A method for designing components of nickel-based superalloys based on machine learning and multi-objective optimization

Abstract

This invention discloses a method for designing the composition of nickel-based superalloys based on machine learning and multi-objective optimization. First, it defines design objectives and an initial composition space, including high-temperature strength and crack sensitivity indices. An initial dataset is constructed through sampling and thermodynamic calculations. Based on this dataset, a machine learning surrogate model capable of predicting multiple indices is trained, and polynomial feature engineering is preferably employed to improve prediction accuracy. Subsequently, this surrogate model is embedded into a multi-objective optimization algorithm to search for Pareto optimal solutions that satisfy the constraints in the composition space. Finally, the solution set is thermodynamically verified and harmful phases are evaluated to select the final alloy composition. This method achieves efficient synergistic optimization of the strength and crack resistance of nickel-based superalloys, shortening the design cycle from months or even years in traditional trial-and-error methods to days, significantly reducing R&D costs, and providing an effective means for the rapid development of high-performance superalloys for additive manufacturing.

Description

Technical Field

[0001] This invention relates to the field of metal material design and optimization technology, specifically to a method for designing the composition of nickel-based superalloys, and more particularly to a method that combines machine learning and multi-objective optimization techniques to rapidly design the composition of nickel-based superalloys that possess both excellent high-temperature strength and good additive manufacturing crack resistance. Background Technology

[0002] Additive manufacturing (also known as 3D printing) technology has provided a revolutionary means for the integrated molding of complex metal components (such as engine turbine disks and blades) in the aerospace field. Nickel-based superalloys, due to their excellent high-temperature strength, creep resistance, and corrosion resistance, have become core candidate materials for critical components in these extreme environments. However, the extremely high cooling rates and complex thermal cycles during additive manufacturing make nickel-based superalloys highly susceptible to solidification cracks and solid-state cracks (such as strain-aging cracks), which severely restricts the formability, reliability, and service life of components.

[0003] To address the cracking problem in additive manufacturing, traditional solutions primarily focus on alloy composition design and process optimization. In composition design, there has long been a heavy reliance on a trial-and-error approach, involving numerous, repetitive melting-processing-testing cycles to explore the relationship between composition, microstructure, and properties (especially crack resistance). This method is not only costly and time-consuming (often measured in years), but also struggles to systematically find compositional points that simultaneously satisfy high strength and high crack resistance due to the highly nonlinear and complex relationship between alloy composition, process, and properties. Typically, to improve high-temperature strength, the content of γ' strengthening phase-forming elements such as Al and Ti needs to be increased, but this often widens the alloy's solidification temperature range, increasing its susceptibility to hot cracking; conversely, controlling the content of these elements to reduce crack sensitivity sacrifices the alloy's high-temperature strength. This inherent contradiction between strength and crack resistance makes it difficult for the traditional trial-and-error method to achieve a breakthrough.

[0004] With the development of computational materials science, several design-aided techniques have emerged to accelerate the design process. For example, the CALPHAD (CALculation of PHAse Diagrams) method can utilize thermodynamic databases to calculate phase equilibrium of alloys, simulate solidification paths, and evaluate sensitivity indicators such as the solidification crack index. However, CALPHAD calculations remain computationally intensive for complex multi-component alloys, and its prediction accuracy is limited by the completeness of the database. In recent years, machine learning techniques have been introduced into materials research and development. By learning from historical experimental or computational data, mapping models between composition / process and properties are established to predict the properties of new materials and achieve initial screening. However, existing machine learning-based design methods often focus on predicting and optimizing single performance indicators (such as strength or a specific crack index), lacking a systematic and synergistic optimization framework for multiple conflicting key objectives such as "high-temperature strength" and "multiple crack susceptibility." Furthermore, for indicators like crack susceptibility, which are influenced by multiple complex mechanisms, simple machine learning models have limited prediction accuracy and cannot reliably guide the final composition determination.

[0005] In summary, existing technologies lack a compositional design method that can efficiently, accurately, and systematically optimize the high-temperature strength and additive manufacturing crack resistance of nickel-based superalloys. Therefore, there is an urgent need to develop a new design paradigm to break through the limitations of the "trial and error" approach, overcome the shortcomings of existing computationally assisted design methods, and rapidly obtain high-performance nickel-based superalloy compositions suitable for additive manufacturing. Summary of the Invention

[0006] The technical problem this invention aims to solve is to provide a method for designing nickel-based superalloy compositions based on machine learning and multi-objective optimization. This method can efficiently and systematically optimize the mutually restrictive high-temperature strength and crack sensitivity indices, quickly screen out nickel-based superalloy compositions suitable for additive manufacturing that possess both excellent high-temperature strength and good crack resistance, significantly shorten the R&D cycle, and reduce development costs.

