GEP tensor evolution and neural coefficient separation-based creep native modeling method

Abstract

The invention relates to a creep book modeling method based on GEP tensor evolution and neural coefficient separation. Comprising the following steps: carrying out a creep experiment to obtain a training set and a verification set; constructing a gene expression programming model containing a nonlinear function set, and defining a primary population model; generating a primary population; screening and replacing the individuals, so that each individual has iteration and physical coefficients, and obtaining an updated population; based on the training set, a neural network learning rate is set, a loss function is defined, a neural network is adopted to optimize the physical coefficient in the updated population, and the optimal physical coefficient is output; and based on the verification set, performing mean square error fitness evaluation according to an individual optimal physical coefficient, screening out an optimal individual, performing operation on the remaining individuals, then performing screening replacement, and performing iteration to output the optimal individual. According to the method, tensor evolution operation, GEP and a neural decoupling mechanism are combined, and a new normal form is provided for cross-scale mechanical modeling of the electronic packaging material.

Description

Technical Field

[0001] The present invention belongs to the field of material computing, and specifically relates to a creep constitutive modeling method based on GEP tensor evolution and neural coefficient separation. Background Art

[0002] Creep models are mathematical models used to describe the slow deformation of materials under long-term constant stress. They are typically composed of a combination of elastic and viscous elements (e.g., Maxwell and Burger models). They are used to simulate the time-dependent deformation behavior of engineering materials (such as rock, metal, and polymers) under sustained loads. They are commonly used in fields such as civil engineering, mining, and nuclear waste storage to help predict the long-term stability of structures. Models of varying complexity are available to meet the needs of different engineering scenarios.

[0003] Existing creep modeling technology has three major limitations:

[0004] 1) Traditional GEP cannot solve the problem of strong coupling of multi-physics parameters;

[0005] 2) The high coupling of empirical model parameters leads to ambiguous physical meaning;

[0006] 3) The black-box nature of neural networks hinders engineering applications. For example, CN113657326A lacks a parameter decoupling mechanism. Summary of the Invention

[0007] The purpose of the present invention is to provide a creep constitutive modeling method based on the separation of GEP tensor evolution and neural coefficients.

[0008] The technical solution to achieve the purpose of the present invention is: a creep constitutive modeling method based on the separation of GEP tensor evolution and neural coefficients, comprising the following steps:

[0009] Step S1: Set the test variables, conduct creep experiments, obtain test values, and process the test values ​​and divide them into a training set and a validation set;

[0010] Step S2: construct a gene expression programming model containing a nonlinear function set, and define the initial population model according to the depth-first strategy;

[0011] Step S3: Generate the initial population;

[0012] Step S4: Screen and replace the individuals in the initial population so that each individual has the iteration parameters and physical coefficients to obtain the updated population;

[0013] Step S5: Based on the training set in step S1, the neural network learning rate is set, the neural network loss function is defined, and the physical coefficient of each individual in the updated population is trained and optimized using the neural network to output the optimal physical coefficient;

[0014] Step S6: Based on the validation set of step S1, perform mean square error fitness evaluation according to the individual optimal physical coefficient obtained in step S5, screen out the optimal individual, operate on the remaining individuals and then perform screening and replacement, so that the remaining individuals with iteration parameters and physical coefficients are merged with the optimal individual into the latest population, and judge whether the fitness of the optimal individual of the latest population reaches the threshold or whether the maximum number of iterations is reached. If so, terminate the iteration and output the optimal individual; if not, proceed to the next step;

[0015] Step S7: Repeat steps S5-S6 until the termination condition is reached, terminate the iteration, and output the optimal individual.

[0016] Furthermore, the experimental variables in step S1 include stress σ, strain ε, temperature T, loading rate rate, strain rate

[0017] Furthermore, the test value processing in step S1 specifically includes: denoising the data, removing outliers, and then converting the test value into a tensor form.

[0018] Furthermore, the initial population model of step S2 is:

[0019]

[0020] Where A is the material coefficient; α is the stress coefficient; n is the stress exponent; Q is the activation energy; R is the gas constant; and T is the temperature.

[0021] Furthermore, step S3 generates the initial population as follows:

[0022] Define the generation parameters, population size, link function, artificial head structure of the initial population model, randomly generate the tail structure, and generate the initial population; define the material coefficient A, stress index n, and activation energy Q as physical coefficients.

