Multi-target particle swarm optimization crystal plastic model parameter calibration method based on coupled machine learning

Abstract

The invention relates to a multi-target particle swarm optimization crystal plastic model parameter calibration method based on coupled machine learning, comprising the following steps: S1, based on a parameter range of a crystal plastic model, generating a parameter sample set through Latin hypercube sampling, and obtaining a stress-strain curve by using crystal plastic finite element simulation; s2, taking the parameter sample set in the S1 and the corresponding stress-strain curve as a data set of machine learning, training through an artificial neural network ANN, and constructing a data-driven agent model; and S3, coupling the proxy model in the S2 with a multi-target particle swarm optimization algorithm, and obtaining an optimal parameter combination meeting the consistency of multi-orientation experimental data through iterative optimization. According to the method, through finite element data generation, proxy model replacement and multi-objective optimization iteration, the calculation cost is reduced; the artificial neural network is trained for different material orientations, and the prediction pertinence is improved.

Description

Technical Field

[0001] This invention belongs to the field of material mechanical property simulation technology, specifically relating to a method for calibrating crystal plasticity model parameters based on multi-objective particle swarm optimization using coupled machine learning. Background Technology

[0002] Crystal plastic finite element model (CPFEM) is an important tool for studying the mechanical behavior of polycrystalline materials, but its parameter calibration relies on a lot of trial and error or traditional optimization algorithms, which has problems such as high computational cost and a lot of manual intervention.

[0003] Traditional methods rely on repeated parameter adjustments based on human experience, requiring multiple runs of finite element simulations and comparisons with experimental data. This is time-consuming and highly subjective. Traditional optimization algorithms, such as gradient descent and genetic algorithms, require frequent calls to finite element simulations, with each simulation taking more than 5 minutes. The optimization process requires tens of thousands of iterations, with a total time consumption of tens of thousands of minutes, resulting in excessively high computational costs. Furthermore, samples with different material orientations require simultaneous optimization of multiple conflicting objectives (such as multiple features of the stress-strain curve), which traditional single-objective optimization algorithms cannot effectively handle. While multi-objective particle swarm optimization (MOPSO) can generate Pareto fronts, its reliance on high-frequency simulation calculations leads to an explosive increase in computational resource requirements.

[0004] To address the aforementioned issues, this invention proposes a phased parameter calibration method that combines finite element simulation, machine learning proxy models, and multi-objective optimization algorithms. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings and deficiencies of existing technologies by providing a method for calibrating crystal plasticity model parameters based on multi-objective particle swarm optimization using coupled machine learning, which significantly improves efficiency and accuracy.

[0006] The technical problem solved by this invention is achieved through the following technical solution: A method for calibrating parameters of a crystal plasticity model based on multi-objective particle swarm optimization using coupled machine learning, the method comprising the following steps: S1. Based on the parameter range of the crystal plasticity model, a parameter sample set is generated by Latin hypercube sampling, and the stress-strain curve is obtained by crystal plasticity finite element simulation. S2, the initial parameter sample set and corresponding stress-strain curves generated based on S1 are used as the dataset for machine learning, and trained by artificial neural network (ANN) to build a data-driven surrogate model. S3. Couple the surrogate model of S2 with the multi-objective particle swarm optimization algorithm, and obtain the optimal parameter combination that satisfies the consistency of multi-orientation experimental data through iterative optimization.

[0007] Furthermore, the parameter range of S1 takes into account the base plane.Slip ({0001}<11-20>), cylindrical surface Slip ({10-10}<11-20>) and second-order cone<c+a> Three slip systems ({-1-122}<-1-123>) and one stretching twin system ({10-12}<-1011>); Latin hypercube sampling fills a 20-parameter space, generating 100 sets of parameter sample sets. These parameter sample sets are then used to perform crystal plasticity finite element simulations on the samples, resulting in 100 sets of stress-strain curves. Unconverged simulation data are then removed, and the obtained stress-strain curves are smoothed and preprocessed.

[0008] Furthermore, the artificial neural network of S2 adopts a single hidden layer structure, with 128 neurons in the hidden layer, the activation function being LeakyReLU, the optimization algorithm being Adam, and the loss function being mean squared error.

