Method for optimizing titanium alloy heat treatment process through machine learning assisted by uncertainty quantification

Abstract

The invention discloses a method for optimizing a titanium alloy heat treatment process through uncertainty quantification assisted machine learning. The method comprises the steps that S1, a four-factor five-level orthogonal experiment is designed, and a machine learning database is constructed; s2, performing modeling prediction on the heat treatment process and the high-temperature tensile property by using machine learning, considering uncertainty quantization of the model in combination with a resampling method, taking a result of the uncertainty quantization as an index of model screening, selecting a final model, and performing training; and S3, generating a virtual space, carrying out modeling prediction on the high-temperature tensile property of the data in the virtual space by utilizing the selected model, carrying out multi-objective optimization on the high-temperature tensile property to calculate an EIH value, and predicting optimal processing parameters of strong-plasticity matching improvement. According to the method for optimizing the titanium alloy heat treatment process through uncertainty quantification assisted machine learning, the problems that in the prior art, the heat treatment process needs to be continuously adjusted through a trial-and-error method, the cost is too high, and the period is long are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of machine learning applications, and specifically relates to a method for optimizing a titanium alloy heat treatment process by aiding machine learning with uncertainty quantification. Background Art

[0002] Recently, machine learning (ML) has been applied to research in materials science to accelerate material discovery and optimization. Typically, machine learning maps from input to output, where the input is usually features such as composition, processing parameters, and experimental conditions, while the output is related properties such as tensile strength, yield strength, elastic modulus, tensile strain, etc. In terms of heat treatment process optimization of titanium alloys, the traditional method is to continuously adjust the heat treatment process through "trial and error", which is too costly and has a long cycle. Therefore, it is necessary to study a theory-based optimization strategy method that can simultaneously consider a full set of multi-scale information and improve the prediction accuracy of target performance. Summary of the invention

[0003] The purpose of the present invention is to provide a method for optimizing the heat treatment process of titanium alloy by using uncertainty quantification-assisted machine learning, which solves the problem in the prior art that the heat treatment process needs to be continuously adjusted through the "trial and error method", which results in high cost and long cycle.

[0004] The technical solution adopted by the present invention is: a method for optimizing the heat treatment process of titanium alloy by using uncertainty quantification-assisted machine learning, and the specific steps are as follows: S1. Use SPSSAU to design a four-factor five-level orthogonal experiment and build a machine learning database; S2. Use machine learning to model and predict the heat treatment process and high-temperature tensile properties. Combined with the resampling method, the uncertainty quantification of the model is considered, and the results of uncertainty quantification are used as indicators for model screening. The final model is selected and trained. S3, generate the virtual space used for prediction, use the model selected in S2 to model and predict the high-temperature tensile properties of the data in the virtual space, perform multi-objective optimization on the high-temperature tensile properties to calculate the EIH value, and predict the optimal processing parameters for improving the strength-plasticity matching.

[0005] The present invention is also characterized in that: The specific method of S1 is: Based on different processing conditions of titanium alloy, SPSSAU was used to design a four-factor five-level orthogonal experiment. The features of the training model included solution temperature, solution time, aging temperature, and aging time. The aging temperature values ​​were 670℃, 700℃, 730℃, 760℃, and 790℃, respectively; the aging time values ​​were 1h, 2h, 3h, 4h, and 5h, respectively; the solution temperature values ​​were 900℃, 950℃, 1000℃, 1050℃, and 1100℃, respectively; the solution time values ​​were 1h, 2h, 3h, 4h, and 5h, respectively; The corresponding target test performance is output for the orthogonal test, and the target test performance includes high-temperature yield strength and high-temperature fracture elongation. The machine and its learning database are constructed based on the output data.

[0006] S2 medium and high temperature tensile properties include high temperature yield strength and high temperature elongation at break; The specific operation process of S2 is: S2.1. Set up different machine learning models, train them using the original data set, and use the test set to evaluate the trained machine learning models, thereby filtering out the models with the worst overall performance. S2.2. Perform the next step of model training on the remaining machine learning models, model the high temperature yield strength and high temperature fracture elongation respectively, evaluate the performance of different machine learning models, select the best machine learning models corresponding to the high temperature yield strength and high temperature fracture elongation respectively, and use the resampling method to quantify the uncertainty for the next step of optimization; S2.3. Through the analysis of the above model performance and uncertainty quantification indicators, the machine learning models with high regression coefficients and small uncertainties in the test set are selected as the best prediction models for high-temperature yield strength and high-temperature fracture elongation.

[0007] The specific methods for evaluating machine learning models in S2.1~S2.3 are: evaluate the performance of the selected machine learning models respectively. The performance indicators of machine learning models include: regression coefficient R 2 , mean absolute error (MAE) and root mean square error (RMSE), and use the accuracy of the above indicators to evaluate the trained model and select the model with the best performance.

[0008] The original data set in S2.1 is that three parallel samples are taken for each parameter to perform high temperature tensile property test at 700℃, and a total of 25 sets of experimental data are obtained. The experimental data is the average value of the three horizontal samples, which is the original data set; The specific process of S2.1 is: setting support vector regression model SVR, Gaussian regression model GP, random forest RF, calling linear regression model LR and extreme gradient boosting model XGB and other machine learning models from Sklearn, randomly dividing the original data set into test set and training set in a ratio of 2:8, standardizing the training set and test set with the mean and variance of the training set samples, and then using the standardized data to train different machine learning models respectively, and resample the training set data, and select the best machine learning models corresponding to high-temperature yield strength and high-temperature fracture elongation according to the sampled data.

