimum representative threshold, this invention adopts the empirical ratio setting method to set R min It is set to 0.8, which requires that the selected combination subset covers at least 80% of the central area in the full set clustering structure.

[0136] In order to enhance the stability and expressiveness of representative coverage metrics in continuous space, the present invention divides the entire set of candidate combinations into M clusters using a clustering algorithm, with the centers being {μ1,μ2,…,μ M}Define the distance threshold ε>0, then the representative coverage function of the final subset S is:

[0137]

[0138] Among them, M represents the total number of clusters obtained by the clustering algorithm, represents the center of the j′th cluster, dist(·,·) represents the Euclidean distance, ε′>0 represents the coverage tolerance radius, and II[·] represents the indicator function. Although the above optimization problem is formally expressed in terms of a fixed number of combinations K * Based on this, a greedy incremental search mechanism is further proposed to explore the optimal subset size in the combination quantity space:

[0139] Set the combination quantity search interval [K min ,K max ], each round of iteration constructs the current candidate subset according to the number of combinations k And perform a greedy selection process:

[0140] 1. Initialization: Set k = K min , set the selected combination subset Let the remaining candidate set be

[0141] 2. Greedy choice: from Select the combination that maximizes the comprehensive score function Join S k .

[0142] 3, constraint check: if adding c * satisfies the constraints:

[0143]

[0144] then the loop continues, otherwise the current k-round search or backtracking removes c * .

[0145] 4, update calculator: if |S k | = k, then the subset S k is recorded as a feasible solution under the current combination number, and its comprehensive score function

[0146] 5, incremental search: let k = k + 1, repeat steps 2-4 until k = K max

[0147] Finally, from all the combination subsets satisfying the constraints the subset with the maximum comprehensive score is selected as the optimal solution:

[0148]

[0149] wherein, represents the set of all feasible subsets satisfying the constraints. Through the above greedy incremental search process, not only can the legal combination subset S k satisfying the budget and representative requirements be gradually constructed, but also the test combination S * with the maximum comprehensive score function value under all feasible combination numbers k can be screened out, and the optimal combination number K * and the optimal test combination variable are determined.

[0150] The application first constructs a life influence modeling framework based on Bayesian neural network, combines weak physical constraints to encode the relationship between test variables (such as acceleration stress level, sampling frequency and sample number) and life, and introduces a virtual sample expansion mechanism to enhance the generalization ability and physical interpretability of the model in the input space. On this basis, an accelerated test value function is designed to integrate prediction uncertainty, test cost and sample coverage, realize the quantification and unified measurement of test information utility, and guide the test resource allocation as the optimization objective function. Further, a batch enhancement type test design strategy for acceleration scenarios is proposed, which selects multiple optimal stress-time combination points in each round of design to improve the uncertainty convergence efficiency and the robustness of model structure identification, and finally realizes the global optimization of resource-limited accelerated test and the improvement of modeling accuracy.

[0151] Embodiment:

[0152] To evaluate the reliability problem of MOSFET devices in typical failure mechanism bias temperature instability (BTI), the proposed PINN-based electronic component accelerated test design optimization method is introduced in this case to achieve optimal modeling accuracy with limited test resources. The variables of this test optimization are: test stress, test sample size, and test frequency.

[0153] First, train the Bayesian neural network model according to historical test data:

[0154]

[0155] Where μ(Z) represents the BNN network predicted life mean, and σ(Z) represents the BNN network prediction uncertainty.

[0156] Then, determine the test variable value range, where the test stress selection range is [110℃-150℃], the sample size selection range is [5-10], and the sampling frequency selection range is [1-3] days. Combine the actual situation to construct the candidate design point set Z * :

[0157] Table 1 Test stress candidate design points

[0158]

[0159] According to engineering experience and simplified model, the target trend function is constructed as follows:

[0160] T target (z k )=-0.8·σ+1.2·logt+2

[0161] This is used to reflect the trend of life decline with voltage rise and stronger life response with longer use time. The optimization function is constructed as follows:

[0162]

[0163] Where the weight is taken The reinforcement learning strategy function is constructed: a deterministic policy network (two-layer MLP) is used to simulate policy behavior, and outputs a set of stress-test stress-test sample size-test frequency combinations in the state space (existing test conditions). Reinforcement learning is used to optimize policy parameters θ to generate a total of candidate combination sets As shown in Table 2:

[0164] Table 2 Candidate accelerated test results

[0165]

[0166] The acceleration test comprehensive score function is calculated according to formula (24), a greedy incremental algorithm is adopted, the combination with the highest current score is selected in each round to join the subset, the search is terminated when the gain is less than the threshold value ε=0.01, and finally the test combination subset scale K is determined * =3, and the optimal test combination is output as follows:

[0167] Table 3 optimal design result of the acceleration test

[0168]

[0169]

[0170] The above examples of the present application are only used to illustrate the calculation model and the calculation process of the present application, and are not intended to limit the embodiments of the present application. Based on the above description, other different forms of changes or variations can be made by those skilled in the art, and it is impossible to enumerate all the embodiments here. Any obvious changes or variations derived from the technical solutions of the present application still fall within the protection scope of the present application.