[0009] Moreover, S2 uses additional samples to validate the surrogate model, with the stress-strain response of each sample orientation predicted by an independent ANN model.

[0010] Furthermore, the multi-objective particle swarm optimization algorithm of S3 uses R 2 The value is the fitness function, used to evaluate the consistency between simulated and experimental stress-strain curves; the initial particle swarm of the multi-objective particle swarm optimization algorithm is filled with the initial particle swarm coordinates using the LHS method within the specified crystal plasticity parameter range. P 0 The number of particles is 100, and the initial velocity V0 is randomly assigned to the swarm. The reference velocity range is set to ±0.3 times the parameter boundary width. In step S3, a trained ANN surrogate model is used to replace the crystal plastic finite element model, and the particle swarm coordinates are input. P 0 Output stress-strain curves.

[0011] Moreover, the S3 uses R 2 The consistency (fitness) between the actual unidirectional orientation of each sample and the corresponding simulation results is evaluated using the following expression: ; (1) in: and This represents the simulated stress and experimental stress under plastic deformation. It is the average value of the simulated stress. Based on the fitness results, an external archive is created to store all the current non-dominated solutions, namely the Pareto front. The non-dominated solutions are stored through the Pareto front, and adaptive mesh filtering is used to ensure the diversity of the solution set.

[0012] Furthermore, S3 updates the particle velocity and position. For the i-th particle, it is based on the optimal position (particle optimal solution) from the previous t steps. The global optimal position in the previous t steps (Global optimal solution) Update its velocity and position. The global optimal solution is selected from the non-dominated solutions of the Pareto front, and the update equation is as follows: ; (2) ; (3) in: and ω and c1 are the coordinates and velocity vectors of the i-th particle at step t, respectively; ω, c1 and c2 are hyperparameters.

[0013] Moreover, the method is applicable to the calibration of material parameters for materials exhibiting crystalline plastic deformation behavior, such as magnesium alloys or titanium alloys.

[0014] The advantages and beneficial effects of this invention are as follows: 1. This invention forms a three-stage coupled framework: generating data through finite element method → ​​substitution by proxy model → multi-objective optimization iteration, thereby reducing computational costs.

[0015] 2. This invention forms a multi-orientation independent agent model: artificial neural networks are trained separately for different material orientations to improve the predictive accuracy. Attached Figure Description

[0016] Figure 1 This is a flowchart of the crystal plasticity model parameter optimization process of the present invention; Figure 2 This is a comparison of the true stress-true strain curves from uniaxial tensile tests and simulations of samples with different orientations in Example 1 of the present invention. Figure 3 This is a comparison of the true stress-true strain curves obtained from uniaxial tensile experiments and simulations using a single multi-objective particle swarm optimization algorithm in Embodiment 2 of the present invention, under the same computation time. Detailed Implementation

[0017] The present invention will be further described in detail below through specific embodiments. The following embodiments are merely descriptive and not limiting, and should not be used to limit the scope of protection of the present invention.

[0018] Example 1 An innovative method for calibrating parameters of a crystal plasticity model based on multi-objective particle swarm optimization with coupled machine learning is proposed. Step (1): To avoid orientation inaccuracies caused by local test locations, EBSD tests were performed at 5 different locations. The obtained orientation information was combined and input into Dream3D software as the overall material texture to generate orientation data representing the volume element (RVE) model. An assembly of 1080 single crystals (grains) was used to model the polycrystalline sample. Each grain was modeled using a single eight-node linear hexahedral unit. A tensile displacement is applied in the y-direction to simulate a uniaxial tensile test, with symmetrical boundary conditions applied on three adjacent faces.

[0019] Step (2): Set the elastic constants of pure magnesium at room temperature as shown in Table 1, and the latent hardening coefficients of all deformation systems. q Set to 1. Twin parameters are set to... f 0 = 0.03, f max = 0.85, its value can be simply calibrated based on the start and end of twinning in the T-0 sample, and the reference range of the initial parameters of each deformation system is set, as shown in Table 2.

