Uncertainty Quantification Method for Adapter Strain Field Prediction Based on Conditional Normalized Flow

Abstract

The present invention proposes a method for quantifying uncertainty in adapter strain field prediction based on conditional standardized flow, which belongs to the field of uncertainty quantification of prediction results, including: S1, extracting implicit feature vectors from the adapter structure using an information fusion balanced neural operator network; S2, building a standardized flow model; S3, building and training an uncertainty quantification model based on conditional standardized flow according to the implicit feature vector and the standardized flow model; S4, inputting the implicit feature vector into the uncertainty quantification model based on conditional standardized flow to obtain an approximate strain distribution of the adapter strain field; S5, using forward propagation to calculate the approximate strain distribution to obtain the uncertainty quantification result of the adapter strain field. This application uses an uncertainty quantification model based on conditional standardized flow to predict the strain distribution of each point of the adapter according to the implicit feature vector and the standardized flow model, giving accurate mean and variance results, quantifying the uncertainty of the strain field, and improving the accuracy of uncertainty quantification.

Description

Technical Field

[0001] The present invention relates to the technical field of uncertainty quantification of prediction results, and in particular to a method for quantifying uncertainty in prediction of an adapter strain field based on conditional standardized flow. Background Art

[0002] As a powerful machine learning model, deep neural network (DNN) has achieved good prediction performance in many fields. However, it is not enough to focus on prediction accuracy. In practical applications, the model also needs to give a reliable uncertainty measure to assist decision making. When predicting the strain field of the adapter, the model needs to perform extrapolation predictions for geometric structures that do not appear in the training set. Due to the lack of generalization ability of the model, the prediction error often has a large error. In the optimization process, this error will lead to inaccurate objective functions. Therefore, the uncertainty quantification of DNN is to analyze the various sources of neural network prediction errors and give the uncertainty size caused by various sources, so that the model can give reliable results.

[0003] Among the existing uncertainty quantification methods, the Bayesian method and the integration method are inefficient when processing high-dimensional adapter strain field data due to their high computational complexity and high storage cost. The single model determination method is simple and efficient, but it requires manual setting of the distribution type of the output layer. Due to the uneven distribution of adapter strain, the distribution forms at different positions are also different, which makes it difficult for the model to converge.

[0004] Therefore, finding a method that can effectively quantify various uncertainties in the strain field prediction of the adapter and obtain the conditional probability distribution of the strain field data without assuming the prior distribution of the real data is a technical problem that needs to be solved urgently by technical personnel in this field. Summary of the invention

[0005] In view of this, the present invention proposes an uncertainty quantification method for adapter strain field prediction based on conditional standardized flow, which can utilize the uncertainty quantification model based on conditional standardized flow to predict the strain distribution of each point of the adapter according to the implicit eigenvector and the standardized flow model, give accurate mean and variance results, quantify the uncertainty of the strain field, and improve the accuracy of uncertainty quantification.

[0006] The technical solution of the present invention is implemented as follows: The present invention provides an adapter strain field prediction uncertainty quantification method based on conditional standardized flow, comprising the following steps:

[0007] S1, extract implicit feature vectors from adapter structures using information fusion balanced neural operator networks;

[0008] S2. construct a standardized flow model; the standardized flow model includes a single-layer fully connected network;

[0009] S3, constructing and training an uncertainty quantification model based on conditional standardized flow according to the implicit feature vector and the standardized flow model;

[0010] S4, inputting the implicit eigenvector into the uncertainty quantification model based on conditional normalized flow to obtain the approximate strain distribution of the adapter strain field;

[0011] S5. Use forward propagation to calculate the approximate strain distribution to obtain an uncertainty quantification result of the adapter strain field, wherein the uncertainty quantification result includes a mean value and a variance of the strain distribution of each point of the adapter.

[0012] On the basis of the above technical solutions, preferably, the uncertainty quantification model based on conditional standardized flow includes 4 fully connected neural networks, a reversible transformation matrix module, a standardized flow transformation module and a distributed parameter learning module.

