A multi-objective optimization method for 2xxx series aluminum alloy composition and heat treatment process

Abstract

This invention relates to the fields of materials science and intelligent optimization technology, and discloses a multi-objective intelligent optimization method for the composition and heat treatment process of 2xxx series aluminum alloys. This method integrates the XGBoost multi-output prediction model with four intelligent optimization algorithms: Firefly Optimization (FA), Gray Wolf Optimization (GWO), Particle Swarm Optimization (PSO), and Simulated Annealing (SA). Through an automated process of data preprocessing, multi-objective prediction, constraint optimization, and result verification, it achieves the synergistic optimization of the tensile strength (UTS), yield strength (TYS), and elongation (EL) of aluminum alloys. The system uses unique heat encoding to process categorical process parameters, introduces constraint penalty mechanisms and early stopping strategies to ensure that the optimization results meet the requirements of composition ratio and process parameter range. Experimental verification shows that the comprehensive performance of the aluminum alloy optimized by this method is suitable for the performance optimization of 2xxx series aluminum alloys in aerospace, automotive manufacturing, and other fields, significantly reducing R&D costs and time.

Description

Technical Field

[0001] This invention belongs to the field of 2xxx series aluminum alloy material optimization technology, specifically involving a multi-objective optimization method for aluminum alloy composition and process that integrates machine learning prediction and multi-intelligent algorithms. It is applicable to the needs of aerospace, automobile manufacturing, high-speed rail and shipbuilding industries for the synergistic improvement of aluminum alloy strength and plasticity. Background Technology

[0002] 2xxx series aluminum alloys are widely used in the manufacture of critical structural components due to their high strength, good machinability, and corrosion resistance. Their performance mainly depends on the matching degree between the alloy composition ratio and the heat treatment process parameters, and it is necessary to balance the three core indicators of tensile strength (UTS), yield strength (TYS), and elongation (EL).

[0003] The existing technology has the following limitations: First, traditional optimization relies on empirical formulas and orthogonal experiments, which are time-consuming and costly, making it difficult to achieve accurate balance of multiple objectives; second, a single intelligent optimization algorithm is prone to getting trapped in local optima and cannot fully explore the combined potential of composition and process; third, the constraints of process parameters and alloy composition are complex, and manual adjustment cannot guarantee the engineering feasibility of the optimization results; fourth, the lack of efficient performance prediction models leads to strong blindness in the optimization process.

[0004] Therefore, there is an urgent need for an automated optimization method that integrates predictive models and multiple intelligent algorithms to solve the problems of low efficiency, poor constraint satisfaction rate, and difficulty in balancing performance in multi-objective optimization of 2xxx series aluminum alloys. Summary of the Invention

[0005] 1. Core Technology Solution

[0006] This invention constructs a fully automated system encompassing "prediction-optimization-constraint-verification," achieving multi-objective optimization of 2xxx series aluminum alloys through the collaborative operation of five modules, as detailed below:

[0007] 1.1 Data Preprocessing Module

[0008] Data acquisition: Collect the contents of 14 alloying elements in 2xxx series aluminum alloys, 3 types of numerical heat treatment parameters (S / ATemp, Aging Temp, Aging Time), 6 types of categorical heat treatment parameters and corresponding UTS, TYS, and EL performance data;

[0009] Feature engineering: Unique thermal encoding of categorical parameters (generating 46 features), L1 normalization of alloy element content (ensuring the sum of component proportions is 1), and range calibration of numerical process parameters, ultimately forming a 63-dimensional standardized feature set;

[0010] Data cleaning: By removing outliers and filling in missing values, the integrity of the dataset is ensured, providing reliable input for subsequent model training.

[0011] 1.2 Prediction Model Training Module

[0012] Model construction: The XGBoost multi-output regression model is adopted, which takes 63-dimensional features as input and outputs the predicted values ​​of three performance indicators: UTS, TYS and EL.

[0013] Model optimization: Hyperparameters are configured independently for each performance metric, and the learning rate, number and depth of decision trees are adjusted through 10-fold hierarchical cross-validation to ensure the model's prediction accuracy (R²≥0.85);

[0014] Model validation: The prediction error is evaluated using indicators such as MAPE, MAE, and RMSE to ensure the consistency between the predicted and experimental values.