[0020] Step (3): Using the crystal plasticity model parameters and stress-strain curves as the dataset for machine learning, an artificial neural network (ANN) was used for training to construct a data-driven surrogate model. An ANN model with one hidden layer was selected, with 128 neurons in the hidden layer. LeakyReLU was used as the activation function, the learning rate was set to 0.001, and Adam was used as the optimization algorithm. The mean squared error (MSE) loss function was used to evaluate the training results.

[0021] Step (4): Initialize the particle swarm. Within the range of crystal plasticity parameters specified in Table 2, fill the initial particle swarm coordinates using the LHS method. P 0 The number of particles is 100. The initial velocity V0 is randomly assigned to the population, and the reference velocity range is set to ±0.3 times the parameter boundary width.

[0022] Step (5): Replace the crystal plastic finite element model with the previously trained ANN surrogate model, and input the particle swarm coordinates. P 0 Output stress-strain curves.

[0023] Step (6): Use R 2 The consistency between the actual single-pull orientation of each sample and the corresponding simulation results was evaluated. Step (7): Update particle velocity and position. For the i-th particle, update its optimal position (particle optimal solution) based on its previous t-step position. The global optimal position in the previous t steps (Global optimal solution) Update its velocity and position.

[0024] Step (8): Update the external archive using the Pareto dominance principle.

[0025] Step (9): After the algorithm terminates at the maximum number of iterations (100), the non-dominated solution set in the external archive is output as the solution to the multi-objective optimization problem (calibrated model parameters). The optimized crystal plasticity model parameters are shown in Table 3. The experimental and simulated stress-strain curves are compared as follows: Figure 2 As shown, the calibration effect is verified.

[0026] Table 1. Elastic constants (MPa) of pure magnesium at room temperature

[0027] Table 2 Reference range of initial parameters for each deformation system

[0028] Table 3. Relevant parameters of the ZK60 magnesium alloy model calibrated using the present invention.

[0029] Table 4. Relevant parameters of the ZK60 magnesium alloy model after calibration using an independent multi-objective particle swarm optimization algorithm.

[0030] Example 2 Example 2 uses an independent multi-objective particle swarm optimization algorithm to calibrate the parameters of the same crystal plasticity model, and the process loop machine learning surrogate model in step 3 is no longer used in the implementation. In step 5, all stress-strain curves are obtained from real-time simulation of crystal plasticity. Theoretically, without considering time costs, the method in Example 2 can obtain the same optimization results as in Example 1. However, in practice, the independent multi-objective particle swarm optimization algorithm must consider time costs. Therefore, we reduced the number of particles in step 4 to 10 and limited the number of iterations to 10 steps to ensure that the parameter optimization time of Example 2 is similar to that of Example 1. After the parameter optimization process is completed, the global optimal solution is selected and compared with the experimental results, as shown in the figure. Figure 3 .

[0031] As can be seen, the simulation and experimental curves of Example 2 show significant deviations in all directions, R 2 The values ​​were all low, only greater than 0.9 in the T-0 and T-22 directions, close to 0.5 in the T-45 direction, and even negative in the T-67 and T-90 directions, indicating a significant difference between the simulated and experimental values. However, in Example 1, the R... 2 The values ​​are generally above 0.983, with the highest reaching 0.9974. The fitting effect of the simulated curve and the experimental data is significantly better than that of Example 2.

[0032] The results show that the global optimal solution obtained by the multi-objective particle swarm optimization algorithm alone in the same amount of time is far less ideal than that obtained by the multi-objective particle swarm optimization algorithm coupled with machine learning. This is because it is extremely difficult to explore the ideal optimal solution within the 20-dimensional parameter space shown in Table 3 using only 10 particles and 10 iterations. Increasing the number of particles and iterations will improve the chances of finding the ideal optimal solution, but this will significantly increase the time cost. This invention, however, focuses the main time cost on training experimental samples. After training the ANN surrogate model using machine learning, the computation time for subsequent stress-strain curves can be reduced from minutes to milliseconds. This allows more particles to fully explore the parameter space through more iterations to obtain the ideal optimal solution without increasing the time cost.

