Material flow stress prediction method and system based on transfer learning algorithm

Abstract

A method and system for predicting the flow stress of materials based on a transfer learning algorithm. After combining auxiliary training data and target training data to generate a model training set, an improved two-stage TrAdaBoost.R2 algorithm is used to train a flow stress prediction model on the model training set. A model with the minimum regression error on the target training data is obtained through cross-validation, and the algorithm hyperparameters are adjusted until an optimal model is obtained. The optimal model is used to predict the material flow stress curve, and the obtained stress-strain prediction curve is used for the numerical simulation of the material. The present invention only needs to conduct a small number of mechanical experiments on this batch of metals, and apply the transfer learning algorithm to the current experimental data and known data sets for training, and then a relatively accurate flow stress prediction result within the temperature and strain rate ranges included in the data set for this batch of metals can be obtained.

Description

Technical Field

[0001] The present invention relates to a prediction technology in the field of material mechanics, specifically a method and system for predicting material flow stress based on an improved two-stage TrAdaBoost.R2 algorithm. Background Art

[0002] The constitutive relationship refers to the situation where the flow stress of a material changes under the influence of factors such as temperature, strain rate, and strain during the deformation process, which plays an important role in material numerical simulation. The accuracy of numerical simulation largely depends on the accuracy of the constitutive relationship. Therefore, the research on material constitutive relationship has important engineering application value and significance in the aerospace field. Since the response of the deformation behavior of materials at high temperature and high strain rate is highly nonlinear, and many factors affecting the flow stress are also nonlinear, the accuracy of predicting flow stress by regression methods is relatively low and the applicable range is limited. In recent years, a material flow stress prediction model based on machine learning has been developed to make its performance similar to or better than that of traditional constitutive equations.

[0003] However, because the acquisition of flow stress data of materials under different conditions is relatively expensive, if the existing experimental data of material flow stress can be fully utilized, the predictable range of the model can be effectively expanded and the prediction ability of the model can be enhanced. Since the existing experimental data come from different sources, the experimental conditions and the compositional properties of the materials cannot be exactly the same as those of the material to be modeled, that is, the independent and identically distributed conditions are not satisfied. Therefore, training a model on this data set belongs to a transfer learning problem. And in previous studies, there has been no relevant research on applying transfer learning algorithms to the prediction modeling of material flow stress. Summary of the Invention

[0004] Aiming at the limitation that the current machine learning methods applied to flow stress prediction are limited to independently and identically distributed data in the prior art, the present invention proposes a method and system for predicting material flow stress based on a transfer learning algorithm. Only a small number of mechanical experiments need to be carried out on this batch of metals, and the transfer learning algorithm is applied to the current experimental data and the known data set for training, and then relatively accurate prediction results of the flow stress of this batch of metals within the temperature and strain rate ranges included in the data set can be obtained. For example, if the data set contains data at high temperature and high strain rate, and the experimental conditions are insufficient, mechanical experiments can be carried out at normal temperature and low strain rate, and through the transfer learning algorithm, training is carried out on the data set and the existing experimental data to obtain a constitutive relationship model capable of predicting the flow stress of this batch of metals at high temperature and high strain rate. To achieve the effects of reducing experimental costs, improving R & D efficiency, and guiding production practice.

[0005] The present invention is realized through the following technical solutions:

[0006] The present invention relates to a method for predicting the flow stress of materials based on a transfer learning algorithm. After combining the auxiliary training data and the target training data to generate a model training set, an improved two-stage TrAdaBoost.R2 algorithm is used to train the flow stress prediction model on the model training set. A model with the minimum regression error on the target training data is obtained through cross-validation, and the algorithm hyperparameters are adjusted until the optimal model is obtained. The optimal model is used to predict the material flow stress curve, and the obtained stress-strain prediction curve is used for the numerical simulation of the material.

[0007] The method specifically includes:

[0008] Step 1: Collect and organize the known flow stress experimental data of materials similar to the material to be predicted as a reusable auxiliary training data set;

[0009] The auxiliary training data set contains at least three sets of flow stress experimental data of similar materials from different sources, and the data in the auxiliary training data set covers at least the temperature and strain rate ranges of the flow stress data of the material to be predicted obtained through experiments.