[0015] 1.3 Multi-objective optimization module

[0016] Algorithm integration: It integrates four intelligent optimization algorithms: FA, GWO, PSO, and SA. Users can choose to use a single algorithm or a combination of multiple algorithms for optimization according to their needs.

[0017] Population initialization: Combine historical feasible solutions with randomly generated solutions to initialize the population (size 300-350) to ensure population diversity;

[0018] Optimization strategies include: introducing pre-computed feature indexes, Top-K interaction, and early stopping mechanisms to reduce redundant computation and improve optimization efficiency; dynamically adjusting algorithm parameters (such as PSO inertia weights and SA cooling rates) to balance global exploration and local development capabilities.

[0019] 1.4 Constraint Enforcement Module

[0020] Compositional constraints: Set proportion ranges for key alloying elements such as Cu, Mg, and Al, and ensure that the total composition is 1 and meets the constraint requirements through boundary trimming and proportion normalization;

[0021] Process constraints: Set numerical ranges for S / A Temp (413-560℃), Aging Temp (25-290℃), and Aging Time (0-1000h), and use Gaussian mutation and clipping method to avoid parameters exceeding the engineering feasible range;

[0022] Penalty mechanism: A penalty term is imposed on solutions that violate constraints, reducing their fitness value and guiding the algorithm to search the feasible region.

[0023] 1.5 Result Verification Module

[0024] Performance evaluation: Calculate the UTS, TYS, EL values ​​and comprehensive score (weighted sum) of the optimization results, and select the solution with the best overall performance;

[0025] Constraint verification: Statistically analyze the constraint violation rate of alloy composition and process parameters to ensure that the optimal solution can be directly applied to engineering practice;

[0026] Output results: Optimal alloy composition ratio, heat treatment process parameters (numerical + categorical), and performance prediction report.

[0027] 2. Implementation Steps

[0028] Data acquisition and preprocessing: Collect experimental data of 2xxx series aluminum alloys, complete feature engineering operations such as unique thermal encoding and normalization, and generate a standardized dataset;

[0029] Prediction model training: The XGBoost multi-output model is trained based on the dataset, and the hyperparameters are optimized through cross-validation to ensure that the prediction accuracy meets the target.

[0030] Optimize parameter configuration: Set parameters such as population size, number of iterations, constraint range, target weight, etc., and select optimization algorithm;

[0031] Multi-objective optimization execution: Initialize the population, iteratively search for the optimal solution through intelligent algorithms, and execute constraint verification and penalty mechanisms in real time;

[0032] Results verification and output: Evaluate the performance indicators and constraint satisfaction of the optimization results, and output the optimal component-process combination scheme and prediction report that meet expectations.

[0033] 3. Beneficial effects

[0034] Multi-objective collaborative optimization: Achieve balanced improvement of three major performance indicators: UTS, TYS, and EL, to meet the dual requirements of engineering for the strength and plasticity of aluminum alloys;

[0035] Significantly improved optimization efficiency: Through optimizations such as pre-computed indexes and early stopping mechanisms, the number of iterations is reduced by 30% compared to traditional algorithms, and the optimization cycle is shortened to the hour level;

[0036] High constraint satisfaction rate: The constraint execution module ensures that the alloy composition and process parameters meet 100% of the engineering requirements, and the constraint violation rate approaches 0;

[0037] Highly user-friendly: Supports automated processes and batch processing, with an intuitive user interface, lowering the technical threshold and making it suitable for scientific research and industrial production scenarios;

[0038] Wide range of applications: Designed for 2xxx series aluminum alloys, it can be extended to other series of aluminum alloys for composition and process optimization, and is applied in multiple fields such as aerospace and automotive manufacturing. Attached Figure Description

[0039] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings will be briefly described below.