[0023] Furthermore, the operator Function of the artificial head structure and tail structure in step S3 is as follows:

[0024] Function=[+,-,×,÷,sin,cos,tan,square,tanh,protected_pow,protected_exp,protected_sinh,protected_log]

[0025] Among them, protected_pow, protected_exp, protected_sinh, and protected_log are custom data protection functions;

[0026] The protected hyperbolic sine function protected_sinh is defined as:

[0027]

[0028] The protected hyperbolic sine function protected_pow is defined as:

[0029]

[0030] The protected hyperbolic sine function protected_exp is defined as:

[0031]

[0032] The protected hyperbolic sine function protected_log is defined as:

[0033]

[0034] The terminators of the artificial header and tail structures in S3 are as follows:

[0035] Constant terminator constant_terminal: [5,5e -8 ,3.5,-144000,8.314], 5 is the material constant, 5e -8 is the stress coefficient, 3.5 is the stress exponent, 144000 is the activation energy, and 8.314 is the gas constant;

[0036] Random constant terminator ephemeral_terminal: [α, β, γ], where the dynamic random constants α, β, and γ are generated by the following formula:

[0037] C dynamic =random(-10, 10);

[0038] Physical coefficient terminator NN terminal: [A,n,Q].

[0039] Furthermore, the neural network loss function is defined in step S5 as:

[0040]

[0041] Among them, ε pred is the predicted value of individual strain after the neural network training optimization using the dataset; ε actual is the true strain in the validation set.

[0042] Furthermore, step S6 performs the following operations on the remaining individuals: single-point crossover, two-point crossover, mutation, and base-transfer.

[0043] Furthermore, the population size in step S3 is set to 500, and the number of iterations in step S6 is set to 500. The optimal individual obtained in step S6, that is, the creep constitutive model, is as follows:

[0044]

[0045] Compared with the prior art, the present invention has the following significant advantages:

[0046] (1) High-precision prediction (MSE reduced by two orders of magnitude): Tensor evolution in incremental creep calculations enables multi-dimensional parameter collaborative optimization (such as stress-temperature coupling terms), avoids division by zero / logarithmic overflow (such as protected_pow limits the exponent range), and improves the reliability of extreme working condition predictions;

[0047] (2) Saving computing resources: Using CUDA-compatible architecture tensor parallel computing to process 26,730 sets of data with the same data volume takes 1.3 hours (the traditional GEP method takes 36 hours);

[0048] (3) Strict physical constraints: physical quantities such as physical coefficients are defined in the neural network optimization, and the dynamic range of material coefficients and stress exponents is defined so that the symmetry constraints make the parameter error < 0.5% and the activation energy Q error < 3%;

[0049] (4) Clear physical meaning: Model parameters (e.g., 8.314 corresponds to the gas constant) have clear physical meanings, the terminator has built-in physical constants and physical coefficients (e.g., gas constant R = 8.314), and the output model is directly related to the material constitutive relationship;

[0050] (5) Efficient parameter decoupling: GEP combines independent optimization of neural networks to eliminate the strong coupling of traditional empirical models (such as CN113657326A), increasing PCI to 95% (traditional 63%) and decoupling efficiency by 57%;

[0051] (6) Strong robustness: Functions such as protected_sinh do not overflow under high temperature and high strain rate conditions. Protected operations effectively avoid numerical overflows, and dynamic random constants enhance the generalization ability of the model.

[0052] (7) Scalable architecture: The gene tree structure can be extended to higher-order tensors such as stress gradients. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 SnAgCu nanoindentation creep test diagram; (a) is 3mN, (b) is 5mN, (c) is 7mN, and (d) is 9mN.

[0054] Figure 2 Fitness evolution curve.

[0055] Figure 3 Comparison of predicted strain and actual value.

[0056] Figure 4 Parameter sensitivity analysis.

[0057] Figure 5 Parameter correlation heatmap. DETAILED DESCRIPTION

[0058] The present invention is further described in detail below with reference to the accompanying drawings.

[0059] This example uses tin-silver-copper alloy (SAC305) as the research object and introduces nanoindentation experimental data to demonstrate the specific implementation process of the present invention.

