Metal JC constitutive model parameter optimization method for metal material analysis

Abstract

The invention discloses a metal JC constitutive model parameter optimization method for metal material analysis, which comprises the following steps of: rearranging and combining experimental data from different sources according to different quantities to describe the influence of the experimental quantity on the uncertainty of JC constitutive model parameters, and wrapping all possible JC constitutive model parameters; according to the method, the uncertainty range of model parameters can be completely described, the uncertainty representation of the current JC constitutive model parameters is obtained by calculating the basic inference allocation, namely, the BBA value, of each interval, the complete JC constitutive model parameter uncertainty representation can be obtained by fusing the JC constitutive model parameters of multiple data sources, and a model with the JC constitutive model parameters as input and the BBA value as output is established. According to the method, a JC constitutive model uncertainty transfer method is established by taking the response of the metal structure as an output proxy model, the calculation amount required by parameter updating is reduced, and the updating of the parameters of the JC constitutive model is completed through the real response of the metal structure in an experiment.

Description

Technical Field

[0001] The present invention belongs to the technical field of metal material analysis, and relates to a metal JC constitutive model parameter optimization method and system for metal material analysis. Background Art

[0002] The performance of metal materials under harsh operating conditions (such as ultra-high temperatures, extreme strain rates, and corrosive environments) has become a core bottleneck for technological breakthroughs in aerospace, energy and chemical engineering, marine engineering, and other fields. With the increasing demand for lightweight equipment design and adaptability to extreme environments, metal materials such as titanium alloys, nickel-based superalloys, and high-strength steels are facing unprecedented challenges in multi-physics coupling. These extreme conditions can trigger complex degradation mechanisms such as dynamic recrystallization, adiabatic shear band formation, and stress corrosion cracking, directly threatening structural integrity and service safety.

[0003] Because metal structures are generally complex, it's impossible to conduct multiple structural-level experiments to verify their safety and stability. Therefore, numerical simulation techniques are often used to simulate and verify the structural limits under harsh operating conditions, aiming to define a safe operating range by exploring the upper limit of the structural tolerance. Constitutive models are mathematical models used to describe the mechanical response of materials under external forces. Over the past decade, significant progress has been made in characterizing material behavior under extreme conditions. Classic constitutive models such as the Johnson-Cook (JC) and Zerilli-Armstrong (ZA) models are widely used to describe the thermal response of metals. These models use mathematical relationships (usually equations or expressions) to describe the relationship between stress and strain in a material, and how these relationships change with time, temperature, or other factors. In short, a constitutive model is a mathematical description of a material's behavior and performance. In numerical simulation, a material's constitutive model determines its properties, which in turn directly influences the structural response.

[0004] For most materials, especially metals, their mechanical behavior, such as yield stress, ductility, and strength, will change significantly with different strain rates and temperatures. In order to fully consider the effects of strain rate and temperature on the rheological behavior of materials, researchers have proposed many theoretical models based on experiments, among which the Johnson-Cook model is the most widely used. The JC model was proposed by Johnson and Cook in 1983 as an empirical model for the rheological behavior of metal materials under large deformation, high strain rate, and high temperature conditions:

[0005]

[0006] Where ε ep is the plastic strain, is the dimensionless strain rate, is the reference strain rate, T * is the dimensionless temperature, T is the test temperature, T room is room temperature, T melt is the melting point temperature of the metal material; A, B, C, n, and m are five unknown coefficients that can be obtained by fitting the experimental values. The three terms on the right side of the equation describe the work hardening effect, strain rate effect, and temperature softening effect of the material, respectively. However, more and more studies have shown that these empirical models have inherent defects. These deviations are mainly due to two factors: (1) the model oversimplifies assumptions and ignores microscopic mechanisms such as dislocation cell structure evolution and phase transformation; (2) the uncertainty of constitutive parameters caused by the sparsity of experimental data and the deviation of the fitting algorithm is not fully quantified. These deviations make it difficult for the simulation results to match the experimental results, and cannot reflect the real changes of metal materials under harsh working conditions.

[0007] Existing research on the uncertainty of JC constitutive model parameters has shown that there is currently no definitive conclusion proving that the parameters follow a precise distribution. Therefore, we collected research data from different researchers on the same material and then used evidence theory to integrate the JC constitutive model parameter ranges from multiple sources to characterize the uncertainty of the JC constitutive model parameters. However, current research has mostly focused on characterizing the uncertainty of JC constitutive model parameters, and there is no complete JC constitutive model parameter uncertainty transfer and update optimization process. As a result, the existing JC constitutive model does not always obtain realistic analysis results when simulating and analyzing complex metal structures, and is unable to truly simulate the service performance of metal materials in harsh environments. Summary of the Invention

[0008] The purpose of the present invention is to solve the problem that the existing technology focuses on the uncertainty characterization of JC constitutive model parameters, and there is no complete set of JC constitutive model parameter uncertainty transmission and update optimization processes. As a result, the existing JC constitutive model always obtains true analysis results when simulating and analyzing the complex structure of metal materials, and is unable to truly simulate the service performance of metal materials in harsh environments. A metal JC constitutive model parameter optimization method and system for metal material analysis are provided.