[0007] To address the aforementioned technical problems, this invention provides a method for designing the composition of nickel-based superalloys based on machine learning and multi-objective optimization, comprising the following steps: S1: Define the design objectives and initial composition space of the alloy. The design objectives include a first type of indicator related to high-temperature strength and a second type of indicator related to crack susceptibility. The first type of indicator includes at least the γ' phase volume fraction V at 1000℃. γ' The second type of index includes at least the solidification crack index (SCI); the variable elements in the initial composition space are Cr, Co, Al, Ti, W, Mo, Ta, and Nb, the fixed trace elements are C, B, and Zr, and the balance is Ni. S2: Sample from the initial composition space using the Latin hypercube sampling method to obtain multi-component component data, and perform thermodynamic calculations through high-throughput solidification simulation to obtain the index value of the design target corresponding to each component data, and construct the initial dataset; S3: Perform quadratic polynomial feature engineering on the input features in the initial dataset to generate a new feature set containing the original features, the squares of each variable element, and the product term between any two variable elements; based on the new feature set and the initial dataset, train a machine learning proxy model for predicting the design target; S4: Using the machine learning proxy model and the non-dominated sorting genetic algorithm, search and select non-dominated solution sets that satisfy preset constraints in the initial component space; the preset constraints include limiting the numerical range of the first type of index and the second type of index. S5: Perform thermodynamic calculations to verify the components in the non-dominated solution set and evaluate harmful phases to screen out the final target alloy components; the evaluation of harmful phases specifically involves: calculating the content of σ phase and / or μ phase in the candidate components during solidification-cooling, excluding components with σ phase and μ phase appearing above 900℃, and components with a total content of σ phase and μ phase exceeding 5% vol between 500℃ and 900℃.

[0008] The above technical solution fully defines the core steps of the nickel-based superalloy composition design method of the present invention, and is the most fundamental technical solution of the present invention. Its core technical effects are as follows: This invention fundamentally solves the inherent contradiction in the industry that it is difficult to balance high-temperature strength and crack resistance in nickel-based superalloys used in additive manufacturing. By dividing the core design objectives into two categories—high-temperature strength-related and crack sensitivity-related—a systematic synergistic optimization framework for multiple conflicting performance indicators is constructed, breaking the technical dilemma in traditional design that "increasing strength inevitably increases crack sensitivity, and reducing crack sensitivity inevitably reduces strength."

[0009] A new design paradigm of "data construction - model training - intelligent optimization - verification and screening" has been established. Machine learning proxy models replace the traditional massive and repetitive thermodynamic calculations and trial-and-error experiments of "melting - processing - testing". The alloy composition research and development cycle has been shortened from months or even years in the traditional method to days, which greatly reduces the human, material and time costs of research and development.

[0010] By introducing quadratic polynomial feature engineering, a new feature set is generated, which includes the original features, element square terms, and inter-element interactive product terms. This accurately fits the mapping relationship between multi-element alloy elements and complex nonlinear indices such as crack sensitivity, significantly improving the prediction accuracy of machine learning models for multi-objective indices and providing a highly reliable surrogate model foundation for subsequent optimization.

[0011] By combining a high-precision surrogate model with a non-dominated sorting genetic algorithm, global intelligent search is achieved in the component space, efficiently obtaining Pareto optimal non-dominated solution sets that satisfy the constraints. This avoids the blindness and local optima defects of traditional trial and error methods, and realizes the mining of global optimal solutions under multiple constraints.

[0012] The dual final screening process of thermodynamic verification and harmful phase assessment not only corrects the prediction error of the machine learning model through precise thermodynamic calculations, but also eliminates components with unqualified microstructure stability through strict TCP phase precipitation control. This ensures the high-temperature long-term service stability of the final alloy composition from the source, and greatly improves the engineering practicality and reliability of the design results.

[0013] The first category of indicators also includes the γ' phase dissolution temperature T. γ' Heat treatment processing window T s -T γ' One or two of the following; the second category of indicators also includes one or two of the following: solidification temperature range (TSI) and strain aging crack index (SAC).