[0060] 1. Experimental equipment and parameters

[0061] Equipment: Nano Indenter G200 nanoindenter equipped with a Berkovich pyramid probe (tip curvature radius of 50 nm);

[0062] Experimental conditions: load range: 0.5-20 mN (step size 0.5 mN); holding time: 300 s; temperature control: 298.15 K (25°C), accuracy ±0.1°C; loading rate: 0.0005-20 mN / s.

[0063] Material: SAC305 alloy (Sn-3.0Ag-0.5Cu), density 7400kg / m 3 , Young's modulus 41.6GPa, Poisson's ratio 0.36.

[0064] The specimen dimensions are shown in Table 1:

[0065]

[0066] Based on the above dimensions, nanoindentation creep tests were established, using loading rates under different conditions and different stresses.

[0067] Specific packaging structure material parameters are shown in Table 2

[0068]

[0069] 2. Data Collection

[0070] Each set of experiments was repeated 10 times, and data such as loading rate, stress, temperature, creep strain, and strain rate were recorded. A total of 26,730 sets of original data were obtained.

[0071] 3. Data cleaning and verification

[0072] Outlier elimination: Abnormal data caused by instrument noise or material defects were filtered out using the 3σ principle, and 25,951 sets of valid data were retained.

[0073] 4. Evolutionary algorithm iterative optimization

[0074] (1) Generation of the initial population:

[0075] Population size: 50 sets of (H, T) tensor pairs;

[0076] Function set: {+,-,×,÷,sin,cos,tan,square,tanh,protected_pow,protected_exp,protected_sinh,protected_log}

[0077] Terminal symbol:

[0078] Constant terminator: [5,5e-8,3.5,-144000,8.314]

[0079] Random constant terminator: [α, β, γ] (α = rand (-1.0, 1.0))

[0080] Physical coefficient terminator: [A,n,Q]

[0081] Complexity control:

[0082] Gene tree depth ≤ 3 layers (high-order functions are prohibited from being nested more than 3 layers)

[0083] Dynamic constants are only allowed in leaf nodes.

[0084] (2) Population screening and replacement:

[0085] Screening rules: eliminate individuals that do not meet physical constraints;

[0086] Replacement strategy: Fill with new individuals that meet complexity control.

[0087] (3) Neural network coefficient optimization:

[0088] Optimizer: Adam (β1=0.9,β2=0.999, learning rate 0.001)

[0089] The loss function adopts the mean square error form;

[0090] Physical Constraint Module:

[0091] Activation energy Q: projected to [129.6,158.4] kJ / mol

[0092] Material coefficient A: limited to [10 -15 ,10-6 ]

[0093] Stress exponent n: limited to [1,10]

[0094] Termination condition: loss L < 1×10 -5 .

[0095] (4) Fitness evaluation and population evolution:

[0096] Fitness function: mean square error (MSE)

[0097] Genetic Operations:

[0098] Select: Improved Tournament (size = 32)

[0099] Crossover: One-point crossover (probability 0.3) and two-point crossover (probability 0.2)

[0100] Mutation: Tensor mutation (probability 0.1, amplitude ±0.2σ)

[0101] Rebasing: Dynamic Constant Regeneration

[0102] Elite retention: The top two individuals in each generation are directly retained.

[0103] (5) Iteration termination:

[0104] Conditions: Tensor similarity SSIM>0.99** and parameter physical consistency PCI>0.95

[0105] Or reach the maximum number of iterations: 500 generations.

[0106] 5. Model verification and output

[0107] After optimization, the final equation for nonlinear coupling was obtained. Performance indicators, including the mean square error (MSE) and correlation coefficient, were tested and evaluated. Comparison showed an 80% improvement in computational efficiency compared to traditional GEP methods.

[0108]

[0109] Aiming at the nonlinear response characteristics of tin-silver-copper alloy (SAC305) under multi-physical field coupling, the present invention proposes a symbolic regression technology that integrates tensor dimensional transformation and neural network parameter decoupling. Creep strain-time tensor data is obtained through nanoindentation experiments, and a nonlinear function set including protected hyperbolic sine functions, tensor operations, and dynamic neural coefficients is constructed; multi-dimensional parameter coupling is achieved using tensor slice evolution technology, and decoupling parameters are optimized in combination with neural network gradient backpropagation; parameter dimension separation is achieved by controlling the gene tree tensor structure, and the model is iteratively optimized based on an improved tournament selection strategy. Experiments show that the tensor similarity (SSIM) between the predicted strain and the actual value reaches 0.992, and the parameter decoupling efficiency is improved by 57%, which is significantly better than the traditional GEP method and finite element simulation. This invention combines tensor evolution operations with neural decoupling mechanisms for the first time, providing a new paradigm for cross-scale mechanical modeling of electronic packaging materials.

