Alloy design method based on CALPHAD representation and application of cross-system knowledge transfer

Abstract

The application discloses a CALPHAD-based cross-system knowledge transfer alloy design method, which comprises the following steps: performing CALPHAD balance calculation on a source aluminum alloy and a target Al-Mg-Zn alloy to construct an initial feature set; deriving mean value and variance of phase fraction weighting and multi-step heat treatment addition / difference features; locking an optimal feature subset through three-step feature selection assisted by source data set; training 300 base models through bagging, integrating mean value and standard deviation to obtain a high-stability predictor; and coupling NSGA-II and high-throughput CALPHAD to search for a Pareto frontier with double targets of strength and elongation and determine a composition-process scheme; and the application significantly improves the model interpretability and generalization performance by constructing a CALPHAD descriptor with physical interpretability as a model feature, thereby improving the alloy design efficiency and reducing the experimental workload.

Description

Technical Field

[0001] This invention relates to the field of aluminum alloy material design and development technology, and in particular to a cross-system knowledge transfer alloy design method based on CALPHAD representation and its application. Background Technology

[0002] Commercial aluminum alloys generally suffer from limitations in balancing strength, plasticity, and corrosion resistance. The emerging Al-Mg-Zn system has attracted attention due to its excellent high-temperature performance and corrosion / radiation resistance; however, its complex phase structure (T phase contains 162 atoms) and composition-sensitive precipitation sequences make traditional experience-based trial-and-error methods inefficient. While machine learning has been used in materials design, it is prone to overfitting when target data is scarce; simple transfer learning fails due to large differences in composition and process distribution. The CALPHAD method can provide thermodynamic descriptors but cannot directly output performance-related features. Therefore, a physically interpretable, small-sample-usable cross-system knowledge transfer scheme is urgently needed to achieve efficient Al-Mg-Zn alloy design. Summary of the Invention

[0003] The purpose of this invention is to provide a cross-system knowledge transfer alloy design method based on CALPHAD representation and its application, thereby solving the aforementioned problems existing in the prior art.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A cross-system knowledge transfer alloy design method based on CALPHAD representation enables efficient design of high-strength and high-toughness Al-Mg-Zn aluminum alloys under small sample data conditions by transferring knowledge from the source aluminum alloy system to the target Al-Mg-Zn alloy system. The method includes the following steps:

[0006] (a) Feature construction: Thermodynamic equilibrium calculations were performed on the composition-heat treatment temperature data of the source aluminum alloy and the target Al-Mg-Zn alloy using CALPHAD software to extract phase properties. With system properties Construct the initial CALPHAD feature set;

[0007] (b) Feature derivation: Using the fraction of each phase as the weight, the thermodynamic and thermophysical properties in the initial CALPHAD feature set are weighted and the weighted mean and weighted variance are calculated. Additive and differential features are constructed for multi-step heat treatment processes to form a CALPHAD derived feature pool that can characterize the coupling effect of composition and heat treatment.

[0008] (c) Source auxiliary feature selection steps:

[0009] For the CALPHAD-derived feature pool obtained in step (b), perform a three-step feature selection assisted by the source dataset:

[0010] (i) Recursive feature elimination: Iteratively eliminate the features that contribute the least using a tree-based regression model until the main features are retained;

[0011] (ii) Sequential backward selection: Based on the results of (i), features that increase cross-validation error are gradually removed to optimize feature combinations;

[0012] (iii) Exhaustive feature selection: Perform a full combination evaluation on the features obtained in (ii) and select the optimal feature subset that maximizes the accuracy and robustness of the target performance prediction;

[0013] (d) Machine learning modeling:

[0014] Perform bagging modeling on the key CALPHAD-derived features selected in step (c): each time, randomly sample 80% of the target dataset and merge it with all source datasets as the training set, and use the remaining 20% ​​of the target dataset as the test set; repeat this sampling-training-testing process no less than 300 times to obtain 300 base models, integrate the mean and standard deviation of their prediction results to form a stable performance predictor with uncertainty quantification.

[0015] (e) Multi-objective optimization and alloy design steps:

[0016] The bagging predictor obtained in step (d) is coupled with high-throughput CALPHAD calculation and NSGA-II genetic algorithm, and executed sequentially with the dual objectives of maximizing tensile strength and elongation:

[0017] (i) Randomly generate an initial population and perform thermodynamic equilibrium calculations for each individual;

[0018] (ii) Calculate the value of each feature in the optimal feature subset of step (c) and input it into the bagging model to obtain the performance prediction value;

[0019] (iii) Non-dominated ranking and crowding distance calculation are performed based on the predicted values, and the Pareto-optimal individuals are retained;

[0020] (iv) Select, crossover, and mutate the current population to generate the next generation, and repeat (i)–(iii);

[0021] (v) The convergence was monitored using hypervolume indices, and the process was iterated until the Pareto front stabilized. Finally, a representative composition-process scheme was selected from the front to complete the rapid design of the Al-Mg-Zn alloy.

[0022] (f) Experimental verification steps:

[0023] The Al-Mg-Zn alloy composition selected in step (e) was sequentially subjected to melting, homogenization, hot rolling, intermediate annealing, cold rolling, solution treatment and artificial aging treatment to prepare plates and test their mechanical properties. The tensile strength obtained was 569±12MPa and the elongation was 14.9±0.3%, which verified that the designed alloy achieved high strength and toughness at the same time.

[0024] Furthermore, the system properties and phase properties in step (a) include at least one of Gibbs free energy, enthalpy, entropy, volume, density, phase fraction, phase stability function, Curie temperature, and Bohr magneton number.