[0014] The above technical solution supplements and defines the design target indicator system, and the incremental technical effects it brings are as follows: By supplementing the γ' phase dissolution temperature and heat treatment processing window as high-temperature strength-related indicators, while ensuring the stability of the alloy's high-temperature microstructure, the quantitative control of the heat treatment window ensures that the designed alloy has a heat treatment process margin that can be implemented industrially, thus solving the pain point of "emphasizing service performance and neglecting process feasibility" in traditional alloy design.

[0015] By supplementing the solidification temperature range and strain aging crack index as crack sensitivity-related indicators, we have achieved full coverage control of the two core crack types, solidification crack and strain aging crack, throughout the entire additive manufacturing process. This has comprehensively reduced the cracking risk of the alloy under extreme thermal cycling in additive manufacturing and further improved the formability of the alloy and the service reliability of the components.

[0016] The mass fraction range of each variable element in the initial composition space is: Cr 6wt.%-9wt.%, Co 5wt.%-13wt.%, Al 3wt.%-6wt.%, Ti 0wt.%-3wt.%, W 6wt.%-9wt.%, Mo 0wt.%-3wt.%, Ta 6wt.%-9wt.%, Nb 0wt.%-3wt.%; the mass fraction of the fixed trace elements is: C 0.02wt.%, B 0.02wt.%, Zr 0.03wt.%.

[0017] The above technical solution precisely defines the range of element content in the initial composition space, and the incremental technical effects it brings are as follows: Based on phase diagram patterns and engineering experience, the mass fraction ranges of eight variable elements and the content of fixed trace elements were precisely defined. This identified the effective component range for stable formation of the γ' phase and low precipitation of harmful phases from the source, eliminating the range of ineffective components that were likely to result in substandard performance and unstable structure. This significantly reduced the design space and greatly improved the efficiency of subsequent sampling, modeling and optimization processes.

[0018] By fixing the contents of trace elements C, B, and Zr, the high-temperature mechanical properties of the alloy can be guaranteed by utilizing the grain boundary strengthening effect of trace elements, while avoiding the adverse interference of trace element content fluctuations on crack sensitivity and harmful phase precipitation, thus ensuring the consistency of the training dataset and the stability of the optimization results.

[0019] In step S2, the number of samples in the Latin hypercube sampling is no less than 2000 sets, and the high-throughput solidification simulation is completed by the phase diagram calculation module of the Pandat thermodynamics software. The calculation uses a Ni-based alloy-specific thermodynamic database.

[0020] The above technical solution imposes parameter constraints on the initial dataset construction stage, and the resulting incremental technical effects are as follows: The Latin hypercube sampling sample size is limited to no less than 2000 sets, which ensures uniform coverage and representativeness of the samples in the eight-dimensional high-dimensional component space, avoids model training distortion caused by sampling bias, provides sufficient and balanced training data for machine learning models, and fully guarantees the generalization ability of the models.

[0021] High-throughput solidification simulations were performed using Pandat thermodynamic software and a dedicated thermodynamic database for Ni-based alloys. This ensured the professionalism and accuracy of the thermodynamic calculation results and guaranteed the authenticity and reliability of the training dataset from the data source, laying a core data foundation for high-precision predictions by subsequent machine learning models.

[0022] In step S3, the machine learning surrogate model is a gradient boosting regression model, an extreme gradient boosting regression model, a random forest model, a Bayesian ridge regression model, or a Gaussian process regression model. After training, the coefficient of determination R², mean absolute error MAE, and root mean square error RMSE are used as evaluation criteria, and the model with the best prediction accuracy is selected as the final surrogate model through 10-fold cross-validation.

[0023] The above technical solution limits the selection and verification methods for machine learning proxy models, and the incremental technical effects it brings are as follows: It covers mainstream high-performance machine learning regression models such as gradient boosting regression, extreme gradient boosting regression, and random forest. Through horizontal comparison of multiple models, it can adapt to the nonlinear prediction needs of different performance indicators and select the model with the best comprehensive prediction performance for various indicators such as high temperature strength and crack sensitivity.

[0024] Using multi-dimensional evaluation criteria such as coefficient of determination R², mean absolute error (MAE), and root mean square error (RMSE), combined with 10-fold cross-validation, the prediction accuracy and generalization ability of the model were comprehensively verified. This effectively avoided the risk of model overfitting, ensured the prediction reliability of the surrogate model in the unknown component space, and provided a stable and accurate prediction foundation for subsequent multi-objective optimization.