Claims

1. A method for optimizing the design of accelerated tests for electronic components taking uncertainty into account, characterized in that: The following steps are involved: Step 1: Build a prediction architecture based on a Bayesian neural network with the test variables as input and the electronic component lifespan as output. Use variational inference methods to approximate the posterior distribution of model parameters, thereby building a Bayesian neural network. Step 2: Based on the Bayesian neural network built in step 1, introduce weak physical constraints into the variational inference framework of the Bayesian neural network model to achieve coordinated optimization of the model's expressiveness and physical credibility; Step 3: Based on the Bayesian neural network obtained in step 2, a reward function is obtained, and a reinforcement learning strategy function is used to guide the generation of candidate trial combinations to obtain the full set of candidate trial combinations; Step 4: Based on the full set of candidate combinations in step 3, based on the greedy incremental search mechanism, explore the optimal subset size in the combination quantity space and obtain the optimal combination quantity K * and the optimal experimental combination variables.

2. The method for optimizing the design of accelerated test for electronic components taking uncertainty into consideration according to claim 1, characterized in that: The specific implementation process of step 1 includes the following steps: Let the experimental variable be d represents the dimension, i.e., the type of experimental variable; the output electronic component life is recorded as y. It is assumed that the logarithmic life of the electronic component log(y) is obtained by mapping a set of experimental variables x through the Bayesian neural network f(·). It is assumed that the Bayesian neural network weight w satisfies the prior uncertainty distribution p(w), and p(w) adopts an independent Gaussian distribution. The predicted output of the Bayesian neural network model is expressed as z represents the value after the model performs logarithmic transformation on the output variable, which represents the predicted target; x represents the input variable, which is the combination of the experimental design variables. represents the observation dataset used to train the model; p(z|x,w) represents the predicted distribution of the model for the input x given the network weight w; Represents the posterior distribution of network weights after BNN model training; Indicates that the observed data After that, the overall predicted distribution of input x; For the posterior distribution Variational inference is used to approximate the true posterior distribution, transforming the Bayesian inference problem into a variational optimization problem, and constructing the joint variational distribution q for all weights in the network. φ (w), by minimizing q φ (w) and The KL divergence between φ (w) approximates the true posterior distribution 3. The method for optimizing the design of accelerated test for electronic components taking uncertainty into consideration according to claim 2, characterized in that: The Bayesian neural network f(·) is as follows: z=log(y)=f(x;w),w~p(w) (1) Among them, z represents the logarithmic life of the real data, and the Gaussian likelihood modeling assumption is made, obeying It indicates that there is a certain degree of unexplained error between the model prediction value f(x; w) and the true observation value log(y), that is, the observation value will not fall exactly on the BNN model prediction value; f(·) represents the BNN model mapping function, w represents the BNN model weight, and p(w) represents the prior uncertainty distribution.

4. The method for optimizing the design of accelerated test for electronic components taking uncertainty into consideration according to claim 3, characterized in that: Joint variational distribution q φ (w) are as follows: Where q φ (w) is controlled by a set of trainable variational parameters φ, Represents the weight of the j-th neuron in the l-th layer of BNN connected to the i-th neuron; in the variational inference framework, in order to achieve the weight of each neural network Approximation of the posterior distribution, introducing a set of trainable variational parameters are used to characterize the mean and standard deviation of the weights respectively; σ ij Use Softplus function to calculate a free variable ρ ij Mapping, that is, σ ij =log(1+exp(ρ ij )).

