A tungsten-energetic high-entropy alloy mechanical and combustion performance synergistic prediction and multi-objective optimization method and product

Abstract

The application discloses a tungsten-energetic high-entropy alloy mechanical and combustion performance synergistic prediction and multi-objective optimization method and product, relates to the technical field of material informatics and energetic structural material design, and comprises the following steps: obtaining a base chemical composition to be optimized, a tungsten particle volume fraction and preparation process parameters, and calculating a combustion activity index, a d electron concentration and a system oxygen affinity difference; inputting the above parameters and calculation results into an input feature vector, respectively inputting four models in a pre-trained support vector regression model group, and obtaining prediction values of tensile strength, elongation after fracture, ignition delay time and combustion speed; taking the prediction values as a target function, searching for a Pareto optimal solution set by using a multi-objective evolutionary algorithm, and optimizing the target to maximize the tensile strength, minimize the deviation of the elongation after fracture from the target value, minimize the ignition delay time and maximize the combustion speed. The application can simultaneously predict the mechanical and combustion performances, and solves the multi-objective optimization problem of the strength-burning speed trade-off.

Description

Technical Field

[0001] This application relates to the fields of materials informatics and energetic structural materials design technology, and in particular to a method and product for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys. Background Technology

[0002] Machine learning technology has been widely applied in the field of alloy material design, forming a relatively mature technical process. The mainstream approach in this field involves building independent prediction models for single properties, such as using support vector machines, random forests, or neural networks to predict the yield strength, hardness, or corrosion resistance of alloys. These methods are primarily geared towards structural material design, and their typical workflow includes five steps: first, collecting experimental data to build a database; second, calculating physical descriptors based on alloy composition as input features for the model; third, using correlation analysis and other methods for feature selection and dimensionality reduction; fourth, training a single machine learning model to predict the target performance; and finally, verifying the model's accuracy through experiments. Existing technologies mainly focus on the performance prediction of explosives and propellants, especially for novel materials like tungsten-high-entropy alloys, where mature machine learning design methods are still lacking.

[0003] Existing technologies primarily predict the mechanical properties (such as strength and hardness) or physical properties (such as corrosion resistance) of structural materials, neglecting performance indicators involving complex physicochemical processes, such as combustion performance. Current methods typically construct separate prediction models for each performance indicator, such as separate strength and hardness models, with each model trained and optimized independently, lacking a unified prediction framework. For materials like tungsten-energetic high-entropy alloys, which require simultaneous optimization of four performance indicators, independent modeling leads to fragmented computational processes, low efficiency, and an inability to leverage the physical correlations between different performance indicators to improve prediction accuracy. Existing general physical descriptors are mainly designed for structural stability and cannot effectively characterize the thermodynamic driving forces and kinetic characteristics of combustion reactions. While existing optimization techniques have applications in structural materials, energetic structural materials face a unique "strength-burning rate tradeoff": increasing tungsten improves strength but reduces combustion activity, while increasing aluminum increases burning rate but sacrifices strength. This multi-objective conflict is particularly prominent in energetic structural materials, and existing methods have not established a systematic optimization process to address this issue, especially lacking quantitative guidance for the synergistic optimization of combustion activity and mechanical properties. Summary of the Invention

[0004] The purpose of this application is to provide a method and product for the synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys, which can simultaneously predict mechanical and combustion properties and solve the multi-objective optimization problem of the trade-off between mechanical and combustion properties.

[0005] To achieve the above objectives, this application provides the following solution: Firstly, this application provides a method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys, including: Obtain the matrix chemical composition, tungsten particle volume fraction, and preparation process parameters of the tungsten-energetic high-entropy alloy to be optimized; Based on the matrix chemical composition and the tungsten particle volume fraction, the combustion activity index, d-electron concentration, and oxygen affinity difference of the tungsten-energetic high-entropy alloy to be optimized are calculated. The combustion activity index, the d-electron concentration, the oxygen affinity difference of the system, the matrix chemical composition, the tungsten particle volume fraction, and the preparation process parameters are used to form an input feature vector. The combustion activity index is used to characterize the relative content of active elements and refractory elements to reflect the chemical activity of the alloy, the d-electron concentration is used to characterize the valence electron structure strength, and the oxygen affinity difference of the system is used to characterize the thermodynamic driving force of the oxidation reaction. The input feature vectors are respectively input into four models in the pre-trained support vector regression model group to simultaneously obtain predicted values ​​of tensile strength, elongation after fracture, ignition delay time, and combustion rate. The support vector regression model group includes four independent support vector regression models. The four independent support vector regression models are used to predict tensile strength, elongation after fracture, ignition delay time, and combustion rate, respectively. Each support vector regression model shares the same input feature space and uses a radial basis function as the kernel function. Using the predicted value as the objective function value for multi-objective optimization, a multi-objective evolutionary algorithm is used to search within the design space defined by the matrix chemical composition, tungsten particle volume fraction, and preparation process parameters. The multi-objective optimization aims to maximize tensile strength, minimize the deviation of elongation after fracture from the target value, minimize ignition delay time, and maximize combustion rate. The output is a Pareto optimal solution set for balancing mechanical properties and combustion performance.

[0006] In a second aspect, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys as described above.

[0007] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys described above.

[0008] Fourthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys as described above.