[0010] The more different sources of similar material data are included in the auxiliary training data set, the greater the possibility that the improved two-stage TrAdaBoost.R2 algorithm selects data that has a positive effect on predicting the flow stress of the material to be predicted through weight change, and the better the knowledge transfer effect. At the same time, the temperature and strain rate ranges covered by the data in the auxiliary data set determine the upper limit of the model's predictable range. Therefore, the data in the auxiliary training data set should be as much as possible, that is, it includes more flow stress experimental data of similar materials from different sources and a larger temperature and strain rate range covered by the experimental data.

[0011] The TrAdaBoost.R2 algorithm is described in Pardoe D, Stone P. "Boosting for Regression Transfer" ([C] / / Proceedings of the 27th International Conference on Machine Learning (ICML-10), June 21-24, 2010, Haifa, Israel. DBLP, 2010.)

[0012] The materials similar to the material to be predicted refer to: materials with similar but not necessarily identical compositions, and similar but not necessarily identical processing technologies, that is, materials belonging to the same category but not completely identical, and processes belonging to the same operation means but with not completely identical process parameters.

[0013] The specific flow stress experimental data mentioned above refer to: the data points corresponding to the stress-strain curves of the material at different temperatures and different strain rates. The units of these data points are: temperature T (K), strain rate strain ε, and stress σ (MPa).

[0014] The auxiliary training data set mentioned above is a plurality of reusable instances, where each instance is all the flow stress data from the same material.

[0015] Step 2: Obtain the flow stress experimental data of the material to be predicted through mechanical experiments as the target training data set;

[0016] The target training data set mentioned above contains a plurality of instances, where each instance is a data point of the experimental data of the material to be predicted.

[0017] For the mechanical experiments mentioned above, obtain the data included in at least 3 flow stress curves with different combinations of temperature and strain rate.

[0018] Step 3: Combine the auxiliary training data and the target training data as the data set for training the flow stress prediction model;

[0019] For the flow stress prediction model mentioned above, its input is temperature, strain rate, and strain, and the output is stress. Specifically, the model is: y i = σ, and the model is a mapping from the input space to the output space mapping

[0020] Step 4: Use the improved two-stage TrAdaBoost.R2 algorithm for model training, and obtain the model with the minimum regression error on the target training data through cross-validation. Adjust the algorithm hyperparameters until the optimal model is obtained.

[0021] The improved two-stage TrAdaBoost.R2 algorithm mentioned above belongs to an instance-based transfer learning algorithm, and its base regressor is the K-nearest neighbor regression. The specific steps include:

[0022] Step ① Intersect the sample spaces of the instances in the target training data set T target and the auxiliary training data set T source , take the data in the intersection of the two sample spaces to obtain the current target training data set T', target the current auxiliary training data set T'. source . Use the current target training data set T' target , the current auxiliary training data set T' sourceCall two-stage TrAdaBoost.R2 for the input. Except that the output of two-stage TrAdaBoost.R2 is the weight distribution vector when the error is minimized, it is exactly the same as two-stage TrAdaBoost.R2, using the current auxiliary training dataset T' source The weight corresponding to each instance in source is to uniformly sample the data points in each instance with probability, and incorporate the sampled data into the target training dataset T target ;

[0023] The two-stage TrAdaBoost.R2 algorithm described in step ① includes:

[0024] 1.1 Gradually reduce the weight and the proportion in the total weight of the instances in all auxiliary training sets T source and obtain the optimal solution of the weight ratio through cross-validation. This stage aims to determine the appropriate total weight of the instances in the target training set T target to avoid the problem of too low initial weight of the target training set T target caused by the much smaller data volume of the target training set T than the auxiliary training set T source and update the weights of the instances in the auxiliary training set T target . The way of weight update is to call the base regressor to obtain a learner on the combined training set T, then calculate the weight adjustment error of each instance, and reduce the weight according to the error value. source

[0025] 1.2 On the basis of the determined weight ratio, update the weight distribution of the target domain instances according to the weight update strategy of the Adaboost.R2 algorithm, that is, weight the data points with larger errors. In this stage, the weights of the instances in the auxiliary training set T source remain unchanged. Only save the generated model. Through cross-validation, find the model with the smallest regression error value on the target training set T target as the final training result. source

[0026] Step ② repeats step ① until the current target training dataset T' source after the intersection of the instances in the unvisited auxiliary training dataset T target and the target training dataset T target , and the current auxiliary training dataset T' source are both empty sets. This process aims to perform data augmentation on the target training dataset T target to expand the temperature and strain rate ranges covered by the data in the target training dataset T target and provide more references for subsequent training.