[0025] Furthermore, the formulas for calculating the weighted mean and weighted variance in step (b) are as follows:

[0026] weighted mean With weighted variance as follows:

[0027]

[0028]

[0029] in, Represents the heat treatment state lower phase The phase fraction, which is used as a weighting factor;

[0030] The formulas for calculating the summation feature and the difference feature are as follows:

[0031]

[0032]

[0033] in , and These represent the characteristic values ​​under the first and second heat treatment states, respectively.

[0034] Furthermore, step (c) source auxiliary feature selection further includes:

[0035] (i) The recursive feature elimination stage uses XGBoost as the base model. When the RMSE of the target dataset starts to rise, the elimination stops and 30 features are retained.

[0036] (ii) The sequential backward selection stage uses the SVR model for evaluation, and 10 features are obtained after 29 rounds of iteration;

[0037] (iii) In the exhaustive feature selection stage, the SVR model was used to evaluate the 10 features in a 2^10 combination, and finally 7 key features of tensile strength and 5 key features of elongation were determined. All key features have clear thermodynamic or thermophysical meanings.

[0038] Furthermore, the multi-objective optimization in step (e) is further defined as follows:

[0039] With a population size of 400, a crossover probability of 0.9, a mutation index of 20, and 100 iterations, a total of ≥40,800 CALPHAD thermodynamic calculations were completed. Convergence was determined when the hypervolume index changed by <0.1% over 10 consecutive generations. Finally, in the high-strength region, an Al-Mg-Zn alloy scheme with the composition of 5.1Mg-2.8Zn-0.4Cu-0.5Mn-0.3Ag-0.2Sc-0.1Zrwt% was selected, with a solution treatment temperature of 470℃ / 1h and an aging temperature of 120℃ / 16h.

[0040] Furthermore, the Al-Mg-Zn alloy composition determined in step (e) was smelted according to the mass percentage of 5.1Mg-2.8Zn-0.4Cu-0.5Mn-0.3Ag-0.2Sc-0.1Zr. After homogenization at 430℃ for 6 hours and 460℃ for 24 hours, hot rolling at 430℃ to 2.8 mm, intermediate annealing at 375℃ for 75 minutes, cold rolling to 2 mm, solution quenching at 470℃ for 1 hour, and artificial aging at 120℃ for 16 hours, a plate was prepared and its mechanical properties were tested. The measured tensile strength was 569±12MPa and the elongation was 14.9±0.3%, verifying the acquisition of a high-strength and high-toughness Al-Mg-Zn alloy.

[0041] Based on the same concept, a high-strength and high-toughness Al-Mg-Zn aluminum alloy was designed and prepared by the above method, and its composition, in mass percentage, is as follows:

[0042] Mg 4.0–5.5%, Zn 2–3.2%, Cu ≤0.5%, Mn ≤0.8%, Ag ≤0.8%, Sc ≤0.3%, Zr ≤0.15%, Cr ≤0.11%, Ti ≤0.06%, Fe ≤0.06%, Si ≤0.06%, balance being Al and unavoidable impurities;

[0043] The alloy has a tensile strength of 569±12MPa, a yield strength of 479±11MPa, and an elongation of 14.9±0.3% under single-stage aging conditions.

[0044] Furthermore, the microstructure contains diffusely distributed nano-T-Mg 32 (Al,Zn) 49 The phase and Al3(Sc,Zr) particles, recrystallization volume fraction <10%, low-angle grain boundary ratio >70%.

[0045] Furthermore, this method can be applied to magnesium alloys, titanium alloys, high-entropy alloys, or other multi-component alloy systems. Under the condition that the number of samples in the new alloy system is ≤50, the method can directly complete the composition-process design of strength-plasticity synergistic optimization, reduce the number of experiments by ≥70%, and obtain alloy materials with simultaneous improvement in tensile strength and elongation.

[0046] The beneficial effects of this invention are:

[0047] 1. Improve prediction accuracy with small samples: By introducing the CALPHAD method and source-assisted feature engineering, the model can achieve stable and accurate performance prediction with only a small amount of target domain data, avoiding the overfitting problem of traditional black-box machine learning methods.

[0048] 2. Enables cross-system knowledge transfer: Effectively utilizes knowledge from other widely studied material systems, significantly reducing experimental costs and time for the target material system.

[0049] 3. Strong physical interpretability: The selected CALPHAD-derived features all have clear thermodynamic or thermophysical meanings, which can be used to explain the alloy strengthening mechanism, facilitating subsequent mechanism research and process optimization.

[0050] 4. Overcoming performance trade-offs: The designed Al-Mg-Zn alloy can achieve a synergistic improvement in strength and elongation under single-stage aging conditions, which is significantly better than other Al-Mg-Zn alloys.

[0051] 5. Versatility and scalability: This method is not only applicable to Al-Mg-Zn alloys, but can also be extended to multi-component systems such as magnesium alloys, titanium alloys, and high-entropy alloys, enabling computation-driven accelerated material design. Attached Figure Description

[0052] Figure 1 This is a flowchart of the CALPHAD-based representation transfer method for accelerating alloy design used in Embodiment 1 of the present invention.

[0053] Figure 2 This refers to the thermodynamic calculations of the presence and distribution of each single phase in the source dataset and target dataset under solid solution and aged states in Embodiment 1 of the present invention.

[0054] Figure 3 This is the specific process for source domain-assisted feature filtering in Embodiment 1 of the present invention;

[0055] Figure 4 This is the source-domain assisted feature selection result of tensile strength (UTS) and elongation (EL) in Embodiment 1 of the present invention;

[0056] Figure 5It is the bagging-based model trained with various strategies to measure tensile strength (UTS) and elongation (EL) in Embodiment 1 of the present invention;

[0057] Figure 6 This is the multi-objective optimization and experimental verification in Embodiment 1 of the present invention;

[0058] Figure 7 These are the statistical results of grain distribution (a) and grain orientation (b) of the alloy in the aging state of the design in Example 1 of this invention.