[0013] On the basis of the above technical solution, preferably, the training process of the uncertainty quantization model based on the conditional normalized flow specifically includes:

[0014] Step 1: Set the initial variable z0 to obey the Gaussian distribution N(μ;σ 2 ), where μ represents the mean of the initial variable z0, σ 2 represents the variance of the initial variable z0;

[0015] Step 2: Use the uncertainty quantification model based on conditional normalized flow to input the load, unit cell design parameters and their coordinates to obtain implicit eigenvectors, and then input the implicit eigenvectors into four fully connected neural networks to obtain the matrix v full , bias vector b, vector v r1 and vector v r2 ;

[0016] Step 3: Transform the matrix v full , vector v r1 and vector v r2 Input to the reversible transformation matrix module to obtain matrix R and matrix R';

[0017] Step 4: Use the bias vector b and the matrices R and R' to transform the variable z0 K times to obtain the new variable z k , the conditional probability distribution is p(z k ), the conditional probability distribution p(z k ), the bias vector b, and the matrix R and the matrix R' are input into the distribution parameter learning module, and the mean and variance of the Gaussian distribution are set as trainable parameters. The optimal distribution parameters of the uncertainty quantization model based on conditional normalized flow are obtained according to network learning.

[0018] On the basis of the above technical solution, preferably, the matrix v full Including upper triangular matrices and the lower triangular matrix Step three specifically includes:

[0019] The vector v r1 As an upper triangular matrix The diagonal of , we get the matrix R;

[0020] The vector v r2 As a lower triangular matrix The diagonal of , we get the matrix R'.

[0021] On the basis of the above technical solution, preferably, the process of the distribution parameter learning module specifically includes:

[0022] Use Monte Carlo sampling to calculate the conditional probability distribution p(z k ) expectation of negative entropy;

[0023] Use adaptive nonparametric kernel density estimation to estimate the conditional probability distribution p(z k )’s probability density function;

[0024] According to the conditional probability distribution p(z k )The expectation and conditional probability distribution of the negative entropy p(z k ) is used to obtain the approximate strain distribution and conditional probability distribution p(z k )

[0025] The approximate strain distribution and conditional probability distribution p(z k ) is minimized to obtain the optimal parameters of the uncertainty quantification model based on conditional normalized flow.

[0026] On the basis of the above technical solution, preferably, the method of estimating the probability density function of the initial Gaussian distribution using an adaptive non-parametric kernel density estimation method specifically includes:

[0027] For the initial Gaussian distribution conditional probability distribution p(z k ) to perform random sampling and obtain m sample points {z1,…,z i ,…z m};

[0028] For the sample points {z1,…,z i ,…z m}Use Scott's theorem to determine the adaptive bandwidth;

[0029] Determine the conditional probability distribution p(zk ) is the probability density function of .

[0030] On the basis of the above technical solution, preferably, the conditional probability distribution p(z k The calculation formula of the probability density function of ) is as follows:

[0031]

[0032]

[0033] in, represents the estimated value of the probability density function at the sample point z, z represents the point for which the probability density needs to be estimated, m is the number of sample points, z i represents the i-th sample point among m sample points, b2 is the conditional probability distribution p(z k ) is the bandwidth, Ψ is the Gaussian kernel function, represents the sample points {z1,…,z i ,…z m} is an unbiased estimate of the standard deviation, std({z1,…,z i ,…z m}) represents the sample point {z1,…,z i ,…z m} standard deviation.

[0034] On the basis of the above technical solution, preferably, the approximate strain distribution of the uncertainty quantification model is similar to the conditional probability distribution p(z k The calculation formula for minimizing the KL divergence between ) is:

[0035]

[0036] Among them, θ * The approximate strain distribution and conditional probability distribution p(z k ), q θ (z k ) represents the approximate strain distribution, p(D|z k ) represents the variable z k The expected value of the log probability in the observed data D, E q p(z k ) represents the prior distribution, s represents the true value of the data, I m represents the m×m identity matrix, diag represents the conversion of a vector into a diagonal matrix, σ' represents the derivative of the activation function, Q T represents the transpose of the orthogonal matrix Q, z k represents the random variable after K transformations, and z0 represents the input variable of the uncertain quantitative model.