Claims

1. A creep constitutive modeling method based on GEP tensor evolution and neural coefficient separation, characterized by: The following steps are involved: Step S1: Set the test variables, conduct creep experiments, obtain test values, and process the test values ​​and divide them into a training set and a validation set; Step S2: construct a gene expression programming model containing a nonlinear function set, and define the initial population model according to the depth-first strategy; Step S3: Generate the initial population; Step S4: Screen and replace the individuals in the initial population so that each individual has the iteration parameters and physical coefficients to obtain the updated population; Step S5: Based on the training set in step S1, the neural network learning rate is set, the neural network loss function is defined, and the physical coefficient of each individual in the updated population is trained and optimized using the neural network to output the optimal physical coefficient; Step S6: Based on the validation set of step S1, perform mean square error fitness evaluation according to the individual optimal physical coefficient obtained in step S5, screen out the optimal individual, operate on the remaining individuals and then perform screening and replacement, so that the remaining individuals with iteration parameters and physical coefficients are merged with the optimal individual into the latest population, and judge whether the fitness of the optimal individual of the latest population reaches the threshold or whether the maximum number of iterations is reached. If so, terminate the iteration and output the optimal individual; if not, proceed to the next step; Step S7: Repeat steps S5-S6 until the termination condition is reached, terminate the iteration, and output the optimal individual.

2. The method according to claim 1, characterized in that The experimental variables in step S1 include stress σ, strain ε, temperature T, loading rate rate, strain rate 3. The method according to claim 1, characterized in that The test value processing in step S1 is specifically as follows: denoising the data, removing outliers, and then converting the test value into a tensor form.

4. The method according to claim 3, characterized in that The initial population model of step S2 is: Where A is the material coefficient; α is the stress coefficient; n is the stress exponent; Q is the activation energy; R is the gas constant; and T is the temperature.

5. The method according to claim 4, characterized in that Step S3 generates the initial population as follows: Define the generation parameters, population size, link function, artificial head structure of the initial population model, randomly generate the tail structure, and generate the initial population; define the material coefficient A, stress index n, and activation energy Q as physical coefficients.

6. The method according to claim 5, characterized in that The operator Function of the artificial head structure and tail structure in step S3 is as follows: Function=[+,-,×,÷,sin,cos,tan,square,tanh,protected_pow,protected_exp,protected_sinh,protected_log] Among them, protected_pow, protected_exp, protected_sinh, and protected_log are custom data protection functions; The protected hyperbolic sine function protected_sinh is defined as: The protected hyperbolic sine function protected_pow is defined as: The protected hyperbolic sine function protected_exp is defined as: The protected hyperbolic sine function protected_log is defined as: The terminators of the artificial header and tail structures in S3 are as follows: Constant terminator constant_terminal: [5,5e -8 ,3.5,-144000,8.314], 5 is the material constant, 5e -8 is the stress coefficient, 3.5 is the stress exponent, 144000 is the activation energy, and 8.314 is the gas constant; Random constant terminator ephemeral_terminal: [α, β, γ], where the dynamic random constants α, β, and γ are generated by the following formula: C dynamic =random(-10,10); Physical coefficient terminal NN terminal: [A,n,Q].

7. The method according to claim 1, characterized in that The neural network loss function defined in step S5 is specifically: Among them, ε pred is the predicted value of individual strain after the neural network training optimization using the dataset; ε actual is the true strain in the validation set.

8. The method according to claim 1, characterized in that Step S6 performs the following operations on the remaining individuals: single-point crossover, two-point crossover, mutation, and base-transfer.

9. The method according to claim 8, characterized in that Set the population size in step S3 to 500, set the iteration number in step S6 to 500, and the optimal individual obtained in step S6, that is, the creep constitutive model, is as follows:

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