Method for Determining Visco-Plastic Constitutive Parameters of Solder Joint Materials Based on Bayesian Optimization

Abstract

The present invention relates to the technical field of electronic packaging reliability and solder joint material modeling, and specifically discloses a method for determining the viscoplastic constitutive parameters of solder joint materials based on Bayesian optimization, including: constructing an experimental sampling set and a simulation sampling set of the target solder joint material under multiple combinations of loading conditions; determining the form of the material viscoplastic constitutive model to be identified, and then constructing an optimization space for the viscoplastic constitutive parameter vector; constructing an objective function for the viscoplastic constitutive parameters based on the experimental sampling set and the simulation sampling set; using the Bayesian optimization method to iteratively optimize the objective function to obtain the optimal viscoplastic constitutive parameters of the solder joint material. The present invention solves the problem that the existing methods cannot efficiently search the parameter space and accurately identify the viscoplastic constitutive model parameters of the solder joint material under the premise of limited simulation times, and is applicable to accurately identifying the high-dimensional parameters of the viscoplastic constitutive model of the solder joint material through finite element simulation.

Description

Technical Field

[0001] The present invention belongs to the technical field of electronic packaging reliability and solder joint material modeling, and particularly relates to a method for determining the viscoplastic constitutive parameters of solder joint materials based on Bayesian optimization. Background Art

[0002] Solder joint materials (such as lead-free solders like SAC305 and SAC405, and leaded solders like SnPb63 / 37) are widely used in microelectronic packaging structures and are key materials for achieving electrical connection and mechanical support between chips and circuit boards. Such materials will experience complex thermo-mechanical loading environments during service, such as temperature cycling, power loading, vibration shock, etc. Therefore, their viscoplastic behavior and creep characteristics have a crucial impact on the reliability of the packaging structure.

[0003] In order to accurately simulate the service response of solder joint materials in finite element simulations, a viscoplastic constitutive model that conforms to the true deformation mechanism of the material needs to be established, and multiple parameters thereof (such as initial yield strength, hardening modulus, viscosity coefficient, creep index, etc.) need to be accurately identified. Since these parameters cannot be directly obtained through experimental measurement, inversion methods are usually relied on to inversely deduce the parameters by fitting with the experimental stress-strain data according to the finite element simulation results.

[0004] However, currently widely used parameter identification methods, such as gradient descent method, genetic algorithm, particle swarm algorithm, etc., have problems such as slow convergence speed, high calculation cost, and serious local optimum. Especially in the case where the model parameter dimension is relatively high (such as 8 dimensions) and multiple working condition curves (such as 12 combined working conditions under different strain rates and temperatures) are involved in comparison, these methods often have difficulty effectively completing the parameter identification task.

[0005] At the same time, each parameter evaluation in the inversion process requires calling a finite element software (such as Abaqus) for simulation, and extracting stress-strain data from the simulation file, which makes the calculation cost of the objective function extremely high and difficult to support large-scale searches.

[0006] Therefore, there is an urgent need for a method for determining the viscoplastic constitutive parameters of solder joint materials that can efficiently search the parameter space and accurately identify the parameters of the viscoplastic constitutive model of solder joint materials on the premise of a limited number of simulations. Summary of the Invention

[0007] The purpose of the present invention is to solve the problem that the existing methods cannot efficiently search the parameter space and accurately identify the parameters of the viscoplastic constitutive model of solder joint materials on the premise of a limited number of simulations, and a method for determining the viscoplastic constitutive parameters of solder joint materials based on Bayesian optimization is proposed, which is applicable to accurately identifying the high-dimensional parameters of the viscoplastic constitutive model of solder joint materials through finite element simulations.

[0008] The technical solution of the present invention is as follows: A method for determining the viscoplastic constitutive parameters of solder joint materials based on Bayesian optimization, comprising the following steps:

[0009] Obtain the stress-strain curve experimental data of the target solder joint material under multiple combinations of loading conditions, and then obtain the experimental sampling set;

[0010] Determine the form of the viscoplastic constitutive model of the material to be identified, and then construct the optimization space of the viscoplastic constitutive parameter vector;

[0011] Based on the optimization space of the viscoplastic constitutive parameters, construct the simulation sampling set of the target solder joint material under multiple combinations of loading conditions;

[0012] Based on the experimental sampling set and the simulation sampling set, construct the objective function of the viscoplastic constitutive parameters;

[0013] Use the Bayesian optimization method to iteratively optimize the objective function to obtain the optimal viscoplastic constitutive parameters of the solder joint material.

