Method for predicting alpha / beta phase transition temperature of titanium alloy and related device

Abstract

This invention belongs to the field of computational materials science and alloy design optimization technology, specifically involving a method and related apparatus for predicting the α / β phase transformation temperature of titanium alloys. It utilizes a linear regression algorithm to establish a basic prediction model for the α / β phase transformation temperature. Through symbolic regression calculation based on a genetic algorithm, a population of correction terms for the basic prediction model is generated. Based on a non-dominated sorting algorithm, according to the length of each individual in the correction term population and the prediction accuracy of the basic prediction model after adding correction terms, a set of correction terms on the Pareto front is selected, and the optimal correction term is chosen. The basic prediction model and the optimal correction term are then fused to obtain the prediction model for the α / β phase transformation temperature of titanium alloys. This model is then used to calculate the α / β phase transformation temperature of the titanium alloy to be predicted. This invention addresses the problem of insufficient physical interpretability in existing machine learning methods.

Description

Technical Field

[0001] This invention belongs to the field of computational materials science and alloy design optimization technology, specifically relating to a method and related apparatus for predicting the α / β phase transformation temperature of titanium alloys. Background Technology

[0002] The mechanical properties of titanium alloys are strongly dependent on their microstructure, and the α / β phase transformation temperature is a key thermodynamic parameter determining the phase composition and microstructure of titanium alloys, directly affecting the optimization of the final mechanical properties. Studies have shown that the α / β phase transformation temperature is closely related to the content ratio of α-stabilizing elements (including aluminum) and β-stabilizing elements (including vanadium and molybdenum). By changing the chemical composition of these elements, the α / β phase transformation temperature can be directly controlled, thereby indirectly obtaining the target microstructure and mechanical properties.

[0003] The determination of the α / β phase transition temperature mainly relies on experimental methods, empirical formulas, and machine learning methods, but all of these methods currently have certain limitations. Traditional experimental methods are cumbersome and costly, making it difficult to establish an explicit quantitative relationship between composition and temperature. Existing empirical formulas (such as piecewise linear models based on the α / β phase transition temperature of pure titanium), while simple in form, generally ignore the complex nonlinear interactions between elements. They are applicable in binary systems, but their predictive reliability drops significantly in multi-component titanium alloys. Although machine learning methods perform well in terms of prediction accuracy and efficiency, effectively overcoming the shortcomings of relying on experimental methods and empirical formulas, their "black box" nature prevents them from outputting analytical expressions with clear physical meaning, limiting their practical application in composition design.

[0004] In summary, existing machine learning methods have shortcomings in interpretability, which restricts the further development of titanium alloy design. Summary of the Invention

[0005] To address the problems existing in the prior art, the present invention aims to provide a method and related apparatus for predicting the α / β phase transformation temperature of titanium alloys. The present invention can solve the problem of insufficient physical interpretability of existing machine learning methods.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for predicting the α / β phase transformation temperature of titanium alloys includes the following process:

[0008] The content of alloying elements of a titanium alloy with known composition is input into a pre-constructed titanium alloy α / β phase transformation temperature prediction model, and the α / β phase transformation temperature of the titanium alloy is calculated using the titanium alloy α / β phase transformation temperature prediction model.

[0009] The construction process of the titanium alloy α / β phase transformation temperature prediction model includes:

[0010] Using a linear regression algorithm, a basic prediction model for the α / β phase transformation temperature is established based on a pre-constructed titanium alloy dataset. The titanium alloy dataset includes the chemical composition information of the titanium alloy and the measured values ​​of the α / β phase transformation temperature corresponding to the chemical composition information. The chemical composition information includes the types of alloying elements contained in the titanium alloy and the content of each alloying element.

[0011] A population of correction terms for the basic prediction model is generated by symbolic regression calculation based on a genetic algorithm.