[0009] The specific process of S2.2 is as follows: The random forest model RF, support vector regression model SVR, extreme gradient boosting model XGB and Gaussian regression model GP were selected for re-machine learning modeling; the uncertainty was quantified using the resampling method. The resampling method was to divide the data set after S2.1 standardization into a test set and a training set in a ratio of 2:8, and then use the same model training method as S2.1 to further train the remaining models. The models were trained 1000 times in total to obtain 1000 prediction values.

[0010] The specific process of S2.3 is: by predicting the mean, the standard deviation and the true value, the miscalibration area and the regression coefficient R are calculated. 2 , and then the final model is selected through the uncertainty quantification ability and accuracy of different models.

[0011] The specific operations of S3 are: S3.1. Generate a virtual space for prediction. The virtual space sets four parameters: solution temperature, solution time, aging time and aging temperature. S3.2. The two selected models are used to predict the corresponding high-temperature tensile properties respectively, and the predicted mean and variance are used to perform multi-objective optimization EIH calculation, and the process parameters are sorted from large to small according to the EIH value, and finally the optimal processing parameters are obtained.

[0012] The specific operation of setting the four parameter ranges in S3.1 is as follows: the solution temperature range is determined according to the β phase transformation point of the titanium alloy, the β phase transformation point of the titanium alloy is 1050℃, the two-phase region is 930℃~1050℃, a certain temperature T below the α phase region is determined as the starting temperature, the upper boundary of the solution treatment temperature is T1, the step length is N1℃, where T is 900℃, T1 is 1200℃, N1 is 10℃, and the solution temperature range is 500℃~800℃; The aging temperature is above the service temperature of the titanium alloy, the temperature range is 500~800℃, the step length is N1℃, and the value of N1 is 10℃; The time range used for both solution time and aging time is 0.5~7h, with a step size of N2h and N2 value of 0.5h.

[0013] The specific operation method of S3.2 is as follows: The two models trained in step S2.2 are used to predict the samples in the virtual space, and the heat treatment process with high EIH value is obtained, thereby obtaining the Pareto frontier that takes into account both strength and plasticity indicators; The specific method to obtain the Pareto frontier is as follows: using the expected improvement method based on hypervolume, represents Pareto advantage, and defines Am as all A R m A collection of A: , the elements of m are called approximation sets, and the hypervolume index H (i.e., hypervolume) of the approximation set A is defined as The volume of the dominated subspace (i.e., the points dominated by every element in A) is given by the following formula: H(A)=Vol (1) Improved function based on hypervolume I:R m ×Am→R is defined as I(y, A)=H —H(A)(2) where y R m , and A Am; Given the predictions of the regression model, for some x in X X, in the form of a with mean and standard deviation Independent m-dimensional normal distribution of; The expected improvement at a point X of the approximation set A, denoted as EIH(x,A), is defined as follows: EIH(x,A)= PDFx(y)dy(3) Where the integration region R is R m ; The EIH value is an evaluation indicator for a multi-objective problem. If the EIH value of a data point is larger, it means that this point has the greatest mathematical expectation for pushing the Pareto front forward.

[0014] The beneficial effects of the present invention are: (1) The present invention integrates traditional ML models, such as XGBoost, linear regression model, extreme gradient regression, random forest and other single models to enhance prediction, effectively utilizes existing data, and constructs a quantitative relationship model between solution temperature, solution time, aging temperature and aging time and target characteristics. On this basis, the uncertainty of the model is quantified by the resampling method, and a multi-objective optimization method based on the expected improvement method of the hypervolume is used. The hypervolume index does not require prior knowledge about the Pareto frontier. The set of maximized hypervolume indexes is a subset of the effective set, and the corresponding target vector covers the Pareto frontier. The present invention regards the expected gain of the hypervolume as a generalization of the expected improvement in the multi-objective domain, providing a method from the prediction of material strength or plasticity to the improvement of material strength-plasticity matching. (2) Data-driven modeling in the optimization method of the present invention: using machine learning to predict high-temperature tensile properties improves the accuracy of model prediction; Uncertainty quantification: Evaluate the reliability of model predictions through resampling techniques to ensure the credibility of the results; Multi-objective optimization: Use multi-objective optimization algorithms to balance strength and plasticity and find the best heat treatment process parameters; Virtual space generation: Construct virtual space to predict unknown parameters, reduce the number of experiments, and improve research efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 is an operation flow chart of the optimization method of the present invention; Figure 2 is a graph of the true value and predicted value of the yield strength model in Example 1 of the optimization method of the present invention and its 95% confidence interval; Figure 3 It is a graph of the true value and predicted value of the elongation at break model in Example 1 of the optimization method of the present invention and its 95% confidence interval. DETAILED DESCRIPTION