[0009] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides a method and product for the synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys. This application achieves, for the first time, the simultaneous prediction of combustion and mechanical properties of energetic structural materials, filling a gap in machine learning prediction of combustion performance. By constructing a dedicated physical descriptor system including combustion activity index, d-electron concentration, and system oxygen affinity difference, the thermodynamic driving force of combustion reaction and valence electron structure strength are incorporated into the feature space. This allows the support vector regression model to effectively capture the nonlinear mapping relationship between combustion performance and composition / processing. For the first time, quantitative prediction of ignition delay time and combustion rate is achieved, solving the technical problem that existing technologies cannot predict the combustion performance of energetic structural materials. This application establishes a unified computational framework for the synergistic prediction of mechanical and combustion properties, significantly improving the efficiency of multi-performance design. It employs four independent but shared input feature space support vector regression models, and through a parallel prediction strategy, simultaneously outputs predicted values ​​for four key performance indicators: tensile strength, elongation after fracture, ignition delay time, and combustion rate. This avoids repetitive feature engineering and data processing work, achieving synergistic prediction of multiple properties while ensuring the independent optimization accuracy of each model, greatly improving the design efficiency of energetic structural materials. This application constructs an integrated "prediction-optimization" design closed loop, specifically addressing the unique multi-objective conflict problem of "strength-burning rate trade-off" in energetic structural materials. Using a pre-trained support vector regression model set as the fitness function, a multi-objective evolutionary algorithm is employed to maximize tensile strength, minimize the deviation of elongation at break from the target value, minimize ignition delay time, and maximize combustion rate as optimization objectives. It searches for Pareto optimal solutions in the composition-process design space, providing designers with a series of uncompromising optimal composition-process combinations. This achieves quantitative synergistic optimization of high strength and high combustion activity, filling the gap in multi-objective optimization design for energetic structural materials. This application develops a dedicated physical descriptor, establishing a quantitative correlation between composition and performance, enhancing the model's interpretability and extrapolation capability. It is the first to propose a combustion activity index (characterizing the relative content of active and refractory elements) and a system oxygen affinity difference (characterizing the driving force of oxidation reactions based on the electronegativity difference between elements and oxygen). Combined with d-electron concentration (characterizing the strength of valence electron structure and metallic bonding force), a complete descriptor system from composition to combustion and mechanical properties is established. These descriptors have clear physical meanings, which makes model predictions not only dependent on data fitting, but also have a physical theoretical basis, significantly enhancing the extrapolation ability and interpretability of the model, and providing new theoretical tools for the intelligent design of energetic high-entropy alloys. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 This is an application environment diagram of a method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of a tungsten-energetic high-entropy alloy according to an embodiment of this application; Figure 2 A flowchart illustrating a method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys, provided in an embodiment of this application; Figure 3 A schematic diagram illustrating the prediction accuracy of support vector regression according to an embodiment of this application; Figure 4 A schematic diagram of SHAP interpretability analysis results provided in an embodiment of this application; Figure 5 A schematic diagram showing the order of importance of post-fracture elongation characteristics according to an embodiment of this application; Figure 6 This is a partial illustration of the tensile strength of a single sample provided in an embodiment of this application; Figure 7 This is a three-dimensional visualization diagram of Pareto optimality obtained by NSGA-II multi-objective optimization according to an embodiment of this application; Figure 8 This is a schematic diagram illustrating the overall steps of a method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys, provided in an embodiment of this application. Figure 9 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0012] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0013] This application belongs to the field of materials informatics and energetic structural materials design technology, and relates to the application of machine learning technology in alloy material design. Specifically, it relates to a method for synergistic prediction and multi-objective optimization design of mechanical and combustion properties of tungsten-energetic high-entropy alloys based on support vector regression.

[0014] Energetic structural materials with a certain kinetic energy need to simultaneously meet two functional requirements when acting on a target: firstly, sufficient structural strength to ensure integrity during the action; and secondly, the ability to undergo a violent combustion reaction after the action to release a large amount of energy and enhance the destructive effect. Traditional single materials struggle to simultaneously meet these seemingly contradictory requirements—structural materials prioritize high strength and high stability, while energetic structural materials prioritize high reactivity and rapid energy release. Tungsten-energetic high-entropy alloys are a new type of energetic structural material developed in recent years. They are composed of high-density, high-melting-point tungsten particles as the reinforcing phase, combined with highly reactive high-entropy alloys such as Ti-Zr-V-Nb-Al as the matrix phase, possessing both high density (>12 g / cm³) and high energy density (>12 g / cm³). 3 With its characteristics of high strength (>800 MPa) and high combustion activity (rapid ignition and intense combustion), it has important application value in military and aerospace fields such as energetic structural components and space debris protection.

[0015] However, the design of tungsten-energetic high-entropy alloys faces significant challenges. These materials require simultaneous optimization of four key properties: tensile strength (ensuring structural integrity), elongation after fracture (avoiding premature failure and ensuring complete breakage after impact), ignition delay time (achieving rapid response), and combustion rate (fully releasing energy). These properties are inherently conflicting: increasing tungsten content improves density and strength but reduces combustion activity; increasing the content of active elements such as aluminum and titanium increases combustion rate and reduces ignition delay but sacrifices strength and density. Traditional trial-and-error methods require extensive experimental screening in multi-component space and high-dimensional process parameter space, resulting in high costs, long cycles, and difficulty in finding the optimal balance between strength and combustion activity. Therefore, the development of efficient intelligent material design methods is urgently needed.

[0016] The main shortcomings of existing technologies are as follows: First, there is a lack of machine learning methods for predicting combustion performance. Existing technologies mainly predict the mechanical properties (such as strength and hardness) or physical properties (such as corrosion resistance) of structural materials, and have not yet addressed performance indicators such as combustion performance, which involve complex physicochemical processes. Combustion performance is fundamentally different from mechanical performance: mechanical properties mainly depend on the microstructure and crystal structure of the material, while combustion performance involves multi-physics coupling processes such as oxidation reaction kinetics, heat transfer, and product diffusion, exhibiting stronger nonlinear characteristics, and cannot be directly applied to existing prediction models.

