A rheological stress prediction optimization method based on convergent Monte Carlo optimization model

Abstract

The present invention discloses a rheological stress prediction optimization method based on a convergent Monte Carlo optimization model, which is specifically as follows: the input source data is imported in a slice-like manner, a multi-layer coupled strain variable factor is constructed to obtain a multi-order improved constitutive model, and a fifth-order fitting equation of the constitutive model is obtained by fitting; the thermal activation energy calculated by the traditional constitutive model is used as the exploration space reference point, the random space exploration range of the thermal activation energy is initialized, and a convergent Monte Carlo optimization model is constructed; the convergent Monte Carlo simulation randomly generates new thermal activation energy, calculates the mean square error of the new stress and the real stress, and compares it with the result predicted by the constitutive model until the number of cycles is met or the optimization target is reached. Compared with the prior art, the present invention optimizes the thermal activation energy in the improved constitutive model, and improves the accuracy of the corresponding activation energy of all strain variable nodes by feedback correction.

Description

Technical Field

[0001] The invention belongs to the field of physical property prediction model construction in metal hot processing process, and specifically designs a rheological stress prediction optimization method based on a convergent Monte Carlo optimization model. Background Art

[0002] The hot compression process of metal materials is an important processing procedure in the machinery manufacturing industry. Materials can only become parts or blanks after hot processing, which not only enables the materials to obtain a certain geometric shape, but more importantly, gives the materials the final composition, organization and performance. In the high-temperature deformation process, the flow stress is one of the plasticity indicators of the material. It refers to the yield strength exhibited when the material reaches the yield limit under a certain deformation temperature, strain and strain rate. It is a comprehensive reflection of the evolution of the internal microstructure and performance changes of the metal during the deformation process. There is a relatively complex relationship between the flow stress value of the material and the deformation parameters. The Arrhenius type equation is usually used to apply mathematical statistics methods to establish the traditional phenomenological constitutive equation of metal materials. This model is generally used for steady-state stress or the stress value corresponding to a certain strain variable to describe the relationship between strain rate, deformation temperature and stress. So far, a large number of metal materials have established thermal deformation constitutive relations based on this equation, and multi-order improved constitutive models can be obtained by coupling strain variable factors.

[0003] However, the traditional constitutive relationship based on the Arrhenius equation cannot be well applied to all deformation conditions and metal material types, resulting in insufficient prediction accuracy. At the same time, the traditional polynomial lacks comprehensive consideration of the interaction of multiple deformation parameters and cannot effectively describe the behavior of metal materials under complex deformation conditions. Summary of the invention

[0004] Purpose of the invention: In response to the problems in the background technology, the present invention discloses a rheological stress prediction optimization method based on a convergent Monte Carlo optimization model. A Monte Carlo optimization model is added to the traditional phenomenological constitutive equation, the corresponding thermal activation energy Q in all strain variable stages is corrected, and the final rheological stress prediction value is determined.

[0005] Technical solution: The present invention discloses a rheological stress prediction optimization method based on a convergent Monte Carlo optimization model, establishes an improved constitutive model of coupled strain variables, and fits a fifth-order fitting equation of all parameters required by the constitutive model including activation energy; introduces a convergent Monte Carlo optimization model to optimize and correct the thermal activation energy, and further optimizes the rheological stress prediction.

[0006] Furthermore, establishing a fifth-order fitting improved constitutive model of coupled strain variables includes the following steps:

[0007] Step 1: Based on the traditional phenomenological constitutive equation, the strain variable is taken as λ as a gradient, combined with the thermal activation energy formula and the Zener-Hollomon parameter equation, and the parameters required to predict the flow stress equation are obtained by linear regression: α, n, Q and lnA;

[0008] Thermal activation energy formula:

[0009] Zener-Hollomon parameter equation:

[0010] The parameters A, n1, n, α, and β are obtained by fitting the following formula and the flow stress detected by the material;

[0011]

[0012] Where: T is Kelvin temperature (K), R is the gas constant (8.314 J mol -1 ·K -1 ), is the strain rate (s -1 ), Q is the activation energy (J·mol -1 ), σ is the flow stress (MPa), and its value is the peak stress; A, n1, n, α, β are material constants, all of which are obtained based on the flow stress curve of the material, and the strain factor α = β / n1; the traditional phenomenological constitutive equation is constructed to predict the flow stress σ, and the phenomenological constitutive equation can be expanded into the following formula:

[0013]

[0014] Step 2: Calculate the polynomial function under the coupled strain variable. First, the original experimental data needs to be sliced ​​and classified. After the original data is imported, the flow stress data is arranged in ascending order according to the three groups of variable parameters: temperature, strain rate, and strain variable. The corresponding stress value is taken out for each interval of λ strain variable. The obtained data is a layer and is superimposed on the slice list one by one.