[0025] Furthermore, the specific process of step S4 is as follows: S41: Randomly generate an initial population of size 1000 in the initial component space; S42: Use the machine learning proxy model to predict the indicator value of the design objective corresponding to each individual in the population; S43: Divide the feasible region according to the preset constraints and select individuals belonging to the feasible region; S44: Use a non-dominated sorting genetic algorithm to perform non-dominated sorting and crowding calculation on individuals in the feasible region to obtain the Pareto front of the current generation. S45: Determine whether the termination condition of 500 iterations is met. If not, perform genetic operations such as selection, crossover, and mutation on the current population to generate a new generation of population and return to step S42. If yes, output the current Pareto front as the non-dominated solution set.

[0026] The above technical solution limits the selection and verification methods for machine learning proxy models, and the incremental technical effects it brings are as follows: It covers mainstream high-performance machine learning regression models such as gradient boosting regression, extreme gradient boosting regression, and random forest. Through horizontal comparison of multiple models, it can adapt to the nonlinear prediction needs of different performance indicators and select the model with the best comprehensive prediction performance for various indicators such as high temperature strength and crack sensitivity.

[0027] Using multi-dimensional evaluation criteria such as coefficient of determination R², mean absolute error (MAE), and root mean square error (RMSE), combined with 10-fold cross-validation, the prediction accuracy and generalization ability of the model were comprehensively verified. This effectively avoided the risk of model overfitting, ensured the prediction reliability of the surrogate model in the unknown component space, and provided a stable and accurate prediction foundation for subsequent multi-objective optimization.

[0028] In step S4, the numerical range of the preset constraint condition is: the volume fraction V of the γ' phase at 1000℃. γ' ≥0.50, γ' phase dissolution temperature T γ' ≥1200℃, heat treatment processing window T s -T γ' ≥50℃, solidification temperature range T SI≤350℃, solidification crack index SCI≤5000, strain aging crack index SAC≤0.01.

[0029] The above technical solution specifically limits the numerical range of the preset constraints, and the incremental technical effects it brings are as follows: The quantitative constraints of each design objective were clearly defined. Based on the requirements of high-temperature service at 1000℃ and additive manufacturing process, a feasible domain that takes into account high-temperature strength, crack resistance and process feasibility was delineated. Invalid solutions that do not meet the requirements of engineering applications were directly eliminated during the optimization process, which greatly improved the efficiency and pertinence of multi-objective optimization.

[0030] The numerical settings of various constraint indicators not only ensure that the alloy has sufficient γ' phase volume fraction and high temperature stability to meet the requirements of extreme high temperature service in aerospace and other fields, but also strictly limit the crack sensitivity index to ensure that the alloy has excellent crack resistance and formability during additive manufacturing, thus achieving precise control over both service performance and manufacturing process.

[0031] In step S5, the thermodynamic calculation verification specifically involves: using the CALPHAD method to perform full-process thermodynamic calculations on all components in the non-dominated solution set, obtaining the actual calculated values ​​of each design objective, and eliminating components whose actual values ​​do not meet the preset constraint conditions.

[0032] The above technical solution further limits the thermodynamic calculation verification process, and the incremental technical effects it brings are as follows: The CALPHAD method is used to perform full-process thermodynamic calculations on the non-dominated solution set to obtain the true calculated values ​​of performance indicators. This can effectively correct the prediction errors of the machine learning surrogate model, avoid the failure of component design due to model prediction bias, and ensure that the finally selected components truly meet the preset performance constraints.

[0033] By eliminating unqualified components through secondary verification, a dual-insurance mechanism of "rapid model prediction and optimization - precise thermodynamic verification and check" is formed, which greatly improves the accuracy and engineering usability of the final design results and avoids the ineffective investment of human and material resources in the subsequent experimental verification stage.

[0034] In step S5, the content of the σ phase and μ phase is calculated using Pandat thermodynamic software combined with the PanNi2023_TH+MB nickel-based alloy database.

[0035] The above technical solution further defines the harmful phase assessment process, and the incremental technical effects it brings are as follows: The calculation of TCP phase content was performed using Pandat thermodynamic software in conjunction with the PanNi2023_TH+MB nickel-based alloy database. This ensured the professionalism and accuracy of the calculation results for harmful phases such as σ and μ phases, and provided a reliable calculation basis for the assessment of harmful phases.