[0017] Second, there is a lack of an efficient computational framework for simultaneously predicting mechanical and combustion properties. Existing methods typically construct separate prediction models for each performance index, such as establishing separate strength and hardness models. Each model is trained and optimized independently, without establishing a unified prediction framework. For materials like tungsten-energetic high-entropy alloys, which require simultaneous optimization of four performance indices (tensile strength, elongation after fracture, ignition delay time, and combustion rate), independent modeling leads to fragmented computational processes, low efficiency, and an inability to utilize the physical correlation information between different performance indices (such as the strength-plasticity tradeoff and the ignition-combustion coupling relationship) to improve prediction accuracy.

[0018] Third, there is a lack of quantitative descriptors for the combustion mechanisms of energetic structural materials. Existing general physical descriptors (such as enthalpy of mixing, valence electron concentration, and atomic size difference) are mainly designed for structural stability and cannot effectively characterize the thermodynamic driving force and kinetic characteristics of combustion reactions. For example, traditional valence electron concentration (VEC) is mainly used to predict crystal structure stability and cannot reflect the reactivity of elements with oxygen; enthalpy of mixing (ΔH) mix It primarily characterizes alloying ability but cannot depict the exothermic oxidation process. This results in a lack of physical basis for combustion performance prediction and poor model extrapolation ability.

[0019] Fourth, there is a lack of multi-objective optimization design methods for energetic structural materials. While existing optimization techniques have applications in structural materials, energetic structural materials face a unique "strength-burning rate trade-off"—increasing tungsten improves strength but reduces combustion activity, while increasing aluminum increases burning rate but sacrifices strength. This multi-objective conflict is particularly prominent in energetic structural materials, and existing methods have not established a systematic optimization process to address this issue, especially lacking quantitative guidance for the synergistic optimization of combustion activity and mechanical properties.

[0020] This application employs support vector regression to establish prediction models for mechanical and combustion performance, and achieves collaborative prediction through shared feature engineering and hyperparameter optimization processes. It develops dedicated physical descriptors such as the combustion activity index and establishes a complete design closed loop from performance prediction to multi-objective optimization. It has the advantages of high prediction accuracy, strong interpretability, and high design efficiency, and has important practical significance for the rapid development of tungsten-energetic high-entropy alloys.

[0021] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0022] The method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys provided in this application embodiment can be applied to, for example... Figure 1In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be set up independently, integrated into server 104, or placed in the cloud or on other servers.

[0023] The terminal 102 can be, but is not limited to, various desktop computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can include smart speakers, smart TVs, smart air conditioners, and smart in-vehicle devices. Portable wearable devices can include smartwatches, smart bracelets, and head-mounted devices. The server 104 can be implemented using a standalone server or a server cluster composed of multiple servers, or it can be a cloud server.

[0024] In one exemplary embodiment, such as Figure 2 As shown, a method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys is provided. This method is executed by computer equipment, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is applied to... Figure 1 Taking server 104 as an example, the explanation includes the following steps S1 to S5. Wherein: S1. Obtain the matrix chemical composition, tungsten particle volume fraction, and preparation process parameters of the tungsten-energetic high-entropy alloy to be optimized.

[0025] S2. Based on the matrix chemical composition and the tungsten particle volume fraction, calculate the combustion activity index, d-electron concentration, and oxygen affinity difference of the tungsten-energetic high-entropy alloy to be optimized.

[0026] S3. The combustion activity index, the d-electron concentration, the oxygen affinity difference of the system, the matrix chemical composition, the tungsten particle volume fraction, and the preparation process parameters are combined to form an input feature vector; wherein, the combustion activity index is used to characterize the relative content of active elements and refractory elements to reflect the chemical activity of the alloy, the d-electron concentration is used to characterize the valence electron structure strength, and the oxygen affinity difference of the system is used to characterize the thermodynamic driving force of the oxidation reaction.

[0027] S4. Input the input feature vector into the four models in the pre-trained support vector regression model group to simultaneously obtain the predicted values ​​of tensile strength, elongation after fracture, ignition delay time, and combustion rate. The support vector regression model group includes four independent support vector regression models. The four independent support vector regression models are used to predict tensile strength, elongation after fracture, ignition delay time, and combustion rate, respectively. Each support vector regression model shares the same input feature space and uses the radial basis function as the kernel function.

[0028] S5. Using the predicted value as the objective function value for multi-objective optimization, a multi-objective evolutionary algorithm is used to search within the design space defined by the matrix chemical composition, tungsten particle volume fraction, and preparation process parameters. The multi-objective optimization aims to maximize tensile strength, minimize the deviation between the elongation after fracture and the target value, minimize the ignition delay time, and maximize the combustion rate. The Pareto optimal solution set is output to balance mechanical properties and combustion performance.

[0029] This application achieves, for the first time, the simultaneous prediction of combustion and mechanical properties of energetic structural materials, filling a gap in machine learning prediction of combustion performance. By constructing a dedicated physical descriptor system including combustion activity index, d-electron concentration, and system oxygen affinity difference, the thermodynamic driving force of combustion reaction and valence electron structure strength are incorporated into the feature space. This enables the support vector regression model to effectively capture the nonlinear mapping relationship between combustion performance and composition / processing. For the first time, quantitative prediction of ignition delay time and combustion rate is achieved, solving the technical challenge of predicting the combustion performance of energetic structural materials in existing technologies. This application establishes a unified computational framework for the collaborative prediction of mechanical and combustion properties, significantly improving the efficiency of multi-performance design. It employs four independent but shared input feature space support vector regression models, using a parallel prediction strategy to simultaneously output predicted values ​​for four key performance indicators: tensile strength, elongation after fracture, ignition delay time, and combustion rate. This avoids repetitive feature engineering and data processing, achieving collaborative prediction of multiple properties while ensuring the independent optimization accuracy of each model, thus significantly improving the design efficiency of energetic structural materials. This application constructs an integrated "prediction-optimization" design closed loop, specifically addressing the unique multi-objective conflict problem of "strength-burning rate trade-off" in energetic structural materials. Using a pre-trained support vector regression model set as the fitness function, a multi-objective evolutionary algorithm is employed to maximize tensile strength, minimize the deviation of elongation at break from the target value, minimize ignition delay time, and maximize combustion rate as optimization objectives. It searches for Pareto optimal solutions in the composition-process design space, providing designers with a series of uncompromising optimal composition-process combinations. This achieves quantitative synergistic optimization of high strength and high combustion activity, filling the gap in multi-objective optimization design for energetic structural materials. This application develops a dedicated physical descriptor, establishing a quantitative correlation between composition and performance, enhancing the model's interpretability and extrapolation capability. It is the first to propose a combustion activity index (characterizing the relative content of active and refractory elements) and a system oxygen affinity difference (characterizing the driving force of oxidation reactions based on the electronegativity difference between elements and oxygen). Combined with d-electron concentration (characterizing the strength of valence electron structure and metallic bonding force), a complete descriptor system from composition to combustion and mechanical properties is established. These descriptors have clear physical meanings, which makes model predictions not only dependent on data fitting, but also have a physical theoretical basis, significantly enhancing the extrapolation ability and interpretability of the model, and providing new theoretical tools for the intelligent design of energetic high-entropy alloys.