[0009] In order to achieve the above object, the present invention adopts the following technical solutions:

[0010] A method for optimizing parameters of a metal JC constitutive model for metal material analysis comprises the following steps:

[0011] S1: Obtain metal experimental data and metal JC constitutive models from multiple different sources, fit the metal experimental data from multiple different sources into multiple sets of metal JC constitutive model parameters, calculate the BBA value of the metal JC constitutive model corresponding to the metal experimental data from each source, fuse all BBA values, convert the fused BBA values ​​into interval probabilities, and obtain the distribution probability of the metal JC constitutive model parameters based on the interval probabilities;

[0012] S2: Construct a proxy model. According to the distribution probability of the JC constitutive model parameters, extract some metal JC constitutive model parameters as the input of the proxy model. The response of the metal structure is used as the output. The proxy model is iteratively trained to obtain an updated proxy model.

[0013] S3: Extract N samples from the distribution probability of the parameters of the metal JC constitutive model as prior samples, use the prior samples as the input of the updated surrogate model, output the response observation value, screen out the posterior samples that meet the requirements from the response observation value, update and optimize the parameters of the metal JC constitutive model based on the posterior samples, and analyze the metal material based on the updated and optimized metal JC constitutive model.

[0014] A further improvement of the present invention is:

[0015] In S1, a plurality of metal experimental data and metal JC constitutive models from different sources are obtained, and the metal experimental data from the different sources are fitted into a plurality of sets of parameters of the metal JC constitutive model, including:

[0016] Obtain stress-strain curves of metal materials under different experimental conditions, and group the experimental data, with each group including at least two stress-strain curves of metal materials under different experimental conditions;

[0017] The yield strength A, hardening modulus B and material hardening index n of the metal material at the fitting reference temperature;

[0018] Fitting the temperature softening parameter m of the metal material;

[0019] Fitting the strain rate hardening parameter C of metal materials;

[0020] N data of each parameter are obtained through yield strength A, hardening modulus B, material hardening index n, temperature softening parameter m and strain rate hardening parameter C.

[0021] In S1, the BBA value of the metal JC constitutive model corresponding to each source metal experimental data is calculated, including:

[0022] Divide N data into regions, of which Take the integer part;

[0023] Count the data points in each area and calculate the weight of the current interval The weight As the BBA value of the current interval, where N i is the number of data points falling into the i-th interval;

[0024] The interval with the largest weight is selected as the benchmark interval I1. The uncertain BBA construction of the benchmark interval I1 and the adjacent intervals includes:

[0025] The interval with the largest weight is selected as the reference interval I1. If the weight of the adjacent interval m({I2}) is less than 1 / 2 of the weight of the reference interval m({I1}), then the adjacent interval is an inaccurate expression of the reference interval, and the BBA value of the reference interval is:

[0026]

[0027] If m({I2})>0.8*m({I1}), the adjacent interval is merged with the benchmark interval, and the BBA value is:

[0028]

[0029] If 0.5*m({I1})<m({I2})<0.8*m({I1}), then the adjacent interval and the reference interval are in a contradictory relationship, and their BBA remains unchanged;

[0030] The uncertain BBA construction of the reference interval I1 and the next adjacent interval I3 includes:

[0031] When m({I2})<0.5*m({I1}), if m({I3})<0.5*m({I2}), the BBA value is: If m({I3})>0.5*m({I2}), the BBA value is:

[0032] When 0.5*m({I2})<m({I3})<0.8*m({I2}), the next adjacent interval is a separate uncertainty interval and the BBA remains unchanged.

[0033] In S1, all BBA values ​​are integrated, including:

[0034] For the BBA of metal experimental data from different sources, if there are intersecting intervals x, the fusion of the BBA of the intersecting intervals is expressed as: Among them, m i (x i ) is the region x in the i-th source that contains the intersecting interval x i The remaining intervals are contradictory intervals. The BBAs of the contradictory intervals are put into the full set for fusion calculation:

[0035] Convert the fused BBA value into the corresponding interval probability Separate the probability of the entire set and add it to the probability of the corresponding interval to obtain the cumulative distribution function F of the parameter T (t).

[0036] The S2 comprises the following steps:

[0037] S2.1: Construct a Taylor rod collision finite element model. According to the distribution probability of the metal JC constitutive model parameters, extract the input parameter sample pool S(t) from the metal JC constitutive model parameters. Select the sample group T from the sample pool S(t) i (i=1,...,10) as the input of Taylor bar collision finite element model, and the output response value f(T i ), according to the response value f(T i ) Construct the initial training sample set S e ={(T i ,f(T i ))}(i=1,...,10);

[0038] S2.2: Based on the initial training sample set S e ={(T i ,f(T i ))}(i=1,...,10) Construct the initial Kriging proxy model g of the finite element model k (t), calculate the initial Kriging proxy model g of the finite element model k The leave-one-out error E of (t) loo (T i )(i=1,...,N0), obtain the leave-one-error training set S eloo ={(T i ,E loo (T i ))}(i=1,...,N0);

[0039] S2.3: Based on the leave-one-error training set S eloo ={(T i ,E loo (T i ))}(i=1,...,N0)Construct the leave-one-error Kriging surrogate model Calculate the leave-one-out error value corresponding to each sample point in the sample pool S(t), and update the initial Kriging proxy model g according to the leave-one-out error value corresponding to each sample point k (t).

[0040] The initial Kriging surrogate model is updated in S2.3, including:

[0041] According to the leave-one-out error value corresponding to each sample point, it is judged whether the current Kriging proxy model meets the preset accuracy:

[0042] If the root mean square error at the training sample point Then the current Kriging proxy model meets the preset accuracy;

[0043] If the root mean square error at the training sample point The initial Kriging proxy model is iteratively trained until the model accuracy meets the preset requirements.