[0012] Calculate the length of each correction term in the correction term population and the prediction accuracy of the base prediction model after adding correction terms;

[0013] Based on the non-dominated sorting algorithm, according to the length of each correction term in the correction term population and the prediction accuracy of the basic prediction model after adding correction terms, all correction terms in the correction term population are traversed to form a Pareto front.

[0014] Select the optimal correction term from the correction terms on the Pareto front;

[0015] By integrating the basic prediction model and the optimal correction term, the prediction model for the α / β phase transformation temperature of the titanium alloy is obtained.

[0016] Preferably, the prediction accuracy of the basic prediction model after adding the correction term is the average absolute error between the measured value of the α / β phase transition temperature and the α / β phase transition temperature predicted by the basic prediction model after adding the correction term.

[0017] Preferably, the process of selecting the optimal correction term from the correction terms on the Pareto front includes:

[0018] Calculate the crowding distance of all correction terms on the Pareto front, and select the correction term with the largest crowding distance as the optimal correction term.

[0019] Preferably, the fusion method of the basic prediction model and the optimal correction term is to linearly sum the basic prediction model and the optimal correction term.

[0020] Preferably, the titanium alloy contains at least one of the alloying elements selected from Al, Mo, V, Cr, Fe, Nb, Sn, Zr, Cu, Si, C, H, O, and N.

[0021] Preferably, the process of constructing the titanium alloy dataset includes:

[0022] An initial dataset for titanium alloys was constructed using at least one of historical experimental data and literature data.

[0023] The initial titanium alloy dataset is filled with missing values ​​and outliers are removed to obtain the titanium alloy dataset.

[0024] Preferably, the specific process of filling missing values ​​and removing outliers in the initial titanium alloy dataset includes:

[0025] The missing values ​​in the initial dataset of the titanium alloy were filled with 0, and outlier data were identified and removed using the Laida criterion.

[0026] This invention also provides a system for predicting the α / β phase transformation temperature of titanium alloys, used to implement the method for predicting the α / β phase transformation temperature of titanium alloys as described above, comprising:

[0027] Input module: Used to input the content of alloying elements of titanium alloys with known compositions into the pre-built titanium alloy α / β phase transformation temperature prediction model;

[0028] Calculation module: used to calculate the α / β phase transformation temperature of the titanium alloy using a titanium alloy α / β phase transformation temperature prediction model and the content of the alloying elements;

[0029] Output module: Used to output the α / β phase transformation temperature calculated by the titanium alloy α / β phase transformation temperature prediction model;

[0030] The construction process of the titanium alloy α / β phase transformation temperature prediction model includes:

[0031] Using a linear regression algorithm, a basic prediction model for the α / β phase transformation temperature is established based on a pre-constructed titanium alloy dataset. The titanium alloy dataset includes the chemical composition information of the titanium alloy and the measured values ​​of the α / β phase transformation temperature corresponding to the chemical composition information. The chemical composition information includes the types of alloying elements contained in the titanium alloy and the content of each alloying element.

[0032] A population of correction terms for the basic prediction model is generated by symbolic regression calculation based on a genetic algorithm.

[0033] Calculate the length of each correction term in the correction term population and the prediction accuracy of the base prediction model after adding correction terms;

[0034] Based on the non-dominated sorting algorithm, according to the length of each correction term in the correction term population and the prediction accuracy of the basic prediction model after adding correction terms, all correction terms in the correction term population are traversed to form a Pareto front.

[0035] Select the optimal correction term from the correction terms on the Pareto front;

[0036] By integrating the basic prediction model and the optimal correction term, the prediction model for the α / β phase transformation temperature of the titanium alloy is obtained.

[0037] The present invention also provides an electronic device, comprising:

[0038] One or more processors;

[0039] A memory on which one or more programs are stored;

[0040] When the one or more programs are executed by the one or more processors, the one or more processors implement the titanium alloy α / β phase transformation temperature prediction method of the present invention as described above.

[0041] The present invention also provides a storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the method for predicting the α / β phase transition temperature of titanium alloys as described above.