[0030] In another exemplary embodiment of this application, the training process of the support vector regression model group includes: Step A1: Construct a tungsten-energetic high-entropy alloy database; the database includes the matrix chemical composition, tungsten particle volume fraction, preparation process parameters, and the corresponding tensile strength, elongation after fracture, ignition delay time, and combustion rate.

[0031] In this embodiment, a tungsten-energetic high-entropy alloy database was constructed. High-throughput experimental methods were used to systematically prepare and test tungsten-energetic high-entropy alloy samples with different compositions. Experimental data including preparation process parameters, matrix chemical composition, tungsten particle volume fraction, mechanical properties, and combustion performance were collected and organized in a unified format.

[0032] The tungsten-energetic high-entropy alloy is a tungsten particle-reinforced Ti-Zr-V-Nb-Al-W high-entropy alloy matrix composite material, wherein the matrix chemical composition satisfies Ti+Zr+V+Nb+Al+W=100 at.%, and the tungsten particle volume fraction is 0-80 vol.%. The preparation process parameters include laser power (W), printing laser scanning speed (mm / min), and heat treatment temperature (°C), covering the key process window of laser instantaneous liquid phase sintering technology. The mechanical properties include tensile strength (MPa) and elongation after fracture (%), and the combustion properties include ignition delay time (s) and average volumetric combustion rate (mm). 3 / s).

[0033] Step A2: Based on the matrix chemical composition and tungsten particle volume fraction in the database, calculate the combustion activity index, d-electron concentration, and system oxygen affinity difference to obtain training calculation parameters.

[0034] In this embodiment, feature engineering is performed to calculate the combustion activity index, d-electron concentration, and oxygen affinity difference based on the alloy composition (in this embodiment, the matrix chemical composition and tungsten particle volume fraction) to construct a high-dimensional feature set.

[0035] The calculation formula and physical meaning of the dedicated physical descriptor are as follows: (1) Burning Activity Index (BAI): In the formula, Indicates the combustion activity index, , , , The values ​​represent the atomic percentages (at.%) of Ti, Zr, V, Al, W, and Nb in the matrix of the tungsten-energetic high-entropy alloy to be optimized. The equivalent atomic percentage of tungsten particles is obtained by conversion using the number of atoms, density, and relative molecular mass: In the formula, The volume fraction of tungsten particles (vol.%). =19.25 g / cm 3 , =183.84 g / mol, which are the density and molar mass of tungsten, respectively. and These are the density and average molar mass of the base alloy, respectively, obtained through weighted calculation of the base composition.

[0036] The combustion activity index (BAI) represents the relative content of active elements (Ti, Zr, V, Al) and refractory elements (W, Nb), reflecting the overall chemical activity of the alloy. This index is the first quantitative characterization parameter proposed for the combustion activity of energetic high-entropy alloys, established based on the high-temperature oxidation reaction mechanism: active elements have a high affinity for oxygen, promoting rapid exothermic oxidation; refractory elements form a dense oxide film, hindering the reaction. A higher BAI value indicates stronger combustion activity, shorter ignition delay time, and faster combustion rate.

[0037] (2) d-electron concentration (Nd): In the formula, Indicates d-electron concentration. Let represent the atomic percentage of the i-th element in the matrix of the tungsten-energetic high-entropy alloy to be optimized. Let be the number of d electrons of the i-th element (the number of d electrons of Ti, Zr, V, Nb, Al and W are 2, 2, 3, 4, 0 and 4, respectively). denoted as d electron number of tungsten.

[0038] The d-electron concentration characterizes the valence electron structure strength of the alloy system and is directly related to the metallic bond strength and lattice stability. d-electrons participate in metallic bonding; the higher their concentration, the stronger the interatomic bonding force, the greater the resistance to dislocation movement, and macroscopically, this manifests as increased tensile strength. Al, as a non-transition metal element, has zero d-electrons, which is consistent with the physical fact that Al mainly plays a role in solid solution softening in alloys and contributes relatively little to strength.

[0039] (3) System Oxygen Affinity Difference ): In the formula, This indicates that the system has poor oxygen affinity. The average oxygen affinity of the active components in the system. The average oxygen affinity of the refractory components in the system. , , , , and Pauling electronegativity differences between Ti, Zr, V, Al, W and Nb and oxygen (Ti: 1.54, Zr: 1.33, V: 1.63, Al: 1.61, Nb: 1.60, W: 0.68).

[0040] The oxygen affinity difference in the system characterizes the thermodynamic driving force of the oxidation reaction, based on Wagner's oxidation theory: the larger the difference, the stronger the affinity of the active component for oxygen relative to the refractory component, the greater the thermodynamic tendency of the oxidation reaction, and the stronger the driving force of the reaction. This descriptor is the first proposed dedicated thermodynamic descriptor for predicting the combustion reactivity of energetic structural materials, and can effectively distinguish the ignition ease and combustion intensity of alloys with different compositions.