[0027] Step ③ is based on the target training set T target obtained in step ① and combines it with the auxiliary dataset Tsource Merge

[0028] Step ④: Call the two-stage TrAdaBoost.R2 algorithm on the merged training set to obtain the final model.

[0029] Step ⑤: Predict the material flow stress curve, and the prediction result can be used for the numerical simulation of the material.

[0030] The present invention relates to a system for implementing the above method, including: a data acquisition module, a training set generation module, a merging module, a hyperparameter verification module, and a prediction module, where: the data acquisition module collects and organizes a large amount of flow stress data of materials similar to the material to be predicted as a reusable auxiliary training data set (T source ); the training set generation module obtains a small amount of flow stress data of the material to be predicted through experiments as the target training data set (T target ); the merging module merges the auxiliary training data set and the target training data set as the data set (T) for training; the hyperparameter verification module adjusts and improves the hyperparameters of the two-stage TrAdaBoost.R2 algorithm, and through cross-validation, obtains the model with the minimum regression error on the target training data set; the prediction module predicts the material flow stress curve, and the prediction result can be used for the numerical simulation of the material.

[0031] Technical effects

[0032] The present invention as a whole solves the defects / insufficiencies of the prior art that only uses non-transfer learning algorithms (including neural networks and support vector machine regression) to model on the independently and identically distributed flow stress data sets obtained through experiments;

[0033] Compared with the prior art, the present invention first applies the transfer learning algorithm to the prediction of the flow stress curve. Based on the function of the machine learning method to automatically discover and capture the relationship between multi-dimensional inputs and outputs without manual derivation, and can model the response of the highly non-linear deformation behavior of materials at high temperature and high strain rate, the transfer learning algorithm (improved two-stage TrAdaBoost.R2 algorithm) used in the present invention has the ability to obtain knowledge beneficial to the prediction of the flow stress of the material to be predicted from the auxiliary training data set, makes full use of the existing experimental data of the material flow stress, and compared with the non-transfer learning algorithm, only requires a small amount of experimental data of the material to be predicted. It achieves the effects of effectively expanding the predictable range of the model, enhancing the prediction ability of the model, and reducing the time and cost of mechanical experiments. Description of the drawings

[0034] Figure 1 is the flow chart of the method of the present invention;

[0035] Figure 2 is the schematic diagram of the existing transfer learning algorithm;

[0036] Figure 3 This is a schematic diagram of the transfer learning algorithm of the present invention.

[0037] Figure 4 These are the experimental results of the AdaBoost.R2 algorithm (non-transfer learning algorithm), the two-stage TrAdaBoost.R2 algorithm (transfer learning algorithm), and the improved two-stage TrAdaBoost.R2 algorithm (transfer learning algorithm improved for the flow stress prediction problem). Detailed implementation manners

[0038] As Figure 1 shown, this embodiment relates to a method for predicting the flow stress of materials based on a transfer learning algorithm, including:

[0039] Step 1) Collect and organize a large amount of flow stress data of materials similar to the material to be predicted as a reusable auxiliary training dataset (T source ). Among them, the data can come from different sources, such as literature, books, or open-source datasets. If there is already a flow stress dataset of the material to be predicted, it can be directly used without collection and organization. When only temperature, strain rate, and strain are used as input features, similar materials are defined as having similar compositions, processing technologies, and experimental conditions. If the composition or other factors are significantly different, input features should be appropriately increased.

[0040] Step 2) Obtain a small amount of flow stress data of the material to be predicted through experiments as the target training dataset (T target ).

[0041] Step 3) Combine the auxiliary training dataset and the target training dataset as the dataset for training. Among them, the auxiliary training dataset takes the same material from the same source as one instance, and the target training dataset takes each data point obtained through experiments as one instance.