[0042] The present invention has the following beneficial effects:

[0043] This invention presents a method for predicting the α / β phase transformation temperature of titanium alloys. It constructs a prediction model for the α / β phase transformation temperature of titanium alloys that integrates a basic prediction model based on a linear regression algorithm with a correction term calculated using a genetic algorithm-based symbolic regression. The basic prediction model is derived from a titanium alloy dataset using a linear regression algorithm; therefore, it is a mathematical analytical formula containing elemental information and content information of the alloying elements in the titanium alloy. Thus, the basic prediction model is an analytical formula for the α / β phase transformation temperature with clear physical meaning. Since the prediction model for the α / β phase transformation temperature of titanium alloys is further optimized based on the basic prediction model, it is also an analytical formula for the α / β phase transformation temperature with clear physical meaning. Therefore, it effectively solves the limitation of insufficient physical interpretability in the prediction of the α / β phase transformation temperature of titanium alloys by existing machine learning models. In the technical solution of this invention, the basic prediction model obtained by the linear regression algorithm has a clear mathematical analytical formula, which contains elemental information of the alloying elements contained in the titanium alloy and the content information of each alloying element. Therefore, it avoids the black box characteristics of existing machine learning methods. This basic prediction model gives the final titanium alloy α / β phase transformation temperature prediction model of this invention basic interpretability. The correction term generated by the symbolic regression calculation based on the genetic algorithm can accurately capture the nonlinear interaction relationship between alloying elements. The optimal correction term selected by Pareto front construction and non-dominated sorting algorithm not only makes up for the fitting defects of the basic prediction model and improves the prediction accuracy, but also ensures the basic prediction accuracy by controlling the length of the correction term. The model is practical and simple. The resulting prediction model for the α / β phase transformation temperature of titanium alloys has both clear physical meaning and high prediction accuracy, clearly demonstrating the quantitative relationship between the chemical composition information of titanium alloys and the α / β phase transformation temperature. Furthermore, this model only requires the input of the alloying element content of the titanium alloy to quickly output the predicted α / β phase transformation temperature, thus significantly improving the efficiency of obtaining the α / β phase transformation temperature in titanium alloy design and reducing the cost waste caused by blind experiments. The selection of the optimal correction term also ensures the stability and reliability of the prediction model, enhancing its application value in titanium alloy design. Attached Figure Description

[0044] Figure 1 This is a flowchart illustrating the construction process of the prediction model for the α / β phase transformation temperature of titanium alloys in an embodiment of the present invention.

[0045] Figure 2 This is a Pareto front distribution diagram of the expression in the symbolic regression calculation in this embodiment of the invention.

[0046] Figure 3This is an expression tree structure diagram of the prediction model for the α / β phase transformation temperature of titanium alloy in an embodiment of the present invention.

[0047] Figure 4 This is a structural block diagram of the titanium alloy α / β phase transformation temperature prediction system in an embodiment of the present invention.

[0048] Figure 5 This is a schematic diagram of the structure of an electronic device in an embodiment of the present invention. Detailed Implementation

[0049] The present invention will be further described clearly and in detail below with reference to specific embodiments and the accompanying drawings. Those skilled in the art will be able to implement the present invention based on these descriptions. Furthermore, the embodiments of the present invention described below are generally only some, not all, of the embodiments of the present invention. Therefore, all other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0050] Example 1

[0051] See Figure 1 The method for predicting the α / β phase transformation temperature of titanium alloys in this embodiment includes the following steps:

[0052] Step 1: Collect at least one of historical experimental data and literature data to construct an initial dataset of titanium alloy α / β phase transformation temperatures. This initial dataset includes the chemical composition information of the titanium alloy and the corresponding measured α / β phase transformation temperatures. The titanium alloy contains Ti and alloying elements, including at least one of Al, Mo, V, Cr, Fe, Nb, Sn, Zr, Cu, Si, C, H, O, and N. The chemical composition information includes the types of alloying elements in the titanium alloy and the content of each element. The content of each alloying element can be the atomic percentage or mass percentage of the element in the titanium alloy. The initial dataset contains at least 50 sets of data (wherein, for a titanium alloy with a known composition, the chemical composition information of that titanium alloy and the corresponding measured α / β phase transformation temperature are considered as one set of data) to ensure the reliability of the predictions of the basic prediction model established in Step 3.