[0041] Step A3: Combine the matrix chemical composition, tungsten particle volume fraction, preparation process parameters, and training calculation parameters in the database to form a training feature set.

[0042] This embodiment requires feature selection. Initial redundancy removal is performed using the Pearson correlation coefficient to eliminate parameters with low correlation to the target performance and high collinearity with other features. Then, a deep selection is performed using Recursive Feature Elimination Cross-Validation (RFECV). The optimal feature subset is determined through an iterative training-evaluation-elimination process, balancing model complexity and prediction accuracy. Specifically, this includes: Step A31: Combine the matrix chemical composition, tungsten particle volume fraction, preparation process parameters, and training calculation parameters in the database to form an initial training feature set.

[0043] Step A32: Use the Pearson correlation coefficient method to perform preliminary screening of the initial training feature set to remove redundant features, and obtain the screened feature set.

[0044] The specific method for preliminary screening of Pearson correlation coefficients is as follows: calculate the Pearson correlation coefficients between all pairs of features in the initial training feature set. r ij ,when If a feature is deemed highly correlated, its average correlation coefficient with the performance of the four targets is compared, and the feature with the larger average correlation coefficient is retained.

[0045] For any two input features in the initial training feature set X i and X j Its Pearson correlation coefficient r ij The calculation formula is: In the formula, and Let be the values ​​of the k-th sample on the i-th and j-th features, respectively. and Features X i and X j The sample mean, n The total number of samples, Let covariance be the variance of the two features. These are the standard deviations of the two features, respectively. The value range is [-1, 1]. The closer the absolute value is to 1, the stronger the linear correlation between the two features.

[0046] Step A33: The selected feature set is subjected to deep screening using the recursive feature elimination cross-validation method to obtain the training feature set; the recursive feature elimination cross-validation method uses the average relative error of the five-fold cross-validation of the support vector regression model as the evaluation index, and removes the feature with the lowest SHAP importance in each iteration until the model performance no longer improves or the number of features is reduced to a preset number.

[0047] The specific method of the Recursive Feature Elimination Cross-Validation (RFECV) is as follows: using the average relative error of the five-fold cross-validation of the support vector regression model as the evaluation metric, starting from the complete feature set (i.e., the selected feature set), each iteration removes the features with the lowest SHAP importance, retrains the model, and evaluates its performance until the model performance no longer improves or the performance improvement is less than 0.01 for three consecutive iterations. The final number of features retained is 7-13. RFECV automatically determines the optimal number of features through recursion, avoiding the subjectivity of manually setting the number of features.

[0048] The specific method is as follows: (1) Definition of initial feature set: The complete feature set refers to the selected feature set retained after screening by Pearson correlation coefficient.

[0049] (2) SHAP importance calculation and feature ranking: Before each RFECV iteration, a set of support vector regression models (4 independent SVR models) is trained based on the current feature subset. KernelSHAP is used to calculate the average absolute SHAP value of each feature for the four performance prediction values.

[0050] (3) Training and assessment process: RFECV employs a five-fold hierarchical cross-validation strategy, the specific process of which is as follows: The training set (80% of the data) is divided into 5 subsets. Four subsets are used for training and one subset is used for validation each time. For the current feature subset, four independent SVR models are trained, with the average relative error as the main evaluation metric: Calculate the average MRE of the five-fold cross-validation as the performance score of the current feature subset.

[0051] (4) Recursive elimination and determination of the optimal feature number: RFECV employs an iterative backward feature elimination strategy, the specific process of which is as follows: Round 1: Retrain the support vector regression model group using all d0 features (the selected feature set after filtering by Pearson correlation coefficient), and evaluate the performance using five-fold cross-validation to obtain MRE0; calculate and sort the SHAP values ​​of each feature based on the current model, identify the feature with the lowest importance and remove it, and the remaining d0-1 features constitute the candidate subset.

[0052] Round 2: Retrain the model using d0-1 features (hyperparameter optimization needs to be re-executed), use five-fold cross-validation, evaluate the performance to obtain MRE1; recalculate the SHAP value of each feature in the current subset, remove the feature with the lowest importance, and the remaining d0-2 features constitute the candidate subset.

[0053] Round k (k≥3): Retrain the model using d0-k+1 features, and evaluate the performance to obtain the MRE. k-1 Calculate the SHAP value of each feature in the current subset, remove the feature with the lowest importance, and the remaining d0-k features constitute the candidate subset.

[0054] Iteration termination condition: When three consecutive iterations satisfy the condition... (i.e., performance improvement is less than 1%), or the process stops when the number of features drops to 5.

[0055] Optimal selection: Select the subset with the smallest MRE and the fewest features from the iteration history as the optimal feature set. The final number of features retained is usually 7-13.

[0056] Then, a data preprocessing process is performed, which standardizes the selected feature data (Z-score standardization) to eliminate differences in dimensions; a five-fold stratified cross-validation is used to divide the training set and the test set to ensure the consistency of the distribution of the four target performances in each compromise and to avoid the bias introduced by the data partitioning.

[0057] Step A4: Using the training feature set as input, and tensile strength, elongation at break, ignition delay time, and combustion rate as outputs, respectively, and radial basis function as kernel function, train four independent support vector regression networks to obtain a set of support vector regression models; wherein the four support vector regression networks share the same input feature space. Please refer to [link to relevant documentation]. Figure 3 , Figure 3 To improve the prediction accuracy of support vector regression.

[0058] In this embodiment, the model building process is performed first. Four independent support vector regression (SVR) networks are established using the radial basis function (RBF) as the kernel function, and the networks output four performance indicators: tensile strength, elongation at fracture, ignition delay time, and combustion rate. Collaborative prediction is achieved through a shared input feature space and a parallel training strategy. Each model is independently optimized for specific performance while maintaining the consistency of the overall computational framework.