[0015] Step 3: Then import the slice list data into the constitutive equation for calculation, calculate the required parameters: α, n, Q and lnA, and use the quintic polynomial to fit the material constants, as shown in the following formula:

[0016] α(ε)=α0+α1ε+α2ε 2 +α3ε 3 +α4ε 4 +α5ε 5

[0017] n(ε)=n0+n1ε+n2ε 2 +n3ε3 +n4ε 4 +n5ε 5

[0018] Q(ε)=Q0+Q1ε+Q2ε 2 +Q3ε 3 +Q4ε 4 +Q5ε 5

[0019] lnA(ε)=A0+A1ε+A2ε 2 +A3ε 3 +A4ε 4 +A5ε 5

[0020] Among them, α(ε), n(ε), Q(ε), lnA(ε) are the required parameters. The calculation functions of α, n, Q and lnA reflect the relationship between the strain variable ε. i , n i , Q i , A i The parameters are the material parameters obtained in the fifth-order fitting process, i=0~5.

[0021] Furthermore, in step 2, the corresponding stress value is taken for each interval λ strain variable, and the value is taken by averaging the two sets of data before and after the required value is taken.

[0022] Furthermore, the convergent Monte Carlo optimization model optimizes the thermal activation energy, thereby further optimizing the rheological stress prediction. The specific process is as follows:

[0023] Assuming there are m groups of temperature parameters and n groups of deformation rate parameters, a total of mn groups of data are obtained;

[0024] (1) Based on a certain strain value as a slice, mn slice data with different temperatures and strain rates as the sample space will be obtained; the total strain value is α; the slice step size is set to λ, where α is an integer multiple of λ, and the number of slices is α / λ;

[0025] (2) In the sample space, the value of the thermal activation energy Q calculated by the traditional phenomenological constitutive equation is used as the reference point of the exploration space, and the activation energy at this time is defined as the initial activation energy Q i , initialize Q i The random space exploration range is within 10%, and the shrinkage parameter converges to 10 times the range, and a convergent Monte Carlo simulation method is constructed;

[0026] (3) The activation energy Q randomly generated in each Monte Carlo simulation jBring in mn groups of sample spaces with different temperatures and strain rates, and calculate the corresponding mn stresses again according to the constitutive equation. At this time, the mean square error between the new stress and the true stress is compared with the result predicted by the traditional phenomenological constitutive equation. r When it is smaller than the mean square error S0 calculated by the traditional phenomenological constitutive equation, the calculation results are optimized;

[0027] (4) Migrate the exploration space reference point to the newly established Q j At the reference point, in order to ensure that possible optimization points near the sample space are not missed, the exploration is continued with the exploration space with the same intercept. After reaching the set number of cycles, the new thermal activation energy is output and the new predicted stress value is calculated and output.

[0028] Furthermore, the thermal activation energy after Monte Carlo optimization is re-substituted into the traditional phenomenological constitutive equation, and the optimized thermal activation energy is used to replace Q(ε) fitted in the fifth-order polynomial to calculate the flow stress data.

[0029] Furthermore, a threshold is set for the invalid random process in the sample space, and each time a new optimization benchmark point Q is explored j When the invalid random exploration exceeds the threshold setting, it means that the Monte Carlo exploration density is lower than the probability distribution between the new target and the current target. n It is obtained based on a fifth-order fitting function with continuous differentiability. On this basis, the original exploration space is converged with the initialized shrinkage rate, and a convergent Monte Carlo simulation is performed in a smaller range.

[0030] Furthermore, when using the convergent Monte Carlo optimization model for optimization, the relative average error ΔAARE is used to calculate the error. The formula is as follows:

[0031]

[0032] in, is the stress value detected by the experiment, is the predicted stress value, N is the number of data, and the relative average error between the traditional phenomenological constitutive equation and the convergent Monte Carlo simulation can be obtained through calculation.