[0036] Based on the screening of harmful phases under uniform operating conditions, the components of TCP phase precipitated at high temperatures can be accurately eliminated, and the total content of TCP phase in the intermediate temperature range can be strictly controlled. This effectively avoids the weakening effect of TCP phase on alloy grain boundaries, ensuring the long-term structural stability, high-temperature mechanical properties and service life of the alloy.

[0037] The final target alloy composition, after being prepared by laser powder bed fusion additive manufacturing process, has a density ≥99.8%, a tensile strength ≥1200MPa at room temperature, and a tensile strength ≥450MPa at 1000℃.

[0038] The above technical solution defines the performance of the final target alloy composition, and its resulting technical effects are as follows: The core performance indicators of the alloy designed by this method after laser powder bed melting additive manufacturing were clarified. The high density of the formed parts (≥99.8%) directly verified that the designed alloy has excellent additive manufacturing formability and crack resistance, solving the core pain points of easy cracking and insufficient density of nickel-based high-temperature alloys in additive manufacturing.

[0039] The tensile strength at 1000℃ was limited, proving that the alloy designed by this method has excellent mechanical properties in extreme high-temperature environments, which can meet the stringent service requirements of high-end equipment such as aerospace engine turbine components.

[0040] The quantitative performance indicators directly verify the practical engineering application value of the design method of this invention, proving that the method can stably produce nickel-based superalloy compositions that have both excellent additive manufacturing processability and high-temperature service performance, and realize a complete closed loop from theoretical optimization to engineering implementation of the design method.

[0041] The nickel-based superalloy composition design method of this invention effectively solves the core pain points of existing technologies through systematic process innovation, model optimization, and parameter limitation. Compared with traditional nickel-based superalloy composition design methods, it has significant technical advantages and engineering application value, and its beneficial effects are as follows: This invention effectively resolves inherent technical contradictions in the industry and achieves synergistic improvement in multiple performance aspects. By dividing the core design objectives into two categories—high-temperature strength and crack sensitivity—it constructs a synergistic optimization framework for multiple conflicting performance indicators, completely breaking the technical dilemma in traditional design where "increasing high-temperature strength inevitably increases crack sensitivity, and reducing crack sensitivity inevitably results in a loss of high-temperature strength." Simultaneously, it supplements key performance and process-related indicators, achieving comprehensive control over solidification cracks and strain-aging cracks, while balancing the high-temperature microstructure stability of the alloy with the feasibility of heat treatment processes. This results in a designed nickel-based superalloy that possesses excellent high-temperature mechanical properties, crack resistance, and formability.

[0042] This innovative design paradigm significantly improves R&D efficiency and reduces R&D costs. It establishes a novel design process of "data construction - model training - intelligent optimization - verification and screening," employing machine learning proxy models to replace traditional massive thermodynamic calculations and repetitive trial-and-error experiments involving "melting - processing - testing." Combined with optimization techniques such as Latin hypercube sampling and quadratic polynomial feature engineering, the alloy composition R&D cycle is shortened from the traditional months or even years to just days, significantly reducing the investment of manpower, resources, and time in the R&D process, and drastically lowering R&D costs and the risk of failure.

[0043] This invention enhances design accuracy and reliability, ensuring the engineering applicability of optimized results. It improves design accuracy through multi-dimensional optimization: introducing quadratic polynomial feature engineering to accurately fit the nonlinear mapping relationship between multi-element alloying elements and performance indicators; screening the optimal machine learning proxy model and verifying it using multiple standards and methods to avoid overfitting risks; combining a non-dominated sorting genetic algorithm to achieve global intelligent search of the composition space and obtain the globally optimal Pareto non-dominated solution set; and setting up a dual final screening process of thermodynamic verification and harmful phase evaluation to correct prediction errors and control TCP phase precipitation, ensuring the high-temperature long-term service stability of the final alloy composition from the source, and ensuring that the design results can be directly applied to industrial applications.

[0044] This invention optimizes the design process and parameters to improve the standardization and repeatability of designs. It precisely limits parameters for key aspects such as the initial composition space, dataset construction, model selection, optimization process, and constraints, clarifying the execution standards and boundary requirements for each step. This not only reduces the ineffective design space and improves the efficiency of each step, but also ensures the consistency of the training dataset, the stability of the optimization process, and the repeatability of the design results. It avoids the blindness and randomness of traditional design methods, making the alloy composition design process more standardized and scientific.