[0042] Step 4) Adjust the hyperparameters of the improved two-stage TrAdaBoost.R2 algorithm. The hyperparameters of the algorithm include the number of iterations, the number of base regressors, the number of cross-validation folds, and the learning rate. All follow the method of first trying hyperparameters in a large range and then fine-tuning within the range of better hyperparameter combinations. Train to obtain the model with the smallest error obtained through cross-validation on the target training dataset as the final model.

[0043] Step 5) If the data in the auxiliary dataset is sufficient, after training is completed, any parameter combination of temperature, strain rate, and strain can be input to predict the material flow stress curve, and the prediction results can be used for numerical simulation of materials.

[0044] Improving the performance of the two-stage TrAdaBoost.R2 algorithm on real datasets proves that it can accurately predict the flow stress curve, and the effect is better than the current common constitutive relation models, such as the Johnson-Cook model. At the same time, as a transfer learning algorithm, it can learn knowledge from the auxiliary dataset, only requiring a small number of mechanical experiments. The prediction accuracy of the obtained model is better than that of the non-transfer neural network algorithm, and it also has a certain prediction ability for the abnormal section of the flow stress curve. For example, it can predict the abnormal hardening phenomenon that occurs in commercially pure titanium in the quasi-static medium temperature section, achieving the effect of guiding production practice.

[0045] In this embodiment, experiments were specifically carried out on the uniaxial compression dataset of commercially pure titanium. The experiments used the data collected from 11 papers as the auxiliary dataset to predict the flow stress of the target commercially pure titanium. The specific experimental process is as follows: The auxiliary dataset contains data from 11 papers. Taking the data from the same source as one instance, there are a total of 11 instances. The target dataset contains 3 (600 data points) known flow stress curves of the commercially pure titanium to be predicted, with a total of 600 instances. The datasets were merged to obtain the training set. The two-stage TrAdaBoost.R2 algorithm was used to train the model on the merged dataset, and the hyperparameters were adjusted. The optimal hyperparameter combination was obtained as k = 5 for K-nearest neighbor regression, the number of iterations S = 10, the maximum boosting number N = 10, the number of cross-validation folds F = 10, and the learning rate α = 0.7. The improved two-stage TrAdaBoost.R2 algorithm was used to train the model on the merged dataset, and the hyperparameters were adjusted. The optimal hyperparameter combination was obtained as k = 5 for K-nearest neighbor regression, the number of iterations K = 5 in the data augmentation stage of step 1, the maximum boosting number N = 10, the number of cross-validation folds F = 10, the learning rate α = 0.7, the number of iterations K = 10 in the model training stage of step 2, the maximum boosting number N = 10, the number of cross-validation folds F = 10, and the learning rate α = 0.7. The non-transfer learning algorithm AdaBoost.R2 was used to train the model on the target dataset, and the hyperparameter was k = 5 for K-nearest neighbor regression. The data points corresponding to the 4 flow stress curves of the commercially pure titanium to be predicted were used as the test set. Among them, these 4 curves are different from the 3 curves included in the target dataset. Figure 4 For the prediction results of the three algorithms, the real curve is the solid line, and the predicted curve is the dotted line.

[0046] The mean square errors of the three algorithms on the test set are as follows: Improved two-stage TrAdaBoost.R2 algorithm: 8.27, two-stage TrAdaBoost.R2 algorithm: 11.40, AdaBoost.R2 algorithm: 19.91. Comparing the results of the AdaBoost.R2 algorithm and the other two transfer learning algorithms, the regression error of the transfer learning algorithm is significantly smaller, verifying the effectiveness of the transfer learning algorithm in the prediction problem of flow stress curves. The regression error of the improved two-stage TrAdaBoost.R2 algorithm is less than that of the two-stage TrAdaBoost.R2 algorithm, verifying that the improved algorithm is more suitable for the prediction problem of flow stress curves. At the same time, from Figure 4 it can be seen that, compared with the other two algorithms, the improved two-stage TrAdaBoost.R2 algorithm has the best prediction ability for the curve shape.

[0047] In the present invention, since the instance data granularity of the dataset in the two-stage TrAdaBoost.R2 algorithm for the flow stress prediction problem is determined, that is, the auxiliary dataset takes the same source material as one instance, and the target dataset takes a single data point as one instance; the K-nearest neighbor algorithm is used as the base regressor. The two-stage TrAdaBoost.R2 algorithm is improved. Before model training, step 1, the data augmentation stage, is added to solve the flow stress prediction problem. The classical transfer learning algorithm, two-stage TrAdaBoost.R2, is improved for flow stress prediction, and a flow stress prediction modeling process based on the transfer learning algorithm is established.