[0059] Figure 8 The microstructure of the alloy designed in this invention under aging conditions and the energy dispersive spectroscopy results within the white box area are shown. Detailed Implementation

[0060] 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. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. The core idea of ​​this invention is to transform raw features such as alloy composition and heat treatment temperature into physically meaningful CALPHAD-related descriptors. Through feature engineering, key CALPHAD-derived features that characterize the coupling effect of composition and heat treatment temperature are constructed, derived, and screened. This achieves knowledge transfer from the source aluminum alloy to the target aluminum alloy and improves the interpretability and generalization ability of its machine learning model. Furthermore, a multi-objective optimization algorithm enables efficient exploration of the alloy design space. The specific technical solution includes the following steps:

[0061] Reference Figures 1-8 The method shown is a cross-system transfer learning alloy design method based on CALPHAD representation. By transferring knowledge from the source aluminum alloy system to the target Al-Mg-Zn alloy system, it achieves efficient design of high-strength and high-toughness Al-Mg-Zn aluminum alloys under small sample data conditions. The method includes the following steps:

[0062] (a) Feature construction: Thermodynamic equilibrium calculations were performed on the composition-heat treatment temperature data of the source aluminum alloy and the target Al-Mg-Zn alloy using CALPHAD software to extract phase properties. With system properties Construct the initial CALPHAD feature set;

[0063] In this embodiment, this step specifically involves: after collecting the source dataset and target dataset from the literature, using CALPHAD software and its accompanying thermodynamic database, performing thermodynamic equilibrium calculations on the composition and heat treatment temperature data of both datasets, and deriving the phase properties from the calculation results. and system properties ,in Representative phase Or the thermodynamic or thermophysical properties of the entire system. These represent the heat treatment state. These initial results construct the initial CALPHAD feature set.

[0064] (b) Feature derivation: Using the fraction of each phase as the weight, the thermodynamic and thermophysical properties in the initial CALPHAD feature set are weighted and the weighted mean and weighted variance are calculated. Additive and differential features are constructed for multi-step heat treatment processes to form a CALPHAD derived feature pool that can characterize the coupling effect of composition and heat treatment.

[0065] In this embodiment, this step specifically involves: performing phase fraction weighting on the thermodynamic and thermophysical properties of each phase, and calculating their weighted average. With weighted variance This is to reflect the effects of all relative systems.

[0066]

[0067]

[0068] in, Represents the heat treatment state lower phase The phase fraction, which is used as a weighting factor.

[0069] If two heat treatments are involved, then the summation characteristics of the two heat treatments are constructed for each thermodynamic and thermophysical property. and difference features This is to reflect the impact of heat treatment changes on the system.

[0070]

[0071]

[0072] in , and These represent the characteristic values ​​under the first and second heat treatment states, respectively.

[0073] (c) Source auxiliary feature selection steps:

[0074] For the CALPHAD-derived feature pool obtained in step (b), perform a three-step feature selection assisted by the source dataset:

[0075] (i) Recursive feature elimination: Iteratively eliminate the features that contribute the least using a tree-based regression model until the main features are retained;

[0076] (ii) Sequential backward selection: Based on the results of (i), features that increase cross-validation error are gradually removed to optimize feature combinations;

[0077] (iii) Exhaustive feature selection: Perform a full combination evaluation on the features obtained in (ii) and select the optimal feature subset that maximizes the accuracy and robustness of the target performance prediction;

[0078] In this embodiment, this step specifically involves: For the large number of candidate CALPHAD-related features derived from the features, a three-step feature selection strategy based on the source dataset is proposed to extract the key features most relevant to the target performance. The method includes the following steps:

[0079] Step 1, Recursive Feature Elimination: The candidate features are iteratively trained using a tree-based regression model. Each time, one or more features that contribute the least to the model's prediction are removed until the feature set is significantly reduced in size and the main features are retained.

[0080] Step 2, sequential backward selection: Based on the above feature subset, gradually remove the features that contribute the least to the model's cross-validation performance, and further optimize the feature combination to improve the model's generalization performance on the target dataset.

[0081] Step 3, exhaustive feature selection: Perform a full combinatorial traversal and performance evaluation on the features selected by the sequence backward selection to determine the final optimal feature subset, so as to maximize the accuracy and robustness of the model in the target performance prediction.

[0082] In the above steps, the source dataset is always included in the cross-validation training set to prevent overfitting of the target dataset.

[0083] (d) Machine learning modeling:

[0084] Perform bagging modeling on the key CALPHAD-derived features selected in step (c): each time, randomly sample 80% of the target dataset and merge it with all source datasets as the training set, and use the remaining 20% ​​of the target dataset as the test set; repeat this sampling-training-testing process no less than 300 times to obtain 300 base models, integrate the mean and standard deviation of their prediction results to form a stable performance predictor with uncertainty quantification.

[0085] In this embodiment, this step specifically involves: to reduce the randomness of small sample data partitioning, bagging modeling is performed based on the selected key CALPHAD-derived features. Specifically, the dataset is sampled multiple times, with 80% of the target data and all source domain data used as the training set to train the machine learning model each time, and the remaining 20% ​​of the target data used as the test set. This sampling is repeated 300 times to form 300 base models, and the predicted output mean and standard deviation are integrated to improve prediction stability and uncertainty quantification.