[0037] More preferably, step S5 specifically includes:

[0038] Randomly sample M sample points from the approximate strain distribution and perform forward propagation to obtain M outputs

[0039] according to The mean and variance of the strain distribution at each point of the adapter are calculated.

[0040] On the basis of the above technical solution, preferably, in step S2, the determinant of the Jacobian matrix of the probability density distribution of the normalized flow model is simplified using QR decomposition, and the determinant of the simplified Jacobian matrix is:

[0041]

[0042] Among them, w k Represents the output variable of a single-layer fully connected network, w k-1 Represents the previous output variable of a single-layer fully connected network, I m represents the m×m identity matrix, diag represents the conversion of a vector into a diagonal matrix, σ' represents the derivative of the activation function, R1' represents the second upper triangular matrix obtained by QR decomposition, Q T represents the transpose of the orthogonal matrix Q, w represents the input variable of the single-layer neural network, b1 represents the bias term of the single-layer fully connected network, and R1 represents the first upper triangular matrix obtained by QR decomposition.

[0043] The adapter strain field prediction uncertainty quantification method of the present invention has the following beneficial effects compared with the prior art:

[0044] (1) By using the information fusion balanced neural operator network to extract implicit feature vectors from the complex adapter structure, and by constructing a single-layer fully connected standardized flow model, the probability density distribution of the adapter strain field is effectively constructed. Using the uncertainty quantification model based on conditional standardized flow, the strain distribution of each point of the adapter is predicted according to the implicit feature vector and the standardized flow model, and accurate mean and variance results are given to quantify the uncertainty of the strain field and improve the accuracy of uncertainty quantification.

[0045] (2) Rich feature representations are extracted from implicit feature vectors through four fully connected neural networks, and the transformation matrices R and R' are learned using the reversible transformation matrix to ensure accurate modeling of the probability density function. The mean and standard deviation of the Gaussian distribution are adaptively learned through the distribution parameter learning module, so that the uncertainty quantification model based on conditional normalized flow can flexibly fit the probability distribution characteristics of the initial variable z0, thereby enhancing the ability to quantify uncertainty. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0047] Figure 1 Schematic diagram of the basic configuration of the adapter of the adapter strain field prediction uncertainty quantification method of the present invention, wherein (a) is a three-dimensional view, and (b) is a front view;

[0048] Figure 2 A design variable diagram of a unit cell structure in the adapter configuration of the adapter strain field prediction uncertainty quantification method of the present invention;

[0049] Figure 3 A flow chart of the adapter strain field prediction uncertainty quantification method of the present invention;

[0050] Figure 4 A schematic diagram of an uncertainty quantification model based on conditional normalized flow for the adapter strain field prediction uncertainty quantification method of the present invention;

[0051] Figure 5 A schematic diagram of a continuous normalized flow transformation of the adapter strain field prediction uncertainty quantification method of the present invention;

[0052] Figure 6 It is a schematic diagram of non-parametric kernel density estimation of the adapter strain field prediction uncertainty quantification method of the present invention. DETAILED DESCRIPTION

[0053] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0054] like Figure 1 and Figure 2As shown, in the embodiment provided by the present invention, the size of the adapter is 150mm×80mm×60mm, the material is polyurethane, the adapter is composed of a geometric unit cell structure, and the geometric unit cell structure of the adapter is controlled by 6 design parameters L1 to L6, wherein L1 is the distance from the bottom end of the unit cell to the midline, L2 is the width of the unit cell, L3 is the radius of the arc transition between the inner arc and the outer arc, L4 and L5 are the radii of the inner arc and the outer arc respectively, and L6 is the thickness of the upper end surface. The overall peripheral length and height of the adapter are fixed at 25mm, and the distance from the bottom end to the top end is fixed at 30mm.

[0055] like Figure 3 As shown, the present invention provides a method for quantifying uncertainty in adapter strain field prediction based on conditional normalized flow, comprising the following steps:

[0056] S1. Extract implicit feature vectors from adapter structures using information fusion balanced neural operator networks.