[0059] The Support Vector Regression (SVR) model was implemented using sklearn.svm.SVR, establishing four independent SVR models (kernel='rbf') corresponding to tensile strength, elongation after fracture, ignition delay time, and combustion rate, respectively. Each model shares the same input feature space but establishes a performance-specific mapping relationship through independent hyperparameter optimization and training processes. Based on the principle of minimizing structural risk, the SVR model constructs sparse solutions by introducing an insensitivity parameter ε, making it suitable for handling small-sample, high-dimensional material data. The RBF kernel function captures the nonlinear relationships between features, where γ controls the kernel width and affects the model's nonlinear fitting ability.

[0060] The input to the four models is the training feature set. The outputs of the four models are tensile strength, elongation at break, ignition delay time, and combustion rate, respectively; each feature corresponds to one model. Sharing the same input features means that the four models use the exact same subset of features (the same feature engineering) and all undergo standardization. The partitioning of the training and test sets, as well as the partitioning of the five-fold cross-validation data, are consistent during model training. Each model has its own kernel function and optimal parameters. The training process is completely independent of the four models, with no correlation between them.

[0061] In this embodiment, the hyperparameter optimization process utilizes grid search combined with five-fold cross-validation to optimize the penalty coefficient C, kernel function coefficient γ, and insensitivity ε for each SVR model. The mean relative error (MRE) is used as the primary evaluation metric to monitor model prediction accuracy, and the coefficient of determination R0 is used as the metric. 2 To assist in evaluating the model's goodness of fit using evaluation metrics, a hierarchical optimization strategy was used to determine the optimal combination of hyperparameters specific to each performance level. Based on the determined optimal hyperparameters, four independent SVR models were retrained on the complete training set (all 80% of the data). The support vectors, weight coefficients, and kernel function parameters of each model were saved to construct the final performance prediction model set, which serves as the basis for interpretability analysis and multi-objective optimization.

[0062] The hyperparameter search range for the grid search is as follows: penalty coefficient C ∈ [0.001, 1000], kernel function coefficient γ ∈ [0.0001, 10], insensitivity ε ∈ [0.001, 10], with several discrete points evenly distributed within each parameter range. A five-fold cross-validation grid search is used to determine the optimal hyperparameter combination. The total number of hyperparameter combinations exceeds 1000. The mean relative error (MRE) is used as the main evaluation index, and the coefficient of determination R0 is used as the metric. 2 To assist in evaluation, the accuracy of each model in predicting corresponding performance was optimized. MRE directly reflects the relative deviation of predicted values ​​and is suitable for assessing the actual error level of material performance prediction; R... 2 It reflects the model's ability to explain data variation and is used to evaluate the model's goodness of fit.

[0063] In another exemplary embodiment of this application, after inputting the input feature vectors into four models in a pre-trained support vector regression model group to simultaneously obtain predicted values ​​for tensile strength, elongation after fracture, ignition delay time, and combustion rate, an interpretability analysis process is also included. This process employs the SHAP (SHapley Additive exPlanations) value analysis framework to calculate the marginal contribution of each feature to each performance prediction value. Key design factors are identified through global feature importance analysis, the mechanism of action of specific components is analyzed through local interpretation, and the nonlinear relationship between composition, process, and performance is revealed through partial dependency graphs, providing physical guidance for material design. This includes the following steps: Step B1: Based on the pre-trained support vector regression model group, the KernelSHAP algorithm is used to calculate the SHAP value of each feature pair predicted in the input feature vector, so as to obtain the SHAP value matrix of each feature on each sample to be optimized; the sample to be optimized is each sample corresponding to the input feature vector.

[0064] Step B2: Based on the SHAP value matrix, calculate the average absolute SHAP value of each feature on all samples to be optimized, and sort them in descending order of numerical value to obtain the feature importance ranking. From the feature importance ranking, identify the top k features that have the greatest impact on tensile strength, elongation after fracture, ignition delay time and combustion rate as the key feature set.

[0065] Step B3: Based on the key feature set, select typical samples from the samples to be optimized, and based on the SHAP value matrix, extract the specific SHAP contribution value of each key feature to the four performance prediction values ​​of the typical samples. Positive values ​​indicate that the key feature drives the prediction value to increase, and negative values ​​indicate that it drives it to decrease, thus obtaining the local interpretation results of the typical samples.

[0066] Step B4: Based on the key feature set, for each key feature in the key feature set, select several observation points evenly within its value range, keeping other features in the input feature vector unchanged, and calculate the arithmetic mean of the predicted values ​​of all samples to be optimized at each observation point based on the corresponding support vector regression models in the pre-trained support vector regression model group. Connect each observation point and its corresponding average predicted value in sequence to draw a partial dependency graph. Identify the performance inflection point and saturation effect by the change in the slope of the curve, and obtain the nonlinear influence law and optimal range of each key feature on mechanical performance and combustion performance.

[0067] The specific methods of SHAP interpretability analysis include: (1) Global feature importance analysis: calculate the average absolute SHAP value of all features on all samples, obtain the feature importance ranking, and identify the key elements and process parameters that have the greatest impact on mechanical properties and combustion performance; (2) Single sample local interpretation: for a specific component sample, calculate the specific contribution of each feature to the four performance prediction values ​​of the sample; (3) Partial dependency graph analysis: fix other features, let the key features change within the range of values, observe the response curve of the prediction values, reveal the nonlinear influence law and optimal range of components and processes on mechanical properties and combustion performance, and identify performance inflection points and saturation effects.