[0016] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0017] Uncertainty quantification assisted machine learning to optimize the heat treatment process of titanium alloys, such as Figure 1 As shown, the specific steps are as follows: S1. Use SPSSAU to design a four-factor five-level orthogonal experiment and build a machine learning database. The specific method is: Based on different processing conditions of titanium alloy, SPSSAU was used to design a four-factor five-level orthogonal experiment. The features of the training model included solution temperature, solution time, aging temperature, and aging time. The aging temperature values ​​were 670℃, 700℃, 730℃, 760℃, and 790℃, respectively; the aging time values ​​were 1h, 2h, 3h, 4h, and 5h, respectively; the solution temperature values ​​were 900℃, 950℃, 1000℃, 1050℃, and 1100℃, respectively; the solution time values ​​were 1h, 2h, 3h, 4h, and 5h, respectively; The corresponding target test performance is output for the orthogonal test, and the target test performance includes high-temperature yield strength and high-temperature fracture elongation. The machine and its learning database are constructed based on the output data.

[0018] S2. Use machine learning to model and predict the heat treatment process and high-temperature tensile properties, where the high-temperature tensile properties include high-temperature yield strength and high-temperature elongation at break. At the same time, combine the resampling method to consider the uncertainty quantification of the model, and use the uncertainty quantification results as the indicator for model screening. Select the final model and train it. The specific methods for evaluating the machine learning model in the following steps are: Evaluate the performance of the selected machine learning model respectively. The performance indicators of the machine learning model include: regression coefficient R 2 , mean absolute error MAE and root mean square error RMSE, use the accuracy of the above indicators to evaluate the trained model and select the model with the best performance. 2 To evaluate the accuracy of the trained model and to compare different algorithms more systematically, we calculated the mean absolute error (MAE) and root mean square error (RMSE) of different algorithms for comparison, selected the model with better regression coefficient and target performance, modeled the target performance with better parameters and better models, and generated the trained target machine learning model.

[0019] Among them, the specific operation process of S2 is: S2.1. Set different machine learning models and train them respectively through the original data set. The original data set is to take three parallel samples under each parameter to perform high temperature tensile performance test at 700°C, and obtain a total of 25 sets of experimental data. The experimental data is the average value of the three horizontal samples, which is the original data set; and use the test set to evaluate the trained machine learning models respectively, so as to filter out the models with the worst overall performance; The specific process is: set up support vector regression model SVR, Gaussian regression model GP, random forest RF, call linear regression model LR and extreme gradient boosting model XGB and other machine learning models from Sklearn, randomly divide the original data set into test set and training set in a ratio of 2:8, standardize the training set and test set with the mean and variance of the training set samples, and then use the standardized data to train different machine learning models respectively, and resample the training set data, and select the best machine learning models corresponding to high-temperature yield strength and high-temperature fracture elongation according to the sampled data.

[0020] For the yield strength model, the mean absolute error MAE and root mean square error RMSE of different algorithms are similar in size. The Gaussian regression model GP and the extreme gradient boosting model XGB have the smallest errors, while the linear regression model LR, random forest RF and support vector regression model SVR have larger errors. As for the elongation at break, the extreme gradient boosting XGB and random forest RF have the smallest errors, while the errors of the support vector regression model SVR algorithm and the Gaussian regression model GP are greater than the former two, and the linear regression model LR has the largest error.

[0021] S2.2. Perform the next step of model training on the remaining machine learning models, model the high temperature yield strength and high temperature fracture elongation respectively, evaluate the performance of different machine learning models (the method is the same as the above evaluation method), select the best machine learning models corresponding to the high temperature yield strength and high temperature fracture elongation respectively, and use the resampling method to quantify the uncertainty for the next step of optimization; The specific process is: no matter for the selection of prediction models for high-temperature fracture elongation or high-temperature yield strength, there are 2 to 3 models that perform well. At this time, the uncertainty of the model is considered for further screening of the model.

[0022] The random forest model RF, support vector regression model SVR, extreme gradient boosting model XGB and Gaussian regression model GP were selected for re-machine learning modeling; the uncertainty was quantified using the resampling method. The resampling method was to divide the data set after S2.1 standardization into a test set and a training set in a ratio of 2:8, and then use the same model training method as S2.1 to further train the remaining models. The models were trained 1000 times in total to obtain 1000 prediction values.

[0023] S2.3. Through the analysis of the above model performance and uncertainty quantification indicators, the machine learning models with high regression coefficients and small uncertainties in the test set are selected as the best prediction models for high-temperature yield strength and high-temperature fracture elongation.

[0024] The specific process is: the miscalibration area (a method of evaluating uncertainty) is calculated by using the predicted mean, predicted standard deviation and true value, and the regression coefficient R 2 , and then the final model is selected through the uncertainty quantification ability and accuracy of different models.

[0025] S3, generate the virtual space used for prediction, use the model selected in S2 to model and predict the high-temperature tensile properties of the data in the virtual space, perform multi-objective optimization on the high-temperature tensile properties to calculate the EIH value, and predict the optimal processing parameters for improving the strength-plasticity matching. The specific operations are as follows: S3.1. Generate a virtual space for prediction. The virtual space sets four parameters: solution temperature, solution time, aging time and aging temperature. The specific operation of setting the four parameter ranges is as follows: the solution temperature range is determined according to the β phase transition point of titanium alloy, which is 1050℃, the two-phase region is 930℃~1050℃, a certain temperature T below the α phase region is determined as the starting temperature, the upper boundary of the solution treatment temperature is T1, the step length is N1℃, where T is 900℃, T1 is 1200℃, N1 is 10℃, and the solution temperature range is 500℃~800℃; The aging temperature is above the service temperature of the titanium alloy, the temperature range is 500~800℃, the step length is N1℃, and the value of N1 is 10℃; The time range used for both solution time and aging time is 0.5~7h, with a step size of N2h and N2 value of 0.5h.

