A method for inverse calculation of material parameters in sheet metal stamping

Abstract

The present invention discloses a method for inversely seeking material parameters for sheet metal stamping. The method is based on dimensionality reduction analysis. According to the existing FLD forming image, the information generated by PCA dimensionality reduction is used to construct a feature model with a simplified structure and suitable for analysis, and then a substitution model is established between the design parameters and the feature space to construct the forward response model required by the approximate Bayesian. At the same time, the dimensionality reduction feature can be used as the summary statistic of the approximate Bayesian, so that the posterior interval distribution of the design parameters is obtained by using the approximate Bayesian calculation and the adaptive nested point distribution method, so as to achieve the inverse of the material parameters, thereby more comprehensively reflecting the forming quality of the parts.

Description

Technical Field

[0001] The invention relates to the technical field of digital modeling and simulation analysis thereof, and in particular to a method for realizing inverse calculation of parameters of sheet metal stamping forming materials. Background Art

[0002] In the process of sheet metal stamping, material properties such as Poisson's ratio, stiffness, hardening coefficient and process parameters such as stamping speed and blank holding force directly affect the quality of the stamping results. The traditional method uses the designer's experience as a reference and constantly "trial and error" to obtain relevant parameters that meet the forming quality, resulting in a long development cycle, poor flexibility and high cost. Although the finite element method is widely used in engineering software, the current design model is actually still based on experience-based parameter debugging, and the problem of difficulty in obtaining sheet metal stamping forming parameters has not been fundamentally solved. Therefore, finding a parameter acquisition method that does not require subjective experience and manual parameter adjustment is of great significance to the further improvement of sheet metal stamping forming technology.

[0003] At present, the inverse solution of sheet metal stamping forming parameters has not been considered in the probability space. The traditional point estimation makes the uncertainty problem often ignored in the inverse solution process of actual parameters. This patent aims to propose an uncertainty inverse solution method for metal forming.

[0004] At the same time, considering that the most intuitive quantitative standard of forming quality is the FLD forming diagram, this patent uses the image of the FLD forming diagram to directly perform identification, processing and analysis, making full use of the characteristics of the image that can better reflect the actual forming performance characteristics. This avoids the singularity (multiple solutions) of the inverse result caused by the loss of FLD data in the traditional evaluation criteria, and thus achieves the purpose of making full use of the FLD feature information. Summary of the invention

[0005] The purpose of the present invention is to provide a method for inversely seeking material parameters for sheet metal stamping forming. The method is based on dimensionality reduction analysis, identifies existing FLD forming simulation images, and uses information generated by PCA dimensionality reduction to build a simplified feature model suitable for analysis, and then establishes a substitution model between design parameters and feature space to build a forward response model required by approximate Bayesian. At the same time, the dimensionality reduction feature can be used as a summary statistic of approximate Bayesian, so that the posterior interval distribution of the design parameters is obtained by using the Approximate Bayesian Computation (ABC) and Adopted Nested Sampling (ANS) method, and the inverse of material parameters is achieved, so as to more comprehensively reflect the forming quality of the parts as a whole.

[0006] The purpose of the present invention can be achieved through the following technical solutions:

[0007] A method for inversely seeking parameters of sheet metal stamping materials comprises the following steps:

[0008] Step 1: Obtain the FLD forming limit image model of thin plate stamping and store it in the computer;

[0009] Step 2: Preprocess the image model, first synthesize a mask of the working area, overlap the original image through the mask, remove the non-mask area, and obtain the actual working area of ​​the part;

[0010] Step 3: Construct a substitution model between design parameters and image features, where:

[0011] The surrogate models include the PCA dimensionality reduction method for mapping the high-dimensional features of the FLD graph and the GPR regression method for establishing a surrogate model between the design parameters and the feature space;

[0012] Step 4: Construct the inverse model of FLD forming limit diagram image parameters;

[0013] The method includes: using a substitution model established between design material parameters and image features as a forward statistic, and then using an approximate Bayesian parameter sampling-adaptive nested point placement algorithm to obtain the posterior of material parameters.