[0048] The above specific implementation can be locally adjusted by those skilled in the art in different ways without departing from the principles and purposes of the present invention. The protection scope of the present invention is subject to the claims and is not limited by the above specific implementation. All implementation solutions within its scope are subject to the present invention.

Claims

1. A method for predicting the flow stress of materials based on a transfer learning algorithm, characterized in that After merging the auxiliary training data and the target training data to generate a model training set, use the improved two-stage TrAdaBoost.R2 algorithm to train the flow stress prediction model on the model training set. Obtain the model with the minimum regression error on the target training data through cross-validation. Adjust the algorithm hyperparameters until the optimal model is obtained. Use the optimal model to predict the material flow stress curve, and use the obtained stress-strain prediction curve for the numerical simulation of the material, specifically including: Step 1: Collect and organize the known flow stress experimental data of materials similar to the material to be predicted as the reusable auxiliary training data set; The auxiliary training data set contains at least three sets of flow stress experimental data of similar materials from different sources, and the data in the auxiliary training data set covers at least the temperature and strain rate ranges of the flow stress data of the material to be predicted obtained through experiments; The materials similar to the material to be predicted refer to: materials with similar compositions but not necessarily exactly the same, and materials with similar processing techniques but not necessarily exactly the same, that is, materials belonging to the same category but not completely the same, and processes belonging to the same operation means but with incomplete process parameters; The specific flow stress experimental data mentioned above refer to: the data points corresponding to the stress-strain curves of the material at different temperatures and different strain rates, and the units of these data points are: temperature T (K), strain rate , strain , stress ; Step 2: Obtain the flow stress experimental data of the material to be predicted through mechanical experiments as the target training data set; Step 3: Merge the auxiliary training data and the target training data as the data set for training the flow stress prediction model; For the described flow stress prediction model, its inputs are temperature, strain rate, and strain, and its output is stress. Specifically, the model is as follows: , , the model is a mapping from the input space to the output space ; ; Step 4: Use the improved two-stage TrAdaBoost.R2 algorithm for model training. Obtain the model with the minimum regression error on the target training data through cross-validation. Adjust the algorithm hyperparameters until the optimal model is obtained; The improved two-stage TrAdaBoost.R2 algorithm belongs to an instance-based transfer learning algorithm, and its base regressor is the K-nearest neighbor regression. The specific steps include: Step ①: Intersect the example spaces of the instances in the target training dataset T target and the auxiliary training dataset T source , take the data in the intersection of the two example spaces, and obtain the current target training dataset T' target , and the current auxiliary training dataset T' source ; Use the current target training dataset T' target , and the current auxiliary training dataset T' source as the input to call two-stage TrAdaBoost.R2'. Among them, two-stage TrAdaBoost.R2' is exactly the same as two-stage TrAdaBoost.R2 except that the output is the weight distribution vector when the error is minimized. Use the weights corresponding to each instance in the current auxiliary training dataset T' source to uniformly sample the data points in each instance with probability, and incorporate the sampled data into the target training dataset T target ; The two-stage TrAdaBoost.R2 algorithm described in Step ① includes: 1.1 Gradually reduce the proportion of the weights and in the total weights of all instances in the auxiliary training set T, and obtain the optimal solution of the weight ratio through cross-validation. This stage aims to determine the appropriate total weight of the instances in the target training set T to avoid the problem of too low initial weights of the target training set T caused by the much smaller data volume of the target training set T than that of the auxiliary training set T, and update the weights of the instances in the auxiliary training set T; the way of weight update is to call the base regressor to obtain a learner on the combined training set T, then calculate the weight adjustment error of each instance, and reduce the weight according to the error value. source in the auxiliary training set T, and obtain the optimal solution of the weight ratio through cross-validation. This stage aims to determine the appropriate total weight of the instances in the target training set T to avoid the problem of too low initial weights of the target training set T caused by the much smaller data volume of the target training set T than that of the auxiliary training set T, and update the weights of the instances in the auxiliary training set T; the way of weight update is to call the base regressor to obtain a learner on the combined training set T, then calculate the weight adjustment error of each instance, and reduce the weight according to the error value. target in the target training set T to avoid the problem of too low initial weights of the target training set T caused by the much smaller data volume of the target training set T than that of the auxiliary training set T, and update the weights of the instances in the auxiliary training set T; the way of weight update is to call the base regressor to obtain a learner on the combined training set T, then calculate the weight adjustment error of each instance, and reduce the weight according to the error value. target The data volume of the target training set T is much smaller than that of the auxiliary training set T source resulting in the problem of too low initial weights of the target training set T, and update the weights of the instances in the auxiliary training set T; the way of weight update is to call the base regressor to obtain a learner on the combined training set T, then calculate the weight adjustment error of each instance, and reduce the weight according to the error value. target resulting in the problem of too low initial weights of the target training set T, and update the weights of the instances in the auxiliary training set T; the way of weight update is to call the base regressor to obtain a learner on the combined training set T, then calculate the weight adjustment error of each instance, and reduce the weight according to the error value. source in the auxiliary training set T; the way of weight update is to call the base regressor to obtain a learner on the combined training set T, then calculate the weight adjustment error of each instance, and reduce the weight according to the error value. 1.2 On the basis of the determined weight ratio, update the weight distribution of the target domain instance according to the weight update strategy of the Adaboost.R2 algorithm, that is, perform weighted processing on the data points with larger errors. In this stage, the weights of the instances in the auxiliary training set T source remain unchanged; only save the generated model; through cross-validation, find the model with the smallest regression error value on the target training set T target as the final training result; Step ② repeats Step ① until the unvisited auxiliary training dataset T source and the instances in the target training dataset T target The current target training dataset T' after the intersection of the example spaces target and the current auxiliary training dataset T' source are both empty sets. This process aims to perform data augmentation on the target training dataset T target and expand the temperature and strain rate ranges covered by the data in the target training dataset T target to provide more references for subsequent training; Step ③ On the basis of the target training set T target obtained in Step ①, merge it with the auxiliary data set T source ; Step ④ Call the two-stage TrAdaBoost.R2 algorithm on the merged training set to obtain the final model; Step ⑤ Predict the material flow stress curve, and the prediction result can be used for the numerical simulation of the material; The more different sources of similar materials the data in the auxiliary training data set comes from, the greater the possibility that the improved two-stage TrAdaBoost.R2 algorithm selects data that has a positive effect on the prediction of the flow stress of the material to be predicted through weight change; the temperature and strain rate ranges covered by the data in the auxiliary data set determine the upper limit of the model's predictable range. Therefore, the data in the auxiliary training data set includes flow stress experimental data of similar materials from more different sources and a larger temperature and strain rate range covered by the experimental data.