[0045] Possessing extremely high engineering application value and adaptable to the needs of high-end equipment, the nickel-based superalloy designed in this invention, after laser powder bed fusion additive manufacturing, achieves a density of ≥99.8% in the formed parts and exhibits excellent tensile strength at 1000℃. It can directly meet the extreme high-temperature service requirements of high-end equipment such as aerospace engine turbine components, realizing a complete closed loop from theoretical optimization to engineering implementation of alloy design. It fills the technological gap in the field of precision design of high-performance nickel-based superalloys for additive manufacturing, provides reliable technical support for the efficient and low-cost research and development of nickel-based superalloys for high-end equipment, and has broad prospects for promotion and application. Attached Figure Description

[0046] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0047] Figure 1 This is a general flowchart of the nickel-based superalloy composition design method provided in the embodiments of the present invention; Figure 2 This is a schematic diagram illustrating the importance analysis of each feature for different prediction targets after quadratic polynomial feature engineering when using the gradient boosting regression model in an embodiment of the present invention. Figure 3 This is a schematic diagram illustrating the prediction performance of the gradient boosting regression model on the test set for six design target indicators in an embodiment of the present invention. Figure 4 This is a flowchart illustrating the multi-objective optimization algorithm used in this embodiment of the invention. Detailed Implementation

[0048] A method for designing the composition of nickel-based superalloys for additive manufacturing applications, the overall process of which is as follows: Figure 1 As shown. This method aims to design an alloy that can operate at 1000°C while simultaneously possessing low crack sensitivity and good high-temperature mechanical properties. The steps are described in detail below with reference to examples.

[0049] Step S1: Define the design objectives and the initial component space.

[0050] First, the design objective is clearly defined as synergistically optimizing high-temperature strength and crack resistance. Specifically, six key performance indicators are selected: the volume fraction V of the γ' phase at 1000℃, as the first type of indicator (related to high-temperature strength). γ' γ' phase dissolution temperature T γ Heat treatment processing window T s -T γ ; and the solidification temperature range T as a second type of indicator (related to crack sensitivity). SI Solidification crack index (SCI) and strain aging crack index (SAC). The definitions of each index are shown in Table 2.

[0051] Next, the initial composition space was determined. Eight elements—Cr, Co, Al, Ti, W, Mo, Ta, and Nb—were selected as variable elements, and their content ranges were initially determined based on the distribution of the γ' phase and harmful phases in the phase diagram (as shown in Table 1). C, B, and Zr were selected as trace elements with fixed contents (C and B 0.02 wt.%, Zr 0.03 wt.%), with Ni as the balance. Thus, an eight-dimensional composition design space was defined.

[0052]

[0053]

[0054] Step S2: Construct the initial dataset.

[0055] To construct training data for the machine learning model, six index values ​​corresponding to a large number of sample points in the composition space are needed. A Latin hypercube sampling method is used to uniformly extract 2000 components from the aforementioned eight-dimensional composition space. Then, these 2000 component data are input into the phase diagram calculation module of commercial thermodynamic software (such as Pandat) for high-throughput solidification simulation, batch calculating the V corresponding to each component. γ' T γ' T s T l Data such as solidification path curves were used to calculate the values ​​of all six target indicators, including SCI and SAC, based on the definitions in Table 2. Ultimately, a dataset containing 2000 data records was created, with each record containing 8 input features (element content) and 6 output labels (indicator values).

[0056] Step S3: Construct a machine learning agent model.

[0057] First, feature engineering is performed. Due to the complex nonlinear interaction between crack sensitivity indices (such as SCI) and elemental content, directly using the eight original features to train the model has limited prediction accuracy. Therefore, the eight original input features are expanded using a quadratic polynomial to generate a total of 44 new features, including the square of each element (8 terms) and the product of each pair of elements (C(8,2)=28 terms).

[0058] Then, using the expanded features and the corresponding six target values, several different machine learning regression models were trained, including random forest, gradient boosting regression, extreme gradient boosting regression, Bayesian ridge regression, and Gaussian process regression. The coefficient of determination (R²), mean absolute error (MAE), and root mean square error (RMSE) were used as evaluation criteria, and the performance of each model was compared using 10-fold cross-validation (results are shown in Table 3). The comparison revealed that the gradient boosting regression model performed best in terms of both overall prediction accuracy and computational efficiency, especially when dealing with difficult-to-predict indicators such as SCI, where its R² reached 0.6921 (after feature engineering), outperforming other models. Therefore, gradient boosting regression was selected as the final surrogate model. Its feature importance analysis is as follows: Figure 2 As shown, the prediction results are as follows: Figure 3 As shown, the effectiveness of the quadratic polynomial features and the credibility of the model are demonstrated.