5. The method for optimizing the design of accelerated test for electronic components taking uncertainty into consideration according to claim 4, characterized in that: By minimizing q φ (w) and The KL divergence between φ (w) approximates the true posterior distribution The process includes: The approximate posterior distribution constructed based on the variational parameters is determined as follows: Where φ=(μ ij ,ρ ij ) represents the set of all variational parameters in the entire neural network, which is the main object that needs to be optimized during the training process; Minimize the KL divergence, that is The equivalent deformation method in variational inference is introduced, that is, maximizing the evidence lower bound ELBO to indirectly minimize the KL divergence between the posterior distributions, and the variational objective function form is obtained To achieve q φ (w) approximates the true posterior distribution 6. The method for optimizing the design of accelerated test for electronic components taking uncertainty into consideration according to claim 5, characterized in that: Weakly differentiable physical constraints introduced into the variational inference framework of Bayesian neural network models as follows: in, Represents the consistency loss function between the BNN model prediction behavior and the prior physical trend, represents the pseudo-label consistency loss function; Represents trend pseudo-label samples; represents the target response trend function generated by the failure physics trend; represents the operation of extracting trend indicators from the output of the BNN model, that is, it is used to extract information that can be compared with physical trends. D′(·, ·) is the distance metric function for trend consistency; M is the total number of pseudo-label samples; is a numerical pseudo-label sample; M represents the number of pseudo-label samples, Represents the average value of all sample values ​​predicted, represents uncertainty regularization, i.e. the variance of all predicted values, represents mean fitting.

7. The method for optimizing the design of accelerated test for electronic components taking uncertainty into consideration according to claim 6, characterized in that: Introducing a weak physical constraint term into the variational inference framework of the Bayesian neural network model, the objective function for collaborative optimization of the model's expressiveness and physical credibility is as follows:

8. The method for optimizing accelerated test design of electronic components considering uncertainty according to any one of claims 1 to 7, characterized in that: In the process of using reinforcement learning strategy function to guide the generation of candidate trial combinations, "state" s is the current trial variable combination, "action" a represents the newly generated trial combination, and the candidate trial combination agent reward function is: Among them, z k Indicates the kth selection of the initialization test combination, Represents the weighted coefficient of each loss, and the negative sign indicates that the goal is to minimize the loss function term and thus maximize the reward; is the uncertainty driving term, indicating that The variance of the Bayesian neural network's predicted lifespan output on the corresponding input data set, f(x,ω k ) The predicted output of the Bayesian neural network under the input, σ 2 (·) Variance of the predicted output; is the sample representative distance term, which represents the experimental combination The distance between the generated sample distribution and the known distribution, MMD represents the maximum mean difference, Indicates that there is a combination The generated simulated sample distribution, p prior represents the empirical distribution, i.e. determined based on historical data; Reflects the difference between the neural network output under the candidate test combination and the actual failure physical knowledge, T phys (z k ) represents the response trend function that reflects how the lifespan evolves with time or stress, T target (z k ) represents the target response trend function generated based on weak physical principles, ||·|| d represents the Spearman rank consistency distance metric function; The function policy function z that maps from the environment state to the action k =π θ (s k ), z k represents the kth generated trial combination, s k represents the input state; the policy function π θ (s k ) takes the current test state characteristics as input and outputs the next step design variable combination s k '=π θ (s k ); Based on the policy function in all possible state spaces, find the optimal parameters so that the trial combination of the policy output can maximize the full set of candidate trial combinations of the agent reward function.

9. The method for optimizing the design of accelerated test for electronic components taking uncertainty into consideration according to claim 8, characterized in that: The response trend function that reflects how the lifespan evolves with time or stress is as follows: T phys (z k )=log(y)~α·ξ+β·logt+γ Among them, the stress variable ξ and the time variable t are the main physical driving factors, and α, β, and γ are adjustable coefficients.

10. The method for optimizing accelerated test design of electronic components considering uncertainty according to claim 8, characterized in that: Based on the greedy incremental search mechanism, the process of exploring the optimal subset size in the combination quantity space includes: The normalized comprehensive scoring function is determined as: in, for )’s normalized result; represents the adaptive weight coefficient, It represents the normalized probability value of the i'th combination on the j'th indicator; represents the information entropy of the j'th indicator; ε represents a small constant to prevent numerical anomalies; is the upper limit of the total entropy, l represents the total number of scoring indicators; In order to maximize the trial utility score, the optimal trial combination subset is selected from the entire set of candidate trial combinations generated by the policy function based on a greedy incremental search mechanism, while satisfying the resource budget constraint and representative coverage requirements. The formal optimization goal is as follows: s.t.∑Cost(c i′ )≤B,RepCov(S)≥R min Among them, Cost(c i′ ) represents the resource consumption of the i'th experimental combination, RepCov(S) represents the representative coverage of the subset S in the original input variable space; S represents the final selected experimental combination subset, B represents the experimental cost constraint, K * represents the optimal number of experimental combinations, c i′ ∈S indicates that the final subset of experimental combinations is selected, R min Minimum representativeness threshold.

Images