2. The method for predicting the flow stress of materials based on the transfer learning algorithm according to claim 1, characterized in that, The auxiliary training data set is a reusable set of multiple instances, where each instance is all the flow stress data of the same material.

3. The method for predicting the flow stress of materials based on the transfer learning algorithm according to claim 1, characterized in that The target training data set contains multiple instances, where each instance is a data point of the experimental data of the material to be predicted.

4. The method for predicting the flow stress of materials based on the transfer learning algorithm according to claim 1, characterized in that, For the mechanical experiment, obtain the data included in at least three flow stress curves with different combinations of temperature and strain rate.

5. A system for implementing the method for predicting the flow stress of materials based on the transfer learning algorithm according to any one of claims 1 to 4, characterized in that, Including: A data acquisition module, a training set generation module, a merging module, a hyperparameter verification module, and a prediction module, where: The data acquisition module collects and collates a large amount of flow stress data of materials similar to the material to be predicted as a reusable auxiliary training data set; The training set generation module obtains a small amount of flow stress data of the material to be predicted through experiments as the target training data set; The merging module merges the auxiliary training data set and the target training data set as the data set for training; The hyperparameter verification module adjusts and improves the hyperparameters of the two-stage TrAdaBoost.R2 algorithm, and through cross-validation, obtains a model with the smallest regression error on the target training data set; The prediction module predicts the material flow stress curve, and the prediction result can be used for the numerical simulation of the material.

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