[0057] Specifically, the load l of the adapter, the design parameter vector p, and the strain value vector s of the adapter in the x-direction and the y-direction are input into the information fusion balance neural operator network to obtain an implicit feature vector v, where v is a high-dimensional implicit feature vector.

[0058] S2. Construct a standardized flow model; the standardized flow model includes a single-layer fully connected network.

[0059] Specifically, in step S2, the determinant of the Jacobian matrix of the probability density distribution of the standardized flow model is simplified using QR decomposition. The determinant of the simplified Jacobian matrix is:

[0060]

[0061] Among them, w k Represents the output variable of a single-layer fully connected network, w k-1 Represents the previous output variable of a single-layer fully connected network, I m represents the m×m identity matrix, diag represents the conversion of a vector into a diagonal matrix, σ' represents the derivative of the activation function, R1' represents the second upper triangular matrix obtained by QR decomposition, Q T represents the transpose of the orthogonal matrix Q, w represents the input variable of the single-layer neural network, b1 represents the bias term of the single-layer fully connected network, and R1 represents the first upper triangular matrix obtained by QR decomposition.

[0062] The complexity of the determinant of the original Jacobian matrix is ​​simplified by QR decomposition, which effectively avoids the numerical instability problem that occurs when directly calculating the determinant of the Jacobian matrix, improves the computational efficiency, enhances the numerical stability and generalization performance of the standardized flow model, and intuitively reflects the influence of the nonlinear transformation of the hidden layer of the neural network on the probability density distribution through the derivative of the activation function.

[0063] In one embodiment of the present application, it is assumed that there is a d-dimensional random variable h that obeys the distribution p(h), and h is transformed into a random variable w0=T(h) by a transformation function T, and the probability density distribution of the random variable w0 is p(w0);

[0064] in, represents d-dimensional real number space, ∫p(h)dh=1=∫p(w0)dz, then Then we can get in, is the Jacobian matrix, det(·) is the determinant of the matrix;

[0065] but

[0066] Perform K consecutive transformation functions T on the random variable w0 k Get the variable w K , then the variable w K The probability density distribution of

[0067] The transformation function T k Set to w k =w k-1 +Aσ(Bw k-1 +b), where A is a d×m parameter matrix and B is an m×d parameter matrix. s is a nonlinear activation function, such as ReLU, Sigmoid, etc., m≤d, then the determinant of the Jacobian matrix is:

[0068]

[0069] Among them, I d represents the d×d identity matrix, σ' represents the derivative of the activation function;

[0070] According to Sylvester's determinant theorem, the amount of matrix calculation is reduced, that is, the Jacobian matrix is:

[0071]

[0072] Among them, I m Represents the m×m identity matrix.

[0073] Preferably, the determinant of the Jacobian matrix can be simplified using QR decomposition:

[0074] Assume that the parameter matrix A is full column rank and the parameter matrix B is full row rank, then A=QR1,B=R1'Q T , then the determinant of the Jacobian matrix can be simplified to:

[0075]

[0076] It can be seen that the computational complexity of the determinant of the simplified Jacobian matrix is ​​only It is linearly related to d and reduces the computational complexity of the standardized flow model.

[0077] like Figure 4 and Figure 5 As shown, S3, construct and train an uncertainty quantification model based on conditional standardized flow according to the implicit feature vector and the standardized flow model; the uncertainty quantification model based on conditional standardized flow includes 4 fully connected neural networks, a reversible transformation matrix module, a standardized flow transformation module and a distributed parameter learning module.