[0044] The iterative training of the initial Kriging proxy model includes:

[0045] Select the maximum leave-one-out error value corresponding to the sample point in the sample pool S(t) Get the maximum leave-one-out error value The corresponding input sample points The sample point T best In the Taylor rod collision finite element model, the output f(T best );

[0046] {T best ,f(T best )} is added to the initial training sample set, and the new training sample set is S e ={S e ,(T best ,f(T best ))}(i=1,...,N0+1);

[0047] Construct a new Kriging proxy model g of the finite element model based on the current new training sample set k (t) Repeat steps S2.2-S2.3 until the model accuracy meets the preset requirements.

[0048] A metal JC constitutive model parameter optimization system for metal material analysis, comprising:

[0049] The JC constitutive model parameter processing module is used to obtain metal experimental data and metal JC constitutive models from multiple different sources, fit the metal experimental data from multiple different sources into multiple sets of metal JC constitutive model parameters, calculate the BBA value of the metal JC constitutive model corresponding to the metal experimental data from each source, fuse all BBA values, convert the fused BBA values ​​into interval probabilities, and obtain the distribution probability of the metal JC constitutive model parameters based on the interval probabilities;

[0050] The proxy model acquisition module is used to construct a proxy model. According to the distribution probability of the JC constitutive model parameters, some metal JC constitutive model parameters are extracted as the input of the proxy model. The response of the metal structure is used as the output. The proxy model is iteratively trained to obtain an updated proxy model.

[0051] The JC constitutive model update module is used to extract N samples from the distribution probability of the metal JC constitutive model parameters as prior samples, use the prior samples as the input of the updated proxy model, output response observations, screen out posterior samples that meet the requirements from the response observations, update and optimize the parameters of the metal JC constitutive model based on the posterior samples, and analyze the metal material based on the updated and optimized metal JC constitutive model.

[0052] A terminal device comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of any one of the methods of the present invention when executing the computer program.

[0053] A computer-readable storage medium stores a computer program, wherein the computer program implements the steps of any method described in the present invention when executed by a processor.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] The present invention discloses a metal JC constitutive model parameter optimization method for metal material analysis. The method obtains metal experimental data from multiple different sources, rearranges and combines the experimental data according to different quantities to describe the influence of the test quantity on the uncertainty of the JC constitutive model parameters, and can include all possible JC constitutive model parameters, so as to fully describe the uncertainty range of the model parameters. By calculating the basic generalization allocation of each interval, that is, the BBA value, the uncertainty representation of the current JC constitutive model parameters is obtained. The JC constitutive model parameters from multiple data sources are integrated to obtain a complete JC constitutive model parameter uncertainty representation. A proxy model with the JC constitutive model parameters as input and the response of the metal structure as output is established. A JC constitutive model uncertainty transfer method is established, which reduces the amount of calculation required for parameter updating. The JC constitutive model parameters are updated by updating the prior distribution of the JC constitutive model based on the actual response of the metal structure in the experiment. The updated model of the method improves the accuracy of the output response of the structure in the simulated harsh environment, reduces the error between the simulation and the experiment, and solves the problem of output accuracy in simulating complex structures of metal materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0057] Figure 1 Schematic diagram of the Taylor rod experimental results of the present invention. DETAILED DESCRIPTION

[0058] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of 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. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0059] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0060] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0061] In the description of the embodiments of the present invention, it should be noted that if the terms "upper," "lower," "horizontal," "inner," etc. appear, the orientation or positional relationship indicated is based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the inventive product is typically placed when in use. These terms are merely for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or component referred to must have a specific orientation, be constructed, or operate in a specific orientation. Therefore, they should not be construed as limitations on the present invention. In addition, the terms "first," "second," etc. are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0062] In addition, if the term "horizontal" appears, it does not mean that the component must be absolutely horizontal, but can be slightly tilted. For example, "horizontal" only means that its direction is more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0063] In the description of the embodiments of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "disposed," "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0064] The present invention is described in further detail below with reference to the accompanying drawings:

[0065] See also Figure 1 In order to improve the accuracy of the JC constitutive model parameter prediction response and enhance its reliability and safety in practical applications, the present invention provides a new JC constitutive model parameter uncertainty transfer and update optimization process. Main content of the invention: Evidence theory is used to describe the uncertainty of the JC constitutive model. By establishing a real Taylor collision Kriging proxy model; based on this proxy model, the Bayesian update method is further applied to the JC model parameter update, and a method for efficiently optimizing the JC constitutive model parameters is proposed: Based on the evidence theory to characterize the parameter uncertainty, the Kriging proxy model is combined with the Bayesian update to optimize the JC constitutive model parameters.

[0066] Step 1: Characterization of uncertainty in JC constitutive parameters based on evidence theory

[0067] Theory of Evidence is a theory of imprecise reasoning that can flexibly and effectively model uncertainty without prior probabilities. Its basic principles include the framework of discernment, basic brief assignment (BBA), mass function, belief function, plausibility function, and evidence fusion rules.

[0068] Let Ω={x1,x2,...,x N} is the identification frame, x i Represents an event. Evidence theory represents the possible combinations of events as power sets2 Ω :

[0069]

[0070] Where Ω represents the empty set, and each element or event in the power set is called a focal element (FE), denoted by x. The probability of each focal element occurring is represented by the basic belief allocation (BBA) m(x), and must satisfy the following conditions:

[0071]

[0072] When information or data comes from multiple sources of evidence, different BBA structures may be encountered, resulting in different evaluations of the same identification framework. However, uncertainty can only be represented by a single BBA structure. To address this challenge, several methods have been proposed to combine evidence from all information sources.