[0053] Step 2: The initial titanium alloy dataset constructed in Step 1 is imputed for missing values ​​and anomalies are removed to obtain the final titanium alloy dataset. The specific process for imputing missing values ​​and removing anomalies in the initial titanium alloy dataset includes: filling missing values ​​with 0, and identifying and removing anomalies using the Laida criterion. This titanium alloy dataset is similar to the initial titanium alloy dataset in Step 1, including the chemical composition information of the titanium alloy and the corresponding measured α / β phase transformation temperatures.

[0054] Step 3: Using a linear regression algorithm, based on the titanium alloy dataset constructed in Step 2, establish a basic prediction model for the α / β phase transformation temperature. Calculate the prediction residual of the basic prediction model. The prediction residual is the difference between the predicted value and the measured value of the α / β phase transformation temperature, where the predicted value is the α / β phase transformation temperature calculated using the basic prediction model. The equation for calculating the prediction residual is as follows:

[0055]

[0056] in, To predict residuals, These are the measured values ​​of the α / β phase transition temperature, in °C. The values ​​are predicted values ​​for the α / β phase transition temperature, in °C.

[0057] Step 4: Generate a population of correction terms for the basic prediction model obtained in Step 3 through symbolic regression calculation based on a genetic algorithm. The correction terms in this population are used to offset the prediction residuals of the basic prediction model. The symbolic regression calculation process based on a genetic algorithm includes: initializing calculation parameters and iterative evolution. The calculation parameters include population size, number of generations, crossover probability, mutation probability, and initial population generation method. The initial population generation method can be a random generation method.

[0058] Step 5: Calculate the length of each correction term in the correction term population and the prediction accuracy of the basic prediction model after adding correction terms; wherein, the prediction accuracy of the basic prediction model after adding correction terms is the average absolute error between the measured value of the α / β phase transition temperature and the α / β phase transition temperature predicted by the basic prediction model after adding correction terms.

[0059] Step Six: Based on the non-dominated sorting algorithm, according to the length of each correction term in the correction term population and the prediction accuracy of the basic prediction model after adding the correction term, traverse all correction terms in the correction term population to form a Pareto front; select the optimal correction term from the correction terms on the Pareto front; specifically, the process of selecting the optimal correction term from the correction terms on the Pareto front includes: calculating the crowding distance of all correction terms on the Pareto front, and selecting the correction term with the largest crowding distance as the optimal correction term.

[0060] Step 7: Combine the basic prediction model obtained in Step 3 and the optimal correction term obtained in Step 6 to obtain the final prediction model for the α / β phase transformation temperature of the titanium alloy. Specifically, the method for combining the basic prediction model and the optimal correction term is to linearly add them together. The mathematical expression of this prediction model for the α / β phase transformation temperature of the titanium alloy is as follows:

[0061]

[0062] In the formula, This is the predicted final α / β phase transition temperature, in °C. This is the optimal correction term, in °C.

[0063] Step 8: For the titanium alloy whose α / β phase transformation temperature is to be predicted, input the content of the alloying elements of the titanium alloy into the titanium alloy α / β phase transformation temperature prediction model constructed in Step 7, and use the titanium alloy α / β phase transformation temperature prediction model to calculate and obtain the α / β phase transformation temperature of the titanium alloy.