[0014] As a further solution of the present invention: the method further comprises step 2 of performing image recognition on the FLD forming limit image model obtained in step 1 to extract image features, and the recognition method comprises the following steps:

[0015] Step 1: Mark the actual working area of ​​the part as an image sub-block, convert the image sub-block into a row vector, and then form the row vector into a matrix I. After all the image sub-blocks are rearranged and transformed, the carrier image S(N,N) is represented by a matrix I with a size of g×;

[0016] Step 2: Perform PCA transformation on matrix I to obtain the principal component matrix Y, thereby realizing the digital transformation of the effective simulation cloud map.

[0017] As a further solution of the present invention: the extraction of image features can be divided into multiple layers;

[0018] The input of the first feature extraction layer is the FLD image extraction matrix, and the output is the extracted first S feature matrix;

[0019] The input of the second feature extraction layer is the first feature matrix, and the output is the extracted second S feature matrix;

[0020] The first feature matrix and the second feature matrix are spliced ​​into a third S feature matrix as the input of the third feature extraction layer as the third feature matrix, and after multi-layer extraction, the output is the final extracted FLD forming limit diagram feature matrix;

[0021] As a further solution of the present invention: both the input and output data are normalized, and the normalization is performed based on maximum and minimum standardization.

[0022] As a further solution of the present invention: the construction of the inverse model in step 4 specifically includes the following steps:

[0023] Step 1: Construct a training sample set {X, Y}, where X = {,,…,}, N1 represents the total number of related parameters, and Y in the sample is the FLD forming limit diagram feature extraction space corresponding to the material parameters and process parameters;

[0024] Step 2: Use the Gaussian process machine learning model to model the stamping process, establish the mapping relationship between the design parameters and the feature space, and obtain the forward response model required by the approximate Bayesian method;

[0025] Step 3: Use the Gaussian process machine learning model as the approximate Bayesian forward simulation model, adopt approximate Bayesian estimation, use the mapping relationship between the design material parameters and the image features as the forward statistic, and use the approximate Bayesian parameter sampling-adaptive nested point placement algorithm. When the target observation statistic is close enough to the statistic of the forward model, the posterior distribution estimate of the relevant material parameters is obtained.

[0026] As a further solution of the present invention, it also includes adopting a feature extraction method combining PCA, SVD and DWT to obtain a right singular matrix.

[0027] As a further solution of the present invention: DWT performs discrete wavelet decomposition on the carrier image before principal component analysis, and uses principal component analysis on the low-frequency sub-band to extract the principal component coefficients containing both low and high frequencies, and utilizes the transformation of the principal component coefficients to improve the robustness to noise addition, image grayscale value changes, etc.

[0028] Beneficial effects of the present invention: The present invention provides an implementation method for inverse material parameter determination for a thin plate stamping image model, a mapping is established between design parameters and image features, an approximate Bayesian method is constructed to obtain a forward response, thereby obtaining sufficient statistics, and finally, under the premise of good forming quality, the posterior distribution of the material parameters is obtained. Compared with traditional engineering analysis methods, the image modeling method adopted in this patent has the advantages of not requiring feature simplification processing, simpler model processing, and better ability to reflect actual forming features. It can help to more objectively obtain relevant material parameters in thin plate stamping forming, and quickly realize the inverse determination of thin plate stamping material parameters without the need for subjective experience and manual parameter adjustment. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The present invention will be further described below in conjunction with the accompanying drawings.

[0030] Figure 1 It is a structural schematic diagram of a flow chart for digital modeling of an FLD forming limit diagram according to the present invention;

[0031] Figure 2 It is a structural schematic diagram of the FLD forming limit diagram dimensionality reduction method of the present invention. DETAILED DESCRIPTION

[0032] The following will be combined with the drawings in 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.