[0073] Yager's criterion is a rule developed to resolve conflicts between different sources of evidence. Yager introduced the following expression for the basic probability mass distribution of two BBAs: m1 and m2:

[0074]

[0075] Where x is the intersection of subsets y and z, and q(x) represents the basic probability assignment of subset x. It can be seen in the formula that no normalization factor is considered. The combined structure q(x) can be used to aggregate multiple pieces of evidence. If m1,m2,...,m n is the basic probability distribution of n belief structures, and x i Indicates that th Belief structures (m i ) associated with the focal element, then n basic probability distribution structures m i (x i ) are combined into:

[0076]

[0077] When the Yager criterion is used for fusion, the conflicting parts of each evidence source will be retained, and the BBA of the conflicting parts will be assigned to the entire set to maximize the retention of evidence from each source.

[0078] The JC constitutive model is a phenomenological model, so the parameters in the constitutive equation cannot be directly calibrated based on physical properties. Instead, the parameters in the JC constitutive model must be fitted using characteristic points from multiple sets of stress-strain curves under different experimental conditions. However, due to factors such as steel production, experimental errors, and measurement errors, the model parameters calculated by each researcher may vary. Therefore, it is necessary to collect as many constitutive model parameters for the same material as possible to obtain an accurate prior probability model.

[0079] In the research on mechanical properties of materials conducted in China, it is generally based on a deterministic research framework, so in the end, the least squares method will be used to combine all available data to fit a set of parameters with the smallest relative error. The amount of data will affect the research on uncertainty. The more available data, the more reliable the results. In order to fully consider the uncertainty caused by the number of experiments, multiple groups of experiments conducted by the same researcher are grouped and combined, and a set of JC constitutive parameters are fitted for each group of experimental results. In this way, the values ​​of JC constitutive model parameters under different experimental conditions and different numbers of experiments can be obtained, and the uncertainty of the constitutive parameters can be fully characterized. After obtaining the JC constitutive parameter values ​​under different experimental sources, all JC constitutive model parameters are integrated through the evidence theory method to obtain the BBA of each parameter. Then, through the Pignistic transformation criterion of BBA and probability:

[0080]

[0081] Among them, Bet is the probability after conversion. After obtaining the probability of the parameter in each interval, the distribution and distribution range of the JC constitutive model parameters of this material can be obtained, which fully characterizes the uncertainty of the parameter.

[0082] Step 2: Build the Taylor Rod Collision Proxy Model

[0083] For optimization design problems, rapid input and output responses are required to quickly find the optimal point. However, repeatedly calling the finite element model will make the calculation cost extremely high. Therefore, it is necessary to first establish a proxy model of the Taylor collision process, determine the input and output relationship, and speed up the calculation.

[0084] The Taylor rod experimental system mainly consists of a projectile launcher, a long cylindrical projectile and a rigid target that can be regarded as a plane. By comparing the upset diameter and axial elongation of the recovered projectile with the upset diameter and axial elongation calculated by the simulation results, as shown in the attached figure. Figure 1 As shown, the accuracy of the constitutive parameters used can be determined and the constitutive parameters can be optimized according to the theoretical formula. Therefore, this study uses the Taylor bar collision experiment as the research object, uses the JC constitutive model parameters as the output, and uses the upset diameter of the Taylor bar after the collision as the response quantity to construct a Kriging proxy model.

[0085] The Kriging model approximates a single objective function value as:

[0086] y(x)=μ(x)+ε(x),ε(x)~N(0,σ 2 )

[0087] Where μ is the prediction of the regression model F(β,x), that is, μ = Fβ; ε(x) is a Gaussian distribution with zero mean and standard deviation σ. The regression model F(β,x) = β1g1(x) + ... + β l g l (x) is a linear combination of l selected functions and coefficients β.

[0088] In order to reduce the expensive evaluation cost and obtain the approximate value of the objective function from the formula, it is necessary to use training samples to train the Kriging model. Let the matrix Represents the training data in the decision space, and its corresponding target vector where i=1,2,...,N t Indicates the size of the sample number. Also note that the size of X is N I ×n, where n is the number of decision variables, i.e. i = 1, 2, ..., N I , there are x i =[x1,...,x n ]. However, applying all samples to train the Kriging model will reduce the efficiency of the Kriging model, so an adaptive strategy is needed to deal with the low efficiency of the original Kriging model. The ELOO autonomous learning function based on leave-one-out cross-validation can effectively select the training samples that contribute most to fitting the original model. The basic principle of leave-one-out cross-validation is: take the training sample set T = [(x1, y1),…, (x m ,y m )] in m-1 samples T ～i =(x ～i ,y ～i )(i is a positive integer in the interval [1,m]) is used as the training set to construct the kriging proxy model The samples not included in the training set (x i ,y i ) as the validation set. Use the constructed kriging model y k (x) gets x i The deviation between the predicted value and the true value is used as a proxy model for the constructed The score, this deviation is also called the leave-one-out error E LOO :

[0089]

[0090] The comprehensive leave-one-out error of each sample can be used to determine whether the accuracy of the current kriging model needs to be expanded to fit the training sample size. However, this process needs to be repeated m times to obtain the leave-one-out error for each sample. When the sample base becomes large, the calculation will become difficult. After obtaining the leave-one-out error of each training sample, the leave-one-out error training set T is formed.c =[(x1,E LOO (x1)),…,(x m ,E LOO (x m ))] T , taking the error of the training sample as the output, we can construct the training sample set T c The kriging model is used to derive the remaining samples x in the candidate sample pool n-m The leave-one-out error is calculated and the point with the largest prediction value is selected. This point indicates that the current kriging model may have a larger prediction deviation at this point. The sample with the largest leave-one-out error value in the candidate sample pool is added as the optimal point to the training sample set to update the current kriging model until the root mean square error of the kriging proxy model at the training sample is less than the set value.