[0064] In the above-mentioned scheme of the present invention, a prediction framework is constructed by integrating a linear benchmark model (i.e., the basic prediction model obtained in step three) with a symbolic regression correction term (i.e., the optimal correction term). A multi-objective optimization selection mechanism based on the Pareto front based on crowding distance is adopted to generate an analytical formula for the α / β phase transformation temperature with both high prediction accuracy and clear physical meaning (i.e., the final prediction model for the α / β phase transformation temperature of titanium alloys obtained in step seven). This effectively solves the problem of insufficient physical interpretability of traditional machine learning models, provides a reliable theoretical basis and practical calculation tool for titanium alloy design, and significantly improves the efficiency and engineering applicability of titanium alloy design.

[0065] Example 2

[0066] The method for predicting the α / β phase transformation temperature of titanium alloys in this embodiment includes the following steps:

[0067] Step 1: Collect chemical composition information of titanium alloys containing 14 alloying elements (Al, Mo, V, Cr, Fe, Nb, Sn, Zr, Cu, Si, C, H, O, N) and the corresponding measured values ​​of α / β phase transformation temperatures from publicly available literature and experimental data. Construct an initial dataset of titanium alloys containing 200 sets of data using the collected measured values ​​of α / β phase transformation temperatures corresponding to the chemical composition information.

[0068] Step 2: Fill missing values ​​and remove outliers from the initial titanium alloy dataset constructed in Step 1 to obtain the titanium alloy dataset.

[0069] Step 3: Using a linear regression algorithm, based on the titanium alloy dataset constructed in Step 2, establish a basic prediction model for the α / β phase transformation temperature. Calculate the prediction residuals of the basic prediction model.

[0070] Step 4: Generate a population of correction terms for the basic prediction model obtained in Step 3 through symbolic regression calculation based on a genetic algorithm. The correction terms in this population are used to offset the prediction residuals of the basic prediction model. The symbolic regression calculation process based on a genetic algorithm includes: initializing the calculation parameters and iterative evolution. The population size of the calculation parameters is set to 1000, the number of generations is set to 20, the crossover probability is set to 0.2, the mutation probability is set to 0.2, and the initial population is generated randomly.

[0071] Step 5: Calculate the length of each correction term in the correction term population and the prediction accuracy of the basic prediction model after adding correction terms.

[0072] Step Six: Based on the non-dominated sorting algorithm, according to the length of each correction term in the correction term population and the prediction accuracy of the basic prediction model after adding the correction term, traverse all correction terms in the correction term population to form a Pareto front; select the optimal correction term from the correction terms on the Pareto front; specifically, the process of selecting the optimal correction term from the correction terms on the Pareto front includes: calculating the crowding distance of all correction terms on the Pareto front, and selecting the correction term with the largest crowding distance as the optimal correction term.

[0073] Step 7: Linearly sum the basic prediction model and the optimal correction term to obtain the final prediction model for the α / β phase transformation temperature of titanium alloy.

[0074] In step one above, four samples were randomly selected from the initial titanium alloy dataset. These four samples, based on the mass percentage of the alloying elements in the corresponding titanium alloy, are as follows:

[0075] Sample 1: Al: 3.2%, V: 10.3%, Fe: 2.2%, H: 0.016%, N: 0.009%, α / β phase transition temperature: 805℃;

[0076] Sample 2: Al: 6.495%, V: 3.3%, Fe: 0.1%, O: 0.2%, α / β phase transition temperature: 1021℃;

[0077] Sample 3: Al: 2.5%, Mo: 1%, Sn: 11%, Si: 0.2%, α / β phase transition temperature: 925℃;

[0078] Sample 4: Al: 2%, V: 11.5%, Fe: 0.2%, Zr: 11%; C: 0.08%; H: 0.015%, O: 0.015%, N: 0.05%, α / β phase transition temperature: 738℃;

[0079] The measured and original values ​​(i.e., the α / β phase transition temperatures of each sample given in published literature and experimental data) of these four samples are shown in Table 1:

[0080] Table 1

[0081]

[0082] In Table 1, the measured α / β phase transition temperature refers to the measured value of the α / β phase transition temperature of the sample, and the original α / β phase transition temperature refers to the original value of the α / β phase transition temperature of the sample.