[0026] S3.2, respectively use the two selected models to predict the corresponding high temperature tensile properties, and use their predicted mean and variance to perform multi-objective optimization EIH calculation, and sort the process parameters from large to small according to the EIH value, and finally obtain the optimal processing parameters. The specific operation method is as follows: The two models trained in step S2.2 are used to predict the samples in the virtual space, and the heat treatment process with high EIH value is obtained, thereby obtaining the Pareto frontier that takes into account both strength and plasticity indicators; The specific method to obtain the Pareto frontier is as follows: using the expected improvement method based on hypervolume, represents Pareto advantage, and defines Am as all A R m A collection of A: The elements of Am are called approximation sets. The hypervolume index H (i.e., hypervolume) of the approximation set A is defined as The volume of the dominated subspace (i.e., the points dominated by every element in A) is given by the following formula: H(A)=Vol (1) Improved function based on hypervolume I:R m ×Am→R is defined as I(y, A)=H —H(A)(2) where y R m , and A Am; Given the predictions of the regression model, for some x in X X, in the form of a with mean and standard deviation Independent m-dimensional normal distribution of; The expected improvement at a point X of the approximation set A, denoted as EIH(x,A), is defined as follows: EIH(x,A)= PDFx(y)dy(3) Where the integration region R is R m ; The EIH value is an evaluation indicator for a multi-objective problem. If the EIH value of a data point is larger, it means that this point has the greatest mathematical expectation for pushing the Pareto front forward. Example 1 The method of optimizing the heat treatment process of titanium alloy by using uncertainty quantification-assisted machine learning is as follows: Step 1: A four-factor five-level orthogonal experiment was designed using SPSSAU. While building a machine learning database, a preliminary exploration of the effects of different heat treatment systems on high-temperature mechanical properties was also conducted. The data set included different processing conditions of high-temperature alloys and the corresponding test performance. Step 2, determining features used to train the model from the acquired data set, and determining target performance of the model from the acquired data set; Step 3: Set up different machine learning models, train the models with the original data sets, obtain the best model parameters and hyperparameters, and calibrate the models with the data sets; Step 4: Evaluate the model performance and uncertainty quantification indicators, and select the model with the best comprehensive performance and target performance; use the resampling method to consider the uncertainty quantification of the model, and use the uncertainty quantification results as indicators for model screening; Step 5, respectively model and predict the yield strength (YS) and uniform elongation (UE) of the data in the generated virtual space, perform multi-objective optimization on the yield strength and uniform elongation to calculate the EIH value, and predict and recommend the optimal processing parameters for improving the strength-plasticity matching.

[0027] In this embodiment, a support vector regression model, a Gaussian regression model, and a linear regression model and an extreme gradient model boosting model are called from Sklearn to train the models with the original data set; the target machine learning model is trained with the training set data and the optimal parameters and hyperparameters are found, the trained model is tested with the test set data, and the trained model is evaluated with the test set, the random seed of the randomly divided data set is modified, and the data set is adjusted until the optimal model is obtained.

[0028] The regression coefficient R 2 To evaluate the accuracy of the trained model and to compare different algorithms more systematically, the mean absolute error (MAE) and root mean square error (RMSE) of different algorithms were calculated for comparison. The model with better regression coefficient and target performance were selected, and the target performance was modeled with better parameters and better models to generate the trained target machine learning model. Considering the uncertainty of the model, the resampling method was used to quantify the uncertainty to further screen the model. The results of uncertainty quantification were used as indicators for model screening, and the target performance was modeled with the best parameters and the best model to generate the trained target machine learning model.

[0029] In the embodiment, a data set to be applied to machine learning is obtained, including: an initial state is a ZTA35G alloy rolled ingot, and the alloy composition is shown in Table 1.

[0030] Table 1 Element composition of ZTA35G alloy ingot

[0031] The present invention constructs a database (data set) for optimizing heat treatment process parameters based on orthogonal experiments and machine learning, obtains high-temperature alloy data under different processing and testing conditions, and sets different solution temperatures, solution times, aging temperatures and aging times, respectively, wherein the aging temperatures include 670°C, 700°C, 730°C, 760°C and 790°C; the aging times include 1h, 2h, 3h, 4h and 5h; the solution temperatures include 900°C, 950°C, 1000°C, 1050°C and 1100°C; the solution times include 1h, 2h, 3h, 4h and 5h; and different processing conditions are combined into 25 different processing methods (as shown in Table 2) to process the original samples.

[0032] Table 2 High temperature alloy data of ZTA35G alloy ingot under different processing and testing conditions

[0033] The tensile strength and ductility of the above samples at high temperature were tested, a total of 25 groups (as shown in Table 2). The high temperature tensile test was carried out according to the Chinese national standard GB / T228.1-2015 "Tensile test of metallic materials Part 2: High temperature test method".