[0033] See also Figure 1-2 As shown, the present invention is a method for inversely determining parameters of sheet metal stamping materials, comprising the following steps:

[0034] Step 1: Obtain the FLD forming limit diagram of the sheet metal stamping to be analyzed and store it in the computer;

[0035] The FLD forming limit diagram obtained in this step can most clearly reflect the sheet metal stamping forming effect. The green color of the part in the working area represents the best forming quality. However, it is difficult to directly establish the relationship between the parameters and the FLD forming limit diagram using traditional methods. For example, the maximum thinning rate and the maximum thickening rate cannot reflect the overall picture of the part. Therefore, the following steps directly use images for parameter analysis;

[0036] Step 2: Preprocess the image model, first synthesize a mask of the working area, overlap the original image through the mask, remove the non-mask area, and obtain the actual working area of ​​the part;

[0037] In this step, the OpenCV library is used to process the image. The preprocessing of the forming limit diagram specifically refers to the separation of the working area and the non-working area, and only the working area is retained for the inverse search of the forming parameters to prevent the non-working area from interfering with the inverse search results.

[0038] In some embodiments, the step of preprocessing the image further includes: normalizing the pixel matrix set of the image, setting the value of the black pixel point to 0 and setting the value of the white pixel point element from the original 255 to 1, thereby forming a normalized pixel matrix set;

[0039] Step 3: Construct a substitution model between the design parameters and the features of the image. The substitution model includes a PCA dimensionality reduction method for mapping the high-dimensional features of the FLD graph and a GPR regression method for establishing a substitution model between the design parameters and the feature space;

[0040] In this step, it is very important to determine the number of principal components, and the number of principal components is recorded as . If m is small, the number of variables is small, and the corresponding low-dimensional data obtained is also easy to calculate, but at the same time, data dimensionality reduction is also likely to cause the target object to lose some useful information.

[0041] This method extracts the cumulative contribution rate ACR (Accumulative Contribution Rate) of the first m principal components to evaluate the reliability of data information. Let the i-th eigenvalue be, then the cumulative contribution rate ACR(m) of the first m principal components is:

[0042]

[0043] The high or low ACR value before extraction by this method reflects the size of this alternative reliability. In the application scenario referred to in this patent, the m value is generally determined according to ACR ≥ 85%, with the purpose of enabling the extracted information to have a higher total utilization rate and achieve an excellent evaluation state. Then, the principal component matrix is ​​obtained based on the determined m value;

[0044] In this step, in order to build a fast response model, that is, given θ, the sufficient statistic Y can be quickly obtained. This step is based on the regression characteristics of GPR and uses this method to build a mathematical model between the parameter θ and the sufficient statistic Y, Y = φ (θ) T w. Gaussian process is based on Bayesian inference to establish a model between parameter θ and sufficient statistic Y = φ(θ) T w The core idea is to determine whether the training data obtained satisfies a probability distribution. Therefore, the conditional probability P(θ|Y) is the focus of the Gaussian process. In the Gaussian process, the covariance matrix not only describes the shape of this distribution, but also determines the similarity between points by finding the value of the kernel function k, thereby ultimately determining the characteristics of the predicted function and obtaining the sufficient statistic Y.

[0045] In this step, in order to evaluate the response effect of the constructed model, that is, given θ, to judge the goodness of fit of the sufficient statistic Y, according to the evaluation index R 2 To judge the accuracy of the model, the calculation formula is as follows, where i is the sample number, y i is the true value, is the predicted value, is the average of the true values. 2 A value close to 1 indicates that the system response calculated based on the dimensionality reduction vector is consistent with the true response, the dimensionality reduction algorithm has little information loss, and the dimensionality reduction vector can represent the true response.

[0046]

[0047] In some implementation schemes, if the dimension of the sample correlation matrix is ​​large, a faster singular value decomposition method SVD may be used to process the large data matrix using a formula to solve the eigenvalues.