[0091] Bayesian updating method to update JC constitutive parameters

[0092] Define the function of a structure as Y=g(x), where X=(X1, X2,…, X n ) are n-dimensional, mutually independent input variables. In the present invention, the input variables are the uncertain JC constitutive model parameters, and the output is the Taylor impact end upset diameter. The input variables are mutually independent variables, and the uncertainty of the input variables can be described by the joint probability density function:

[0093]

[0094] Where, is the input variable X i When we have the observed values ​​of the response, these observations are recorded as s=(s1,s2,...,s m ), we can use these data to update the parameters, and the updated parameter probability density function is recorded as: f X|s (x|s) is called the posterior distribution.

[0095] The update principle is:

[0096]

[0097] Where L(x) is the likelihood function, which measures the error between the simulated output response and the true observation using the Euclidean distance. The likelihood function for the i-th observation is usually written as:

[0098]

[0099] Where, The mean is 0 and the standard deviation is The probability density function of the normal distribution.

[0100] If the observation errors are independent and additive, the likelihood function is expressed as:

[0101]

[0102] The BUS method expands the input space variable X to [X, P] by introducing an auxiliary variable P that follows a uniform distribution on the interval [0, 1]. The integration operation is avoided by using a simple rejection sampling method. The domain of the augmented space is Ω = {(x, p) | p ≤ c·L(x)}, where Ω is also called the observation domain. c is a constant that satisfies 0 ≤ c·L(x) ≤ 1, so the above formula can be transformed into:

[0103]

[0104] Here, the denominator corresponds to a reliability problem with the performance function h(x,p) = pc·L(x). In this problem, the observation domain actually describes a failure domain: when [x,p]∈Ω, the structure is considered to be in failure mode. I(·) is an indicator function: when [x,p]∈Ω, I(·) = 1; otherwise, I(·) = 0. This transformation allows the MCS digital simulation method used in structural reliability analysis to easily solve the posterior probability density function of the input variables.

[0105] The present invention discloses an embodiment, comprising the following steps:

[0106] Step 1: Obtain the stress-strain curves of metal materials under different experimental conditions through experiments, and group the experiments under different conditions into groups (at least two groups). If there are n groups of experiments, there will be a total of The number of groups, and then perform the following steps of parameter fitting for each group of data:

[0107] Step 1.1: Fitting the yield strength A, hardening modulus B, and material hardening exponent n at the reference temperature

[0108] Select room temperature and reference strain rate (T = T room , ), the strain rate and temperature terms of the constitutive model will degenerate to a constant 1, and the model degenerates to: ep =A+B(ε ep ) n , A is the initial yield stress under the above experimental conditions, and then a simple logarithm of the experimental data can be obtained:

[0109] ln(σ ep -A)=nlnε ep +lnB

[0110] The slope and intercept values ​​obtained through linear fitting can be used to determine the corresponding parameters n and B. Due to experimental limitations and the limited number of room-temperature quasi-static tests, fitting these two parameters generally requires different combinations of points on the curve. This allows the first part of the parameters, A, B, and n, to be determined.

[0111] Step 1.2: Fitting the temperature softening parameter m

[0112] The fitting of temperature softening parameter m is similar to strain rate hardening parameter. Several groups of experiments at different temperatures are carried out at the reference strain rate, and the stress at yield ( ε ep =0) for analysis. Based on the fitting results of the first two steps, the model degenerates into a simple exponential model:

[0113] σ ep =A(1-T *m )

[0114] Similarly, by taking the logarithm of both sides and performing linear fitting, the slope value is the thermal softening index m.

[0115] Step 1.3: Fitting the strain rate hardening parameter C

[0116] The unit was tested at different strain rates at room temperature, and the stress value at yield was fitted (T = T room , ε ep =0). At room temperature, the third temperature term of the model is still 1. Under the same strain, the strain hardening term of the first term of the model also degenerates to a constant value. The size of this constant value can be calculated based on the fitting results of the previous step. At this time, the model degenerates into a simple linear equation:

[0117]

[0118] The strain rate constant C can be obtained by linear fitting of the experimental data.

[0119] Through the above fitting steps, N data for each parameter can be obtained using the least squares fitting method (the number of B,n will be different).

[0120] Step 2: Use the obtained N data points to perform histogram analysis and divide the N data into (Take the integer part) regions, count the data points that fall into each interval and calculate the weight As the BBA of this interval, N i is the number of data points falling into the i-th interval.

[0121] Step 3: Select the interval with the largest weight as the benchmark interval and construct the BBA of the uncertain interval, including:

[0122] If the weight of the adjacent interval m({I2}) is less than 1 / 2 of the weight of the reference interval m({I1}), the adjacent interval should be interpreted as an imprecise representation of the reference interval and the corresponding BBA should be calculated as:

[0123]

[0124] If m({I2})>0.8*m({I1}), the adjacent interval is merged with the reference interval to form an interval with greater uncertainty, which is accepted by the reference interval. Its BBA is calculated as:

[0125]

[0126] If 0.5*m({I1})<m({I2})<0.8*m({I1}), the adjacent interval and the reference interval are in a contradictory relationship, and the BBA of the two should remain unchanged.