[0086] (e) Multi-objective optimization and alloy design steps:

[0087] The bagging predictor obtained in step (d) is coupled with high-throughput CALPHAD calculation and NSGA-II genetic algorithm, and executed sequentially with the dual objectives of maximizing tensile strength and elongation:

[0088] (i) Randomly generate an initial population and perform thermodynamic equilibrium calculations for each individual;

[0089] (ii) Calculate the value of each feature in the optimal feature subset of step (c) and input it into the bagging model to obtain the performance prediction value;

[0090] (iii) Non-dominated ranking and crowding distance calculation are performed based on the predicted values, and the Pareto-optimal individuals are retained;

[0091] (iv) Select, crossover, and mutate the current population to generate the next generation, and repeat (i)–(iii);

[0092] (v) The convergence was monitored using hypervolume indices, and the process was iterated until the Pareto front stabilized. Finally, a representative composition-process scheme was selected from the front to complete the rapid design of the Al-Mg-Zn alloy.

[0093] In this embodiment, this step specifically involves: for multi-objective alloy design problems, a trained bagging model is coupled with high-throughput thermodynamic calculations and a genetic algorithm as a performance predictor to achieve rapid alloy design. The specific steps are as follows: the genetic algorithm randomly generates an initial population, performs thermodynamic calculations on the initial population, and obtains the values ​​of key CALPHAD-derived features through the feature derivation method in the second step. These values ​​are then input into the bagging model to obtain the predicted performance. Subsequently, non-dominated solutions are sorted based on the predicted values ​​to select the non-dominated solutions in the current population. Selection, crossover, and mutation operations are then performed to generate new offspring, forming the next generation population, and the above process is repeated. This iterative evolution is continued, and the convergence of the algorithm is tracked using a hypervolume index until a stable Pareto front is found. Finally, representative alloy compositions and processes are selected at the Pareto front to complete the rapid design.

[0094] (f) Experimental verification steps:

[0095] The Al-Mg-Zn alloy composition selected in step (e) was sequentially subjected to melting, homogenization, hot rolling, intermediate annealing, cold rolling, solution treatment and artificial aging treatment to prepare plates and test their mechanical properties. The tensile strength obtained was 569±12MPa and the elongation was 14.9±0.3%, which verified that the designed alloy achieved high strength and toughness at the same time.

[0096] In this embodiment, this step specifically involves: experimental verification of the designed alloy. After melting, homogenization treatment, hot rolling, intermediate annealing, cold rolling, solution treatment, and artificial aging treatment, the tensile strength was tested to be 569 ± 12 MPa and the elongation was 14.9 ± 0.3%, thus developing a high-strength and high-toughness Al-Mg-Zn alloy.

[0097] Furthermore, the system properties and phase properties in step (a) include at least one of Gibbs free energy, enthalpy, entropy, volume, density, phase fraction, phase stability function, Curie temperature, and Bohr magneton number.

[0098] Furthermore, the formulas for calculating the weighted mean and weighted variance in step (b) are as follows:

[0099] weighted mean With weighted variance as follows:

[0100]

[0101]

[0102] in, Represents the heat treatment state lower phase The phase fraction, which is used as a weighting factor;

[0103] The formulas for calculating the summation feature and the difference feature are as follows:

[0104]

[0105]

[0106] in , and These represent the characteristic values ​​under the first and second heat treatment states, respectively.

[0107] Furthermore, step (c) source auxiliary feature selection further includes:

[0108] (i) The recursive feature elimination stage uses XGBoost as the base model. When the RMSE of the target dataset starts to rise, the elimination stops and 30 features are retained.

[0109] (ii) The sequential backward selection stage uses SVR evaluation, and 10 features are obtained after 29 rounds of iteration;

[0110] (iii) In the exhaustive feature selection stage, a 2^10 full combination evaluation was performed on 10 features, and finally 7 key features of tensile strength and 5 key features of elongation were determined, and all key features have clear thermodynamic meaning.

[0111] Furthermore, the multi-objective optimization in step (e) is further defined as follows:

[0112] With a population size of 400, a crossover probability of 0.9, a mutation index of 20, and 100 iterations, a total of ≥40,800 CALPHAD thermodynamic calculations were completed. Convergence was determined when the hypervolume index changed by <0.1% over 10 consecutive generations. Finally, in the high-strength region, an Al-Mg-Zn alloy scheme with the composition of 5.1Mg-2.8Zn-0.4Cu-0.5Mn-0.3Ag-0.2Sc-0.1Zrwt% was selected, with a solution treatment temperature of 470℃ / 1h and an aging temperature of 120℃ / 16h.

[0113] Furthermore, the Al-Mg-Zn alloy composition determined in step (e) was smelted according to the mass percentage of 5.1Mg-2.8Zn-0.4Cu-0.5Mn-0.3Ag-0.2Sc-0.1Zr. After homogenization at 430℃ for 6 hours and 460℃ for 24 hours, hot rolling at 430℃ to 2.8 mm, intermediate annealing at 375℃ for 75 minutes, cold rolling to 2 mm, solution quenching at 470℃ for 1 hour, and artificial aging at 120℃ for 16 hours, a plate was prepared and its mechanical properties were tested. The measured tensile strength was 569±12MPa and the elongation was 14.9±0.3%, verifying the acquisition of a high-strength and high-toughness Al-Mg-Zn alloy.