[0048] Step 4: Construct an inverse model for FLD forming limit diagram image parameters. The extraction model includes: using a substitution model established between the design material parameters and the image features as a forward statistic, and then using an approximate Bayesian parameter sampling-adaptive nested point placement algorithm to obtain the posterior of the material parameters;

[0049] This step introduces approximate Bayesian theory. Although the general Bayesian method can obtain richer information in obtaining the complete distribution of model parameters, in the Bayesian parameter determination method, it is necessary to define a likelihood function to measure the consistency level between the observed data and the simulated data. However, it is often difficult to determine the likelihood function through numerical calculations or analytical methods. In order to overcome this problem and make the reasoning of complex systems possible, this step introduces the approximate Bayesian algorithm (Approximate Bayesian Computation, ABC). ABC provides the possibility of inferring a given system by using different features to measure the similarity between simulated data and observed data. It uses two consecutive approximations to avoid the problem of solving the likelihood function, and can easily complete the solution of the inverse problem and the quantification of uncertainty parameters.

[0050] First, the low-dimensional sufficient statistics containing image information, namely the principal components after dimensionality reduction, are used to replace the high-dimensional experimental observations, that is,

[0051] p(x|D)≈p(x|S(D))∝p(x)·p(S(D)|x)

[0052] Where S(·) is the summary statistics of the FLD formation diagram, that is, the image features after dimensionality reduction, whose dimension is much smaller than the dimension of the original data. Sufficient statistics are a set of observation statistics, which can fully represent the information contained in the observations. In the above steps, GPR is used to establish a mathematical model between parameters and sufficient statistics Y. However, p(S(D)|x) is still difficult to solve. Therefore, the second step of approximation is introduced:

[0053]

[0054] Where d||·|| is the distance metric, usually the Euclidean distance, ξ≥0 represents the tolerance, when ξ=0, the equation Established.

[0055] In this way, the two-step approximation circumvents the problem of the difficulty in determining the likelihood function in the Bayesian formula and transforms it into the problem of making the statistics of the sample response close to the statistics of the observed value.

[0056] In order to efficiently obtain the posterior distribution of the model parameters, the ANS method is used to calculate the posterior probability in this step. The structure of the algorithm is as follows:

[0057]

[0058] In some embodiments, in order to make the samples obtained by the above sampling method more comprehensive in searching the posterior space of the parameters, an amplification factor is usually applied to the covariance coefficient. Then, based on the forward problem of this sampling, the response of the relevant parameters is obtained. The sufficient statistics of the response are calculated, and the distance between the sufficient statistics and the sufficient statistics of the observed value is calculated. If the Euclidean distance between them is small enough, the sample is accepted, otherwise it is rejected. This cycle is repeated until convergence. In some embodiments, the posterior mean can be substituted into the CAE model, and numerical simulation verification can be performed to observe whether wrinkles or ruptures occur, and the overall effect and the effect diagram of the original sample are observed under the premise of eliminating inherent defects.

[0059] It can be seen that the actual physical parameters and the parameter results extracted by the parameter inversion model of the present invention have good practicality. It can be found that the proposed parameter inversion model has a good inverse proxy modeling ability for the dimensionality reduction inversion of the forming diagram. For parameter design problems with insufficient sample size and high parameter data dimensions, the use of an image-based parameter inversion model can obtain good design results with low information loss, and can reduce the amount of calculation and design time.

[0060] In a specific embodiment: the present application also provides a method for recognizing an image of a FLD forming limit diagram cloud image, which extracts image features to the greatest extent and ensures the accuracy of the objective function. The method comprises the following steps:

[0061] Step 1: Obtain the forming limit image model of the physical object to be analyzed and store it in a computer;

[0062] Step 2: Preprocess the image model to exclude the image features of the non-working area. First, synthesize the mask of the working area, then perform Boolean operation on the original image through the mask, cut the non-mask area, and obtain the actual working area of ​​the part;

[0063] Step 3: Convert the obtained image sub-blocks into row vectors, and then form the row vectors into a matrix I. After all the image sub-blocks are rearranged and transformed, the carrier image S(N,N) is represented by a matrix I of size g × ;

[0064] Step 4: Perform PCA transformation on matrix I to obtain the principal component matrix Y, thereby realizing the digital transformation of the effective simulation cloud map.