[0034] In an embodiment of the present invention, determining features used to train a model from an acquired data set, and determining target performance of the model from an acquired data set include: The obtained solution temperature, solution time, aging temperature and aging time are used as the features of the training model; the obtained yield strength and uniform elongation properties are modeled as target properties respectively.

[0035] Set up different machine learning models and train them with the original data sets, including: using support vector regression model, Gaussian regression model, calling linear regression model from Sklearn, and extreme gradient model boosting to train the models with the original data sets.

[0036] The original data set is used to train the model separately, including: the original data set is divided into a test set and a training set in a ratio of 2:8, and the model is trained with the training set: the target machine learning model is trained with the training set data and the optimal parameters and hyperparameters are found, the trained model is tested with the test set data, and the trained model is evaluated with the test set, the random seed of the randomly divided data set is modified, and the data set is adjusted until the optimal model is obtained. The trained model is evaluated with the test set. In order to compare different algorithms more systematically, we calculate the mean absolute error and root mean square error of different algorithms for comparison.

[0037] For the linear regression model, find its optimal model parameters: modify the random seed that randomly divides the data set and adjust the data until the optimal model is obtained.

[0038] Find the optimal model parameters for the random forest model, support vector regression model, Gaussian regression model, and extreme gradient boosting model respectively.

[0039] Preferably, a grid search method is used to search for hyperparameters of the support vector regression model. Grid search is the simplest and most widely used hyperparameter search algorithm. It determines the optimal value by finding all points within the search range. By setting a suitable range and step size, grid search can find the global optimal value.

[0040] In this embodiment, the optimal model parameters and hyperparameters are obtained, and the model is calibrated with the data set, including: for the generated model and the optimal parameters and hyperparameters, the linear regression model, the random forest model, the support vector regression model, the Gaussian regression model and the extreme gradient boosting model are calibrated with the training set data in the test set and the training set distributed in 2:8.

[0041] Evaluate the model performance and select the best model and target performance, specifically: use the regression coefficient R 2 As the accuracy evaluation of the trained model, the regression coefficient R 2 for: R 2 =1- (4) Among them, m is the total number of data sets in the test set; y i is the corresponding target performance in the test set; is the predicted value of the corresponding performance in the test set; It is also the average value of the corresponding target performance in the test set; In order to compare different algorithms more systematically, we calculated the mean absolute error (MAE) and root mean square error (RMSE) of different algorithms for comparison. The mean absolute error (MAE) and root mean square error (RMSE) are: MAE= (5) RMSE= (6) Based on the performance of several models, the linear regression model (LR) with the worst overall performance was removed, and the remaining four models were used for the next step of model training. The yield strength and uniform elongation were modeled separately, and the best model corresponding to the two properties was selected for the next step of optimization.

[0042] The machine learning modeling RF, SVR, XGB and GP algorithms were re-performed. At this time, no matter whether we are selecting the prediction model for YS or UE, there are 2 to 3 models that perform well. At this time, the uncertainty of the model is considered for further model screening.

[0043] The results of uncertainty quantification are used as indicators for model screening. The training data x_a11 and the target data y_a11 are resampled using random seeds i, and the resampled data are used to train the model. The results of uncertainty quantification are used as indicators for model screening. Finally, the SVR model is selected as the prediction model for yield strength, and the XGB model is selected as the prediction model for uniform elongation.

[0044] From the relationship diagram between the true value and the predicted value of each model (such as Figure 2 , Figure 3 As shown in Figure 2), although the R 2 The values ​​of MAE and RMSE vary, but all the predicted values ​​fall within the 95% confidence interval, which means that the predicted values ​​of the model are accurate.

[0045] The data of the generated virtual space are predicted respectively, and the multi-objective optimization index is calculated. The generation of the virtual space used must first ensure the rationality and diversity of the space range. Four parameters need to be set for the virtual space: solution temperature, solution time, aging time and aging temperature.

[0046] Hypervolume metrics are used for performance evaluation and selection criteria in multi-objective optimization. Hypervolume metrics do not require prior knowledge about the Pareto front. The set that maximizes the hypervolume metric is a subset of the effective set, and the corresponding objective vector covers the Pareto front. This work considers the expected gain of hypervolume as a generalization of the expected improvement in the multi-objective domain. This hypervolume-based improvement has been successfully applied as a preselection criterion in evolutionary algorithms. Hypervolume metrics are used for performance evaluation and selection criteria in multi-objective optimization. This work uses a hypervolume-based expected improvement method to Denotes Pareto advantage. Definition A m For all A R m A collection of A : . A m The elements of are called approximation sets. A The hypervolume index H (i.e., hypervolume) is defined as being constrained by a reference point The volume of the dominated subspace (i.e., the points dominated by every element in A): H ( A )=Vol (1) Improved function based on hypervolume I : R m × Am → R is defined as I ( y, A )= H — H ( A） (2) where y R m ,and A Am .

[0047] Considering the predictions of the regression model, for some of X x X, in the form of a with mean and standard deviation Independent m-dimensional normal distribution.

