Nickel-based superalloy component design and optimization method based on quantum machine learning

Abstract

The invention discloses a nickel-based superalloy component design and optimization method based on quantum machine learning, and belongs to the field of material technologies and machine algorithms, and the method comprises the following steps: firstly, constructing a data set containing nickel-based superalloy components, oxidation environment conditions and oxidation resistance results, and executing preprocessing operation; based on the preprocessed data and a quantum computing framework, designing a quantum feature mapping circuit, extracting high-dimensional nonlinear features of alloy components and environmental parameters, obtaining a mixed kernel function, and performing training and verification; and carrying out optimization design on the alloy components by adopting a multi-objective genetic algorithm for the verified prediction model, and introducing a hyper-volume for evaluation in order to quantitatively evaluate the overall effect of multi-objective optimization. According to the method, the quantum feature enhancement technology is introduced to be combined with the improved multi-target genetic algorithm, so that the complex nonlinear relation is more effectively captured, and a better alloy design scheme is obtained.

Description

Technical Field

[0001] This invention relates to the fields of materials technology and machine algorithms, specifically to a method for designing and optimizing the composition of nickel-based superalloys based on quantum machine learning. Background Technology

[0002] Nickel-based superalloys are widely used in aero-engines, gas turbines, and high-temperature chemical industries due to their excellent high-temperature strength, corrosion resistance, and oxidation resistance. As service conditions become increasingly demanding, the requirements for the oxidation resistance of nickel-based superalloys at high temperatures are constantly increasing. However, existing technologies have several shortcomings in this area. Traditional methods typically require extensive alloy formulation experiments and lengthy high-temperature constant-weight tests to obtain data on the oxidation weight gain of alloys. This experimental process is time-consuming, costly, and involves complex experimental conditions. Furthermore, with the increase in the variety of selectable alloy compositions and the spatial expansion of oxidation environment parameters, it is difficult to efficiently predict the oxidation resistance of alloys and optimize their design using only conventional experiments or classical machine learning methods.

[0003] In scenarios involving small samples and high-dimensional nonlinearity, traditional machine learning models may exhibit insufficient accuracy or overfitting. In particular, when attempting a global search in a high-dimensional space composed of elemental composition and service conditions, classical optimization algorithms are prone to getting trapped in local optima or experiencing a sharp increase in computational cost that hinders convergence. Meanwhile, some improved approaches, such as combining microalloying strategies with automated experimental platforms to accelerate screening, while improving efficiency to some extent, suffer from expensive equipment and still require sophisticated data modeling. Existing research has attempted to use artificial neural networks and random forests to predict the oxidation weight gain of nickel-based alloys, but the improvement is limited when the sample size is limited or the relationship is extremely nonlinear. Regarding alloy composition optimization, traditional single-objective optimization often focuses only on reducing oxidation weight gain, neglecting factors such as model uncertainty and process feasibility, potentially resulting in formulations that are unstable or infeasible in actual preparation.

[0004] In summary, there is currently a lack of technical solutions that can accurately predict the oxidation resistance of nickel-based superalloys under small sample conditions, while simultaneously taking into account multi-objective optimization in terms of performance, uncertainty, and process feasibility. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method for designing and optimizing the composition of nickel-based superalloys based on quantum machine learning.

[0006] To achieve the above technical solution, the specific steps are as follows: S1. Construct a dataset containing the composition, oxidation environment conditions, and oxidation resistance of nickel-based superalloys, and perform preprocessing operations on the dataset; The composition of nickel-based superalloys consists of typical constituent elements and their percentage content. The elements include: Ni, Cr, Co, Mo, W, Al, Ti, Fe, Nb, C, Hf, Si, Mn, Zr and Ta, totaling 15 elements. The oxidation environment conditions refer to the environmental parameters of the oxidation experiment: temperature and time. The antioxidant performance result is the oxidation weight gain of the alloy under preset temperature and time conditions, i.e., the weight gain per unit area, expressed in mg / cm². 2 To ensure data quality, only experimental data with a temperature range of 700℃-1200℃, an oxidation time of 1-10 hours, and an oxidation environment of atmospheric pressure air were collected. The processing operations include: data cleaning, handling of missing and outlier values, and normalization. Data format standardization: All alloy composition contents are uniformly expressed as mass percentage (wt.%), temperature is uniformly expressed as ℃, time is uniformly expressed as hours, and oxidation weight gain is uniformly expressed as mg / cm². The units and measurement conditions of each value are clearly defined. Missing and outlier handling: Data samples lacking information on elemental content, temperature, time, and oxidative weight gain, and for which no inference can be made, are directly deleted. For missing alloy composition data, methods such as average value filling, regression prediction-based filling, or nearest neighbor value filling are used to fill the missing data. When performing thermodynamic calculations, obvious input errors or unit conversion errors can be inferred from the calculation results, and these outliers can be verified and corrected. If the value is confirmed to be unreasonable, the sample is removed to prevent noise from interfering with model training. Feature normalization: Considering the large differences in the dimensions of different features, directly using the original values ​​will lead to unstable model training. Therefore, all input features are normalized. The maximum-minimum scaling method is used to linearly map each feature to the interval [0,1], thereby eliminating the influence of dimensions. After processing, several sets of data are obtained, including 17-dimensional features and corresponding oxidation weight gain results.