[0083] As shown in Table 1, the absolute value of the relative error between the measured and original values ​​of the α / β phase transformation temperature of the four samples does not exceed 1%. Therefore, the α / β phase transformation temperature values ​​recorded in the initial dataset of titanium alloys constructed in step one are used.

[0084] In step two above, the initial dataset of titanium alloy is checked to ensure there are no missing values. Then, the Laida criterion is used to identify and delete outlier data in the initial dataset of titanium alloy.

[0085] In step three above, using all alloying elements as independent variables and the α / β phase transformation temperature as the dependent variable, a basic prediction model for the α / β phase transformation temperature is established using a multiple linear regression algorithm. In this scheme, the process of establishing the basic prediction model for the α / β phase transformation temperature using a multiple linear regression algorithm with all alloying elements as independent variables and the α / β phase transformation temperature as the dependent variable is a conventional process. The specific construction process will not be elaborated upon in this invention. The mathematical expression of the obtained basic prediction model is as follows:

[0086]

[0087] in, for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element.

[0088] Based on this basic prediction model, the predicted values ​​of all samples in the initial dataset of titanium alloys were calculated, and the prediction residuals were obtained. The mean absolute error of this basic prediction model is 12.1℃.

[0089] In step four above, when generating the correction term population of the basic prediction model obtained in step three through symbolic regression calculation based on a genetic algorithm, the function set used includes addition, subtraction, multiplication, division, and square root operations. After iterative evolution, a total of 12,450 individuals with mathematical expressions were finally generated in the correction term population.

[0090] In step five above, the prediction accuracy (mean absolute error) and individual length of the basic prediction model were calculated for each of the 12,450 individuals obtained in step four after adding the correction term. The calculation results show that the mean absolute error of all individuals ranges from 9.24 ℃ to 18.5 ℃, and the individual length ranges from 5 to 30.

[0091] In step six, based on the mean absolute error and individual length calculated in step five, all individuals are non-dominatedly ordered. After screening, eight Pareto optimal solutions are finally identified, forming a Pareto front. The distribution of this Pareto front is as follows: Figure 2 As shown. The crowding distance for each individual in the Pareto front is calculated, and an optimal correction term is selected. The analytical expression of the optimal correction term is... for: = The expression tree structure corresponding to the optimal correction term is as follows: Figure 3 As shown.

[0092] In step seven above, the basic prediction model and the optimal correction term are fused through linear summation to obtain the mathematical expression of the final prediction model for the α / β phase transformation temperature of titanium alloys, as follows:

[0093]

[0094] in, for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The mass percentage of the element for The percentage of the element by mass.

[0095] The model for predicting the α / β phase transformation temperature of titanium alloys has been verified to have an average absolute error of 9.36 ℃, which is 10% higher than the basic prediction model.

[0096] Step 8: The chemical formula of a titanium alloy with the predicted α / β phase transformation temperature is Ti-5Al-2Mo-5Sn-2Zr-0.25Si, and the measured phase transformation temperature is 980℃. The content of the alloying elements in this titanium alloy is input into the titanium alloy α / β phase transformation temperature prediction model for calculation, yielding a predicted α / β phase transformation temperature of 984.0675℃. It can be seen that the predicted value of the titanium alloy α / β phase transformation temperature in this embodiment is close to the actual value, with a deviation of 0.42%, therefore the α / β phase transformation temperature prediction result is relatively accurate. Specifically, when inputting the content of the alloying elements in this titanium alloy into the titanium alloy α / β phase transformation temperature prediction model, the mass percentage of each alloying element in the titanium alloy is used to replace the symbols of each alloying element in the titanium alloy α / β phase transformation temperature prediction model, and then the calculation is performed; the calculation result is the predicted value of the titanium alloy α / β phase transformation temperature.