[0033] Beneficial effects:

[0034] The present invention adds a Monte Carlo optimization model on the basis of the traditional phenomenological constitutive equation, corrects the corresponding thermal activation energy Q in all strain variable stages, and determines the final rheological stress prediction value after the correction. The prediction value is more accurate than the traditional model. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a flow chart of the convergent Monte Carlo optimization model prediction method;

[0036] Figure 2 Activation energy before and after the Monte Carlo model correction. DETAILED DESCRIPTION

[0037] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0038] The present invention discloses a rheological stress prediction optimization method based on a convergent Monte Carlo optimization model, establishes an improved constitutive model of coupled strain variables, and fits the fifth-order fitting equation of all parameters required by the constitutive model, including activation energy; introduces a convergent Monte Carlo optimization model to optimize and correct the thermal activation energy, and further optimizes the rheological stress prediction. Specifically, the following process is included:

[0039] Step 1. Construct a fifth-order improved constitutive model of coupled strain variables.

[0040] On the basis of the traditional phenomenological constitutive equation, the strain variable is taken as λ as a gradient, combined with the thermal activation energy formula: and the Zener-Hollomon parameter equation: The parameters required for predicting the flow stress equation: α, n, Q and lnA are obtained by linear regression.

[0041] The parameters A, n1, n, α, and β are obtained by fitting the following formula and the flow stress detected by the material;

[0042]

[0043] Where: T is Kelvin temperature (K), R is the gas constant (8.314 J mol -1 ·K -1 ), is the strain rate (s -1 ), Q is the activation energy (J·mol -1 ), σ is the flow stress (MPa), and its value is the peak stress; A, n1, n, α, β are material constants, all of which are obtained based on the flow stress curve of the material, and the strain factor α = β / n1; the traditional phenomenological constitutive equation is constructed to predict the flow stress σ, and the phenomenological constitutive equation can be expanded into the following formula:

[0044]

[0045]

[0046] To calculate the polynomial function under the coupled strain variable condition, it is first necessary to slice and classify the original experimental data. After importing the original data, the flow stress data are arranged in ascending order according to the three groups of variable parameters: temperature, strain rate, and strain variable. The corresponding stress value is taken out for each interval of λ strain variable. The value is taken by averaging the two groups of data before and after the required value is taken. The obtained data is a layer, which is superimposed on the slice list one by one.

[0047] Then the slice list data is imported into the constitutive equation for calculation, and the required parameters are calculated: α, n, Q and lnA. The material constants are fitted using a quintic polynomial, as shown in the following formula:

[0048] α(ε)=α0+α1ε+α2ε 2 +α3ε 3 +α4ε 4 +α5ε 5

[0049] n(ε)=n0+n1ε+n2ε 2 +n3ε 3 +n4ε 4 +n5ε 5

[0050] Q(ε)=Q0+Q1ε+Q2ε 2 +Q3ε 3 +Q4ε 4 +Q5ε 5

[0051] lnA(ε)=A0+A1ε+A2ε 2 +A3ε 3 +A4ε 4 +A5ε 5

[0052] Among them, α(ε), n(ε), Q(ε), lnA(ε) are the required parameters. The calculation functions of α, n, Q and lnA reflect the relationship between the strain variable ε. i , n i , Q i , A i The parameters are the material parameters obtained in the fifth-order fitting process, i=0~5.

[0053] Step 2. Convergence Monte Carlo Optimization

[0054] Assuming there are m groups of temperature parameters and n groups of deformation rate parameters, a total of mn groups of data are obtained.

[0055] (1) Based on a certain specific strain value as a slice, mn slice data with different temperatures and strain rates as the sample space will be obtained; the total strain value is α; the slice step size is set to λ (α is an integer multiple of λ), and the number of slices is α / λ.

[0056] (2) In this sample space, the value of thermal activation energy Q calculated by the traditional phenomenological constitutive equation is used as the reference point of the exploration space, and the activation energy at this time is defined as the initial activation energy Q i , initialize Q i The random space exploration range is within 10%, and the shrinkage parameter converges to 10 times the range, and a convergent Monte Carlo simulation method is constructed.

[0057] (3) Q randomly generated in each Monte Carlo simulation j Bring in mn groups of sample spaces with different temperatures and strain rates, and calculate the corresponding mn stresses again according to the constitutive equation. At this time, the mean square error between the new stress and the true stress is calculated and compared with the result predicted by the traditional phenomenological constitutive equation. r When it is smaller than the mean square error S0 calculated by the traditional phenomenological constitutive equation, the calculation results are optimized;

[0058] (4) Migrate the exploration space reference point to the newly established Q j At the reference point, in order to ensure that the possible optimization points near the sample space are not missed, the exploration is continued with the exploration space with the same intercept, and a new predicted stress value is output after reaching the set number of cycles (n is set to 100, m ≥ 10000 in the figure).