[0007] S2. Based on the preprocessed data and the quantum computing framework (Qiskit), a quantum feature mapping circuit is designed to extract high-dimensional nonlinear features of alloy composition and environmental parameters, and a hybrid kernel function is obtained. The specific steps are as follows: S2.1 Each input feature after dimensionality reduction is encoded into the initial state of a qubit. The encoding methods include: S2.1.1 First, principal component analysis (PCA) is applied to the alloy composition characteristics to reduce the 15 elemental components to k principal components, for example, k=8. The principal components are orthogonal linear combinations obtained by linear transformation, so as to retain the main variance contribution while reducing the number of qubits required. In addition, two qubits are selected to encode environmental characteristics, namely temperature and time. S2.1.2 Construct a parameterized quantum circuit, namely a feature mapping circuit, for each quantum bit to map classical eigenvalues ​​to quantum state amplitude or phase; The construction method is as follows: for the first Each feature is used to apply a rotation gate to the corresponding qubit, and the rotation angle is controlled by the value of this feature (e.g., ...). ,in For the first (Normalized values ​​of each feature); After encoding all features, entanglement gates can be applied between multiple (two or more) qubits to capture the interaction between features; S2.1.3 After constructing the quantum feature mapping circuit, each set of input features is mapped to a state in the quantum Hilbert space. ; S2.2 Calculate the similarity between quantum states obtained by mapping any two sets of input features using the fidelity metric quantum kernel function; The specific approach is as follows: The Fidelity Quantum Kernel method provided by the quantum machine learning framework is used, and the kernel function value is defined based on the fidelity of the quantum state; for two different input samples... and Their corresponding quantum states are respectively and The quantum kernel function is defined as the fidelity between two quantum states, and its expression is as follows: In the formula, Represents a kernel function based on quantum characteristics; where the inner product... State of expression with state The overlap magnitude, the squared value represents the fidelity of the two quantum states; S2.3. Introduce the Nyström approximation method to sparsify the quantum kernel; The sparsity reduction method is as follows: randomly sample some data points using the Nyström method as anchors to approximately reconstruct the complete kernel matrix; Assuming from Randomly selected from training samples Using a set of samples as anchor points, by default The corresponding index set is ;remember The quantum kernel matrix between all training samples and anchor samples, its size is... , The quantum kernel matrix between each pair of anchor samples, its size Through the By adding a minor regularization term and taking the generalized inverse, an approximate global kernel matrix can be obtained. The expression is as follows: In the formula, express The transpose of the matrix has a size of At this point, the calculation is approximately equivalent to restricting the original kernel matrix to the rank spanned by the anchor samples. In the subspace; S2.4. The similarity of environmental features is measured using the classical radial basis function (RBF) kernel to obtain the environmental kernel; Besides the alloy composition itself, service environment factors also significantly affect the oxidation performance of alloys. To incorporate the influence of environmental parameters on oxidation behavior into the model, this invention uses a classical radial basis function (RBF) kernel to measure the similarity of environmental features. For the environmental feature vectors of two samples, the two-dimensional vectors composed of temperature and oxidation time are denoted as follows: and The expression is as follows: In the formula, Represents the radial basis function kernel (RBF) based on environmental characteristics; The parameter representing the width of the RBF core; This represents the Euclidean distance between environmental feature vectors; when environmental conditions are similar, the exponent term approaches 1, indicating high environmental similarity; conversely, the similarity decreases. S2.5. Construct a hybrid kernel function by linearly combining the quantum kernel and the environment kernel according to certain weights, as shown in the following expression: In the formula, Represents the fusion coefficient. This is used to balance the contributions of quantum features and environmental features to the overall kernel similarity, i.e., when At higher levels, more emphasis is placed on quantum characteristics, i.e., the effect of the mapped alloy composition; when At lower levels, the role of environmental condition similarity is emphasized. By using a hybrid kernel approach, the model can simultaneously capture the high-dimensional nonlinear correlation of alloy composition space and the influence of oxidation environment conditions, thereby obtaining a more comprehensive and accurate similarity measurement.

[0008] S3. Train and validate the obtained hybrid function kernel; The training method is as follows: Kernel Ridge Regression (KRR) is used, with the mixture kernel matrix as the kernel function of the model; The verification method is as follows: In order to evaluate the model performance and select the optimal combination of hyperparameters, such as quantum kernel weights. Number of anchor points RBF kernel parameters The prediction accuracy index is calculated using the K-fold cross-validation method. The K-fold cross-validation method can also be used as the multi-objective optimization performance index of S4, namely the Pareto hypervolume, to comprehensively measure the generalization ability and multi-objective optimization effect of the model. Based on this, various parameters are adjusted to finally determine the optimal model configuration, providing a reliable evaluation tool for subsequent genetic algorithm optimization.