[0048] The expected improvement at a point X of the approximation set A, denoted as EIH(x,A), is defined as follows: EIH(x,A)= PDFx(y)dy(3) Among them, the integral area R yes R m 。

[0049] The EIH value is an evaluation indicator for a multi-objective problem. If the EIH value of a data point is larger, it means that this point has the greatest mathematical expectation for pushing the Pareto front forward.

[0050] The mean and variance of the predicted values ​​obtained by the support vector regression model for yield strength and the mean and variance obtained by the extreme gradient lifting model for uniform elongation are used to calculate EIH. The EIH and its mean and variance of all parameters in the virtual space are calculated, and the process parameters are sorted from large to small according to the EIH value.

[0051] Table 3 The top 10 largest process parameters of EIH extracted and their prediction performance

[0052] In this embodiment, the optimal processing parameters for improving the strength-ductility matching are predicted and recommended. They include: solution temperature is predicted from 900 to 1200°C with a step length of 10; solution time is predicted from 0.5 to 7h with a step length of 0.5; aging temperature is predicted from 500 to 800°C with a step length of 10; aging time is predicted from 0.5 to 7h with a step length of 0.5; The optimal processing parameters determined are: solution temperature 970℃, solution time 7h; aging temperature 770℃, aging time 7h or aging temperature 500℃, aging time 7h.

[0053] Example 2 The method of optimizing the heat treatment process of titanium alloy by using uncertainty quantification-assisted machine learning is as follows: S1. Use SPSSAU to design a four-factor five-level orthogonal experiment and build a machine learning database; S2. Use machine learning to model and predict the heat treatment process and high-temperature tensile properties. Combined with the resampling method, the uncertainty quantification of the model is considered, and the results of uncertainty quantification are used as indicators for model screening. The final model is selected and trained. S3, generate the virtual space used for prediction, use the model selected in S2 to model and predict the high-temperature tensile properties of the data in the virtual space, perform multi-objective optimization on the high-temperature tensile properties to calculate the EIH value, and predict the optimal processing parameters for improving the strength-plasticity matching.

[0054] Example 3 The method of uncertainty quantification assisted machine learning to optimize the heat treatment process of titanium alloy is as follows: S1. Use SPSSAU to design a four-factor five-level orthogonal experiment and build a machine learning database. The specific method is: based on different processing conditions of titanium alloy, use SPSSAU to design a four-factor five-level orthogonal experiment, in which the characteristics of the training model include solution temperature, solution time, aging temperature, and aging time. The aging temperature values ​​are 670℃, 700℃, 730℃, 760℃, and 790℃, respectively; the aging time values ​​are 1h, 2h, 3h, 4h, and 5h, respectively; the solution temperature values ​​are 900℃, 950℃, 1000℃, 1050℃, and 1100℃, respectively; the solution time values ​​are 1h, 2h, 3h, 4h, and 5h, respectively. The corresponding target test performance is output for the orthogonal test, and the target test performance includes high-temperature yield strength and high-temperature fracture elongation. The machine and its learning database are constructed based on the output data.

[0055] S2. Use machine learning to model and predict the heat treatment process and high-temperature tensile properties. Combined with the resampling method, the uncertainty quantification of the model is considered, and the results of uncertainty quantification are used as indicators for model screening. The final model is selected and trained. S3, generate the virtual space used for prediction, use the model selected in S2 to model and predict the high-temperature tensile properties of the data in the virtual space, perform multi-objective optimization on the high-temperature tensile properties to calculate the EIH value, and predict the optimal processing parameters for improving the strength-plasticity matching.

[0056] Example 4 The method of uncertainty quantification assisted machine learning to optimize the heat treatment process of titanium alloy is as follows: S1. Use SPSSAU to design a four-factor five-level orthogonal experiment and build a machine learning database; S2. Use machine learning to model and predict the heat treatment process and high-temperature tensile properties. Combined with the resampling method, the uncertainty quantification of the model is considered, and the results of uncertainty quantification are used as indicators for model screening. The final model is selected and trained. The specific operation process is as follows: S2.1. Set up different machine learning models, train them using the original data set, and use the test set to evaluate the trained machine learning models, thereby filtering out the models with the worst overall performance. S2.2. Perform the next step of model training on the remaining machine learning models, model the high temperature yield strength and high temperature fracture elongation respectively, evaluate the performance of different machine learning models, select the best machine learning models corresponding to the high temperature yield strength and high temperature fracture elongation respectively, and use the resampling method to quantify the uncertainty for the next step of optimization; S2.3. Through the analysis of the above model performance and uncertainty quantification indicators, the machine learning models with high regression coefficients and small uncertainties in the test set are selected as the best prediction models for high-temperature yield strength and high-temperature fracture elongation.

[0057] S3, generate the virtual space used for prediction, use the model selected in S2 to model and predict the high-temperature tensile properties of the data in the virtual space, perform multi-objective optimization on the high-temperature tensile properties to calculate the EIH value, and predict the optimal processing parameters for improving the strength-plasticity matching.