[0114] Based on the same concept, a high-strength and high-toughness Al-Mg-Zn aluminum alloy was designed and prepared by the above method, and its composition, in mass percentage, is as follows:

[0115] Mg 4.0–5.5%, Zn 2–3.2%, Cu ≤0.5%, Mn ≤0.8%, Ag ≤0.8%, Sc ≤0.3%, Zr ≤0.15%, Cr ≤0.11%, Ti ≤0.06%, Fe ≤0.06%, Si ≤0.06%, balance being Al and unavoidable impurities;

[0116] The alloy has a tensile strength of 569±12MPa, a yield strength of 479±11MPa, and an elongation of 14.9±0.3% under single-stage aging conditions.

[0117] Furthermore, the microstructure contains diffusely distributed nano-T-Mg32(Al,Zn)49 phase and Al3(Sc,Zr) particles, with a recrystallization volume fraction of <10% and a low-angle grain boundary ratio of >70%.

[0118] Furthermore, this method can be applied to magnesium alloys, titanium alloys, high-entropy alloys, or other multi-component alloy systems. Under the condition that the number of samples in the new alloy system is ≤50, the method can directly complete the composition-process design of strength-plasticity synergistic optimization, reduce the number of experiments by ≥70%, and obtain alloy materials with simultaneous improvement in tensile strength and elongation.

[0119] Example 1:

[0120] Al-Mg-Zn alloy design flow based on CALPHAD representation

[0121] The overall process is shown in Figure 1 .

[0122] (1) Data preparation

[0123] Source dataset: 727 data points of aluminum alloys in the 2xxx, 6xxx and 7xxx series were collected from the literature, including 13 alloying element compositions (Mg, Zn, Cu, Mn, Ag, Sc, Zr, Cr, Ti, Fe, Si, Ni and V), two-step heat treatment parameters (solution temperature and aging temperature), and two mechanical property indicators (tensile strength and elongation).

[0124] Target dataset: 20 data points of Al-Mg-Zn alloy were collected from the literature, ensuring that the Zn / Mg mass ratio was <1. The dataset includes 11 alloying elements (Mg, Zn, Cu, Mn, Ag, Sc, Zr, Cr, Ti, Fe and Si), two heat treatment parameters (solution temperature and aging temperature), and two mechanical property indicators (tensile strength and elongation).

[0125] (2) Initial characteristics are obtained by thermodynamic calculations

[0126] Using the commercial Thermo-Calc software, the TCA15 commercial aluminum alloy database was accessed. Thermodynamic equilibrium calculations were performed on the alloy composition and corresponding solution and aging temperatures of each sample in both the source and target datasets. The system properties were then derived from the calculation results. ) and phase properties ( The results are used as the initial CALPHAD features. Among them, Represents a specific phase The thermodynamic or thermophysical properties of the entire system are summarized in Table 1. This represents the heat treatment conditions, namely, solution treatment (SS) or artificial aging (AA).

[0127] Table 1. Physical quantities calculated using CALPHAD.

[0128] Common properties of the system and phase Unique properties of phase Gibbs free energy (G) Phase fraction (NP) Helmholtz free energy (A) Phase stability function (QF) Internal energy (U) Curie temperature (TC) Enthalpy (H) Bohr number (BMAG) Entropy (S) Volume (V) Density

[0129] A total of 1494 thermodynamic calculations were performed, resulting in 38 phases, the distribution of which is as follows: Figure 2 As shown, the aluminum alloy matrix phase (FCC_A1) appeared in all samples, while other secondary phases such as Al2Cu and Al3Zr appeared in less than 50% of the samples, indicating that the phase composition of the dataset is very complex.

[0130] (3) Feature Derivation and Selection

[0131] While preserving system properties Phase properties with matrix Based on this, the thermodynamic and thermophysical properties of each phase are weighted by phase fraction, and their weighted average is calculated using formulas (1) and (2). With weighted variance This is to reflect the influence of all relative systems, thus omitting all specific thermodynamic and thermophysical properties of the second phase. Subsequently, summation features of the solid solution state and the aged state are constructed using formulas (3) and (4) respectively for the retained features. and difference features This is to reflect the impact of changes in the solid solution state and the time-dependent state on the system. To date, a total of 152 CALPHAD-related features have been derived.

[0132] Subsequently, as shown in Figure 3 The source-assisted three-step feature selection method is used to obtain the features most relevant to intensity and elongation. The feature selection results are shown in... Figure 4 . Figure 4 This is the result of source-domain assisted feature selection for tensile strength (UTS) and elongation (EL) in Embodiment 1 of this invention. Specifically, a and b represent recursive feature elimination, c and d represent sequential backward selection, and e and f represent exhaustive feature selection. (Solid markers represent model scores under optimal feature combinations, and hollow green markers represent model scores under non-optimal feature combinations.) The first step uses recursive feature elimination to efficiently remove non-informative features from the initial 152 CALPHAD-related features, such as... Figure 4As shown in ab. Since the removed features are mainly dominated by the source dataset, and the model performance needs to be evaluated based on the target dataset, performance fluctuations occur in the early stages of recursive feature elimination, indicating that the removed features are not important to either dataset. However, the prediction accuracy of the ultimate tensile strength (UTS) of the extreme gradient boosting (XGB) model then drops sharply, indicating that features crucial to the target dataset are being removed. To avoid the loss of such target-related features, the recursive feature elimination process is terminated when performance begins to decline, ultimately resulting in a feature space with reduced dimensionality but richer information. In the second step, to further optimize the feature space, the 30 features retained after recursive feature elimination are evaluated using Sequential Backward Selection, such as... Figure 4 As shown in cd. During the 29 iterations (including 435 hyperparameter optimizations), the cross-validation error steadily decreased as non-informative features were removed, with performance only declining when the number of features was too small. Among all models, the Support Vector Regression (SVR) model consistently performed best. Even using only 10 features, its performance was superior to the model performance results in the first step of the selection process. In the third step, since the sequential backward selection method is a greedy algorithm and may not be able to find the globally optimal feature subset, exhaustive feature selection was used to further test the final 10 features. After evaluating all possible subsets of these 10 features, it was found that the model performance gradually improved as the subset size increased, but performance decreased after including redundant variables. Throughout the selection process, the SVR model consistently outperformed the XGB model and the Random Forest Regression model. Finally, 7 CALPHAD-derived key features most relevant to tensile strength and 5 features most relevant to elongation were selected. For tensile strength, the seven optimal characteristics include: the phase stability function of the matrix phase in the solution-treated state ( ), the variance of Gibbs free energy between phases under time-dependent conditions ( ), the difference in variance between the solution-treated state and the aged state ( Internal energy of the system under time-dependent conditions The sum of the matrix phase fractions in the solution-treated and aged states ( ) and difference ( ), and the matrix phase fraction under aging conditions ( For elongation (EL), the optimal 5 feature subsets also include... and It also includes with Similar internal energy variance difference ( Furthermore, this subset also covers the entropy of the matrix phase in the time-dependent state ( ); ), and the system volume in the solution-treated state ( Compared to original characteristics such as alloy composition and heat treatment temperature, these CALPHAD-derived descriptors provide a more physically theoretical basis for representing alloy behavior.