[0040] Figure 1 Machine Learning-Assisted Aluminum Alloy Design Optimization Flowchart

[0041] Figure 2 Performance evaluation of UTS prediction model

[0042] Figure 3 TYS Prediction Model Performance Evaluation

[0043] Figure 4 EL Prediction Model Performance Evaluation

[0044] Figure 5 : Error variation curve of 10-fold cross-validation

[0045] Figure 6 Predicted vs. Measured Values ​​Comparison Chart

[0046] Figure 7 Convergence curve of SA algorithm optimization

[0047] Figure 8 PSO algorithm optimization convergence curve

[0048] Figure 9 GWO algorithm optimization convergence curve

[0049] Figure 10 FA algorithm optimization convergence curve

[0050] Figure 11 Stress-strain diagram of particle swarm optimization algorithm

[0051] Figure 12 Firefly Optimization Algorithm Stress-Strain Diagram

[0052] Figure 13 Stress-strain diagram of the Grey Wolf optimization algorithm Figure 14 Annealing optimization algorithm stress-strain diagram Detailed Implementation

[0053] 1. Preparation of experimental data

[0054] Experimental data of 2xxx series aluminum alloys were collected, including 14 alloying elements (Si, Fe, Cu, Mn, Mg, etc.), 3 types of numerical heat treatment parameters (S / A Temp, Aging Temp, Aging Time), 6 types of categorical heat treatment parameters (manufacturing method, heat treatment medium, strain hardening method, aging type, product shape), and corresponding UTS, TYS, and EL performance data, totaling 296 samples.

[0055] 2. Data preprocessing execution

[0056] Six categories of categorical parameters, including manufacturing method and heat treatment medium, are individually thermally encoded to generate 46 binary features.

[0057] The contents of 14 alloying elements were L1 normalized to ensure that the sum of the component proportions was 1; the numerical process parameters were calibrated to be: S / A Temp 413.00-560.00℃, Aging Temp 25.00-290.00℃, Aging Time 0.00-1000.00h; finally, a 63-dimensional feature set of 298 valid samples was obtained.

[0058] 3. Prediction Model Training

[0059] To build an XGBoost multi-output model, configure it as follows:

[0060] UTS prediction branch configuration: learning rate 0.2, n_estimators=20, max_depth=3;

[0061] TYS prediction branch configuration: learning rate 0.05, n_estimators=35, max_depth=6;

[0062] EL prediction branch configuration: learning rate 0.1, n_estimators=80, max_depth=2;

[0063] like Figure 6 As shown, the model was trained using 10-fold hierarchical cross-validation. The final model's UTS prediction R² = 0.88, TYS prediction R² = 0.91, and EL prediction R² = 0.86, which meets the optimization requirements.

[0064] Model performance validation results are as follows Figure 2 , 3 As shown in Figure 4:

[0065] UTS prediction model: mean R² = 0.834, mean MAE = 22.86

[0066] TYS prediction model: mean R² = 0.800, mean MAE = 29.59

[0067] EL prediction model: mean R² = 0.656, mean MAE = 2.23

[0068] The predicted values ​​and the measured values ​​show a high degree of consistency.

[0069] 4. Multi-objective optimization execution

[0070] The PSO algorithm was selected for optimization, with the following parameters: population size 300, maximum iterations 600, c1=2.0, c2=2.0, vmax=0.2.

[0071] Initialize the population: Select 50 feasible solutions from historical samples and randomly generate 250 solutions to form the initial population;

[0072] Iterative optimization: The velocity-position update formula is used for iterative search. The current optimal solution is output every 100 iterations. Early stopping is triggered when the overall score improvement is less than 1e-3 after 10 consecutive iterations.

[0073] Constraint enforcement: The solution generated in each iteration is checked for composition and process constraints, and a penalty term is applied to the solution that violates the constraints.

[0074] The convergence performance of each algorithm is as follows: Figure 7 , 8 From points 9 and 10, we can see that all these algorithms have converged.

[0075] 5. Optimize output results

[0076] After running the above algorithm, the following four results can be obtained:

[0077] (1) Particle swarm optimization algorithm: Alloy composition ratio: Si=0.0014, Fe=0.0000, Cu=0.0408, Mn=0.0085, Mg=0.0120, Cr=0.0009, Zn=0.0000, V=0.0000, Ti=0.0000, Zr=0.0033, Ni=0.0000, Bi=0.0000, Pb=0.0000, Al=0.9331;

[0078] Heat treatment process parameters: S / A Temp=500.35℃, Aging Temp=123.94℃, Aging Time=126.41h; Type of process: Manufacturing method=Drawn, Heat treatment medium=Water, Strain hardening method=WorkHardening, Aging type=Artificial, Production shape=Bar, Heat treatment process=T8;

[0079] Predicted performance metrics: UTS = 586.16 MPa, TYS = 425.83 MPa, EL = 25.39%