[0078] Specifically, the training process of the uncertainty quantization model based on conditional normalization flow includes:

[0079] Step 1: Set the initial variable z0 to obey the Gaussian distribution N(μ;σ 2 ), where μ represents the mean of the initial variable z0, σ 2 represents the variance of the initial variable z0;

[0080] Step 2: Use the uncertainty quantification model based on conditional normalized flow to input the load, unit cell design parameters and their coordinates to obtain implicit eigenvectors, and then input the implicit eigenvectors into four fully connected neural networks to obtain the matrix v full , bias vector b, vector v r1 and vector v r2 ;

[0081] Step 3: Transform the matrix v full , vector v r1 and vector v r2 Input to the reversible transformation matrix module to obtain matrix R and matrix R';

[0082] Step 4: Use the bias vector b and the matrices R and R' to transform the variable z0 K times to obtain the new variable z k , the conditional probability distribution is p(z k ), the conditional probability distribution p(z k), the bias vector b, and the matrix R and the matrix R' are input into the distribution parameter learning module, and the mean and variance of the Gaussian distribution are set as trainable parameters. The optimal distribution parameters of the uncertainty quantization model based on conditional normalized flow are obtained according to network learning.

[0083] Among them, the matrix vector vector Bias Vector σ=Tanh(·)∈[−1,1].

[0084] Rich feature representations are extracted from implicit feature vectors through four fully connected neural networks, and the transformation matrices R and R' are learned using the reversible transformation matrix to ensure accurate modeling of the probability density function. The mean and standard deviation of the Gaussian distribution are adaptively learned through the distribution parameter learning module, so that the uncertainty quantification model based on conditional standardized flow can flexibly fit the probability distribution characteristics of the initial variable z0, thereby enhancing the ability to quantify uncertainty.

[0085] In one embodiment of the present application, z is used k =z k-1 +QRtanh(R'Q T z k-1 +b) Perform k reversible transformations on the initial variable z0. By introducing the Tanh activation function, the nonlinear fitting ability of the transformation function T(h) is enhanced, so that the uncertainty quantification model based on conditional normalized flow can adaptively adjust the probability distribution characteristics of the initial variable z0.

[0086] In one embodiment of the present application, for the vector v r1 and vector v r2 Tanh nonlinear activation function is added to constrain the value range between -1 and 1. full , the bias vector b is not constrained. By r1 and vector v r2 To constrain the value range, improve the stability of numerical calculations, and reduce the errors of numerical calculations, the matrix v full If the bias vector b is not constrained, more original information of the data can be retained, which is conducive to the uncertainty quantification model based on conditional normalized flow to capture the complexity of the data.

[0087] In one embodiment of the present application, the diagonal elements of the matrix R and the matrix R' are r jj , r j ' j ∈[-1,1], -1 / ||σ'|| ∞ =-1.

[0088] Furthermore, the matrix vfull Including upper triangular matrices and the lower triangular matrix Step three specifically includes:

[0089] The vector v r1 As an upper triangular matrix The diagonal of , we get the matrix R;

[0090] The vector v r2 As a lower triangular matrix The diagonal of , we get the matrix R'.

[0091] By adding the vector v r1 and vector v r2 As the diagonal elements of the matrix R and the matrix R', they improve the efficiency of parameter utilization, ensure numerical stability, and enhance the expressive power and the ability to fit complex relationships of the uncertainty quantification model based on conditional normalized flow.

[0092] Furthermore, the process of the distribution parameter learning module specifically includes:

[0093] Use Monte Carlo sampling to calculate the conditional probability distribution p(z k ) expectation of negative entropy;

[0094] Use adaptive nonparametric kernel density estimation to estimate the conditional probability distribution p(z k )’s probability density function;

[0095] According to the conditional probability distribution p(z k )The expectation and conditional probability distribution of the negative entropy p(z k ) is used to obtain the approximate strain distribution and conditional probability distribution p(z k )

[0096] The approximate strain distribution and conditional probability distribution p(z k ) is minimized to obtain the optimal parameters of the uncertainty quantification model based on conditional normalized flow.

[0097] By using the prior knowledge of Gaussian distribution and Monte Carlo sampling method to calculate the negative entropy of conditional probability distribution, the adaptive nonparametric kernel density estimation method is used to better capture the characteristics of complex distribution, improve the accuracy of probability density function estimation, and compare the approximate strain distribution of the uncertainty quantification model with the conditional probability distribution p(z k) is minimized, the parameters of the deep neural network of the uncertainty quantification model based on conditional standardized flow are optimized, and efficient parameter learning of the parameters of the deep neural network of the uncertainty quantification model based on conditional standardized flow is achieved, thereby improving its fitting ability for approximate strain distribution.