[0058] Example 5 The method of uncertainty quantification assisted machine learning to optimize the heat treatment process of titanium alloy is as follows: S1. Use SPSSAU to design a four-factor five-level orthogonal experiment and build a machine learning database; S2. Use machine learning to model and predict the heat treatment process and high-temperature tensile properties. Combined with the resampling method, the uncertainty quantification of the model is considered, and the results of uncertainty quantification are used as indicators for model screening. The final model is selected and trained. The specific operation process is as follows: S2.1. Set different machine learning models, train different machine learning models respectively through the original data set, and use the test set to evaluate the trained machine learning models respectively, so as to screen out the models with the worst overall performance; the specific process of S2.1 is: set support vector regression model SVR, Gaussian regression model GP, random forest RF, call linear regression model LR and extreme gradient boosting model XGB from Sklearn and other machine learning models, randomly divide the original data set into test set and training set in a ratio of 2:8, standardize the training set and test set with the mean and variance of the training set samples, and then use the standardized data to train different machine learning models respectively, and resample the training set data, and select the best machine learning models corresponding to high-temperature yield strength and high-temperature fracture elongation according to the sampled data.

[0059] S2.2. Perform the next step of model training on the remaining machine learning models, model the high temperature yield strength and high temperature fracture elongation respectively, evaluate the performance of different machine learning models, select the best machine learning models corresponding to the high temperature yield strength and high temperature fracture elongation respectively, and use the resampling method to quantify the uncertainty for the next step of optimization; S2.3. Through the analysis of the above model performance and uncertainty quantification indicators, the machine learning models with high regression coefficients and small uncertainties in the test set are selected as the best prediction models for high-temperature yield strength and high-temperature fracture elongation.

[0060] S3, generate the virtual space used for prediction, use the model selected in S2 to model and predict the high-temperature tensile properties of the data in the virtual space, perform multi-objective optimization on the high-temperature tensile properties to calculate the EIH value, and predict the optimal processing parameters for improving the strength-plasticity matching.

[0061] Example 6 The method of uncertainty quantification assisted machine learning to optimize the heat treatment process of titanium alloy is as follows: S1. Use SPSSAU to design a four-factor five-level orthogonal experiment and build a machine learning database; S2. Use machine learning to model and predict the heat treatment process and high-temperature tensile properties. Combined with the resampling method, the uncertainty quantification of the model is considered, and the results of uncertainty quantification are used as indicators for model screening. The final model is selected and trained. S3, generate the virtual space used for prediction, use the model selected in S2 to model and predict the high temperature tensile properties of the data in the virtual space, perform multi-objective optimization on the high temperature tensile properties to calculate the EIH value, and predict the optimal processing parameters for improving the strength-plasticity matching. The specific operations are: S3.1. Generate a virtual space for prediction. The virtual space sets four parameters: solution temperature, solution time, aging time and aging temperature. S3.2. The two selected models are used to predict the corresponding high-temperature tensile properties respectively, and the predicted mean and variance are used to perform multi-objective optimization EIH calculation, and the process parameters are sorted from large to small according to the EIH value, and finally the optimal processing parameters are obtained.

Claims

1. A method for optimizing titanium alloy heat treatment process by using uncertainty quantification-assisted machine learning, characterized in that: The specific steps are as follows: S1. Use SPSSAU to design a four-factor five-level orthogonal experiment and build a machine learning database; S2. Use machine learning to model and predict the heat treatment process and high-temperature tensile properties. Combined with the resampling method, the uncertainty quantification of the model is considered, and the results of uncertainty quantification are used as indicators for model screening. The final model is selected and trained. S3, generate the virtual space used for prediction, use the model selected in S2 to model and predict the high-temperature tensile properties of the data in the virtual space, perform multi-objective optimization on the high-temperature tensile properties to calculate the EIH value, and predict the optimal processing parameters for improving the strength-plasticity matching.

2. The method for optimizing titanium alloy heat treatment process by using uncertainty quantification-assisted machine learning according to claim 1 is characterized in that: The specific method of S1 is: Based on different processing conditions of titanium alloy, SPSSAU was used to design a four-factor five-level orthogonal experiment, in which the characteristics of the training model included solution temperature, solution time, aging temperature, and aging time. The aging temperature values ​​were 670℃, 700℃, 730℃, 760℃, and 790℃, respectively; the aging time values ​​were 1h, 2h, 3h, 4h, and 5h, respectively; the solution temperature values ​​were 900℃, 950℃, 1000℃, 1050℃, and 1100℃, respectively; the solution time values ​​were 1h, 2h, 3h, 4h, and 5h, respectively; The corresponding target test performance is output for the orthogonal test, wherein the target test performance includes high temperature yield strength and high temperature fracture elongation, and a machine and its learning database are constructed according to the output data.

3. The method for optimizing titanium alloy heat treatment process by using uncertainty quantification-assisted machine learning according to claim 1 is characterized in that: The high temperature tensile properties in S2 include high temperature yield strength and high temperature elongation at break; The specific operation process of S2 is as follows: S2.

1. Set up different machine learning models, train them using the original data set, and use the test set to evaluate the trained machine learning models, thereby filtering out the models with the worst overall performance. S2.

2. Perform the next step of model training on the remaining machine learning models, model the high temperature yield strength and high temperature fracture elongation respectively, evaluate the performance of different machine learning models, select the best machine learning models corresponding to the high temperature yield strength and high temperature fracture elongation respectively, and use the resampling method to quantify the uncertainty for the next step of optimization; S2.