[0014] Preferably, the step of obtaining the stress-strain curve experimental data of the target solder joint material under multiple combinations of loading conditions, and then obtaining the experimental sampling set is specifically:

[0015] Determine the stress-strain curve experimental data of the target solder joint material under multiple combinations of loading conditions;

[0016] Select characteristic sampling points for each stress-strain curve experimental data to obtain a characteristic sampling point containing experimental data, and then construct the experimental sampling set.

[0017] Preferably, the expression formula of the experimental sampling set is:

[0018]

[0019] where represents the experimental stress value at the th characteristic sampling point under the th loading condition combination and the th characteristic sampling point.

[0020] Preferably, the step of determining the form of the viscoplastic constitutive model of the material to be identified, and then constructing the optimization space of the viscoplastic constitutive parameter vector is specifically:

[0021] Determine the form of the viscoplastic constitutive model of the material to be recognized, and then obtain the dimensions and physical meanings of each viscoplastic constitutive parameter in the form of the viscoplastic constitutive model of the material;

[0022] According to the dimensions and physical meanings of each viscoplastic constitutive parameter, set the value ranges of each viscoplastic constitutive parameter to form the optimization space of the viscoplastic constitutive parameter vector with

[0023] Preferably, the setting of the value ranges of each viscoplastic constitutive parameter forms the optimization space of the viscoplastic constitutive parameter vector with

[0024] Construct the viscoplastic constitutive parameter vector with :

[0025]

[0026] wherein, represents the th viscoplastic constitutive parameter, represents the real number field;

[0027] Each viscoplastic constitutive parameter satisfies , represents the value range of the viscoplastic constitutive parameter , and then obtain the optimization space of the viscoplastic constitutive parameter with

[0028]

[0029] wherein, represents the optimization space of the viscoplastic constitutive parameter vector with .

[0030] Preferably, based on the optimization space of the viscoplastic constitutive parameter, construct a simulation sampling set of the target solder joint material under multiple loading condition combinations, specifically:

[0031] For loading condition combinations, respectively prepare n finite element simulation files and user subroutine files of the viscoplastic constitutive equation;

[0032] For the user subroutine file of the viscoplastic constitutive equation, automatically update and set p the viscoplastic constitutive parameter vector with during the parameter optimization and determination process, and submit the simulation tasks in sequence to obtain the stress-strain curve simulation data under

[0033] For each stress-strain curve, the same number of characteristic sampling points as the experimental data of the stress-strain curve are selected, obtaining characteristic sampling points containing

[0034] As an option, the expression formula of the simulation sampling set is:

[0035]

[0036] where, represents the simulated stress value of the th combination of loading conditions at the th characteristic sampling point.

[0037] As an option, the objective function of the viscoplastic constitutive parameters is the mean square error between the simulation sampling set and the experimental sampling set, and its calculation formula is:

[0038]

[0039] where, represents the objective function of the viscoplastic constitutive parameters, represents the total number of combinations of loading conditions, represents the total number of characteristic sampling points on each stress-strain curve, represents the experimental stress value of the th combination of loading conditions at the th characteristic sampling point in the experimental sampling set, represents the simulated stress value of the th combination of loading conditions at the th characteristic sampling point in the simulation sampling set.

[0040] As an option, the Bayesian optimization method is used to iteratively optimize the objective function to obtain the optimal viscoplastic constitutive parameters of the solder joint material, specifically:

[0041] Based on the Gaussian process, a surrogate model of the objective function is constructed, and the maximum number of iterations of Bayesian optimization is set;

[0042] According to the surrogate model of the objective function, the expected improvement criterion is used to select the next set of p -dimensional viscoplastic constitutive parameter vectors to be evaluated, and the objective function is iteratively optimized, and each round of calculation is numbered , and is used as a label to organize the finite element simulation files generated in each round until the maximum number of iterations of Bayesian optimization or the preset error convergence is reached, and the process ends, and the optimal viscoplastic constitutive parameter vector is output:

[0043]

[0044] Among them, represents the corresponding when the minimum value of the is obtained for the viscoplastic constitutive parameter vector ; represents the optimization space of the

[0045] Preferably, the surrogate model of the objective function is:

[0046]

[0047] Among them, represents the estimated value of the objective function, that is, the surrogate model of the objective function, represents the Gaussian process, represents the p predicted mean function of the -dimensional viscoplastic constitutive parameter vector, and is the covariance kernel function of, represents the currently predicted p -dimensional viscoplastic constitutive parameter vector, represents a set of constitutive parameter vectors in the known historical samples;

[0048] The expression formula for the next set of p -dimensional viscoplastic constitutive parameter vectors to be evaluated is:

[0049]

[0050] Among them, represents the next set of p -dimensional viscoplastic constitutive parameter vectors to be evaluated, represents the -dimensional viscoplastic constitutive parameter vector corresponding to the maximum expectation, ; represents the maximum value, represents the expectation, represents the currently known optimal objective function value.