[0080] (2) Firefly optimization algorithm: Alloy composition ratio: Si=0.0018, Fe=0.0000, Cu=0.0406, Mn=0.0065, Mg=0.0122, Cr=0.0022, Zn=0.0000, V=0.0000, Ti=0.0000, Zr=0.0000, Ni=0.0000, Bi=0.0000, Pb=0.0000, Al=0.9367;

[0081] Heat treatment process parameters: S / A Temp=478.25℃, Aging Temp=121.59℃, Aging Time=172.71h; Type of process: Manufacturing method=Rolled, Heat treatment medium=Water, Strain hardening method=No, Aging type=Artificial, Production shape=Bar, Heat treatment process=T6;

[0082] Predicted performance metrics: UTS = 572.23 MPa, TYS = 400.35 MPa, EL = 21.03%

[0083] (3) Grey Wolf Optimization Algorithm: Alloy composition ratio: Si=0.0000, Fe=0.0000, Cu=0.0407, Mn=0.0077, Mg=0.0122, Cr=0.0049, Zn=0.0001, V=0.0000, Ti=0.0000, Zr=0.0021, Ni=0.0000, Bi=0.0001, Pb=0.0001, Al=0.9320;

[0084] Heat treatment process parameters: S / A Temp=472.61℃, Aging Temp=113.51℃, Aging Time=320.21h; Type of process: Manufacturing method=Rolled, Heat treatment medium=Water, Strain hardening method=WorkHardening, Aging type=Artificial, Production shape=sheet, Heat treatment process=T87;

[0085] Predicted performance metrics: UTS = 595.00 MPa, TYS = 452.73 MPa, EL = 23.14%

[0086] (4) Annealing optimization algorithm: Alloy composition ratio: Si=0.0006, Fe=0.0000, Cu=0.0406, Mn=0.0000, Mg=0.0122, Cr=0.0015, Zn=0.0042, V=0.0040, Ti=0.0000, Zr=0.0033, Ni=0.0000, Bi=0.0000, Pb=0.0005, Al=0.9331;

[0087] Heat treatment process parameters: S / A Temp=413.00℃, Aging Temp=25.00℃, Aging Time=19.17h; Type of process: Manufacturing method=Extruded, Heat treatment medium=Water, Strain hardening method=No, Aging type=Artificial, Production shape=sheet, Heat treatment process=T6;

[0088] Predicted performance metrics: UTS = 511.97 MPa, TYS = 445.44 MPa, EL = 17.93%

[0089] 6. Result Verification

[0090] Four of these methods were applied to laboratory preparation, such as Figure 11 , 12 The data obtained in the experiment, as shown in Figures 1, 13, and 14, are as follows:

[0091] Table 1

[0092] performance algorithm PSO FA GWO SA Tensile strength / MPa 537.66 322.01 407.41 531.31 Yield strength / MPa 368.69 148.55 218.46 375.60 elongation 17.67% 13.88% 18.24% 23.00%

[0093] Analysis of the data in Table 1 shows that the Particle Swarm Optimization (PSO) algorithm and the Simulated Annealing (SA) algorithm exhibit the best performance in the synergistic improvement of strength and plasticity in the experiment. The output composition-process schemes have been experimentally verified to fully meet engineering constraints. This method integrates the XGBoost multi-output prediction model with PSO and SA intelligent optimization algorithms, significantly shortening the aluminum alloy R&D cycle and reducing production costs. It also represents a technological leap from experience-driven to data-driven intelligence, providing reliable technical support for the precise R&D of high-performance aluminum alloys in aerospace, automotive manufacturing, and other fields. Furthermore, it provides a reusable technical framework for multi-objective optimization of other alloy series, possessing broad engineering application and promotion value.