[0009] S4. The alloy composition is optimized using a multi-objective genetic algorithm on the verified prediction model. The steps include: S4.1 Optimization Variables and Encoding Method: Alloy composition content and environmental parameters are encoded as decision variables of the genetic algorithm; In this invention, an individual code contains 14 gene positions corresponding to the percentage content of elements such as Cr and Co, and 2 gene positions corresponding to temperature and time. Each gene is represented by a real number, and its initial value range is set according to metallurgical experience and process specifications. The specific range is shown in S4.2. Because the alloy element content needs to meet the constraint of a total of 100%, the encoding using real numbers is not simply independent; each gene must jointly satisfy the linear constraint condition. Therefore, this invention retains nickel as a filler element in the encoding. That is, the Ni content is not directly stored in the individual gene, but is calculated using the gene values ​​of other elements. After the other element genes are assigned values, the Ni content is set as the remainder, thus ensuring that the total is always equal to 100%. S4.2 Initial Population Generation and Boundary Pruning: An initial population is randomly generated, ensuring that the elemental content of each individual is randomly selected within a preset reasonable range and satisfies necessary element combination restrictions. The content ranges of the main elements are set as follows: Ni (40%–70%), Cr (15%–21%), Co (10%–16%), Mo (1%–5%), W (0%–10%), Al (1%–5%), Ti (0%–3%), Fe (0%–5%), Nb (0%–3%), with other trace elements set to fixed constants. When generating the initial individuals, each non-Ni element is first randomly assigned a value according to the range, and then the Ni balance is calculated to ensure a total of 100%. If the initial value of the main element exceeds the range, a main element trimming step is performed. The trimming step cuts off the excess content of the element to the minimum or maximum allowed value, and the Ni content is readjusted after trimming. After trimming and normalization, it is also necessary to check whether the metallurgical constraints of specific element combinations are met. For example, ensure that the Ni matrix element is not less than 50%, the total amount of strengthening phase forming elements does not exceed 10% (Al, Nb, Ta), and the total amount of refractory elements does not exceed 8% (W, Mo, Ta, Nb). If an individual violates these basic constraints, the individual is discarded or the corresponding gene is adjusted until it meets the requirements. Through the above measures, the population obtained after initialization is a metallurgically feasible alloy formulation. S4.3 Fitness Evaluation and Multi-Objective Computation: Define the objective function of the genetic algorithm to evaluate the performance of each individual on multiple objectives; The objective function of a genetic algorithm includes: For each individual in the population, its alloy composition and environmental parameters are used as inputs. After undergoing the same feature preprocessing as in the model training phase, the data is input into a pre-trained hybrid kernel regression model to predict the oxidation weight gain of the candidate formulation under corresponding conditions. This is the primary optimization objective, which needs to be minimized, in line with the common sense that better antioxidant performance results in less weight gain. Meanwhile, to quantify the uncertainty of the model predictions, an uncertainty measure can be introduced as a secondary objective for each prediction result. For example, the prediction bias can be estimated using the model's residual distribution or by introducing an auxiliary Gaussian process, thus obtaining the standard deviation or confidence interval width of the candidate formulation's predicted value. It is used as an indicator of uncertainty, with the goal of minimizing it. ; Third, define a constraint breach metric or feasibility score for the process feasibility objective. Based on the key metallurgical parameters of the formulation, a penalty function is calculated. This function is defined as the prediction of the solidus (T_solidus) and dissolution temperature (T_solvus) according to the model's heat treatment characteristic temperatures. If a formulation causes the predicted T_solvus to be significantly higher than T_solidus or deviate from the empirical safety range, a larger penalty value is assigned; otherwise, the penalty is zero. Similarly, whether or not prior constraints are violated—namely, the aforementioned lower limit for Ni content and upper limits for Al and Ti—is converted into accumulated penalty scores. A higher penalty value indicates greater difficulty in process implementation or worse material stability. We define the process feasibility objective as minimizing this value. ; In summary, each individual corresponds to three target values. This genetic algorithm aims to reduce these three values ​​simultaneously. S4.4 Non-dominated sorting selection: This invention uses the NSGA-II algorithm to perform selection operations under multiple objectives; The sum of neighborhood distances for each individual in each objective dimension of the current frontier is calculated. Individuals with larger distances indicate that their region is sparse and contributes to diversity, and will receive a higher retention priority. Finally, based on the non-dominated level and crowding distance, the population is selected through tournament selection or direct optimal replication to generate parent candidates for the next generation of genetic algorithms. S4.5 Crossover and Mutation: After the selection operation generates a new generation of parents, the parents are reproduced, i.e., crossover and mutation, in order to explore a wider solution space; Single-point crossover is used, and crossover operations are performed according to the set crossover probability; Mutation operations are performed using a preset mutation rate; S4.6 Iterative Evolution and Termination: After completing one round of selection, crossover, and mutation operations, the next generation of population is generated, and the algorithm repeats the process of steps S4.3-S4.5. The termination condition set by the algorithm can be reaching the predetermined maximum number of generations or the Pareto front convergence no longer showing significant improvement.

[0010] S5. In order to quantitatively evaluate the overall effect of multi-objective optimization, hypervolume (HV) is introduced for evaluation. With reference point The maximum tolerable levels for oxidation weight gain, uncertainty, and penalty value are represented. Then, the multidimensional volume enclosed between the reference point and the Pareto front is calculated. The larger the HV value, the larger the volume covered by the Pareto solution set towards the ideal small objective value, which means the better the overall optimization result. Since directly calculating the hypervolume of complex shapes in three-dimensional space can be difficult, this invention employs a hypervolume approximation method based on a genetic algorithm to estimate the HV value. Specifically, under the premise of a fixed reference point, a small-scale genetic algorithm is designed for the current Pareto solution set to optimize using the HV value as the fitness. This genetic algorithm-based hypervolume approximation method attempts to fill more volumes dominated by Pareto solutions in the target space, and its fitness peak is the approximate estimated hypervolume. This method can calculate the HV index efficiently while ensuring accuracy. By comparing the HV values ​​of the Pareto front obtained under different model parameters or algorithm settings, the performance of the method in multi-objective optimization can be intuitively measured.

[0011] Beneficial effects of the present invention This invention combines quantum feature enhancement technology with an improved multi-objective genetic algorithm to more effectively capture complex nonlinear relationships and obtain better alloy design schemes.

[0012] This invention, by leveraging quantum feature mapping and fidelity metric quantum kernels, can capture complex nonlinear relationships between elements under high-dimensional, small-sample conditions, exhibiting higher fitting accuracy and generalization ability compared to classical machine learning methods. The hybrid kernel integrates information from material composition and environmental factors, enabling the model to consider both the intrinsic compositional differences and external condition changes when predicting the oxidation weight gain of alloys, thus improving the reliability of the prediction.