[0065] The above is a detailed description of an embodiment of the present invention, but the content is only a preferred embodiment of the present invention and cannot be considered to limit the scope of implementation of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the patent coverage of the present invention.

Claims

1. A method for inversely calculating the parameters of sheet metal stamping materials, characterized in that: The following steps are involved: Step 1: Obtain the FLD forming limit image model of thin plate stamping and store it in the computer; Step 2: Preprocess the image model, first synthesize a mask of the working area, overlap the original image through the mask, remove the non-mask area, and obtain the actual working area of ​​the part; Step 3: Construct a substitution model between design parameters and image features, where: The alternative models include the PCA dimensionality reduction method to map the high-dimensional features of the FLD graph and the GPR regression method to establish an alternative model between the design parameters and the feature space; Step 4: Construct the inverse model of FLD forming limit diagram image parameters; Including: using the substitution model established between the design material parameters and the image features as the forward statistic, and then using the approximate Bayesian parameter sampling-adaptive nested point distribution algorithm to obtain the posterior of the material parameters; The construction of the inverse model in step 4 specifically includes the following steps: Step 1: Construct a training sample set {X, Y}, where X = {, , …,}, N1 represents the total number of related parameters, and Y in the sample is the FLD forming limit diagram feature extraction space corresponding to the material parameters and process parameters; Step 2: Use the Gaussian process machine learning model to model the stamping process, establish the mapping relationship between the design parameters and the feature space, and obtain the forward response model required by the approximate Bayesian method; Step 3: Use the Gaussian process machine learning model as the approximate Bayesian forward simulation model, adopt approximate Bayesian estimation, use the mapping relationship between the design material parameters and the image features as the forward statistic, and use the approximate Bayesian parameter sampling-adaptive nested point placement algorithm. When the target observation statistic is close enough to the statistic of the forward model, the posterior distribution estimate of the relevant material parameters is obtained.

2. A method for inversely determining parameters of sheet metal stamping materials according to claim 1, characterized in that: The method further includes step 2 of performing image recognition on the FLD forming limit image model obtained in step 1 to extract image features. The recognition method includes the following steps: Step 1: Mark the actual working area of ​​the part as an image sub-block, convert the image sub-block into a row vector, and then form the row vector into a matrix I. After all the image sub-blocks are rearranged and transformed, the carrier image S(N,N) is represented by a matrix I with a size of g×; Step 2: Perform PCA transformation on matrix I to obtain the principal component matrix Y, thereby realizing the digital transformation of the effective simulation cloud map.

3. A method for inversely determining parameters of sheet metal stamping materials according to claim 2, characterized in that: The extraction of image features can be divided into multiple layers; The input of the first feature extraction layer is the FLD image extraction matrix, and the output is the extracted first S feature matrix; The input of the second feature extraction layer is the first feature matrix, and the output is the extracted second S feature matrix; The first feature matrix and the second feature matrix are concatenated into a third S feature matrix, which is used as the input of the third feature extraction layer as the third feature matrix. After multiple layers of extraction, the output is the final extracted FLD forming limit diagram feature matrix.

4. A method for inversely determining parameters of sheet metal stamping materials according to claim 3, characterized in that: The input and output data are normalized based on maximum and minimum standardization.

5. The method for inversely determining the parameters of sheet metal stamping materials according to claim 1, characterized in that: It also includes a feature extraction method that uses PCA, SVD, and DWT fusion to find the right singular matrix.

6. The method for inversely determining the parameters of sheet metal stamping materials according to claim 5 is characterized in that: Before principal component analysis, DWT performs discrete wavelet decomposition on the carrier image, and uses principal component analysis on the low-frequency sub-band to extract the principal component coefficients containing both low and high frequencies. The transformation of the principal component coefficients is used to improve the robustness to noise addition and changes in image grayscale values.

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