[0098] Specifically, the conditional probability distribution p(z k )The calculation formula of negative entropy is:

[0099]

[0100] logp(z0)=-log2π-logσ1-logσ2-(z 01 -μ1) 2 / 2σ1 2 -(z 02 -μ2) 2 / 2σ2 2

[0101] Among them, σ1 and σ2 represent the input variable z0 in [z 01 ,z 02 ], μ1 and μ2 represent the standard deviation of the input variable z0 in [z 01 ,z 02 ] is the mean of the two dimensions, z 01 Represents the value of the first dimension of the input variable z0, z 02 Represents the value of the second dimension of the input variable z0.

[0102] like Figure 6 As shown, further, the method of estimating the probability density function of the initial Gaussian distribution using the adaptive non-parametric kernel density estimation method specifically includes:

[0103] For the initial Gaussian distribution conditional probability distribution p(z k ) to perform random sampling and obtain m sample points {z1,…,z i ,…z m};

[0104] For the sample points {z1,…,z i ,…z m}Use Scott's theorem to determine the adaptive bandwidth;

[0105] Determine the conditional probability distribution p(z k ) is the probability density function of .

[0106] Distribution sample points are obtained by random sampling, and the adaptive bandwidth selection method of Scott's theorem is used to improve the flexibility and accuracy of kernel density estimation. The Gaussian kernel function is combined with the adaptive bandwidth to obtain an accurate probability density function estimate of the initial Gaussian distribution conditional probability distribution, providing reliable probability density distribution information for KL divergence calculation.

[0107] Furthermore, the conditional probability distribution p(z k The calculation formula of the probability density function of ) is as follows:

[0108]

[0109] in, represents the estimated value of the probability density function at the sample point z, z represents the point for which the probability density needs to be estimated, m is the number of sample points, z i represents the i-th sample point among m sample points, b2 is the conditional probability distribution p(z k ) is the bandwidth, Ψ is the Gaussian kernel function, represents the sample points {z1,…,z i ,…z m} is an unbiased estimate of the standard deviation, std({z1,…,z i ,…z m}) represents the sample point {z1,…,z i ,…z m} standard deviation.

[0110] Furthermore, the approximate strain distribution of the uncertainty quantification model is similar to the conditional probability distribution p(z k The calculation formula for minimizing the KL divergence between is:

[0111]

[0112] Among them, θ * The approximate strain distribution and conditional probability distribution p(z k ), q θ (z k ) represents the approximate strain distribution, p(D|z k ) represents the variable z k The expected value of the log probability in the observed data D, E q p(z k ) represents the prior distribution, s represents the true value of the data, I m represents the m×m identity matrix, diag represents the conversion of a vector into a diagonal matrix, σ' represents the derivative of the activation function, Q T represents the transpose of the orthogonal matrix Q, z krepresents the random variable after K transformations, and z0 represents the input variable of the uncertain quantitative model.

[0113] S4. Input the implicit eigenvector into the uncertainty quantification model based on conditional normalized flow to obtain the approximate strain distribution of the adapter strain field.

[0114] S5. Use forward propagation to calculate the approximate strain distribution to obtain an uncertainty quantification result of the adapter strain field, wherein the uncertainty quantification result includes a mean value and a variance of the strain distribution of each point of the adapter.

[0115] Specifically, step S5 specifically includes:

[0116] Randomly sample M sample points from the approximate strain distribution and perform forward propagation to obtain M outputs

[0117] according to The mean and variance of the strain distribution at each point of the adapter are calculated.