[0013] This invention employs the multi-objective NSGA-II algorithm, which simultaneously considers maximizing antioxidant performance, minimizing model uncertainty, and satisfying process feasibility constraints in a single optimization. This avoids the problem of traditional single-objective optimization, which unilaterally pursues performance and leads to infeasible solutions. The non-dominated sorting and crowding distance mechanism of NSGA-II ensure that the search process is not prone to getting trapped in local optima and can produce diverse candidate solutions for decision-making. Compared with manual allocation or single-objective genetic algorithms, the method of this invention has significant improvements in global search efficiency and solution set quality.

[0014] This invention combines the hypervolume index with a hypervolume approximation calculation method based on a genetic algorithm to evaluate the overall performance of a multi-objective optimization model. Hypervolume, as an effective indicator of Pareto front quality, can quantify the model's trade-off ability across different objectives. By comparing the HV values ​​of different models or algorithms, it is possible to objectively analyze which scheme is better overall, providing guidance for model improvement and parameter adjustment. This evaluation method provides a new quantitative analysis tool for multi-objective material design. Attached Figure Description

[0015] Figure 1 This is a flowchart of the present invention; Figure 2This is a quantum circuit diagram of the present invention; Figure 3 This is a Pareto 3D scatter plot of the present invention; Figure 4 This is a grid heatmap of the present invention. Detailed Implementation

[0016] The present invention will be further described in detail below with reference to specific embodiments.

[0017] See Figures 1-4 A method for designing and optimizing the composition of nickel-based superalloys based on quantum machine learning includes the following steps: S1. Construct a dataset containing the composition, oxidation environment conditions, and oxidation resistance of nickel-based superalloys, and perform preprocessing operations on the dataset; The dataset was collected from academic papers and patents; The composition of nickel-based superalloys consists of typical constituent elements and their percentage content. The elements include: Ni, Cr, Co, Mo, W, Al, Ti, Fe, Nb, C, Hf, Si, Mn, Zr and Ta, totaling 15 elements. The oxidation environment conditions refer to the environmental parameters of the oxidation experiment: temperature and time. The antioxidant performance result is the oxidation weight gain of the alloy under preset temperature and time conditions, i.e., the weight gain per unit area, expressed in mg / cm². 2 To ensure data quality, only experimental data with a temperature range of 700℃-1200℃, an oxidation time of 1-10 hours, and an oxidation environment of atmospheric pressure air were collected. Since the data sources may be not synchronized across multiple documents, databases, or patents, preprocessing is required, including: data cleaning, handling of missing and outlier values, and normalization. Data format standardization: All alloy composition contents are uniformly expressed as mass percentage (wt.%), temperature is uniformly expressed as ℃, time is uniformly expressed as hours, and oxidation weight gain is uniformly expressed as mg / cm². The units and measurement conditions of each value are clearly defined. Missing and outlier handling: For data samples with missing key features, such as element content, temperature, time, and oxidation weight gain, and whose missing features cannot be inferred, they are directly deleted; for missing data with non-key features, such as alloy composition, methods such as average value filling, regression prediction-based filling, or nearest neighbor value filling are used to fill the missing features; for suspected outlier data, such as outliers caused by obvious input errors (infinity, infinitesimal) or unit conversion errors that can be inferred from the calculation results during thermodynamic calculations, verification and correction are performed; if the value is confirmed to be unreasonable, the sample is removed to prevent noise from interfering with model training; Feature normalization: Considering the large differences in the dimensions of different features, directly using the original values ​​will lead to unstable model training. Therefore, all input features are normalized. The maximum-minimum scaling method is used to linearly map each feature to the interval [0,1], thereby eliminating the influence of dimensions. After processing, several sets of data are obtained, including 17-dimensional features and corresponding oxidation weight gain results.