[0127] The uncertainty of the BBA of the reference interval and the BBA of the left and right adjacent intervals are constructed using this method.

[0128] Step 4: Consider the uncertain BBA construction of the benchmark interval I1 and the next adjacent interval I3. There are:

[0129] When m({I2})<0.5*m({I1}):

[0130] If m({I3}) < 0.5*m({I2}), the relationship between I2 and I3 is not considered, and BBA should be calculated as:

[0131] If m({I3})>0.5*m({I2}), then

[0132] When 0.5*m({I2})<m({I3})<0.8*m({I2}), the next adjacent interval is a separate uncertainty interval and BBA remains unchanged.

[0133] When 0.5*m({I1})<m({I2})<0.8*m({I1}), I2 is a separate uncertainty interval, and only the relationship with I3 needs to be considered according to step 3.

[0134] Through the above classification, the relationship between all intervals and the benchmark interval is established and the BBA is constructed for the corresponding interval. The BBA value described in this embodiment is interpreted as the basic belief distribution.

[0135] Step 5: Use steps 1-5 to construct the BBA for each data source.

[0136] For a parameter, different sources will have different BBAs. If there are intersecting intervals x, the BBA of the intersecting intervals follows Among them, m i (x i ) is the region x in the i-th source that contains the intersecting interval x i The remaining intervals are contradictory, so their BBAs are put into the full set for calculation.

[0137] Step 6: According to the BBA to probability conversion formula, convert the fused BBA into the probability of the corresponding interval It is important to separate the probability of the entire set and add it to the probability of the corresponding interval, and finally obtain the cumulative distribution function F of the parameter T (t).

[0138] Step 7: Establish the Taylor rod collision finite element model, and calculate the cumulative distribution function of the constitutive model parameters F T (t) Extract the input parameter sample pool S and randomly select N0 samples T of input parameter T from the sample pool S. i (i=1,...,N0), bring this group of samples into the function function of the real result model to calculate the corresponding response value f(T i ), and then construct the initial training sample set S e ={(T i ,f(T i ))}(i=1,...,N0).

[0139] Step 8: Construct a Kriging proxy model of the finite element model, including:

[0140] According to the current initial training sample set S e ={(T i ,f(T i ))}(i=1,...,N0), use the DACE toolbox to establish the initial Kriging proxy model g of the JC constitutive model parameters and the Taylor collision model k (t).

[0141] Step 9: Calculate the leave-one-out error E of the current Kriging surrogate model loo (T i )(i=1,...,N0), forming a leave-one-error training set S eloo ={(T i ,E loo (T i ))}(i=1,...,N0). According to the current leave-one-error training set S eloo ={(T i ,Eloo (T i ))}(i=1,...,N0)Construct the leave-one-error Kriging surrogate model

[0142] Step 10: Determine whether the Kriging proxy model error of the finite element model meets the accuracy. If the root mean square error at the training sample point is It is considered that the current Kriging model accuracy meets the requirements and the adaptive learning process ends. Iterate the Kriging model according to the following steps.

[0143] Step 11: Predict the leave-one-out error value corresponding to each sample point in the sample pool S Find the input variable corresponding to the maximum value Indicates the Kriging model g of the current finite element model k (t) in T best The error at the sample point is the largest. best Substitute into the finite element model to obtain the output f(T best ).

[0144] Step 12: best ,f(T best )}Add to training sample set S e ={(T i ,f(T i ))}(i=1,...,N0), that is, the new training sample set is S e ={S e ,(T best ,f(T best ))}(i=1,...,N0+1), according to the current S e Construct a new Kriging proxy model g for the finite element model k (t), return to step 9 and step 10 until the model accuracy meets the requirements.

[0145] Establish Kriging model Y = g k (t) After that, the model is used to update the parameters instead of the performance function in the Bayesian update.

[0146] Step 13: Extract N from the cumulative distribution function of the JC constitutive model parameters obtained in step 6 t samples as prior samples, and bring the prior samples into Y=g k (t) Calculate the output response of the Taylor collision.

[0147] Step 14: Construct a likelihood function based on experimental results in the literature Set the standard deviation to 5% of the observed value and set N t The output is brought into the likelihood function to calculate the likelihood value of the prior sample

[0148] Step 15: Introduce N that obeys uniform distribution on [0,1] t Auxiliary variables Construct auxiliary function h(t,p)=pc*L(t), where c=max L, and N t The likelihood value of the prior sample and the auxiliary variable P are brought into the auxiliary function to calculate the failure situation When h(T i ,p i )>0, it is considered that g k (T i ) is close enough to the true value, T i is the posterior sample. By summarizing the mean and variance of all posterior samples, we can get the posterior mean and variance and complete the update.

[0149] The method disclosed in this paper uses evidence theory to characterize the uncertainty of JC constitutive model parameters. Experimental data are rearranged and combined according to the number of tests to describe the effect of the number of tests on the uncertainty of JC constitutive model parameters. This method can include all possible JC constitutive model parameters and fully describe the uncertainty range of the model parameters.

[0150] Furthermore, by using evidence theory to calculate the basic generalization distribution of each interval, we can obtain the uncertainty representation of the current JC constitutive model.

[0151] Furthermore, the JC constitutive model parameters from multiple data sources can be fused using fusion theory to obtain a complete uncertainty representation of the JC constitutive model parameters.

