A Machine Learning-Based Method for Predicting the Thermal Conductivity of Titanium Alloys

Abstract

This invention discloses a machine learning-based method for predicting the thermal conductivity of high thermal conductivity titanium alloys, belonging to the field of physical property prediction technology for metallic materials. It addresses the problems of poor accuracy and limited reference data in current titanium alloy thermal conductivity prediction models. This method constructs an enhanced dataset by fusing experimental and computational data, and builds alloy factors based on physical features. Through alloy factor screening and machine learning model training, a multidimensional nonlinear mapping relationship is established between titanium alloy composition, alloy factor features, and thermal conductivity. This enables rapid and relatively accurate prediction of the thermal conductivity of titanium alloys with different compositions. It provides an efficient and reliable composition design reference for the subsequent development of high thermal conductivity titanium alloys.

Description

Technical Field

[0001] This invention relates to the fields of metallic material preparation and computational materials science, specifically to a method for designing the composition of high thermal conductivity titanium alloys based on machine learning. Background Technology

[0002] Traditional titanium alloys, due to their high specific strength, excellent corrosion resistance, and biocompatibility, have been widely used in aerospace, biomedical, and automotive industries. In recent years, with the increasing demand for high-performance heat dissipation materials in the 3C electronics industry, the potential of titanium alloys as backplates or packaging substrates has gradually emerged. However, pure titanium has a low thermal conductivity (approximately 22 W / (m·K)), and the introduction of alloying elements further disrupts the crystal morphology, generating strong phonon scattering and reducing electron mobility, resulting in the thermal conductivity of most engineering-grade titanium alloys (such as Ti-6Al-4V) generally being below 10 W / (m·K). This low thermal conductivity not only easily causes localized thermal stress concentration in electronic components, affecting their service life, but also leads to heat accumulation in the cutting zone and accelerated tool wear during processing, increasing manufacturing difficulty and cost. Therefore, overcoming the bottleneck in improving thermal conductivity and designing titanium alloys that combine high thermal conductivity with high strength and toughness is key to expanding the processing applications of titanium alloys.

[0003] Traditional titanium alloy design methods often rely on trial-and-error approaches based on physical metallurgical experience or high-throughput experimental screening. However, the thermal conductivity of titanium alloys is subject to complex coupling effects from multiple physical mechanisms, including electron transport and phonon scattering, resulting in a vast compositional space and highly nonlinear evolution. Furthermore, research on the thermal conductivity of titanium alloys is limited, with small datasets. Traditional methods are not only time-consuming and inefficient but also cannot extend predictions to other alloying conditions. Moreover, existing commercial thermodynamic simulation software (such as JmatPro) exhibits significant biases in predicting the thermal conductivity of titanium alloys, making it difficult to provide reliable support for the compositional design of high-thermal-conductivity titanium alloys. With the advent of the big data era, machine learning methods, with their powerful nonlinear mapping capabilities, have been increasingly applied to the performance prediction and reverse compositional design of various high-performance materials.

[0004] Predicting titanium alloy properties using machine learning typically involves data acquisition, feature engineering, model training, and validation. Current mainstream research on titanium alloy performance prediction often uses the amount of each element added as direct input features to construct a "black box" regression model. However, these methods often focus only on numerical fitting, lacking the mechanism by which the intrinsic physical properties of alloying elements regulate thermal conductivity evolution, resulting in weak physical interpretability of the model. Furthermore, due to the small sample size of experimental data on titanium alloy thermal conductivity, conventional machine learning feature engineering is prone to model overfitting, making it difficult to guide the accurate design of low-alloy systems. Therefore, how to utilize feature selection methods that combine small sample data with physical feature fusion is particularly important for using machine learning to assist in the prediction of titanium alloy thermal conductivity. Summary of the Invention

[0005] Based on the above problems, the purpose of this invention is to provide a machine learning-based method for predicting the thermal conductivity of titanium alloys. This method constructs an enhanced dataset by fusing experimental data and computational data, and constructs an alloy factor by combining physical features. It establishes a multidimensional nonlinear mapping relationship between titanium alloy composition, alloy factor features, and thermal conductivity, thereby solving the problems existing in the prior art.

[0006] The technical solution adopted in this invention is as follows: Step 1: Obtain 40 sets of experimental data on the composition and thermal conductivity of titanium alloys through MatWeb and scientific literature.