[0018] S2. Based on the preprocessed data and the quantum computing framework (Qiskit), a quantum feature mapping circuit is designed to extract high-dimensional nonlinear features of alloy composition and environmental parameters, and a hybrid kernel function is obtained. The specific steps are as follows: S2.1 Each input feature after dimensionality reduction is encoded into the initial state of a qubit. The encoding methods include: S2.1.1 To balance the contradiction between limited qubit resources and high feature dimensionality, principal component analysis (PCA) is first applied to the alloy composition characteristics to reduce the dimensionality, reducing the 15 elemental components to k principal components, for example, k=8. The principal components are orthogonal linear combinations obtained through linear transformation, so as to retain the main variance contribution while reducing the number of qubits required. In addition, two qubits are selected to encode environmental features, namely temperature and time. S2.1.2 Construct a parameterized quantum circuit, namely a feature mapping circuit, for each quantum bit to map classical eigenvalues ​​to quantum state amplitude or phase; The construction method is as follows: for the first Each feature is used to apply a rotation gate, such as an RY rotation, to the corresponding qubit. The rotation angle is controlled by the numerical value of this feature (e.g., ...). ,in For the first (Normalized values ​​of each feature); After encoding all features, entanglement gates, such as ZZ coupling gates, can be applied between multiple (two or more) qubits to capture the interaction between features; S2.1.3 After constructing the quantum feature mapping circuit, each set of input features is mapped to a state in the quantum Hilbert space. ; S2.2 Calculate the similarity between quantum states obtained by mapping any two sets of input features using the fidelity metric quantum kernel function; The specific approach is as follows: The FidelityQuantumKernel method provided by the quantum machine learning framework is used, and the kernel function value is defined based on the fidelity of the quantum state; for two different input samples... and Their corresponding quantum states are respectively and The quantum kernel function is defined as the fidelity between two quantum states, and its expression is as follows: In the formula, Represents a kernel function based on quantum characteristics; where the inner product... State of expression with state The overlap magnitude is used to determine the fidelity between the two quantum states, and the squared value represents the fidelity between them. Intuitively, if the quantum states mapped from two samples are very close, the fidelity is close to 1; conversely, if they differ significantly, the fidelity is close to 0. By calculating the fidelity between training samples, a quantum kernel function can be constructed. Its scale is The matrix, where N The number of training samples, the elements in the matrix Reflecting the sample With sample The degree of similarity in quantum feature space; S2.3. Introduce the Nyström approximation method to sparsify the quantum kernel; Since the dimension of the quantum kernel matrix increases quadratically with the number of samples, directly calculating and storing the entire kernel matrix is ​​extremely costly when there are many samples. To improve computational efficiency, this invention introduces the Nyström approximation method to sparsify the quantum kernel. The sparsity reduction method is as follows: randomly sample some data points using the Nyström method as anchors to approximately reconstruct the complete kernel matrix; In specific implementation, assuming from Randomly selected from training samples Using a set of samples as anchor points, by default The corresponding index set is ;remember The quantum kernel matrix between all training samples and anchor samples, its size is... , The quantum kernel matrix between each pair of anchor samples, its size Through the By adding a minor regularization term and taking the generalized inverse, an approximate global kernel matrix can be obtained. The expression is as follows: In the formula, express The transpose of the matrix has a size of At this point, the calculation is approximately equivalent to restricting the original kernel matrix to the rank spanned by the anchor samples. In the subspace; by selecting an appropriate number of anchor points The Nyström approximation can achieve a value much lower than This generates sparse quantum kernel representations with computational complexity, significantly reducing the overhead of subsequent model training and prediction; simultaneously, while ensuring... Given a sufficiently large size, this sparse approximation can preserve the discriminative information of the original quantum nucleus relatively well; S2.4. The similarity of environmental features is measured using the classical radial basis function (RBF) kernel to obtain the environmental kernel; Besides the alloy composition itself, service environment factors also significantly affect the oxidation performance of alloys. To incorporate the influence of environmental parameters on oxidation behavior into the model, this invention uses a classical radial basis function (RBF) kernel to measure the similarity of environmental features. For the environmental feature vectors of two samples, the two-dimensional vectors composed of temperature and oxidation time are denoted as follows: and The expression is as follows: In the formula, Represents the radial basis function kernel (RBF) based on environmental characteristics; The parameter representing the width of the RBF core; This represents the Euclidean distance between environmental feature vectors; when environmental conditions are similar, the exponent term approaches 1, indicating high environmental similarity; conversely, the similarity decreases. S2.5. Construct a hybrid kernel function by linearly combining the quantum kernel and the environment kernel according to certain weights, as shown in the following expression: In the formula, Represents the fusion coefficient. This is used to balance the contributions of quantum features and environmental features to the overall kernel similarity, i.e., when At higher levels, more emphasis is placed on quantum characteristics, i.e., the effect of the mapped alloy composition; when At lower levels, the role of environmental condition similarity is emphasized. By using a hybrid kernel approach, the model can simultaneously capture the high-dimensional nonlinear correlation of alloy composition space and the influence of oxidation environment conditions, thereby obtaining a more comprehensive and accurate similarity measurement.

[0019] S3. Train and validate the obtained hybrid function kernel; The training method is as follows: based on the mixture function kernel, the kernel method is used to perform regression modeling of antioxidant performance, that is, using algorithms such as kernel ridge regression (KRR) or Gaussian process regression (GPR), and using the mixture kernel matrix as the kernel function of the model; taking kernel ridge regression as an example, this invention solves the double dual coefficients by adding a preset regularization term to the kernel matrix to achieve fitting of the training data; after the model training is completed, for any new alloy composition and environmental input, firstly calculate the quantum kernel feature between the input and the anchor sample of the training set, as well as the environmental RBF kernel feature, then obtain the kernel vector of the input relative to the training set according to the mixture kernel function, and finally predict the corresponding oxidation weight gain value through the trained kernel regression model; The verification method is as follows: In order to evaluate the model performance and select the optimal combination of hyperparameters, such as quantum kernel weights. Number of anchor points RBF kernel parameters The K-fold cross-validation method is used to calculate the prediction accuracy index and the multi-objective optimization performance index, namely the Pareto hypervolume, to comprehensively measure the model's generalization ability and multi-objective optimization effect. Based on this, various parameters are adjusted to finally determine the optimal model configuration, providing a reliable evaluation tool for subsequent genetic algorithm optimization.