[0152] The present invention uses Taylor collision as a verification model to verify the correctness of the JC constitutive model parameters, and uses the upset diameter of the impact end after the Taylor collision as the output to correct the JC constitutive model parameters. A Kriging proxy model is constructed with the JC constitutive model parameters as input and the upset length of the impact end after the Taylor collision as the output, which greatly reduces the amount of calculation required for parameter updating. Subsequently, the Bayesian update method is used to update the prior distribution of the JC constitutive model using the upset diameter in the experiment as the observation value, and the prediction of the output before and after the update is compared. It can be found that the updated JC constitutive model parameters have higher prediction accuracy for the output, thereby establishing a complete JC constitutive model parameter uncertainty transfer and update optimization process.

[0153] This embodiment discloses a metal JC constitutive model parameter optimization system for metal material analysis, comprising:

[0154] The JC constitutive model parameter processing module is used to obtain metal experimental data and metal JC constitutive models from multiple different sources, fit the metal experimental data from multiple different sources into multiple sets of metal JC constitutive model parameters, calculate the BBA value of the metal JC constitutive model corresponding to the metal experimental data from each source, fuse all BBA values, convert the fused BBA values ​​into interval probabilities, and obtain the distribution probability of the metal JC constitutive model parameters based on the interval probabilities;

[0155] The proxy model acquisition module is used to construct a proxy model. According to the distribution probability of the JC constitutive model parameters, some metal JC constitutive model parameters are extracted as the input of the proxy model. The response of the metal structure is used as the output. The proxy model is iteratively trained to obtain an updated proxy model.

[0156] The JC constitutive model update module is used to extract N samples from the distribution probability of the metal JC constitutive model parameters as prior samples, use the prior samples as the input of the updated proxy model, output response observations, screen out posterior samples that meet the requirements from the response observations, update and optimize the parameters of the metal JC constitutive model based on the posterior samples, and analyze the metal material based on the updated and optimized metal JC constitutive model.

[0157] A JC constitutive model parameter update process has been established. JC constitutive model parameters are typically fitted through mechanical experiments (such as uniaxial tension and uniaxial compression), but deviations often occur when simulating the output response of structures under harsh environments. This patent, using the Taylor model as a reference, verifies that this method can update and optimize JC constitutive model parameters based on experimental results, reducing the error between simulation and experiment, and solving the problem of output accuracy in simulating complex metal structures.

[0158] A schematic diagram of a terminal device provided in one embodiment of the present invention. The terminal device in this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of each of the aforementioned method embodiments are implemented. Alternatively, when the processor executes the computer program, the functions of each module / unit in each of the aforementioned device embodiments are implemented.

[0159] The computer program may be divided into one or more modules / units, which are stored in the memory and executed by the processor to accomplish the present invention.

[0160] The terminal device may be a computing device such as a desktop computer, a notebook computer, a PDA, a cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0161] The processor can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0162] The memory may be used to store the computer programs and / or modules, and the processor implements various functions of the terminal device by running or executing the computer programs and / or modules stored in the memory and calling the data stored in the memory.

[0163] If the module / unit integrated in the terminal device is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the process in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, it can implement the steps of each of the above-mentioned method embodiments. The computer program includes computer program code, which can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal and software distribution medium. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electric carrier signals and telecommunication signals.

[0164] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for optimizing parameters of a metal JC constitutive model for metal material analysis, characterized in that: The following steps are involved: S1: Obtain metal experimental data and metal JC constitutive models from multiple different sources, fit the metal experimental data from multiple different sources into multiple sets of metal JC constitutive model parameters, calculate the BBA value of the metal JC constitutive model corresponding to the metal experimental data from each source, fuse all BBA values, convert the fused BBA values ​​into interval probabilities, and obtain the distribution probability of the metal JC constitutive model parameters based on the interval probabilities; S2: Construct a proxy model. According to the distribution probability of the JC constitutive model parameters, extract some metal JC constitutive model parameters as the input of the proxy model. The response of the metal structure is used as the output. The proxy model is iteratively trained to obtain an updated proxy model. S3: Extract N samples from the distribution probability of the parameters of the metal JC constitutive model as prior samples, use the prior samples as the input of the updated surrogate model, output the response observation value, screen out the posterior samples that meet the requirements from the response observation value, update and optimize the parameters of the metal JC constitutive model based on the posterior samples, and analyze the metal material based on the updated and optimized metal JC constitutive model.

2. The method for optimizing parameters of a metal JC constitutive model for metal material analysis according to claim 1, characterized in that: In S1, a plurality of metal experimental data and metal JC constitutive models from different sources are obtained, and the metal experimental data from the different sources are fitted into a plurality of sets of parameters of the metal JC constitutive model, including: Obtain stress-strain curves of metal materials under different experimental conditions, and group the experimental data, with each group including at least two stress-strain curves of metal materials under different experimental conditions; The yield strength A, hardening modulus B and material hardening index n of the metal material at the fitting reference temperature; Fitting the temperature softening parameter m of the metal material; Fitting the strain rate hardening parameter C of metal materials; N data of each parameter are obtained through yield strength A, hardening modulus B, material hardening index n, temperature softening parameter m and strain rate hardening parameter C.