[0007] Step 2: Construct an augmented dataset of experimental and computational data based on JMatPro. The computational data is sampled in three regions within a two-dimensional subspace: the sparse region, the boundary region, and the region near the experimental points obtained after PCA dimensionality reduction mapping. This yields a uniformly distributed virtual alloy composition scheme that conforms to physical metallurgical constraints. The corresponding thermal conductivity is calculated using JMatPro material property simulation software to expand the computational data. The data is then filtered based on the distribution range of thermal conductivity in pure titanium and conventional titanium alloys to ensure the breadth of sample distribution and the rationality of the calculated thermal conductivity.

[0008] Step 3: Map the 18 physical characteristics of the 10 alloying elements to macroscopic alloying factors. Combine the amount of alloying elements added to calculate the mean factor reflecting the influence of the magnitude of the characteristic quantities and the variance factor reflecting the influence of the degree of dispersion of the properties.

[0009] Step 4: Dimensionality reduction of feature factors is performed using Pearson analysis, recursive feature elimination, and exhaustive search.

[0010] Step 5: Establish an SVR regression model and determine the optimal hyperparameters through grid search and five-fold cross-validation.

[0011] Step 6: Using the SHAP attribution analysis method, extract the feature SHAP values ​​of all samples, and characterize the specific mapping relationship between physical parameter changes and thermal conductivity response through a global feature importance summary plot and a univariate dependency plot.

[0012] This invention has the following advantages: by introducing a physically meaningful alloy factor, it significantly improves the model's generalization ability and physical interpretability, and increases the test set determination coefficient. It reached 0.93. Attached Figure Description

[0013] The present invention can be better understood by referring to the description given below in conjunction with the accompanying drawings, which together with the following detailed description are included in and form part of this specification, and are used to further illustrate preferred embodiments of the invention and explain the principles and advantages of the invention.

[0014] Figure 1 A flowchart illustrating the composition design of high thermal conductivity titanium alloys provided for this invention.

[0015] Figure 2 This is a comparison chart of the element distribution of experimental data and supplementary calculated data in an embodiment of the present invention.

[0016] Figure 3 This is a scatter plot comparing the prediction results of the SVR model with the actual values ​​in an embodiment of the present invention.

[0017] Figure 4 The results of the SHAP analysis show the importance of key alloying factor characteristics in the embodiments of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that, for clarity and brevity, this specification focuses on describing the core steps related to thermal conductivity prediction and attribution analysis, omitting known details of conventional material experiments and basic algorithms. Example

[0019] like Figure 1 As shown, the machine learning-based method for predicting the thermal conductivity of titanium alloys provided by this invention includes the following steps: Step 1: Construct a titanium alloy composition-thermal conductivity dataset.

[0020] By searching the MatWeb database and publicly available academic literature, and after rigorous data cleaning, 40 high-quality datasets of "composition-thermal conductivity" for room-temperature annealed titanium alloys were finally selected. These datasets contain 10 alloying elements besides Ti: Al, Cu, Cr, Mo, Si, V, Nb, Fe, Zr, and Sn. To address the sparsity problem of small sample data in a high-dimensional composition space, this embodiment employs principal component analysis (PCA) combined with a three-region sampling algorithm for data augmentation; specifically, the alloying elements in the augmented data are all included within the alloying element range of the original data.

[0021] Specifically, in constructing the composition generation space, this embodiment sets mass fraction boundaries for each alloying element (see Table 1 for details). These mass fraction boundaries are determined based on the distribution characteristics of alloy components in existing experimental datasets, combined with the commonly used content ranges of specific alloying elements in the titanium alloy system. Furthermore, to ensure that the generated virtual samples have a reasonable physical metallurgical basis and facilitate the prediction of high thermal conductivity titanium alloys, additional global constraints are imposed: the total addition of alloying elements <10 wt.%, and the number of non-zero added elements in a single generation is limited to 1 to 5.

[0022] Table 1. Range of original alloying mass fraction in supplementary data points Content (wt.%) 0-8 0-6 0-5 0-4 0-3 0-6 0-4 0-5 0-3 0-4 Furthermore, a three-region component generation algorithm was designed, consisting of "sparse region, boundary region, and region near the experimental point," with the generation ratio set to 5:2:3.