[0059]

[0060] Step S4: Multi-objective optimization screening.

[0061] The trained gradient boosting regression surrogate model is embedded into a multi-objective optimization framework. A non-dominated sorting genetic algorithm is used as the optimization engine, and its process is as follows: Figure 4 As shown.

[0062] First, constraints for the optimization problem are set. Based on the alloy service requirements (1000℃) and process experience, boundaries are set for the six target indicators, as shown in Table 4, such as V. γ' ≥ 0.50, SCI ≤ 5000, etc., to define the feasible search area.

[0063] Then, the NSGA-II algorithm is initiated. A population of size 1000 is randomly generated in the initial component space. Using the surrogate model trained in step S3, the six objective values ​​of all individuals in the population (i.e., the component scheme) are quickly predicted. Individuals located within the feasible region are selected according to the constraints in Table 4. Next, non-dominated ranking and crowding calculation are performed on these feasible individuals to obtain the first-generation Pareto front.

[0064] The algorithm determines whether the termination condition has been met (in this example, it is set to 500 iterations). If not, genetic operations such as selection, crossover, and mutation are performed on the current population to generate a new generation. The process of prediction, selection, and sorting is repeated. As the iterations proceed, the Pareto front continuously evolves towards a better direction. After 500 iterations, the algorithm converges and outputs the final non-dominated solution set. Each component in this solution set achieves some optimal trade-off across the six objectives, and there is no other solution that is superior to it in all objectives.

[0065]

[0066] Step S5: Final verification and screening.

[0067] Because machine learning models have some error in predicting indicators such as SCI, to ensure the absolute reliability of the final components, all components in the non-dominated solution set obtained in step S4 are recalculated using CALPHAD thermodynamic software to obtain the true values ​​of their six indicators. Components whose true values ​​do not meet the constraints in Table 4 are then removed.

[0068] Furthermore, a harmful phase assessment was performed on the remaining candidate components. The precipitation of topologically close-packed phases such as the σ phase and μ phase was calculated for each component during the entire cooling process from the liquid phase to room temperature. Components exhibiting TCP phases above 900℃, or with excessively high TCP phase content between 500-900℃, were excluded. This step is crucial because TCP phases severely impair the long-term microstructural stability and mechanical properties of the alloy, which the surrogate model does not directly predict.

[0069] After rigorous verification and screening, an optimal alloy composition was finally obtained, the specific composition of which is shown in Table 5, and the calculated key performance indicators are shown in Table 6. This composition, while ensuring a sufficiently high γ' phase volume fraction (>0.50) to provide high-temperature strength, successfully controls the solidification crack index (SCI) below 5000, achieving a good balance between high strength and low crack sensitivity.

[0070] verify

[0071] The above two groups of preferred alloy compositions were prepared and tested by additive manufacturing using laser powder bed melting (LPBF) process. The process parameters were: laser power 280W, scanning speed 1000mm / s, layer thickness 30μm, scanning spacing 80μm, and substrate preheating temperature 200℃.

[0072] Test results show that the additively manufactured parts with the preferred composition have a density of ≥99.8%, with no macroscopic cracks or obvious microscopic cracks; the tensile strength at room temperature is ≥1200MPa, the yield strength is ≥880MPa, and the elongation is ≥10%; the tensile strength at 1000℃ is ≥450MPa, the yield strength is ≥270MPa, and the elongation is ≥5%; meeting the service requirements of high-temperature additively manufactured components in the aerospace field, and verifying the reliability and practicality of the design method of this invention.