[0059] To ensure effective convergence of the model, a threshold is set for the invalid random process in the sample space. j When the invalid random exploration exceeds the threshold setting, it means that the Monte Carlo exploration density is lower than the probability distribution between the new target and the current target. n It is obtained based on a fifth-order fitting function and is continuously differentiable. On this basis, the original exploration space can be converged with the initialized shrinkage rate, and a convergent Monte Carlo simulation can be performed in a smaller range.

[0060] Step 3. Model error calculation

[0061] The model error is calculated using the relative average error ΔAARE calculation method. Since the average relative error is unbiased in the analysis of the predictive performance of the constitutive model, it can better evaluate the accuracy of the prediction model. The formula is as follows:

[0062]

[0063] in, is the stress value detected by the experiment, is the predicted stress value, n is the number of data, and the relative average error between the traditional phenomenological constitutive equation and the convergent Monte Carlo simulation can be obtained through calculation.

[0064] In this embodiment, the experimental material data is selected as the flow stress curve of 18CrNiMo7-6 material to calculate all parameters of the fifth-order improved constitutive model for constructing coupled strain variables, and the fitting parameters of the fifth-order polynomial are shown in the following table:

[0065] Table 1 Quintic polynomial fitting coefficients

[0066]

[0067] The flow stress data of each stage calculated by the quintic polynomial is compared with the stress data in the flow stress curve in the original test, and the error value is obtained by combining the relative average error ΔAARE calculation method to obtain the traditional phenomenological constitutive equation prediction error value ΔAARE A =4.75%.

[0068] On the basis of the traditional phenomenological constitutive equation, a Monte Carlo optimization model is added to correct the corresponding thermal activation energy Q in all strain variable stages, and a new set of thermal activation energy data is obtained after correction, as follows Figure 2 shown.

[0069] Substitute the thermal activation energy after Monte Carlo optimization back into the traditional phenomenological constitutive equation calculated in step 1, replace the Q(ε) fitted in the fifth-order polynomial with the optimized thermal activation energy, calculate the flow stress data and compare it with the stress data in the flow stress curve in the original test, and combine the relative average error ΔAARE calculation method to obtain the error value, and the relative average error of the convergent Monte Carlo simulation is ΔAARE M =2.12%.

[0070] The above contents described in the present invention are merely examples of the present invention. Those skilled in the art may make various modifications to the specific embodiments described or replace them with similar methods, which shall fall within the protection scope of the present invention as long as they do not deviate from the contents of the present invention description or exceed the scope defined in the claims.

Claims

1. A rheological stress prediction optimization method based on a convergent Monte Carlo optimization model, characterized in that: An improved constitutive model of coupled strain variables is established, and the fifth-order fitting equations of all parameters required by the constitutive model, including the activation energy, are fitted; a convergent Monte Carlo optimization model is introduced to optimize and correct the thermal activation energy, and further optimize the rheological stress prediction.

2. The method for rheological stress prediction and optimization based on a convergent Monte Carlo optimization model according to claim 1, characterized in that: The establishment of the fifth-order fitting improved constitutive model of coupled strain variables includes the following steps: Step 1: Based on the traditional phenomenological constitutive equation, the strain variable is taken as λ as a gradient, combined with the thermal activation energy formula and the Zener-Hollomon parameter equation, and the parameters required to predict the flow stress equation are obtained by linear regression: α, n, Q and lnA; Thermal activation energy formula: Zener-Hollomon parameter equation: The parameters A, n1, n, α, and β are obtained by fitting the following formula and the flow stress detected by the material; Where: T is Kelvin temperature (K), R is the gas constant (8.314 J mol -1 ·K -1 ), is the strain rate (s -1 ), Q is the activation energy (J·mol -1 ), σ is the flow stress (MPa), and its value is the peak stress; A, n1, n, α, β are material constants, all of which are obtained based on the flow stress curve of the material, and the strain factor α = β / n1; the traditional phenomenological constitutive equation is constructed to predict the flow stress σ, and the phenomenological constitutive equation can be expanded into the following formula: Step 2: Calculate the polynomial function under the coupled strain variable. First, the original experimental data needs to be sliced ​​and classified. After the original data is imported, the flow stress data is arranged in ascending order according to the three groups of variable parameters: temperature, strain rate, and strain variable. The corresponding stress value is taken out for each interval of λ strain variable. The obtained data is a layer and is superimposed on the slice list one by one. Step 3: Then import the slice list data into the constitutive equation for calculation, calculate the required parameters: α, n, Q and lnA, and use the quintic polynomial to fit the material constants, as shown in the following formula: α(ε)=α0+α1ε+α2ε 2 +a3e 3 +a4e 4 +a5e 5 n(ε)=n0+n1ε+n2ε 2 +n3e 3 +n4e 4 +n5e 5 Q(ε)=Q0+Q1ε+Q2ε 2 +Q3e 3 +Q4e 4 +Q5e 5 lnA(ε)=A0+A1ε+A2ε 2 +A3e 3 +A4e 4 +A5e 5 Among them, α(ε), n(ε), Q(ε), lnA(ε) are the required parameters. The calculation functions of α, n, Q and lnA reflect the relationship between the strain variable ε. i , n i , Q i , A i The parameters are the material parameters obtained in the fifth-order fitting process, i=0~5.