[0020] S4. The alloy composition is optimized using a multi-objective genetic algorithm on the verified prediction model. Unlike traditional optimization methods that target only a single performance index, this invention takes three aspects as optimization objectives: antioxidant performance, model uncertainty, and process feasibility. It uses the non-dominated sorting genetic algorithm (NSGA-II) to consider all three aspects simultaneously in order to obtain an alloy formulation scheme that performs well in all three dimensions. The steps include: S4.1 Optimization Variables and Encoding Method: Alloy composition content and environmental parameters are encoded as decision variables in the genetic algorithm. Each candidate solution (individual in the genetic algorithm) includes several gene positions, representing the percentage content of each element and optional service temperature, time and other parameters. In this invention, the encoding of an individual includes 14 gene positions corresponding to the percentage content of elements such as Cr and Co, and 2 gene positions corresponding to temperature and time. Each gene is represented by a real number, and its initial value range is set according to metallurgical experience and process specifications. The specific range is shown in S4.2. Because the alloy element content needs to meet the constraint of a total of 100%, the encoding using real numbers is not simply independent; each gene must jointly satisfy the linear constraint condition. To this end, this invention retains nickel as a filler element in the encoding. That is, the Ni content is not directly stored in the individual gene, but is calculated through the gene values ​​of other elements. After the other element genes are assigned values, the Ni content is set as the remainder, thereby ensuring that the total is always equal to 100%. This strategy effectively reduces dimensionality and naturally satisfies the composition constraint. S4.2 Initial Population Generation and Boundary Pruning: An initial population is randomly generated, ensuring that the element content of each individual is randomly selected within a preset reasonable range and satisfies necessary element combination restrictions. The content ranges of the main elements are set as follows: Ni (40%–70%), Cr (15%–21%), Co (10%–16%), Mo (1%–5%), W (0%–10%), Al (1%–5%), Ti (0%–3%), Fe (0%–5%), Nb (0%–3%). Other trace elements are set to fixed constants or a narrow range. When generating the initial individuals, each non-Ni element is first randomly assigned a value according to the above range, and then the Ni balance is calculated to meet the overall requirements. If the initial value of the main element exceeds the range, a main element trimming step is performed. The trimming step cuts off the excess content of the element to the minimum or maximum allowed value. After trimming, the Ni content is readjusted. After trimming and normalization, it is also necessary to check whether the metallurgical constraints of specific element combinations are met. For example, ensure that the Ni matrix element is not less than 50%, the total amount of strengthening phase forming elements does not exceed 10% (Al, Nb, Ta), and the total amount of refractory elements does not exceed 8% (W, Mo, Ta, Nb). If an individual violates these basic constraints, the individual is discarded or the corresponding gene is adjusted until it meets the requirements. Through the above measures, the population obtained after initialization is a metallurgically feasible alloy formulation. S4.3 Fitness Evaluation and Multi-Objective Computation: Define the objective function of the genetic algorithm to evaluate the performance of each individual on multiple objectives, including: For each individual in the population, its alloy composition and environmental parameters are used as inputs. After undergoing the same feature preprocessing as in the model training phase, the data is input into a pre-trained hybrid kernel regression model to predict the oxidation weight gain of the candidate formulation under corresponding conditions. This is the primary optimization objective, which needs to be minimized, in line with the common sense that better antioxidant performance results in less weight gain. Meanwhile, to quantify the uncertainty of the model predictions, an uncertainty measure can be introduced as a secondary objective for each prediction result. For example, the prediction bias can be estimated using the model's residual distribution or by introducing an auxiliary Gaussian process, thus obtaining the standard deviation or confidence interval width of the candidate formulation's predicted value. It is used as an indicator of uncertainty, with the goal of minimizing it. ; Third, define a constraint breach metric or feasibility score for the process feasibility objective. Specifically, a penalty function can be calculated based on the key metallurgical parameters of the formulation. This function is defined as the prediction of the solidus (T_solidus) and dissolution temperature (T_solvus) according to the model's heat treatment characteristic temperatures. If a formulation causes the predicted T_solvus to be significantly higher than T_solidus or deviate from the empirical safe range, a larger penalty value is assigned; otherwise, the penalty is zero. Similarly, whether or not prior constraints are violated—namely, the aforementioned lower limit for Ni content and upper limits for Al and Ti—is converted into an accumulation of penalty scores. A higher penalty value indicates greater difficulty in process implementation or worse material stability. We define the process feasibility objective as minimizing this value. ; In summary, each individual corresponds to three target values. This genetic algorithm aims to reduce these three values ​​simultaneously. S4.4 Non-dominated sorting selection: This invention uses the NSGA-II algorithm to perform selection operations under multiple objectives. Unlike single-objective genetic algorithms, NSGA-II classifies individuals in the population through non-dominated sorting. First, the current population is divided into several Pareto Fronts according to the Pareto dominance relationship: the first front contains non-dominated solutions in the population that are not inferior to other individuals in any objective; the second front is a new set of non-dominated solutions formed after removing individuals from the first front; and so on. The algorithm prioritizes retaining individuals located at the higher fronts because these individuals do not have a significant disadvantage in any objective. Then, within each front, individuals are sorted according to the crowding distance to maintain the diversity of the solution set. Specifically, the sum of neighborhood distances of each individual in each target dimension of the current frontier is calculated. Individuals with larger distances indicate that their region is sparse and contributes to diversity, and will be given a higher retention priority. Finally, based on the non-dominance level and crowding distance, the population is selected through tournament selection or direct optimal replication to generate parent candidates for the next generation of genetic algorithms. S4.5 Crossover and Mutation: After the selection operation generates a new generation of parents, the parents are reproduced, i.e., crossover and mutation, in order to explore a wider solution space; The crossover operation is performed according to the set crossover probability. This invention adopts single-point crossover: two chromosomes (alloy formula individuals) are randomly selected as parents, and the latter half of the gene is cut and exchanged at a random position in their gene string to generate two new offspring individuals; if the random crossover is not triggered, the offspring are direct copies of the parents; for each offspring, its alloy element part is immediately normalized and the boundary is trimmed, the Ni content is recalculated to ensure that the total is 100%, and it is checked whether it meets the constraints of each element. If there is a violation, the gene is corrected or the offspring is discarded. The mutation process then proceeds: the genes of individuals in the population are scanned bit by bit at a preset mutation rate, and each bit is perturbed with a certain probability. For element content genes, mutation can be achieved by randomly changing its value to another legal value within the allowable range of the corresponding element; for environmental genes such as temperature and time, the value is randomly changed to another value within the range; after each mutation, the alloy composition needs to be renormalized and the validity of the constraints needs to be verified; if the mutation causes an individual to no longer meet the constraints, the mutation is discarded and the original individual before the mutation is retained; by introducing new combinations through crossover, introducing random perturbations through mutation, and combining this with the pruning correction mechanism after each reproduction, the diversity of the population can be guaranteed while limiting the search to the physically feasible area; S4.6 Iterative Evolution and Termination: After completing one round of selection, crossover, and mutation operations, the next generation of the population is generated. The algorithm repeats steps S4.3-S4.5 to continuously evolve the population. At the end of each generation iteration, the solution set in the current population and its distribution in the target space are recorded. As the number of generations increases, the multi-objective genetic algorithm will gradually approach the Pareto optimal front. On the one hand, the performance of the first front individuals in each generation on the three objectives will tend to improve. On the other hand, the distribution of solutions within the first front in the target space will become more diversified, thereby comprehensively exploring the trade-off between performance, uncertainty, and process feasibility. The algorithm can be set to terminate by reaching a predetermined maximum number of generations or by the Pareto front no longer showing significant improvement. When the termination condition is met, the algorithm outputs the final non-dominated solution set, which is the Pareto optimal alloy formulation set. These formulations represent the optimal solutions with different trade-offs. For example, some formulations focus on extremely low oxidation weight gain but sacrifice a certain process margin, while others achieve higher reliability and machinability with slightly higher weight gain. Decision-makers can select a suitable alloy design scheme from the Pareto solution set according to actual needs.