[0033] Although embodiments and drawings of the present invention have been disclosed for illustrative purposes, those skilled in the art will understand that various substitutions, variations and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A method for calibrating parameters of a crystal plasticity model based on multi-objective particle swarm optimization using coupled machine learning, characterized in that: The steps of the method are as follows: S1. Based on the parameter range of the crystal plasticity model, a parameter sample set is generated by Latin hypercube sampling, and the stress-strain curve is obtained by crystal plasticity finite element simulation. S2, the initial parameter sample set and corresponding stress-strain curves generated based on S1 are used as the dataset for machine learning, and trained by artificial neural network (ANN) to build a data-driven surrogate model. S3. Couple the surrogate model of S2 with the multi-objective particle swarm optimization algorithm, and obtain the optimal parameter combination that satisfies the consistency of multi-orientation experimental data through iterative optimization.

2. The method for calibrating crystal plasticity model parameters based on multi-objective particle swarm optimization using coupled machine learning according to claim 1, characterized in that: The parameter range of S1 takes into account the base plane. Slip ({0001}<11-20>), cylindrical surface Slip ({10-10}<11-20>) and second-order cone<c+a> Three slip systems ({-1-122}<-1-123>) and one stretching twin system ({10-12}<-1011>); Latin hypercube sampling fills a 20-parameter space, generating 100 sets of parameter sample sets. These parameter sample sets are then used to perform crystal plasticity finite element simulations on the samples, resulting in 100 sets of stress-strain curves. Unconverged simulation data are then removed, and the obtained stress-strain curves are smoothed and preprocessed.

3. The method for calibrating crystal plasticity model parameters based on multi-objective particle swarm optimization using coupled machine learning according to claim 1, characterized in that: The artificial neural network of S2 adopts a single hidden layer structure, with 128 neurons in the hidden layer, the activation function being LeakyReLU, the optimization algorithm being Adam, and the loss function being mean squared error.

4. The method for calibrating crystal plasticity model parameters based on multi-objective particle swarm optimization using coupled machine learning according to claim 1, characterized in that: The S2 uses additional samples to validate the surrogate model, with the stress-strain response of each sample orientation predicted by an independent ANN model.

5. The method for calibrating crystal plasticity model parameters based on multi-objective particle swarm optimization using coupled machine learning according to claim 1, characterized in that: The multi-objective particle swarm optimization algorithm of S3 uses R 2 The value is the fitness function, used to evaluate the consistency between simulated and experimental stress-strain curves; the initial particle swarm of the multi-objective particle swarm optimization algorithm is filled with the initial particle swarm coordinates using the LHS method within the specified crystal plasticity parameter range. P 0 The number of particles is 100, and the initial velocity V0 is randomly assigned to the swarm. The reference velocity range is set to ±0.3 times the parameter boundary width. In step S3, a trained ANN surrogate model is used to replace the crystal plastic finite element model, and the particle swarm coordinates are input. P 0 Output stress-strain curves.

6. The method for calibrating crystal plasticity model parameters based on multi-objective particle swarm optimization using coupled machine learning according to claim 5, characterized in that: The S3 uses R 2 The consistency (fitness) between the actual unidirectional orientation of each sample and the corresponding simulation results is evaluated using the following expression: ； （1） in: and This represents the simulated stress and experimental stress under plastic deformation. It is the average value of the simulated stress. Based on the fitness results, an external archive is created to store all the current non-dominated solutions, namely the Pareto front. The non-dominated solutions are stored through the Pareto front, and adaptive mesh filtering is used to ensure the diversity of the solution set.

7. The method for calibrating crystal plasticity model parameters based on multi-objective particle swarm optimization using coupled machine learning according to claim 5, characterized in that: S3 updates the particle velocity and position. For the i-th particle, it is based on the optimal position (particle optimal solution) of the previous t steps. The global optimal position in the previous t steps (Global optimal solution) Update its velocity and position. The global optimal solution is selected from the non-dominated solutions of the Pareto front, and the update equation is as follows: ； （2） ； （3） in: and ω and c1 are the coordinates and velocity vectors of the i-th particle at step t, respectively; ω, c1 and c2 are hyperparameters.

8. The method for calibrating crystal plasticity model parameters based on multi-objective particle swarm optimization using coupled machine learning according to claim 1, characterized in that: The method is applicable to the calibration of material parameters for materials exhibiting crystalline plastic deformation behavior, such as magnesium alloys or titanium alloys.

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