[0051] The beneficial effects of the present invention are:

[0052] 1. High recognition efficiency: By using the Bayesian optimization algorithm, through constructing pThe surrogate model of the objective function for viscoplastic constitutive parameters can quickly locate the optimal solution of viscoplastic constitutive parameters under the condition of limited simulation times.

[0053] 2. Strong adaptability: The present invention supports the optimization of constitutive model parameters in any dimension and is applicable to the stress response behavior modeling of various solder joint materials (such as SAC305, SAC405, SnPb, etc.) under different temperature and strain rate loading conditions, having good engineering applicability and popularization value.

[0054] 3. High degree of automation of simulation tasks: Through the calculation number k identification mechanism and the batch submission framework, the automatic organization and invocation of.inp files and.for subroutine files are realized, greatly reducing the burden of manual intervention and realizing an end-to-end fully automatic constitutive inversion process.

[0055] 4. Results can be traced and high stability: Each round of simulation results is marked with a unique number k, which supports the cache mechanism and the breakpoint restart mechanism, improving the stability and repeatability of the identification process and facilitating result verification and version management.

[0056] 5. Strong accuracy guarantee ability: By controlling the point-by-point error between the experimental curve and the simulation result curve at multiple sampling points and designing a reasonable objective function, it is ensured that the final identification result has good physical interpretability and engineering prediction ability. Description of the Drawings

[0057] Figure 1 Shown is a flow chart of a method for determining viscoplastic constitutive parameters of solder joint materials based on Bayesian optimization.

[0058] Figure 2 Shown is the change process of the objective function of viscoplastic constitutive parameters during the typical Bayesian optimization process. Detailed Embodiments

[0059] Now, the exemplary embodiments of the present invention will be described in detail with reference to the drawings. It should be understood that the embodiments shown and described in the drawings are merely exemplary, intended to explain the principles and spirit of the present invention, and not to limit the scope of the present invention.

[0060] Embodiment:

[0061] As Figure 1 shown, a method for determining viscoplastic constitutive parameters of solder joint materials based on Bayesian optimization includes the following steps:

[0062] S1. Obtain the experimental data of the stress-strain curves of the target solder joint material under multiple combinations of loading conditions, and then obtain the experimental sampling set;

[0063] Obtaining the stress-strain curve experimental data of the target solder joint material under multiple combinations of loading conditions, and then obtaining the experimental sampling set, specifically:

[0064] Determine the stress-strain curve experimental data of the target solder joint material under combinations of loading conditions (such as combinations of strain rate, temperature, etc.); among them, the strain rates are 0.001 / s, 0.0001 / s, 0.00001 / s; the temperatures are 25°C, 50°C, 75°C, 100°C, 125°C;

[0065] For each stress-strain curve experimental data, characteristic sampling points are selected, which can be key feature point sampling or equal strain interval sampling, and a characteristic sampling point containing experimental data is obtained, and then an experimental sampling set is constructed :

[0066]

[0067] Among them, represents the th combination of loading conditions at the th characteristic sampling point of the experimental stress value.

[0068] In this embodiment, , , among which, the strain rates are 0.001 / s, 0.0001 / s, 0.00001 / s; the temperatures are 25°C, 50°C, 75°C, 100°C, 125°C; the stress data under strain conditions of 0.002, 0.004, 0.006, and 0.02 respectively are used to obtain the experimental sampling set, with a total of 48 characteristic sampling points of experimental data, as shown in Table 1.