[0133] (4) Machine learning modeling and integration

[0134] Machine learning models were trained based on the selected key Calphad-derived features. Since small datasets are highly sensitive to the training-test set split, this study employed a bagging method to evaluate model robustness: 80% of the target set data and the entire source dataset were randomly sampled as the training set for training three models: Support Vector Regression, Random Forest Regression, and Extreme Gradient Boosting Tree. The remaining 20% ​​of the target set data served as the out-of-bag (OOB) validation set. The RMSE of the three models was evaluated, and the best model was selected as the base model. This sampling was repeated 300 times to form 300 base models, and the mean and standard deviation of the predicted outputs were integrated to improve prediction stability and the ability to quantify uncertainty.

[0135] The performance of a bagging model trained using key CALPHAD-derived features was compared with that of bagging models trained using other alternative strategies. The alternative strategies were: (i) using only the original target dataset; (ii) directly combining the original source dataset and the original target dataset without feature engineering; and (iii) performing feature engineering only on the target dataset. Figure 5 This describes the distribution of RMSE of bagging base models trained with various strategies for tensile strength (UTS) and elongation (EL) in Embodiment 1 of the present invention on the corresponding out-of-bag (OOB) set (where Target: only the original target dataset is used; Target+Source: a combination of the original source dataset and the original target dataset is used; Target+FE: feature engineering is performed only on the target dataset; Target+Source+FE: feature engineering is performed on both the source dataset and the target dataset). Figure 5ab presents the distribution of RMSE of bagging base models trained with various strategies on the corresponding out-of-bag sets. The average RMSE score represents generalization ability, and the dispersion of RMSE reflects stability. The results show that, compared with using only the original target dataset, adding the original source dataset improves the generalization ability of UTS but slightly reduces the prediction performance of EL; feature engineering only on the target dataset weakens the prediction effect of UTS but improves the prediction performance of EL. In contrast, joint feature engineering on the source and target datasets achieves optimal generalization ability and stability for both UTS and EL, which confirms the effectiveness of the CALPHAD method proposed in this patent that couples the source-assisted feature engineering process, realizing knowledge transfer from 2xxx, 6xxx, and 7xxx series aluminum alloy data to the Al-Mg-Zn dataset.

[0136] (5) Multi-objective optimization and alloy design

[0137] Subsequently, a bagged model of strength and elongation derived from the key CALPHAD model was used to guide alloy design. The composition design space was set as follows: Mg 4–5.5 wt.%, Zn 0–3.2 wt.%, Cu ≤0.5 wt.%, Mn ≤0.8 wt.%, Ag ≤0.8 wt.%, Sc ≤0.3 wt.%, Zr ≤0.15 wt.%, Cr ≤0.11 wt.%, Ti ≤0.06 wt.%, Fe ≤0.06 wt.%, Si ≤0.06 wt.%. To avoid increasing search costs by searching composition temperatures simultaneously, the solution temperature and aging temperature were pre-set to 470 and 120 °C, respectively, to improve design efficiency.

[0138] Within this composition design scope, the bagging model, acting as a performance predictor, coupled high-throughput CALPHAD computation with the NSGA-II algorithm. With maximizing tensile strength and elongation as dual objective functions, a population size of 400, a crossover probability of 0.9, a mutation index of 20, and 100 iterations, a total of 20,400 candidate compositions were evaluated, resulting in 40,800 thermodynamic calculations and the acquisition of the Pareto front. Figure 6 The diagram shows: a) the convergence behavior of the multi-objective optimization process; b) the obtained Pareto front and the selected alloy design candidate schemes; c) the measured stress-strain curves of the designed C1 and C2 alloys; d) the comparison between the experimental measured values ​​(red markers) and the model predicted values ​​(yellow markers) of the mechanical properties, and the performance improvement relative to the initial target dataset.

[0139] The search convergence is indicated by the hypervolume metric, as shown. Figure 6 a. As can be seen, after 20400 component evaluations, the index approaches convergence. The Pareto front obtained by the search is as follows: Figure 6As shown in b, then focusing on strength, an alloy composition was selected in the high-strength region of the Pareto front for experimental verification.