[0023] Specifically, for sparse region supplementation, a random sampling method is used in the constrained space to generate candidate points. The minimum distance between these candidate points and all existing experimental points is calculated; points less than 10% of the average distance are discarded to ensure a reasonable interval between new points and existing data. This process is repeated until the required number of sparse points are collected. Boundary region supplementation also involves sampling within the constrained space, but priority is given to retaining at least one element with a content within 5% of the boundary. Sufficient boundary points are collected through multiple attempts. The area near the experimental points is reduced to two-dimensional space using PCA, followed by K-Means clustering. The cluster center is selected as the base point for local perturbation sampling within ±5%. 150 sets of computational data are obtained through the above process. Using JMatPro software based on phase diagram calculation principles, a heat treatment temperature of 600℃ is set, and a dedicated titanium alloy database is used to calculate the corresponding room temperature thermal conductivity. The final study used the theoretical upper limit of the room temperature thermal conductivity of pure titanium (approximately 21 W / (m·K)) and the statistical range of titanium alloy thermal conductivity in the literature to establish confidence intervals for data cleaning, resulting in 70 sets of calculation data. This led to the construction of a titanium alloy composition-thermal conductivity enhancement dataset containing 110 samples. In this embodiment, principal component analysis was used to distribute the added alloy composition and the alloy composition collected from the literature in a two-dimensional plane as shown in the figure. Figure 2 As shown.

[0024] Step 2: Construction and Screening of Alloy Factors Eighteen intrinsic physical characteristics of titanium alloys were collected, including atomic number, valence electron number, atomic radius, and Md parameter. The mean and variance factors of the alloy factors were calculated using the following formulas, constructing a feature library of 36 alloy factors.

[0025]

[0026] To reduce redundant information in the high-dimensional feature space and the complexity of model training, this study uses the Pearson correlation elimination-recursive elimination-exhaustive method to reduce the dimensionality of alloy factors.

[0027] Specifically, Pearson correlation analysis was used. When |R|>0.95, it was determined that the physical information carried by the two alloy factors was highly similar, and their influence on subsequent thermal conductivity prediction was considered to be similar. One of the alloy factors was then removed. After removal, 33 alloy factors remained. In the recursive elimination phase, each remaining alloy factor was iterated in each iteration. After removing the alloy factor, the mean squared error (MSE) of the remaining K-1 alloy factors trained using the SVR model was calculated. The alloy factor corresponding to the group with the smallest error was removed from the K error results. The remaining K-1 alloy factors entered the next iteration until the model error began to increase three times consecutively. After recursive elimination, 20 alloy factors were successfully removed. For the remaining 11 alloy factors, an exhaustive method was used to iterate through all possible combinations of the 11 alloy factors, and the cross-validation MSE of each combination was calculated using the SVR model. Given that the differences in predicted MSE among multiple candidate subsets are extremely small, in order to ensure high model fidelity while minimizing the complexity of the physical model, this study prioritizes the feature combination with the fewest features as the final key alloy factor combination. The five alloy factors finally selected are shown in Table 2.

[0028] Table 2. Alloying factors obtained and their physical significance Physical meaning mean number of valence electrons Mean atomic radius Md mean Ion radius variance Md variance Step 3: Model Training and Hyperparameter Tuning The dataset was divided into training and test sets in an 8:2 ratio. Support Vector Machine Regression (SVR) was selected as the prediction model. To overcome the sensitivity of SVR to parameters, a 3×3 grid search space was constructed, and five-fold cross-validation was used for system tuning. The final determined hyperparameter combination was: radial basis function kernel (kernel = 'rbf'), penalty parameter C = 10, error tolerance ε = 0.01, and kernel coefficient gamma = 'auto'. The prediction results show (e.g.) Figure 3 (As shown), test set determination coefficient The mean squared error (MSE) is 0.93 and the mean squared error (MSE) is 0.35, indicating that the model has excellent generalization ability.

[0029] Step 4: Attribution and Mechanism Analysis Based on SHAP Values To deeply analyze the influence of five key alloying factors on thermal conductivity, this embodiment uses the SHAP attribution analysis method to extract the characteristic SHAP values ​​of all 110 sets of data. By analyzing the global feature importance summary plot and univariate dependency plot of the key alloying factors, the influence of different alloying factors on model prediction is analyzed.