[0097] Furthermore, embodiments of the present invention also provide a titanium alloy α / β phase transformation temperature prediction system, used to implement the titanium alloy α / β phase transformation temperature prediction method described above, such as... Figure 4 As shown, the system includes:

[0098] Input module: Used to input the content of alloying elements of titanium alloys with known compositions into the pre-built titanium alloy α / β phase transformation temperature prediction model;

[0099] Calculation module: used to calculate the α / β phase transformation temperature of the titanium alloy using a titanium alloy α / β phase transformation temperature prediction model and the content of the alloying elements;

[0100] Output module: Used to output the α / β phase transformation temperature calculated by the titanium alloy α / β phase transformation temperature prediction model;

[0101] The construction process of the titanium alloy α / β phase transformation temperature prediction model includes:

[0102] Using a linear regression algorithm, a basic prediction model for the α / β phase transformation temperature is established based on a pre-constructed titanium alloy dataset. The titanium alloy dataset includes the chemical composition information of the titanium alloy and the measured values ​​of the α / β phase transformation temperature corresponding to the chemical composition information. The chemical composition information includes the types of alloying elements contained in the titanium alloy and the content of each alloying element.

[0103] A population of correction terms for the basic prediction model is generated by symbolic regression calculation based on a genetic algorithm.

[0104] Calculate the length of each correction term in the correction term population and the prediction accuracy of the base prediction model after adding correction terms;

[0105] Based on the non-dominated sorting algorithm, according to the length of each correction term in the correction term population and the prediction accuracy of the basic prediction model after adding correction terms, all correction terms in the correction term population are traversed to form a Pareto front.

[0106] Select the optimal correction term from the correction terms on the Pareto front;

[0107] By integrating the basic prediction model and the optimal correction term, the prediction model for the α / β phase transformation temperature of the titanium alloy is obtained.

[0108] The embodiments of the present invention also provide corresponding electronic devices and computer-readable storage media for implementing the solutions provided in the embodiments of the present invention.

[0109] Among them, such as Figure 5 As shown, the electronic device includes a memory and one or more processors. The memory is used to store one or more programs, and the one or more processors are used to execute the one or more programs to cause the electronic device to perform the titanium alloy α / β phase transformation temperature prediction method according to any embodiment of this application.

[0110] The storage medium stores a computer program, which, when executed by a processor, implements the method for predicting the α / β phase transformation temperature of titanium alloys according to any embodiment of this application.

[0111] In summary, the technical solution of this invention breaks through the black box limitation of existing machine learning methods in predicting the α / β phase transformation temperature of titanium alloys, providing a reliable theoretical tool for titanium alloy design and thus significantly improving R&D efficiency.

[0112] Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort should fall within the scope of protection of the present invention.

Claims

1. A method for predicting the α / β phase transformation temperature of titanium alloys, characterized in that, The process includes the following: The content of alloying elements of a titanium alloy with known composition is input into a pre-constructed titanium alloy α / β phase transformation temperature prediction model, and the α / β phase transformation temperature of the titanium alloy is calculated using the titanium alloy α / β phase transformation temperature prediction model. The construction process of the titanium alloy α / β phase transformation temperature prediction model includes: Using a linear regression algorithm, a basic prediction model for the α / β phase transformation temperature is established based on a pre-constructed titanium alloy dataset. The titanium alloy dataset includes the chemical composition information of the titanium alloy and the measured values ​​of the α / β phase transformation temperature corresponding to the chemical composition information. The chemical composition information includes the types of alloying elements contained in the titanium alloy and the content of each alloying element. A population of correction terms for the basic prediction model is generated by symbolic regression calculation based on a genetic algorithm, wherein the correction terms are mathematical expressions. Calculate the length of each correction term in the correction term population and the prediction accuracy of the basic prediction model after adding correction terms. The prediction accuracy of the basic prediction model after adding correction terms is the average absolute error between the measured value of the α / β phase transition temperature and the α / β phase transition temperature predicted by the basic prediction model after adding correction terms. Based on the non-dominated sorting algorithm, according to the length of each correction term in the correction term population and the prediction accuracy of the basic prediction model after adding correction terms, all correction terms in the correction term population are traversed to form a Pareto front. The optimal correction term is selected from the correction terms on the Pareto front. Specifically, this involves calculating the crowding distance of all correction terms on the Pareto front and selecting the correction term with the largest crowding distance as the optimal correction term. By integrating the basic prediction model and the optimal correction term, the prediction model for the α / β phase transformation temperature of the titanium alloy is obtained.