[0073] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for designing the composition of nickel-based superalloys based on machine learning and multi-objective optimization, characterized in that, Includes the following steps: S1: Define the design objectives and initial composition space of the alloy. The design objectives include a first type of indicator related to high-temperature strength and a second type of indicator related to crack susceptibility. The first type of indicator includes at least the γ' phase volume fraction V at 1000℃. γ' The second type of index includes at least the solidification crack index (SCI); the variable elements in the initial composition space are Cr, Co, Al, Ti, W, Mo, Ta, and Nb, the fixed trace elements are C, B, and Zr, and the balance is Ni. S2: Sample from the initial composition space using the Latin hypercube sampling method to obtain multi-component component data, and perform thermodynamic calculations through high-throughput solidification simulation to obtain the index value of the design target corresponding to each component data, and construct the initial dataset; S3: Perform quadratic polynomial feature engineering on the input features in the initial dataset to generate a new feature set containing the original features, the squares of each variable element, and the product term between any two variable elements; based on the new feature set and the initial dataset, train a machine learning proxy model for predicting the design target; S4: Using the machine learning proxy model and the non-dominated sorting genetic algorithm, search and select non-dominated solution sets that satisfy preset constraints in the initial component space; the preset constraints include limiting the numerical range of the first type of index and the second type of index. S5: Perform thermodynamic calculations to verify the components in the non-dominated solution set and evaluate harmful phases to screen out the final target alloy components; the evaluation of harmful phases specifically involves: calculating the content of σ phase and / or μ phase in the candidate components during solidification-cooling, excluding components with σ phase and μ phase appearing above 900℃, and components with a total content of σ phase and μ phase exceeding 5% vol between 500℃ and 900℃.

2. The design method according to claim 1, characterized in that, The first category of indicators also includes the γ' phase dissolution temperature T. γ' Heat treatment processing window T s -T γ' One or two of the following; the second category of indicators also includes the solidification temperature range T. SI One or two of the strain aging crack index (SAC).

3. The design method according to claim 1, characterized in that, The mass fraction range of each variable element in the initial composition space is: Cr 6wt.%-9wt.%, Co 5wt.%-13wt.%, Al 3wt.%-6wt.%, Ti 0wt.%-3wt.%, W 6wt.%-9wt.%, Mo 0wt.%-3wt.%, Ta 6wt.%-9wt.%, Nb 0wt.%-3wt.%; the mass fraction of the fixed trace elements is: C 0.02wt.%, B 0.02wt.%, Zr 0.03wt.%.

4. The design method according to claim 1, characterized in that, In step S2, the number of samples in the Latin hypercube sampling is no less than 2000 sets, and the high-throughput solidification simulation is completed by the phase diagram calculation module of the Pandat thermodynamics software. The calculation uses a Ni-based alloy-specific thermodynamic database.

5. The design method according to claim 1, characterized in that, In step S3, the machine learning surrogate model is a gradient boosting regression model, an extreme gradient boosting regression model, a random forest model, a Bayesian ridge regression model, or a Gaussian process regression model. After training, the coefficient of determination R², mean absolute error MAE, and root mean square error RMSE are used as evaluation criteria, and the model with the best prediction accuracy is selected as the final surrogate model through 10-fold cross-validation.

6. The design method according to claim 1, characterized in that, The specific process of step S4 is as follows: S41: Randomly generate an initial population of size 1000 in the initial component space; S42: Use the machine learning proxy model to predict the indicator value of the design objective corresponding to each individual in the population; S43: Divide the feasible region according to the preset constraints and select individuals belonging to the feasible region; S44: Use a non-dominated sorting genetic algorithm to perform non-dominated sorting and crowding calculation on individuals in the feasible region to obtain the Pareto front of the current generation. S45: Determine whether the termination condition of 500 iterations is met. If not, perform genetic operations such as selection, crossover, and mutation on the current population to generate a new generation population, and return to step S42. If so, output the current Pareto front as the non-dominated solution set.

7. The design method according to claim 2, characterized in that, In step S4, the numerical range of the preset constraint condition is: the volume fraction V of the γ' phase at 1000℃. γ' ≥0.50, γ' phase dissolution temperature T γ' ≥1200℃, heat treatment processing window T s -T γ' ≥50℃, solidification temperature range T SI ≤350℃, solidification crack index SCI≤5000, strain aging crack index SAC≤0.

01.

8. The design method according to claim 1, characterized in that, In step S5, the thermodynamic calculation verification specifically involves: using the CALPHAD method to perform full-process thermodynamic calculations on all components in the non-dominated solution set, obtaining the actual calculated values ​​of each design objective, and eliminating components whose actual values ​​do not meet the preset constraint conditions.

9. The design method according to claim 1, characterized in that, In step S5, the content of the σ phase and μ phase is calculated using Pandat thermodynamic software combined with the PanNi2023_TH+MB nickel-based alloy database.

10. The design method according to claim 1, characterized in that, The final target alloy composition, after being prepared by laser powder bed fusion additive manufacturing process, has a density ≥99.8%, a tensile strength ≥1200MPa at room temperature, and a tensile strength ≥450MPa at 1000℃.

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