[0068] The specific methods of SHAP interpretability analysis are as follows: (1) Global feature importance analysis: Based on four independent SVR models that have been trained, the KernelSHAP algorithm is used to calculate the Shapley value of each feature in the optimal feature subset retained after recursive feature elimination and cross-validation. For the m-th performance model (m=1,2,3,4 corresponding to tensile strength, elongation after fracture, ignition delay time, and combustion rate, respectively), the global importance of the j-th feature is quantified by the average absolute SHAP value: (see...) Figure 4 , Figure 4 (Figure showing the results of SHAP interpretability analysis) In the formula, N is the total number of samples in the training set. Let be the SHAP value of the j-th feature on the i-th sample in the m-th model. Its calculation is based on Shapley's theory in game theory, estimating the average marginal contribution of this feature among all possible features using a kernel function. Then, sort them in descending order of numerical value to obtain the feature importance ranking for this performance index (see...). Figure 5 The top 3-5 features are identified as the key elements or process parameters that have the greatest impact on the performance.

[0069] (2) Local interpretation of a single sample (see) Figure 6 ): For a specific component sample, calculate the specific contribution of each feature to the four performance prediction values ​​of that sample.

[0070] The “specific component samples” include: ① representative preferred components obtained from Pareto optimality through step 8 NSGA-II optimization; ② typical samples with extreme performance (extremely high intensity or extremely fast burning rate) in the training set; and ③ newly designed components for which the prediction mechanism needs to be explained.

[0071] For a specific sample, the m-th performance prediction value is obtained by linearly superimposing the SHAP values ​​of each feature: In the formula, It is the predicted value of the m-th performance of this sample. It is the baseline value (the average value of the training set predictions, i.e., the output when all features take the baseline value). It is the SHAP value (contribution value) of the j-th feature to the m-th performance prediction of the sample. A positive value indicates that the feature promotes the increase of the prediction value, and a negative value indicates that it promotes the decrease.

[0072] (3) Partial Dependency Graph (PDP) Analysis: Partial Dependency Graph Analysis: By fixing other features and allowing key features to vary within their range, the response curves of the predicted values ​​are observed to reveal the nonlinear influence of composition and process on mechanical and combustion properties and their optimal range, and to identify performance inflection points and saturation effects.

[0073] The “key features” refer to the top 3-5 features that have the greatest impact on each performance identified through global importance analysis, and the “other features” refer to the remaining features other than the key features of the current subset.

[0074] The specific implementation process is as follows: First, a key feature is selected, and a series of observation points are uniformly selected within its value range. For each observation point, keeping other process parameters and compositional characteristics of all alloy samples in the training set unchanged, only the value of the key feature is uniformly replaced with the value of the current observation point. The performance prediction value of all samples at this time is calculated using the trained support vector regression model, and the arithmetic mean is taken. The average prediction values ​​corresponding to each observation point are connected sequentially to obtain a PDP curve reflecting the average response relationship between the feature and the predicted performance. This curve shows the average change trend of the model output as the value of the key feature changes under the background of real sample distribution.

[0075] Inflection point identification: When the slope of the curve changes abruptly from being significantly non-zero to close to zero (or the sign changes), this point is the inflection point, indicating that the impact of this feature on performance has a threshold effect; Saturation effect identification: When the curve gradually becomes horizontal (slope approaches 0) as the feature value increases, it indicates that the performance has entered the saturation region, and further increasing the input of this feature will not significantly improve the performance.

[0076] In another exemplary embodiment of this application, step S5 above can be specifically implemented by the following steps: Multi-objective evolutionary optimization and Pareto optimal search were employed, using a pre-trained support vector regression model set as the fitness function. NSGA-II (Non-dominated sorting genetic algorithm II) was used for multi-objective optimization in the composition-process design space, with the target value for elongation after fracture set within the range of 1%-5%. Constraints included: composition conservation, element content ranges, tungsten particle volume fraction ranges, process parameter ranges, and matrix BCC phase stability constraints. Through non-dominated sorting, crowding calculation, and elite retention strategies, a Pareto optimal composition with high strength, suitable plasticity, and high combustion activity was searched, yielding a series of incompatible optimal solutions for designers to choose from.

[0077] Specifically, such as Figure 7 As shown, the specific settings and optimization objectives of the NSGA-II multi-objective optimization are: population size 100-200, number of iterations 200-500, crossover probability 0.9, and mutation probability 0.1. The optimization objective function is: maximize tensile strength and minimize tensile strength. (deviation from the target plasticity value), minimizing ignition delay time, and maximizing combustion rate, among which... The target elongation after fracture is set within the range of 1%-5% based on specific application requirements. Energetic structural materials require a suitable elongation after fracture (typically 1-5%) to ensure that brittle fracture does not occur during the action, while also enabling sufficient fragmentation after the action. Constraints include: composition conservation ∑c i =100%, elemental content range 10%≤Ti≤70%, 10%≤Zr≤60%, 0%≤V≤15%, 5%≤Nb≤25%, 0%≤Al≤10%, 0%≤W≤10%, tungsten particle volume fraction 0%≤c W_particle ≤80%, process parameters range: laser power 500-2000 W, scanning speed 300-1000 mm / min, heat treatment temperature 500-1500℃, matrix BCC phase stability ΔH mix ∈[-15,5] kJ / mol, δ≤6.6%, 4.5≤VEC≤6.5.

[0078] The specific process is as follows: Element content constraints are verified and normalized. Based on the normalized composition, specific descriptors such as the combustion activity index, d-electron concentration, and oxygen affinity difference are calculated. Process parameters, composition, and descriptors are combined into a feature vector, and the parameters are standardized. These vectors are then input into four independent models to obtain predicted values ​​for tensile strength, elongation at break, ignition delay time, and combustion rate. These predicted values ​​are then converted into objective function values: maximizing tensile strength, minimizing the absolute deviation of elongation at break from the target value, minimizing ignition delay time, and maximizing combustion rate. For violations of composition conservation and element content constraints... Individuals constrained by range, process parameter range, and matrix BCC phase stability are reduced using a penalty function method, where phase stability is verified by mixing enthalpy, atomic size difference, and valence electron concentration. The NSGA-II algorithm evaluates the quality of individuals based on non-dominated sorting and crowding calculation, generates offspring populations through simulated binary crossover and polynomial mutation, generates a new generation population through an elite retention strategy, iterates and evolves to a set number of generations, and outputs a Pareto optimal solution set to obtain the optimal composition-process combination with high strength-suitable plasticity-high combustion activity that balances strength-plasticity-combustion activity.