[0021] S5. In order to quantitatively evaluate the overall effect of multi-objective optimization, hypervolume (HV) is introduced for evaluation. The hypervolume index is defined as: the size of the target space dominated by the Pareto front, given a reference point. The reference point is generally selected as the coordinates of the maximum acceptable values ​​for each target. In this invention, a reference point is used. The maximum tolerable levels for oxidation weight gain, uncertainty, and penalty value are represented. Then, the multidimensional volume enclosed between the reference point and the Pareto front is calculated. The larger the HV value, the larger the volume covered by the Pareto solution set towards the ideal small objective value, which means the better the overall optimization result. Since directly calculating the hypervolume of complex shapes in three-dimensional space can be difficult, this invention employs a hypervolume approximation method based on a genetic algorithm to estimate the HV value. Specifically, under the premise of a fixed reference point, a small-scale genetic algorithm is designed for the current Pareto solution set to optimize using the HV value as fitness. This genetic algorithm-based hypervolume approximation method attempts to fill more volumes dominated by Pareto solutions in the target space, and its peak fitness value is the approximate estimated hypervolume. This method can calculate the HV index efficiently while maintaining accuracy. By comparing the HV values ​​of the Pareto front obtained under different model parameters or algorithm settings, the performance of the method in multi-objective optimization can be intuitively measured. For example, in experimental testing, different quantum kernel weights were used to calculate the HV value. and the number of anchor points The combination underwent multiple optimization runs, and the resulting HV indices were statistically analyzed. The results showed that appropriate quantum feature fusion (such as...) ) and a sufficient number of anchor points (such as This configuration significantly improves the hypervolume of the Pareto frontier, indicating that the model achieves the best balance between performance and feasibility.

[0022] It should be noted that the above are merely preferred embodiments of this application and do not limit the scope of patent protection of this application. Any equivalent structural or procedural changes made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of this application.

Claims

1. A method for designing and optimizing the composition of nickel-based superalloys based on quantum machine learning, characterized in that, Includes the following steps: S1. Construct a dataset containing the composition, oxidation environment conditions, and oxidation resistance of nickel-based superalloys, and perform preprocessing operations on the dataset; S2. Based on the preprocessed data and quantum computing framework, a quantum feature mapping circuit is designed to extract the high-dimensional nonlinear features of alloy composition and environmental parameters, and to obtain a hybrid kernel function. The hybrid kernel function is a weighted function of the quantum kernel function and the environmental kernel function; The quantum kernel is obtained through feature dimensionality reduction, quantum feature encoding, quantum kernel construction, and Nyström sparse approximation operation; S3. Train and validate the obtained hybrid function kernel; S4. The multi-objective genetic algorithm is used to optimize the alloy composition of the verified prediction model, and the design of the nickel-based high-temperature alloy composition design and optimization method is completed. The optimization objectives of the multi-objective genetic algorithm are: antioxidant performance, model uncertainty, and process feasibility; S5. In order to quantitatively evaluate the overall effect of multi-objective optimization, hypervolume is introduced for evaluation.

2. The method for designing and optimizing the composition of nickel-based superalloys based on quantum machine learning according to claim 1, characterized in that, In S1, the nickel-based superalloy composition elements include: Ni, Cr, Co, Mo, W, Al, Ti, Fe, Nb, C, Hf, Si, Mn, Zr, and Ta; the oxidation environment parameters include temperature and time; the oxidation resistance result is the oxidation weight gain of the alloy under preset temperature and time conditions; the preprocessing operation includes: data cleaning, missing and outlier handling, and normalization.