[0069] Table 1 Experimental Sampling Set (MPa)

[0070]

[0071] S2. Determine the form of the material viscoplastic constitutive model to be identified, and then construct the optimization space of the viscoplastic constitutive parameter vector of

[0072] In this embodiment, determine the form of the material viscoplastic constitutive model to be identified, and then construct the optimization space of the viscoplastic constitutive parameter vector of

[0073] Determine the form of the viscoplastic constitutive model of the material to be identified (such as Garofalo, Norton, Chaboche, Anand, etc.), and then obtain the dimensions and physical meanings of each viscoplastic constitutive parameter in the viscoplastic constitutive model of the material (such as elastic modulus E , initial yield strength Y , hardening modulus H , viscosity coefficient α , creep exponent β , etc.);

[0074] In this embodiment, the viscoplastic constitutive model of the electronic packaging solder joint material adopts the Garofalo viscoplastic constitutive model, and the specific model form is:

[0075]

[0076] Among them, is the strain rate, is the equivalent stress, is the temperature, is the material constant, representing the strain rate pre-factor, is the stress sensitivity coefficient (MPa -1 ), is the stress exponent, is the hyperbolic sine function, is the activation energy (J / mol), is the gas constant (J / (mol·K)). In addition, the Young's modulus E , yield strength Y , and hardening modulus H of the electronic packaging solder joint material also need to be defined.

[0077] According to the dimensions and physical meanings of each viscoplastic constitutive parameter, set the value range of each viscoplastic constitutive parameter to form the optimization space of the viscoplastic constitutive parameter vector of dimension;

[0078] The -dimensional viscoplastic constitutive parameter vector is given by the formula:

[0079]

[0080] Among them, represents the th viscoplastic constitutive parameter, represents the real number field;

[0081] Each viscoplastic constitutive parameter satisfies , represents the value range of the viscoplastic constitutive parameter , and we get The optimization space of the dimensional viscoplastic constitutive parameters is:

[0082]

[0083] in, express dimensional viscoplastic constitutive parameter vector Optimization space, dimensional viscoplastic constitutive parameter vector The optimization space is shown in Table 2.

[0084] Table 2 Optimization space of two-dimensional viscoplastic constitutive parameters

[0085]

[0086] S3. Based on The optimization space of the 3D viscoplastic constitutive parameters is used to construct a simulation sampling set of the target weld material under multiple loading condition combinations;

[0087] In this embodiment, the The optimization space of the dimensional viscoplastic constitutive parameters is used to construct a simulation sampling set of the target weld material under multiple loading condition combinations, specifically:

[0088] Establish simulation templates for finite element solutions. For each loading condition combination (such as strain rate, temperature and other condition combinations), prepare 15 finite element simulation files (such as inp files in Abaqus) and user subroutine files of the viscoplastic constitutive equation (such as for files in Abaqus);

[0089] User subroutine files for viscoplastic constitutive equations, automatic update of settings during parameter optimization and determination dimensional viscoplastic constitutive parameter vector , assuming the parameter value is , and submit the simulation tasks in sequence to obtain the stress-strain curve simulation data under 15 loading condition combinations;

[0090] The simulation data of each stress-strain curve is selected to be the same as the experimental data of the stress-strain curve. feature sampling points, and get The characteristic sampling points of the simulation data are then used to construct the simulation sampling set :

[0091]

[0092] in, Indicates The loading condition combination is in The simulated stress values of the characteristic sampling points are shown in Table 3, the simulated sampling set.

[0093] Table 3 Simulated Sampling Set

[0094]

[0095] S4. Based on the experimental sampling set and the simulated sampling set, construct the objective function of the viscoplastic constitutive parameters;

[0096] In this embodiment, the objective function of the viscoplastic constitutive parameters is the mean square error (MSE) between the simulated sampling set and the experimental sampling set. Based on a set of dimensional viscoplastic constitutive parameter vectors , calculate its objective function of the viscoplastic constitutive parameters:

[0097]

[0098] Among them, represents the objective function of the viscoplastic constitutive parameters, represents the total number of combinations of loading conditions, represents the total number of characteristic sampling points on each stress-strain curve, represents the experimental stress value of the th combination of loading conditions at the th characteristic sampling point in the experimental sampling set, represents the simulated stress value of the th combination of loading conditions at the th characteristic sampling point in the simulated sampling set.

[0099] S5. Based on the Gaussian Process (GP), construct a surrogate model of the objective function, and use the Bayesian optimization method to iteratively optimize the surrogate model of the objective function to obtain the optimal viscoplastic constitutive parameters of the solder joint material.

[0100] In this embodiment, the surrogate model of the objective function is:

[0101]

[0102] Among them, represents the estimated value of the objective function, that is, the surrogate model of the objective function, represents the Gaussian process, represents the prediction mean function, represents the covariance kernel function, which is used to express the correlation between parameters, represents the current predicted p dimensional viscoplastic constitutive parameter vector, represents a certain set of constitutive parameter vectors in the known historical samples.