[0140] (6) Alloy preparation and experimental verification

[0141] The raw materials can be high-purity Al, Mg, Zn, and Ag (99.99%), as well as master alloys (Al–50 wt.% Cu, Al–10 wt.% Mn, Al–5 wt.% Zr, Al–2 wt.% Sc, and Al–10 wt.% Ti). The designed alloy was melted in an argon atmosphere and then cast into a cast iron mold with dimensions of 20 mm × 20 mm × 100 mm. The measured composition was 5.1Mg, 2.8Zn, 0.4Cu, 0.5Mn, 0.3Ag, 0.2Sc, and 0.1Zr (mass percentage), with the remainder being an aluminum matrix and very few impurities. The as-cast alloy ingot was first homogenized at 430℃ for 6 hours, then homogenized at 460℃ for 24 hours and air-cooled. Subsequently, it was heated at 430℃ for 30 minutes and hot-rolled to a thickness of 2.8 mm. After intermediate annealing at 375℃ for 75 minutes, it was cold-rolled to a thickness of 2 mm. Solution treatment was performed at 470°C for 1 hour, followed by water quenching to room temperature and artificial aging treatment at 120°C for 16 hours.

[0142] Mechanical property testing involved preparing dumbbell-shaped tensile specimens (effective length 9.5 mm) and performing room temperature tensile testing on an AGS-X testing machine at a loading rate of 0.572 mm / min. Each condition was repeated three times, and the average value was taken. The test results were: tensile strength (UTS) 569 ± 12 MPa, yield strength (YS) 479 ± 11 MPa, and elongation (EL) 14.9 ± 0.3%, as shown in the figure. Figure 6 The experimental results were largely consistent with the model predictions, with an error of less than 5%, verifying the reliability of the model and optimization method. The designed alloy achieved an ultra-high strength of nearly 570 MPa while maintaining an elongation of around 15%. Compared to the original Al-Mg-Zn alloy dataset, the designed alloy achieved a synergistic improvement in both strength and toughness. Figure 6 As shown in Figure d, a rapid design of a high-strength and high-toughness Al-Mg-Zn alloy was achieved. The results were obtained through electron backscattering diffraction (EBSD) pattern analysis. Figure 7 The statistical results of grain distribution and orientation of the designed alloy in the aged state are shown. The extremely high proportion of low-angle grain boundaries and the extremely low recrystallization indicate that the recrystallization process during alloy heat treatment was significantly suppressed, resulting in a large number of subgrain structures. These fine-grained structures not only improve the strength and toughness of the alloy, but also provide a large number of nucleation sites for artificial aging treatment. Figure 8 The microstructure of the designed alloy in its aged state and the energy dispersive spectroscopy results within the white box area are shown. This indicates the formation of a large amount of nano-T-Mg within the alloy. 32(Al,Zn) 49 The Al-Mg-Zn alloy contains Al3(Sc, Zr) phases and dispersed Al3(Sc, Zr) particles. The dispersed Al3(Sc, Zr) particles can significantly inhibit recrystallization during heat treatment, thus improving the toughness of the alloy, while the high-density T phase precipitation ensures the high strength of the alloy. These factors together contribute to the high strength and toughness of the designed Al-Mg-Zn alloy, demonstrating its application potential in the future market.

[0143] The beneficial effects of this invention are:

[0144] 1. Improve prediction accuracy with small samples: By introducing the CALPHAD method and source-assisted feature engineering, the model can achieve stable and accurate performance prediction with only a small amount of target domain data, avoiding the overfitting problem of traditional black-box machine learning methods.

[0145] 2. Enables cross-system knowledge transfer: Effectively utilizes knowledge from other widely studied material systems, significantly reducing experimental costs and time for the target material system.

[0146] 3. Strong physical interpretability: The selected CALPHAD-derived features all have clear thermodynamic or thermophysical meanings, which can be used to explain the alloy strengthening mechanism, facilitating subsequent mechanism research and process optimization.

[0147] 4. Overcoming performance trade-offs: The designed Al-Mg-Zn alloy can achieve a synergistic improvement in strength and elongation under single-stage aging conditions, which is significantly better than other Al-Mg-Zn alloys.

[0148] 5. Versatility and scalability: This method is not only applicable to Al-Mg-Zn alloys, but can also be extended to multi-component systems such as magnesium alloys, titanium alloys, and high-entropy alloys, enabling computation-driven accelerated material design.