3. The method for rheological stress prediction and optimization based on a convergent Monte Carlo optimization model according to claim 2, characterized in that: In step 2, the corresponding stress value is taken out for each interval λ strain variable, and the value is taken in a manner of finding the average of two groups of data before and after the required value is taken.

4. The method for rheological stress prediction and optimization based on a convergent Monte Carlo optimization model according to claim 2, characterized in that: The convergent Monte Carlo optimization model optimizes the thermal activation energy, thereby further optimizing the rheological stress prediction. The specific process is as follows: Assuming there are m groups of temperature parameters and n groups of deformation rate parameters, a total of mn groups of data are obtained; (1) Based on a certain strain value as a slice, mn slice data with different temperatures and strain rates as the sample space will be obtained; The total strain is α; Set the slicing step size to λ, where α is an integer multiple of λ and the number of slices is α / λ; (2) In the sample space, the value of the thermal activation energy Q calculated by the traditional phenomenological constitutive equation is used as the reference point of the exploration space, and the activation energy at this time is defined as the initial activation energy Q i , initialize Q i The random space exploration range is within 10%, and the shrinkage parameter converges to 10 times the range, and a convergent Monte Carlo simulation method is constructed; (3) The activation energy Q randomly generated in each Monte Carlo simulation j Bring in mn groups of sample spaces with different temperatures and strain rates, and calculate the corresponding mn stresses again according to the constitutive equation. At this time, the mean square error between the new stress and the true stress is compared with the result predicted by the traditional phenomenological constitutive equation. r When it is smaller than the mean square error S0 calculated by the traditional phenomenological constitutive equation, the calculation results are optimized; (4) Migrate the exploration space reference point to the newly established Q j At the reference point, in order to ensure that possible optimization points near the sample space are not missed, the exploration is continued with the exploration space with the same intercept. After reaching the set number of cycles, the new thermal activation energy is output and the new predicted stress value is calculated and output.

5. The method for rheological stress prediction and optimization based on a convergent Monte Carlo optimization model according to claim 4, characterized in that: The thermal activation energy after Monte Carlo optimization is re-substituted into the traditional phenomenological constitutive equation, and the optimized thermal activation energy is used to replace the Q(ε) fitted in the fifth-order polynomial to calculate the flow stress data.

6. The method for rheological stress prediction and optimization based on a convergent Monte Carlo optimization model according to claim 4, characterized in that: For the invalid random process in the sample space, the threshold is set, and each time a new optimization benchmark point Q is explored j When the invalid random exploration exceeds the threshold setting, it means that the Monte Carlo exploration density is lower than the probability distribution between the new target and the current target. n It is obtained based on a fifth-order fitting function with continuous differentiability. On this basis, the original exploration space is converged with the initialized shrinkage rate, and a convergent Monte Carlo simulation is performed in a smaller range.

7. The method for rheological stress prediction and optimization based on a convergent Monte Carlo optimization model according to claim 4, characterized in that: When using the convergent Monte Carlo optimization model for optimization, the relative average error ΔAARE is used to calculate the error. The formula is as follows: in, is the stress value detected by the experiment, is the predicted stress value, N is the number of data, and the relative average error between the traditional phenomenological constitutive equation and the convergent Monte Carlo simulation can be obtained through calculation.

Images