[0030] Specifically, by Figure 4 The SHAP values ​​of the ionic radius variance exhibit the largest distribution range, dominating the spectrum. High eigenvalues ​​are concentrated in the negative range of the SHAP values, indicating a strong negative correlation with thermal conductivity. This is because the differentiated ionic radii increase the phonon scattering cross section and shorten the phonon mean free path. The univariate dependency plot clearly shows a strictly monotonically decreasing trend in the ionic radius variance. Furthermore, the Md mean and Md variance show a significantly enhanced effect on thermal conductivity after standardization exceeding 0.5, reflecting the beneficial role of d-orbital energy level states in the reconstruction of the electronic band structure. The influence of the mean valence electron number on thermal conductivity shows an initial increase followed by a decrease. The SHAP values ​​corresponding to the mean atomic radius at the same eigenvalue exhibit significant fluctuations, proving that its control over thermal conductivity is not independent but rather strongly coupled with other characteristics.

[0031] The above-described embodiments merely illustrate implementation methods of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. Those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A method for predicting the thermal conductivity of high thermal conductivity titanium alloys based on machine learning, characterized in that, Includes the following steps: Step 1: Obtain data on the composition and thermal conductivity of titanium alloys to establish an initial dataset.

2. Step 2: Using a three-region composition generation algorithm combined with Principal Component Analysis (PCA) to expand the sampling, a virtual alloy composition scheme with uniform distribution and conforming to physical metallurgical constraints is obtained. The corresponding thermal conductivity is calculated using JMatPro material performance simulation software to expand the calculation data. The three regions include the sparse region, the boundary region, and the region near the experimental point. Calculation samples are generated and merged with the experimental data to form an enhanced dataset. Step 3: Collect the intrinsic physical characteristics of each element in the titanium alloy, and calculate the alloy factor of the enhancement dataset, including the characteristic mean factor, based on the relative content of each element in the alloy and the formula. With characteristic variance factor Construct an initial alloy factor library; Step 4: Use a three-stage dimensionality reduction method to screen out key alloy factors that are strongly correlated with thermal conductivity from the initial alloy factor library; Step 5: Using the key alloy factors of the augmented dataset as input features, a support vector machine regression (SVR) algorithm is used to train the thermal conductivity prediction model. Cross-validation and grid search are then used to optimize the hyperparameters, establishing an alloy factor-thermal conductivity prediction model. Since the key alloy factors are mapped from the alloy composition using a defined physical calculation formula, by combining the alloy factor calculation module with the SVR prediction model, a titanium alloy composition-thermal conductivity prediction model is essentially constructed, with the alloy composition and its content as the original input and the predicted thermal conductivity value as the output. Step 6: Use the SHAP attribution analysis method to calculate the contribution of each key alloy factor to the model prediction results, and characterize the specific mapping relationship between changes in physical parameters and thermal conductivity response.

3. A method based on the step one according to claim 1, characterized in that... The acquired dataset consists of composition and thermal conductivity data of room temperature titanium alloys in the annealed state.

4. The method of step two according to claim 1, characterized in that: The generation ratio of the three-region composition generation algorithm is: sparse region: boundary region: region near the experimental point = 5:2:

3. The spatial constraints for the generated composition are: total element addition <10wt.%, and the number of non-zero added elements in a single generated alloy system is limited to 1 to 5 types.

5. The method in step three according to claim 1, characterized in that... The physical characteristics include 18 physicochemical features, such as atomic number, atomic weight, number of valence electrons, density, molar volume, work function, ionization energy, ionic radius, covalent radius, atomic radius, electronegativity, Bo value, Md value, heat capacity, fusion enthalpy, thermal conductivity, electrical resistance, and linear thermal expansion coefficient.

6. Step four according to claim 1, characterized in that: The screening steps for the key alloying factors include: Step 1: Use Pearson correlation analysis to identify the correlation between alloy factors and filter out redundant variables with a correlation higher than 0.95; Step 2: Based on the recursive feature elimination (RFE) mechanism, filter out noise factors that contribute little to the target performance; Step 3: Use an exhaustive method to traverse the remaining low-dimensional feature combinations and determine the final key alloy factor combination guided by the optimal MSE (Model Evaluation Sequence) index.

7. Step five according to claim 1, characterized in that: The SVR model uses a radial basis function (RBF) with a penalty parameter C set to 10 and an error tolerance ε of 0.01.

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