[0118] This application extracts implicit feature vectors from complex adapter structures by using an information fusion balanced neural operator network, and effectively constructs the probability density distribution of the adapter strain field by constructing a single-layer fully connected standardized flow model. The uncertainty quantification model based on conditional standardized flow is used to predict the strain distribution of each point of the adapter according to the implicit feature vector and the standardized flow model, and accurate mean and variance results are given to quantify the uncertainty of the strain field. Any complex strain field distribution under a given combination of coordinates and conditional parameters is generated without artificially giving a priori distribution form of the strain field. This can effectively solve the problem of instability in the model training process caused by the large difference between the prior strain field distribution and the true distribution, improve the accuracy of uncertainty quantification, and reduce the computational cost and improve the computational efficiency.

[0119] In one embodiment of the present application, a variety of uncertainty quantification methods are used to predict the adapter strain field, such as using multivariate deep evidential regression (MVDER), Hamiltonian Monte Carlo (HMC), Kronecker factored approximation curvature (K-FAC), Monte Carlo dropout (MCD), consistent quantile regression (CQR), Stochastic weight averaging-Gaussian (SWAG), and variational Bayes (VB) for comparison, and using negative log likelihood (NLL), confidence interval coverage (COV), consistent confidence interval coverage (CCOV), interval width (PIW), standard deviation coefficient of variation (Standard deviation coefficient of The credibility of the uncertainty quantification model was evaluated by using standard deviation variation (SDCV) and root mean square calibration error (RMSCE).

[0120] When the probability is the same, the smaller the PIW, the more accurate the confidence interval and the better the uncertainty quantification result. The final comparison results are shown in Table 1:

[0121] Table 1. Uncertainty evaluation index of test set

[0122]

[0123] It can be seen from Table 1 that among the uncertainty indicators, the uncertainty quantification method based on conditional standardized flow (CNFA-UQ) of this application has an average ranking of 2, which is the highest ranking, proving the effectiveness of the uncertainty quantification method based on conditional standardized flow in quantifying the uncertainty of the adapter strain field prediction results.

[0124] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for quantifying uncertainty in adapter strain field prediction based on conditional normalized flow, characterized in that: The following steps are involved: S1, extract implicit feature vectors from adapter structures using information fusion balanced neural operator networks; S2. construct a standardized flow model; the standardized flow model includes a single-layer fully connected network; S3, constructing and training an uncertainty quantification model based on conditional standardized flow according to the implicit feature vector and the standardized flow model; S4, inputting the implicit eigenvector into the uncertainty quantification model based on conditional normalized flow to obtain the approximate strain distribution of the adapter strain field; S5. Calculate the approximate strain distribution using forward propagation to obtain uncertainty quantification results of the strain field of the adapter, wherein the uncertainty quantification results include the mean and variance of the strain distribution of each point of the adapter; The uncertainty quantification model based on conditional standardized flow includes 4 fully connected neural networks, a reversible transformation matrix module, a standardized flow transformation module and a distribution parameter learning module; The training process of the uncertainty quantization model based on conditional normalization flow specifically includes: Step 1: Set the initial variable z0 to obey the Gaussian distribution N(μ;σ 2 ), where μ represents the mean of the initial variable z0, σ 2 represents the variance of the initial variable z0; Step 2: Use the uncertainty quantification model based on conditional normalized flow to input the load, unit cell design parameters and their coordinates to obtain implicit eigenvectors, and then input the implicit eigenvectors into four fully connected neural networks to obtain the matrix v full , bias vector b, vector v r1 and vector v r2 ; Step 3: Transform the matrix v full , vector v r1 and vector v r2 Input to the reversible transformation matrix module to obtain matrix R and matrix R′; Step 4: Use the bias vector b and the matrix R and matrix R′ to transform the variable z0 K times to obtain the new variable z k , the conditional probability distribution is p(z k ), the conditional probability distribution p(z k ), the bias vector b, and the matrix R and the matrix R′ are input into the distribution parameter learning module, and the mean and variance of the Gaussian distribution are set as trainable parameters. The optimal distribution parameters of the uncertainty quantization model based on conditional normalized flow are obtained according to network learning.

2. The adapter strain field prediction uncertainty quantification method based on conditional normalized flow according to claim 1, characterized in that: The matrix v full Including upper triangular matrices and the lower triangular matrix Step three specifically includes: The vector v r1 As an upper triangular matrix The diagonal of , we get the matrix R; The vector v r2 As a lower triangular matrix The diagonal of , we get the matrix R′.