[0103] The surrogate model of the objective function is iteratively optimized by the Bayesian optimization method to obtain the optimal viscoplastic constitutive parameters of the solder joint material, specifically as follows:

[0104] Set the initial number of Bayesian optimizations to , and the maximum number of iterations of Bayesian optimization ;

[0105] Iteratively optimize the surrogate model of the objective function by the Bayesian optimization method. During each round of finite element simulation and optimization parameter update, assign a calculation number to each round. Use as a label to organize the finite element simulation files (such as inp files, for files, odb files, and cache files) generated in each round. The objective function of the viscoplastic constitutive parameters changes gradually with the calculation number of each round. As shown in Figure 2 , until the maximum number of iterations of Bayesian optimization or the preset error convergence is reached, the process ends, and the optimal viscoplastic constitutive parameters of the solder joint material are output; in each iteration, select the next set of p -dimensional viscoplastic constitutive parameters to be evaluated according to the expected improvement (EI) criterion of the surrogate model of the objective function. Its expression formula is:

[0106]

[0107] where represents the next set of p -dimensional viscoplastic constitutive parameters to be evaluated, represents the maximum value, represents the expectation, represents the currently known optimal objective function value;

[0108] The optimal viscoplastic constitutive parameters of the solder joint material are:

[0109]

[0110] where represents the minimum value, represents the objective function of the viscoplastic constitutive parameters, represents -dimensional viscoplastic constitutive parameter vector of the optimization space. The final optimized mean square error is 6.21. Furthermore, the optimal viscoplastic constitutive parameters of the solder joint material are determined, as shown in Table 4.

[0111] Table 4 Optimal viscoplastic constitutive parameters of the solder joint material

[0112]

[0113] The present invention can significantly improve the efficiency and accuracy of viscoplastic constitutive modeling and parameter identification of solder materials in electronic packaging, provide a key supporting means for the design of high-reliability packaging structures, and has important theoretical value and engineering application prospects.

[0114] Those of ordinary skill in the art will realize that the embodiments described herein are for helping the reader understand the principles of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific deformations and combinations that do not depart from the essence of the present invention according to these technical revelations disclosed by the present invention, and these deformations and combinations are still within the protection scope of the present invention.

Claims

1. A method for determining the viscoplastic constitutive parameters of solder joint materials based on Bayesian optimization, characterized in that, Including the following steps: Obtain the stress-strain curve experimental data of the target solder joint material under multiple combinations of loading conditions, and then obtain the experimental sampling set; Determine the form of the viscoplastic constitutive model of the material to be identified, and then construct the optimization space of the viscoplastic constitutive parameter vector with Based on the optimization space of viscoplastic constitutive parameters, a simulation sampling set of the target solder joint material under multiple combinations of loading conditions is constructed; Based on the experimental sampling set and the simulation sampling set, construct the objective function of the viscoplastic constitutive parameters; Use the Bayesian optimization method to iteratively optimize the objective function to obtain the optimal viscoplastic constitutive parameters of the solder joint material.

2. The method for determining the viscoplastic constitutive parameters of the solder joint material based on Bayesian optimization according to claim 1, wherein The obtaining of the stress-strain curve experimental data of the target solder joint material under multiple combinations of loading conditions, and then obtaining the experimental sampling set is specifically as follows: Determine the stress-strain curve experimental data of the target solder joint material under combinations of loading conditions; Selection of experimental data for each stress-strain curve characteristic sampling points are selected to obtain characteristic sampling points with experimental data, and then an experimental sampling set is constructed.

3. The method for determining the viscoplastic constitutive parameters of the solder joint material based on Bayesian optimization according to claim 2, wherein The described experimental sampling set The expression formula is: Among them, represents the th combination of loading conditions at the th characteristic sampling point of the experimental stress value.