2. The method for predicting the α / β phase transformation temperature of titanium alloys according to claim 1, characterized in that, The fusion method of the basic prediction model and the optimal correction term is to linearly sum the basic prediction model and the optimal correction term.

3. The method for predicting the α / β phase transformation temperature of titanium alloys according to claim 1, characterized in that, Titanium alloys contain at least one of the following alloying elements: Al, Mo, V, Cr, Fe, Nb, Sn, Zr, Cu, Si, C, H, O, and N.

4. The method for predicting the α / β phase transformation temperature of titanium alloys according to claim 1, characterized in that, The process of constructing the titanium alloy dataset includes: An initial dataset for titanium alloys was constructed using at least one of historical experimental data and literature data. The initial titanium alloy dataset is filled with missing values ​​and outliers are removed to obtain the titanium alloy dataset.

5. The method for predicting the α / β phase transformation temperature of titanium alloys according to claim 4, characterized in that, The specific process of imputing missing values ​​and removing outliers in the initial titanium alloy dataset includes: The missing values ​​in the initial dataset of the titanium alloy were filled with 0, and outlier data were identified and removed using the Laida criterion.

6. A system for predicting the α / β phase transformation temperature of titanium alloys, characterized in that, include: Input module: Used to input the content of alloying elements of titanium alloys with known compositions into the pre-built titanium alloy α / β phase transformation temperature prediction model; Calculation module: used to calculate the α / β phase transformation temperature of the titanium alloy using a titanium alloy α / β phase transformation temperature prediction model and the content of the alloying elements; Output module: Used to output the α / β phase transformation temperature calculated by the titanium alloy α / β phase transformation temperature prediction model; The construction process of the titanium alloy α / β phase transformation temperature prediction model includes: Using a linear regression algorithm, a basic prediction model for the α / β phase transformation temperature is established based on a pre-constructed titanium alloy dataset. The titanium alloy dataset includes the chemical composition information of the titanium alloy and the measured values ​​of the α / β phase transformation temperature corresponding to the chemical composition information. The chemical composition information includes the types of alloying elements contained in the titanium alloy and the content of each alloying element. A population of correction terms for the basic prediction model is generated by symbolic regression calculation based on a genetic algorithm, wherein the correction terms are mathematical expressions. Calculate the length of each correction term in the correction term population and the prediction accuracy of the basic prediction model after adding correction terms. The prediction accuracy of the basic prediction model after adding correction terms is the average absolute error between the measured value of the α / β phase transition temperature and the α / β phase transition temperature predicted by the basic prediction model after adding correction terms. Based on the non-dominated sorting algorithm, according to the length of each correction term in the correction term population and the prediction accuracy of the basic prediction model after adding correction terms, all correction terms in the correction term population are traversed to form a Pareto front. The optimal correction term is selected from the correction terms on the Pareto front. Specifically, this involves calculating the crowding distance of all correction terms on the Pareto front and selecting the correction term with the largest crowding distance as the optimal correction term. By integrating the basic prediction model and the optimal correction term, the prediction model for the α / β phase transformation temperature of the titanium alloy is obtained.

7. An electronic device, characterized in that, include: One or more processors; A memory on which one or more programs are stored; When the one or more programs are executed by the one or more processors, the one or more processors implement the method for predicting the α / β phase transformation temperature of titanium alloys as described in any one of claims 1-5.

8. A storage medium, characterized in that, It stores a computer program, wherein the computer program, when executed by a processor, implements the method for predicting the α / β phase transformation temperature of titanium alloys as described in any one of claims 1-5.

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