3. The adapter strain field prediction uncertainty quantification method based on conditional normalized flow according to claim 2, characterized in that: The process of the distribution parameter learning module specifically includes: Use Monte Carlo sampling to calculate the conditional probability distribution p(z k ) expectation of negative entropy; Use adaptive nonparametric kernel density estimation to estimate the conditional probability distribution p(z k )’s probability density function; According to the conditional probability distribution p(z k )The expectation and conditional probability distribution of the negative entropy p(z k ) is used to obtain the approximate strain distribution and conditional probability distribution p(z k ) The approximate strain distribution and conditional probability distribution p(z k ) is minimized to obtain the optimal parameters of the uncertainty quantification model based on conditional normalized flow.

4. The adapter strain field prediction uncertainty quantification method based on conditional normalized flow according to claim 3, characterized in that: The method of estimating the probability density function of the initial Gaussian distribution using the adaptive non-parametric kernel density estimation method specifically includes: For the initial Gaussian distribution conditional probability distribution p(z k ) to perform random sampling and obtain m sample points {z1,…,z i ,…z m }; For the sample points {z1,…,z i ,…z m }Use Scott's theorem to determine the adaptive bandwidth; Determine the conditional probability distribution p(z k ) is the probability density function of .

5. The adapter strain field prediction uncertainty quantification method based on conditional normalized flow according to claim 4, characterized in that: The conditional probability distribution p(z k The calculation formula of the probability density function of ) is as follows: in, represents the estimated value of the probability density function at the sample point z, z represents the point for which the probability density needs to be estimated, m is the number of sample points, z i represents the i-th sample point among m sample points, b2 is the conditional probability distribution p(z k ) is the bandwidth, Ψ is the Gaussian kernel function, represents the sample points {z1,…,z i ,…z m } is an unbiased estimate of the standard deviation, std({z1,…,z i ,…z m }) represents the sample point {z1,…,z i ,…z m } standard deviation.

6. The adapter strain field prediction uncertainty quantification method based on conditional normalized flow according to claim 5, characterized in that: The approximate strain distribution of the uncertainty quantification model is similar to the conditional probability distribution p(z k The calculation formula for minimizing the KL divergence between ) is: Among them, θ * The approximate strain distribution and conditional probability distribution p(z k ), q θ (z k ) represents the approximate strain distribution, p(D|z k ) represents the variable z k The expected value of the log probability in the observed data D, E q p(z k ) represents the prior distribution, s represents the true value of the data, I m represents the m×m identity matrix, diag represents the conversion of a vector into a diagonal matrix, σ′ represents the derivative of the activation function, Q T represents the transpose of the orthogonal matrix Q, z k represents the random variable after K transformations, and z0 represents the input variable of the uncertain quantitative model.

7. The adapter strain field prediction uncertainty quantification method based on conditional normalized flow according to claim 1, characterized in that: Step S5 specifically includes: Randomly sample M sample points from the approximate strain distribution and perform forward propagation to obtain M outputs according to The mean and variance of the strain distribution at each point of the adapter are calculated.

8. The adapter strain field prediction uncertainty quantification method based on conditional normalized flow according to claim 1, characterized in that: In step S2, the determinant of the Jacobian matrix of the probability density distribution of the standardized flow model is simplified using QR decomposition. The determinant of the simplified Jacobian matrix is: Among them, w k Represents the output variable of a single-layer fully connected network, w k-1 Represents the previous output variable of a single-layer fully connected network, I m represents the m×m identity matrix, diag represents the conversion of a vector into a diagonal matrix, σ′ represents the derivative of the activation function, R1′ represents the second upper triangular matrix obtained by QR decomposition, Q T represents the transpose of the orthogonal matrix Q, w represents the input variable of the single-layer neural network, b1 represents the bias term of the single-layer fully connected network, and R1 represents the first upper triangular matrix obtained by QR decomposition.

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