4. The method for determining the viscoplastic constitutive parameters of the solder joint material based on Bayesian optimization according to claim 2, wherein Determine the form of the viscoplastic constitutive model of the material to be identified, and then construct the optimization space of the viscoplastic constitutive parameter vector in the -dimensional space, specifically: Determine the form of the viscoplastic constitutive model of the material to be identified, and then obtain the dimensions and physical meanings of each viscoplastic constitutive parameter under the form of the viscoplastic constitutive model of the material; According to the dimensions and physical meanings of each viscoplastic constitutive parameter, the value ranges of each viscoplastic constitutive parameter are set to form the optimization space of the viscoplastic constitutive parameter vector with 5. The method for determining the viscoplastic constitutive parameters of the solder joint material based on Bayesian optimization according to claim 4, wherein The value ranges of the set viscoplastic constitutive parameters form the optimization space of the viscoplastic constitutive parameter vector in the -dimensional space, specifically as follows: Construct viscoplastic constitutive parameter vector : Among them, represents the th viscoplastic constitutive parameter, represents the real number field; Each viscoplastic constitutive parameter satisfies , denotes the value range of the viscoplastic constitutive parameter , and then the optimization space of the -dimensional viscoplastic constitutive parameter is: Among them, denotes the optimization space of the viscoplastic constitutive parameter vector.

6. The method for determining the viscoplastic constitutive parameters of the solder joint material based on Bayesian optimization according to claim 5, wherein The optimization space based on the viscoplastic constitutive parameters is used to construct a simulation sampling set of the target solder joint material under multiple combinations of loading conditions, specifically: For combinations of loading conditions, respectively prepare n finite element simulation files and user subroutine files of viscoplastic constitutive equations; User subroutine file for viscoplastic constitutive equation, automatic update settings during parameter optimization and determination p Viscoplastic constitutive parameter vector , and submit simulation tasks in sequence to obtain simulation data of stress-strain curves under combinations of loading conditions; For each stress-strain curve, the same characteristic sampling points as those of the stress-strain curve experimental data are selected to obtain characteristic sampling points of simulation data, and then a simulation sampling set is constructed.

7. The method for determining the viscoplastic constitutive parameters of the solder joint material based on Bayesian optimization according to claim 6, wherein The simulation sampling set The expression formula is as follows: Among them, represents the th combined loading condition at the th characteristic sampling point of the simulated stress value.

8. The method for determining the viscoplastic constitutive parameters of the solder joint material based on Bayesian optimization according to claim 1, wherein The objective function of the viscoplastic constitutive parameters is the mean square error between the simulation sampling set and the experimental sampling set, and its calculation formula is: Among them, represents the objective function of the viscoplastic constitutive parameters, represents the total number of combinations of loading conditions, represents the total number of characteristic sampling points on each stress-strain curve, represents the -th loading condition combination in the experimental sampling set at the -th characteristic sampling point, represents the simulated stress value of the -th loading condition combination in the simulation sampling set at the -th characteristic sampling point.

9. The method for determining the viscoplastic constitutive parameters of the solder joint material based on Bayesian optimization according to claim 1, wherein The using of the Bayesian optimization method to iteratively optimize the objective function to obtain the optimal viscoplastic constitutive parameters of the solder joint material is specifically as follows: Construct a surrogate model of the objective function based on the Gaussian process, and set the maximum number of iterations of Bayesian optimization; Select the next group of constitutive parameter vectors of viscoplasticity to be evaluated according to the surrogate model of the objective function using the expected improvement criterion, perform iterative optimization on the objective function, and assign a calculation number to each round as p . Organize the finite element simulation files generated in each round with as the label until the maximum number of iterations of Bayesian optimization or the preset error convergence is reached, then the process ends and the optimal constitutive parameter vector of the solder joint material viscoplasticity is output as : ​ Among them, represents the corresponding to the minimum vector of viscoplastic constitutive parameters in dimension , represents the objective function of viscoplastic constitutive parameters, represents the optimization space of the vector of viscoplastic constitutive parameters in dimension .

10. The method for determining the viscoplastic constitutive parameters of solder joint materials based on Bayesian optimization according to claim 9, wherein The surrogate model of the objective function is: Among them, represents the estimated value of the objective function, that is, the surrogate model of the objective function, means subject to, represents a Gaussian process, represents p the predicted mean function of the dimensional viscoplastic constitutive parameter vector, represents regarding and the covariance kernel function of, represents the currently predicted p dimensional viscoplastic constitutive parameter vector, represents a set of constitutive parameter vectors in the known historical samples; The representation formula of the p viscoplastic constitutive parameter vector of the next group to be evaluated is as follows: Among them, represents the next set of p viscoplastic constitutive parameter vectors to be evaluated, represents the corresponding viscoplastic constitutive parameter vectors when maximizing the expectation, , represents the maximum value, represents the expectation, represents the currently known optimal objective function value.

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