3. Through the analysis of the above model performance and uncertainty quantification indicators, the machine learning models with high regression coefficients and small uncertainties in the test set are selected as the best prediction models for high-temperature yield strength and high-temperature fracture elongation.

4. The method of optimizing titanium alloy heat treatment process by using uncertainty quantification-assisted machine learning according to claim 3 is characterized in that: The specific methods for evaluating the machine learning model in S2.1 to S2.3 are: evaluating the performance of the selected machine learning model respectively, and the performance indicators of the machine learning model include: regression coefficient R 2 , mean absolute error (MAE) and root mean square error (RMSE), and use the accuracy of the above indicators to evaluate the trained model and select the model with the best performance.

5. The method of optimizing titanium alloy heat treatment process by using uncertainty quantification-assisted machine learning according to claim 3 is characterized in that: The original data set in S2.1 is obtained by taking three parallel samples under each parameter to perform high temperature tensile property test at 700°C, and a total of 25 sets of experimental data are obtained. The experimental data is the average value of the three horizontal samples, which is the original data set; The specific process of S2.1 is: setting support vector regression model SVR, Gaussian regression model GP, random forest RF, calling linear regression model LR and extreme gradient boosting model XGB and other machine learning models from Sklearn, randomly dividing the original data set into test set and training set at a ratio of 2:8, standardizing the training set and test set with the mean and variance of the training set samples, and then using the standardized data to train different machine learning models respectively, and resample the training set data, and select the best machine learning models corresponding to high-temperature yield strength and high-temperature fracture elongation according to the sampled data.

6. The method of optimizing titanium alloy heat treatment process by using uncertainty quantification-assisted machine learning according to claim 3 is characterized in that: The specific process of S2.2 is as follows: The random forest model RF, support vector regression model SVR, extreme gradient boosting model XGB and Gaussian regression model GP were selected for re-machine learning modeling; the uncertainty was quantified using the resampling method. The resampling method was to divide the data set after S2.1 standardization into a test set and a training set in a ratio of 2:8, and then use the same model training method as S2.1 to further train the remaining models. The models were trained 1000 times in total to obtain 1000 prediction values.

7. The method for optimizing titanium alloy heat treatment process by using uncertainty quantification-assisted machine learning according to claim 3 is characterized in that: The specific process of S2.3 is: by predicting the mean, the standard deviation and the true value, the miscalibration area and the regression coefficient R are calculated. 2 , and then the final model is selected through the uncertainty quantification ability and accuracy of different models.

8. The method for optimizing titanium alloy heat treatment process by using uncertainty quantification-assisted machine learning according to claim 1, characterized in that: The specific operation of S3 is: S3.

1. Generate a virtual space for prediction, wherein four parameters are set in the virtual space: solution temperature, solution time, aging time and aging temperature; S3.

2. The two selected models are used to predict the corresponding high-temperature tensile properties respectively, and the predicted mean and variance are used to perform multi-objective optimization EIH calculation, and the process parameters are sorted from large to small according to the EIH value, and finally the optimal processing parameters are obtained.

9. The method for optimizing titanium alloy heat treatment process by using uncertainty quantification-assisted machine learning according to claim 8 is characterized in that: The specific operation of setting the four parameter ranges in S3.1 is as follows: the solution temperature range is determined according to the β phase transformation point of the titanium alloy, the β phase transformation point of the titanium alloy is 1050°C, the two-phase region is 930°C~1050°C, a certain temperature T below the α phase region is determined as the starting temperature, the upper boundary of the solution treatment temperature is T1, the step length is N1°C, wherein the value of T is 900°C, the value of T1 is 1200°C, the value of N1 is 10°C, and the solution temperature range is 500°C~800°C; The aging temperature is above the service temperature of the titanium alloy, the temperature range is 500-800°C, the step length is N1°C, and the value of N1 is 10°C; The time range used for the solution time and the aging time is 0.5~7h, the step length is N2h, and the value of N2 is 0.5h.

10. The method for optimizing titanium alloy heat treatment process by using uncertainty quantification-assisted machine learning according to claim 8, characterized in that: The specific operation method of S3.2 is as follows: The two models trained in step S2.2 are used to predict the samples in the virtual space, and the heat treatment process with high EIH value is obtained, thereby obtaining the Pareto frontier that takes into account both strength and plasticity indicators; The specific method to obtain the Pareto frontier is as follows: using the expected improvement method based on hypervolume, represents Pareto advantage, and defines Am as all A R m A collection of A: , the elements of m are called approximation sets, and the hypervolume index H (i.e., hypervolume) of the approximation set A is defined as restricted to the reference point The volume of the dominated subspace (i.e., the points dominated by every element in A) is given by the following formula: H(A)=Vol (1) Improved function based on hypervolume I:R m ×Am→R is defined as I(y,A)=H —H(A)(2) where y R m , and A Am; Given the predictions of the regression model, for some x in X X, in the form of a with mean and standard deviation Independent m-dimensional normal distribution of; The expected improvement at a point X of the approximation set A, denoted as EIH(x,A), is defined as follows: EIH(x,A)= PDFx(y)dy(3) Where the integration region R is R m ; The EIH value is an evaluation indicator for a multi-objective problem. If the EIH value of a data point is larger, it means that this point has the greatest mathematical expectation for pushing the Pareto front forward.

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