3. The method for optimizing parameters of a metal JC constitutive model for metal material analysis according to claim 2, characterized in that: In S1, the BBA value of the metal JC constitutive model corresponding to each source metal experimental data is calculated, including: Divide N data into regions, of which Take the integer part; Count the data points in each area and calculate the weight of the current interval The weight As the BBA value of the current interval, where N i is the number of data points falling into the i-th interval; The interval with the largest weight is selected as the benchmark interval I1. The uncertain BBA construction of the benchmark interval I1 and the adjacent intervals includes: The interval with the largest weight is selected as the reference interval I1. If the weight of the adjacent interval m({I2}) is less than 1 / 2 of the weight of the reference interval m({I1}), then the adjacent interval is an inaccurate expression of the reference interval, and the BBA value of the reference interval is: If m({I2})>0.8*m({I1}), the adjacent interval is merged with the benchmark interval, and the BBA value is: If 0.5*m({I1})<m({I2})<0.8*m({I1}), then the adjacent interval and the reference interval are in a contradictory relationship, and their BBA remains unchanged; The uncertain BBA construction of the reference interval I1 and the next adjacent interval I3 includes: When m({I2})<0.5*m({I1}), if m({I3})<0.5*m({I2}), the BBA value is: If m({I3})>0.5*m({I2}), the BBA value is: When 0.5*m({I2})<m({I3})<0.8*m({I2}), the next adjacent interval is a separate uncertainty interval and the BBA remains unchanged.

4. The method for optimizing parameters of a metal JC constitutive model for metal material analysis according to claim 3, characterized in that: In S1, all BBA values ​​are integrated, including: For the BBA of metal experimental data from different sources, if there are intersecting intervals x, the fusion of the BBA of the intersecting intervals is expressed as: Among them, m i (x i ) is the region x in the i-th source that contains the intersecting interval x i The remaining intervals are contradictory intervals. The BBAs of the contradictory intervals are put into the full set for fusion calculation: Convert the fused BBA value into the corresponding interval probability Separate the probability of the entire set and add it to the probability of the corresponding interval to obtain the cumulative distribution function F of the parameter T (t).

5. The method for optimizing parameters of a metal JC constitutive model for metal material analysis according to claim 1, characterized in that: The S2 comprises the following steps: S2.1: Construct a Taylor rod collision finite element model. According to the distribution probability of the metal JC constitutive model parameters, extract the input parameter sample pool S(t) from the metal JC constitutive model parameters. Select the sample group T from the sample pool S(t) i (i=1,...,10) as the input of Taylor bar collision finite element model, and the output response value f(T i ), according to the response value f(T i ) Construct the initial training sample set S e ={(T i ,f(T i ))}(i=1,...,10); S2.2: Based on the initial training sample set S e ={(T i ,f(T i ))}(i=1,...,10) Construct the initial Kriging proxy model g of the finite element model k (t), calculate the initial Kriging proxy model g of the finite element model k The leave-one-out error E of (t) loo (T i )(i=1,...,N0), obtain the leave-one-error training set S eloo ={(T i ,E loo (T i ))}(i=1,...,N0); S2.3: Based on the leave-one-error training set S eloo ={(T i ,E loo (T i ))}(i=1,...,N0)Construct the leave-one-error Kriging surrogate model Calculate the leave-one-out error value corresponding to each sample point in the sample pool S(t), and update the initial Kriging proxy model g according to the leave-one-out error value corresponding to each sample point k (t).

6. The method for optimizing parameters of a metal JC constitutive model for metal material analysis according to claim 5, characterized in that: The initial Kriging surrogate model is updated in S2.3, including: According to the leave-one-out error value corresponding to each sample point, it is judged whether the current Kriging proxy model meets the preset accuracy: If the root mean square error at the training sample point Then the current Kriging proxy model meets the preset accuracy; If the root mean square error at the training sample point The initial Kriging proxy model is iteratively trained until the model accuracy meets the preset requirements.

7. The method for optimizing parameters of a metal JC constitutive model for metal material analysis according to claim 6, characterized in that: The iterative training of the initial Kriging proxy model includes: Select the maximum leave-one-out error value corresponding to the sample point in the sample pool S(t) Get the maximum leave-one-out error value The corresponding input sample points The sample point T best In the Taylor rod collision finite element model, the output f(T best ); {T best ,f(T best )} is added to the initial training sample set, and the new training sample set is S e ={S e ,(T best ,f(T best ))}(i=1,...,N0+1); Construct a new Kriging proxy model g of the finite element model based on the current new training sample set k (t) Repeat steps S2.2-S2.3 until the model accuracy meets the preset requirements.

8. A metal JC constitutive model parameter optimization system for metal material analysis, characterized in that: include: The JC constitutive model parameter processing module is used to obtain metal experimental data and metal JC constitutive models from multiple different sources, fit the metal experimental data from multiple different sources into multiple sets of metal JC constitutive model parameters, calculate the BBA value of the metal JC constitutive model corresponding to the metal experimental data from each source, fuse all BBA values, convert the fused BBA values ​​into interval probabilities, and obtain the distribution probability of the metal JC constitutive model parameters based on the interval probabilities; The proxy model acquisition module is used to construct a proxy model. According to the distribution probability of the JC constitutive model parameters, some metal JC constitutive model parameters are extracted as the input of the proxy model. The response of the metal structure is used as the output. The proxy model is iteratively trained to obtain an updated proxy model. The JC constitutive model update module is used to extract N samples from the distribution probability of the metal JC constitutive model parameters as prior samples, use the prior samples as the input of the updated proxy model, output response observations, screen out posterior samples that meet the requirements from the response observations, update and optimize the parameters of the metal JC constitutive model based on the posterior samples, and analyze the metal material based on the updated and optimized metal JC constitutive model.

9. A terminal device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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