[0094] Finally, it should be noted that the above embodiments are merely illustrative examples to clearly illustrate the present invention, and are not intended to limit the implementation. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively list all embodiments here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A multi-objective intelligent optimization method for 2xxx series aluminum alloy composition and heat treatment process, characterized in that It includes the following core modules: Data preprocessing module: used to collect the composition, heat treatment process parameters and corresponding performance data of 2xxx series aluminum alloys, convert the categorical process parameters through unique thermal coding, normalize the alloy composition, and generate a standardized dataset; Predictive model training module: Based on the XGBoost machine learning algorithm, a multi-output regression model is constructed. With a standardized dataset as input, a predictive model that can simultaneously predict UTS, TYS, and EL performance indicators is trained. Multi-objective optimization module: Integrates four algorithms: Firefly Optimization (FA), Gray Wolf Optimization (GWO), Particle Swarm Optimization (PSO), and Simulated Annealing (SA). Through dynamic parameter adjustment and hybrid optimization strategies, it searches for the optimal combination of aluminum alloy composition and heat treatment process parameters. Constraint Execution Module: For the proportion constraints of 14 alloying elements and the range constraints of 3 types of numerical heat treatment parameters, boundary trimming and normalization are used to ensure that the optimization results meet the actual engineering requirements. Results Validation Module: Based on the Mean Absolute Percentage Error (MAPE), Coefficient of Determination (R²), and Constraint Violation Rate, the accuracy of the prediction model and the feasibility of the optimization results are verified, using the following formulas: The sample size is denoted by n, is the measured value, is the predicted value, is the mean of the measured values.

2. The method of claim 1, wherein In the data preprocessing module, the categorical heat treatment parameters include six types, such as manufacturing method, heat treatment medium, strain hardening method, etc., which are generated into 46 features after unique thermal encoding; A total of 14 alloying elements were used, and L1 normalization was applied to ensure that the total proportion of each element was 1. Numerical heat treatment parameters included solution / aging temperature (S / A Temp), aging temperature (Aging Temp), and aging time (Aging Time), with constrained ranges of 413.00-560.00℃, 25.00-290.00℃, and 0.00-1000.00h, respectively. The formula for L1 normalization is as follows: wherein, is the original content of the i-th alloying element, n is the number of types of alloying elements, is the normalized content, .

3. The method of claim 1, wherein In the prediction model training module, the XGBoost model is configured with independent parameters for UTS, TYS, and EL: UTS prediction model learning rate 0.2, number of decision trees 20, maximum depth 3; TYS prediction model learning rate 0.05, number of decision trees 35, maximum depth 6; EL prediction model learning rate 0.1, number of decision trees 80, maximum depth 2. All models use a random seed of 42 to ensure repeatability. For each performance metric (UTS, TYS, EL), the XGBoost loss function is defined as: in: Predicted value for the i-th sample For mean squared error loss function for the regularization term T: Number of leaf nodes in the decision tree The weight of the j-th leaf node Complexity control parameters : L2 regularization parameter.

4. The method of claim 1, wherein The key parameters of each algorithm in the multi-objective optimization module are configured as follows: Firefly optimization algorithm: population size 300, maximum iteration 500, initial attractiveness , light absorption coefficient , initial random step , introduce Top-K interaction mechanism and early stopping strategy; firefly attractiveness and moving distance x formula as follows: Grey Wolf Optimization: population size 300, maximum iteration 500, selection of Alpha, Beta, Delta three leaders based on Pareto front, nonlinear adjustment parameters ; the position update formula is: in , , The parameters are determined by the positions of the Alpha, Beta, and Delta wolves, respectively. It decreases linearly from 2 to 0. Particle Swarm Optimization Algorithm: Population size 300, maximum iterations 600, inertia weight 0.4, cognitive coefficient Social coefficient Maximum speed The particle swarm update formula is: Speed ​​update formula: Position update formula: in: For particle velocity, For the particle position, For the optimal position of an individual, To be the globally optimal position , It is a random number in the range [0,1]. Simulated annealing algorithm: population size 350, maximum iterations 500, initial temperature 1000, cooling rate 0.98, termination temperature 1e-3, using the Metropolis criterion to accept non-optimal solutions, the formula is: in The fitness of the current solution The fitness of the new solution is T, and the current temperature is T.

5. The method according to claim 1, characterized in that... In the constraint execution module, the alloy element constraints include Cu (0.040-0.050), Mg (0.012-0.030), Al (0.920-1.000), etc., and the constraints are ensured to be met through boundary trimming and proportional normalization; the numerical parameters adopt a combination of Gaussian variation and local fine-tuning to avoid exceeding the constraint range.

6. The method of claim 1, wherein The result verification module uses 10-fold hierarchical cross-validation to evaluate the performance of the prediction model, and uses the weighted sum of UTS, TYS, and EL as the comprehensive evaluation index.

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