3. The method for designing and optimizing the composition of nickel-based superalloys based on quantum machine learning according to claim 1, characterized in that, The steps in S2 include: S2.1 Each input feature after dimensionality reduction is encoded into the initial state of a quantum bit; S2.2 Calculate the similarity between quantum states obtained by mapping any two sets of input features using the fidelity metric quantum kernel function; The calculation method is as follows: the Fidelity Quantum Kernel method provided by the quantum machine learning framework is used, and the kernel function value is defined based on the Fidelity of the quantum state; for two different input samples... and Their corresponding quantum states are respectively and The quantum kernel function is defined as the fidelity between two quantum states, and its expression is as follows: In the formula, Represents a kernel function based on quantum characteristics; where the inner product... Represents the first state With the second state The overlap magnitude, the squared value represents the fidelity of the two quantum states; S2.

3. Introduce the Nyström approximation method to sparsify the quantum kernel; The sparsity reduction method is as follows: randomly sample some data points using the Nyström method as anchor points to approximately reconstruct the complete kernel matrix; S2.

4. The similarity of environmental features is measured using the classical radial basis function kernel (RBF), resulting in the environmental kernel, expressed as follows: In the formula, Represents a radial basis function kernel (RBF) based on environmental characteristics; The parameter representing the width of the RBF core; The Euclidean distance between environmental feature vectors is represented by: The two-dimensional vectors composed of temperature and oxidation time are denoted as: and ; S2.

5. Construct a hybrid kernel function by linearly combining the quantum kernel and the environment kernel according to certain weights, as shown in the following expression: In the formula, Represents a mixture function; This represents the fusion coefficient.

4. The method for designing and optimizing the composition of nickel-based superalloys based on quantum machine learning according to claim 3, characterized in that, The step of encoding each input feature after dimensionality reduction onto an initial state of a qubit includes: S2.1.1 In order to balance the contradiction between limited quantum bit resources and high feature dimension, principal component analysis (PCA) is first applied to the alloy composition characteristics for dimensionality reduction. That is, the 15 elemental components are combined in a pairwise orthogonal manner and the variance of each combination is calculated. The top 8 combinations with the highest variance are retained. In addition, 2 quantum bits are selected to encode environmental features, namely temperature and time. S2.1.2 Construct a parameterized quantum circuit for each qubit, mapping classical eigenvalues ​​to quantum state amplitude or phase; The construction method is as follows: for the first Each feature is used to apply a rotation gate to the corresponding qubit, and the rotation angle is controlled by the value of the feature. After all features are encoded, entanglement gates can also be applied between two or more qubits to capture the interaction between features. S2.1.3 After constructing the quantum feature mapping circuit, each set of input features is mapped to a state in the quantum Hilbert space. .

5. The method for designing and optimizing the composition of nickel-based superalloys based on quantum machine learning according to claim 1, characterized in that, In S3, the training method is as follows: based on the mixture function kernel, the kernel ridge regression algorithm KRR is used, the mixture kernel matrix is ​​used as the kernel function of the model, and the double dual coefficients are solved by adding a preset regularization term to the kernel matrix to achieve fitting of the training data. The verification method is as follows: K-fold cross-validation is used to calculate the prediction accuracy index to evaluate the model performance and select the optimal combination of hyperparameters and quantum kernel weights. Number of anchor points RBF kernel parameters .

6. The method for designing and optimizing the composition of nickel-based superalloys based on quantum machine learning according to claim 1, characterized in that, The steps in S4 include: S4.

1. The alloy composition content and environmental parameters are encoded as decision variables of the genetic algorithm. Each candidate solution contains 14 gene positions corresponding to the percentage of Cr, Co, Mo, W, Al, Ti, Fe, Nb, C, Hf, Si, Mn, Zr and Ta, and 2 gene positions corresponding to temperature and time. Constraints are set based on real number encoding: the Ni content is obtained by subtracting the remaining elements from 100%; S4.

2. Randomly generate an initial population, with the element content range of each individual being: Cr: 15%–21%, Co: 10%–16%, Mo: 1%–5%, W: 0%–10%, Al: 1%–5%, Ti: 0%–3%, Fe: 0%–5%, and Nb: 0%–3%, with the remaining trace elements set to preset fixed constants; When generating the initial individual, each non-Ni element is randomly assigned a value according to the range, and then the Ni balance is calculated to ensure that the total is 100%. If the initial value of the main element exceeds the range, the main element trimming step is performed. The trimming step cuts off the excess content of the element to the minimum or maximum allowed value. After trimming, the Ni content is readjusted. After trimming and normalization, it is also necessary to check whether the metallurgical constraints of the specific element combination are met, including: ensuring that the Ni matrix element is not less than 50%, the total amount of strengthening phase forming elements does not exceed 10%, the strengthening phase forming elements are: Al, Nb and Ta, the total amount of refractory elements does not exceed 8%, the refractory elements are: W, Mo, Ta and Nb. If an individual violates these basic constraints, the individual is discarded. S4.3 Fitness Evaluation and Multi-Objective Computation: Define the objective function of the genetic algorithm to evaluate the performance of each individual on multiple objectives; Each individual corresponds to three target values. The genetic algorithm is used to minimize the three target values. S4.4 Using the NSGA-II algorithm to perform selection operations in multi-objective scenarios; S4.5 After the selection operation generates a new generation of parents, crossover and mutation operations are performed on the parents to explore a wider solution space. S4.6 After completing one round of selection, crossover and mutation operations, the next generation of population is generated. The algorithm repeats the process of steps S4.3-S4.5 to continuously evolve the population. At the end of each iteration, the solution set in the current population and its distribution in the target space are recorded. The termination condition set by the algorithm can be reaching a predetermined maximum number of generations.

7. The method for designing and optimizing the composition of nickel-based superalloys based on quantum machine learning according to claim 1, characterized in that, In S5, a hypervolume approximation calculation method based on a genetic algorithm is used to estimate the hypervolume HV value.

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