[0149] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A cross-system knowledge transfer alloy design method based on CALPHAD representation, characterized in that, By transferring knowledge from the source aluminum alloy system to the target Al-Mg-Zn alloy system, efficient design of high-strength and high-toughness Al-Mg-Zn aluminum alloys is achieved under small sample data conditions. The method includes the following steps in sequence: (a) Feature construction: Thermodynamic equilibrium calculations were performed on the composition-heat treatment temperature data of the source aluminum alloy and the target Al-Mg-Zn alloy using CALPHAD software to extract phase properties. With system properties Construct the initial CALPHAD feature set; (b) Feature derivation: Using the fraction of each phase as the weight, the thermodynamic and thermophysical properties in the initial CALPHAD feature set are weighted and the weighted mean and weighted variance are calculated. Additive features and differential features are constructed for multi-step heat treatment processes to form a CALPHAD derived feature pool that can characterize the coupling effect of composition and heat treatment. (c) Source auxiliary feature selection steps: For the CALPHAD-derived feature pool obtained in step (b), perform a three-step feature selection assisted by the source dataset: (i) Recursive feature elimination: Iteratively eliminate the features that contribute the least using a tree-based regression model until the main features are retained; (ii) Sequential backward selection: Based on the results of (i), features that increase cross-validation error are gradually removed to optimize feature combinations; (iii) Exhaustive feature selection: Perform a full combination evaluation on the features obtained in (ii) to select the optimal feature subset that maximizes the accuracy and robustness of the target performance prediction; (d) Machine learning modeling: Bag modeling is performed on the key CALPHAD-derived features selected in step (c): 80% of the target dataset is randomly sampled each time and merged with all source datasets as the training set, and the remaining 20% ​​of the target dataset is used as the test set; this sampling-training-testing process is repeated no less than 300 times to obtain 300 base models, and the mean and standard deviation of their prediction results are integrated to form a stable performance predictor with uncertainty quantification. (e) Multi-objective optimization and alloy design steps: The bagging predictor obtained in step (d) is coupled with high-throughput CALPHAD calculation and NSGA-II genetic algorithm, and executed sequentially with the dual objectives of maximizing tensile strength and elongation: (1) Randomly generate the initial population and perform thermodynamic equilibrium calculations for each individual; (2) Calculate the value of each feature in the optimal feature subset of step (c) and input it into the bagging model to obtain the performance prediction value; (3) Non-dominated ranking and crowding distance calculation are performed based on the predicted values, and the Pareto-optimal individuals are retained; (4) Select, crossover, and mutate the current population to generate the next generation, and repeat (1)–(3); (5) The convergence was monitored by the hypervolume index, and the process was iterated until the Pareto front stabilized. Finally, a representative composition-process scheme was selected from the front to complete the rapid design of the Al-Mg-Zn alloy. (f) Experimental verification steps: The Al-Mg-Zn alloy composition selected in step (e) was sequentially subjected to melting, homogenization, hot rolling, intermediate annealing, cold rolling, solution treatment and artificial aging treatment to prepare plates and test their mechanical properties. The tensile strength obtained was 569±12MPa and the elongation was 14.9±0.3%, which verified that the designed alloy achieved high strength and toughness at the same time.

2. The method according to claim 1, wherein the system properties and phase properties in step (a) include at least one of Gibbs free energy, enthalpy, entropy, volume, density, phase fraction, phase stability function, Curie temperature and Bohr magneton number.

3. The method according to claim 1, wherein the formulas for calculating the weighted mean and weighted variance in step (b) are: weighted mean With weighted variance The calculation method is as follows: ； ； in, Represents the heat treatment state lower phase The phase fraction, which is used as a weighting factor; The formulas for calculating the summation feature and the difference feature are as follows: ； ； in , and These represent the characteristic values ​​under the first and second heat treatment states, respectively. For: matrix phase properties.

4. The method according to claim 3, wherein, The source-assisted feature selection in step (c) further includes: (i) The recursive feature elimination stage uses XGBoost as the base model. When the RMSE of the target dataset starts to rise, the elimination stops and 30 features are retained. (i) The sequential backward selection stage uses the SVR model for evaluation, and 10 features are obtained after 29 rounds of iteration; (iii) In the exhaustive feature selection stage, the SVR model is used to evaluate the 10 features in a 2^10 combination, and finally 7 key features of tensile strength and 5 key features of elongation are determined. All of the key features have clear thermodynamic and thermophysical meanings.

5. The method according to claim 1, wherein, The multi-objective optimization in step (e) is further defined as follows: With a population size of 400, a crossover probability of 0.9, a mutation index of 20, and 100 iterations, a total of ≥40,800 CALPHAD thermodynamic calculations were completed. Convergence was determined when the hypervolume index changed by <0.1% over 10 consecutive generations. Finally, in the high-strength region, an Al-Mg-Zn alloy scheme with the composition of 5.1Mg-2.8Zn-0.4Cu-0.5Mn-0.3Ag-0.2Sc-0.1Zrwt% was selected, with a solution treatment temperature of 470℃ / 1h and an aging temperature of 120℃ / 16h.

6. The method according to claim 5, wherein, The Al-Mg-Zn alloy composition determined in step (e) was smelted according to the mass percentage of 5.1Mg-2.8Zn-0.4Cu-0.5Mn-0.3Ag-0.2Sc-0.1Zr. After homogenization at 430℃ for 6 hours and 460℃ for 24 hours, hot rolling at 430℃ to 2.8 mm, intermediate annealing at 375℃ for 75 minutes, cold rolling to 2 mm, solution quenching at 470℃ for 1 hour, and artificial aging at 120℃ for 16 hours, a plate was prepared and its mechanical properties were tested. The measured tensile strength was 569±12MPa and the elongation was 14.9±0.3%, verifying that a high-strength and high-toughness Al-Mg-Zn alloy was obtained.

7. A high-strength and high-toughness Al-Mg-Zn aluminum alloy, designed and prepared by the method according to any one of claims 1-6, wherein its composition, by mass percentage, is: Mg 4.0–5.5%, Zn 2–3.2%, Cu ≤0.5%, Mn ≤0.8%, Ag ≤0.8%, Sc ≤0.3%, Zr ≤0.15%, Cr ≤0.11%, Ti ≤0.06%, Fe ≤0.06%, Si ≤0.06%, balance being Al and unavoidable impurities; The alloy has a tensile strength of 569±12MPa, a yield strength of 479±11MPa, and an elongation of 14.9±0.3% under single-stage aging conditions.

8. The alloy according to claim 7, wherein, The microstructure contains diffusely distributed nano-T-Mg 32 (Al,Zn) 49 The phase and Al3(Sc,Zr) particles, recrystallization volume fraction <10%, low-angle grain boundary ratio >70%.

9. The use of the method according to any one of claims 1-6 in the design of magnesium alloys or titanium alloys, characterized in that, Using the method described above, with a sample size of ≤50 for the new alloy system, the composition-process design for strength-plasticity synergistic optimization can be directly completed, reducing the number of experiments by ≥70% and obtaining alloy materials with simultaneous improvement in tensile strength and elongation.

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