[0079] The prediction model set obtained by this method is essentially four independent but shared feature space tungsten-energetic high-entropy alloy “composition-process-performance” mapping models: for composition combinations within the range of laser power 500-2000 W, scanning speed 300-1000 mm / min, heat treatment temperature 500-1500℃, Ti atomic percentage 10-70%, Zr atomic percentage 10-60%, V atomic percentage 0-15%, Nb atomic percentage 5-25%, Al atomic percentage 0-10%, W atomic percentage 0-10%, and tungsten particle volume fraction 0-80%, the tensile strength, elongation after fracture, ignition delay time, and combustion rate are predicted respectively. Figures 3-7 Some of the results are shown below.

[0080] The advantages of this embodiment are: (1) Achieving simultaneous prediction of combustion and mechanical properties, significantly improving computational efficiency. In this embodiment, support vector regression is used to establish prediction models for four performance indicators. Through shared feature engineering, unified data preprocessing, and parallel hyperparameter optimization processes, simultaneous prediction of tensile strength, elongation after fracture, ignition delay time, and combustion rate is achieved. Compared with traditional independent modeling methods, this method integrates the training and prediction processes of the four models through a unified computational framework, avoiding repetitive feature selection and data processing. While ensuring independent optimization and specialization of each model, it significantly improves the computational efficiency of multi-performance collaborative prediction, providing effective technical support for high-throughput material design.

[0081] (2) Develop a physical descriptor specific to energetic structural materials and establish a quantitative correlation between composition and performance. In response to the special performance requirements of energetic high-entropy alloys, this embodiment proposes for the first time the combustion activity index (BAI) and the system oxygen affinity difference (Δχ). O These proprietary physical descriptors, such as d-electron concentration, fill the gap in the quantitative characterization of the combustion performance of energetic structural materials. These descriptors effectively characterize the essential features of the combustion reaction from the perspectives of thermodynamic driving forces and elemental activity. Combined with structural descriptors such as d-electron concentration, a complete descriptor system from composition to combustion and mechanical properties is established. This solves the problem that general descriptors cannot predict combustion performance, providing new theoretical tools and physical guidance for the intelligent design of energetic high-entropy alloys.

[0082] In another exemplary embodiment of this application, such as Figure 8 As shown, a method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys is presented. It employs a parallel independent modeling and synergistic optimization strategy, and through thorough analysis of the variation patterns in high-throughput experimental data, achieves high-precision modeling of the "composition-process-performance" of tungsten-energetic high-entropy alloys, which can further guide multi-objective optimization design of the composition. This method is implemented using Python 3.8 and the Scikit-learn 1.0 machine learning library. The method consists of the following steps: Step 1: Tungsten-high-entropy alloy samples with different compositions were systematically prepared using high-throughput experimental methods to construct a database of tungsten-energetic high-entropy alloys. The alloys were tungsten particle-reinforced Ti-Zr-V-Nb-Al-W high-entropy alloy matrix composites, with a matrix composition satisfying Ti+Zr+V+Nb+Al+W=100 at.%, and tungsten particle volume fraction ranging from 0-80 vol.%. Laser instantaneous liquid-phase sintering technology was employed, with a laser power of 500-2000 W, a scanning speed of 300-1000 mm / min, and a heat treatment temperature of 500-1500℃. The alloys were then subjected to room temperature tensile tests (strain rate 10...). -3 s -1 The tensile strength (MPa) and elongation after fracture (%) were obtained, and the ignition delay time (s) and average volumetric combustion rate (mm) were obtained through laser ignition testing. 3 / s). The data is organized into a CSV format database in the order of laser power, scanning speed, heat treatment temperature, heat treatment time, Ti%, Zr%, V%, Nb%, Al%, W%, tungsten particle volume fraction, tensile strength, elongation after fracture, ignition delay time, and combustion rate.

[0083] Step 2: Calculate the specific physical descriptor based on the alloy composition: Combustion Activity Index (BAI), System d-electron concentration (N) d ), poor oxygen affinity of the system (Δχ) OThe initial feature set contains 10 original parameters + 3 dedicated descriptors = 13-dimensional features.

[0084] Step 3: Using the Pearson correlation coefficient method, calculate the pairwise correlation coefficient matrix between the 13 input features and the 4 target performances. Features deemed highly correlated are compared with the average correlation coefficients of the two features and the four target performance metrics, retaining those with higher average correlation coefficients. After removing redundancy, the remaining features are then subjected to RFECV screening. The average R-value of the five-fold cross-validation of the support vector regression model is used. 2 To evaluate the feature set, low-importance features are recursively eliminated to determine the optimal feature subset.

[0085] Step 4: Standardize the selected features (StandardScaler, mean 0, variance 1). Use 5-fold stratified cross-validation to split the training set (80%) and the test set (20%) to ensure consistency in the performance distribution across all trade-offs.

[0086] Step 5: Use sklearn.svm.SVR to build four independent prediction models (kernel='rbf'), corresponding to tensile strength, elongation after fracture, ignition delay time, and combustion rate, respectively. Each model shares the same input feature space, but is trained separately to establish performance-specific mapping relationships, achieving collaborative prediction through parallel computing.

[0087] Step 6: Optimize hyperparameters using GridSearchCV. The search range is: penalty coefficient C ∈ [0.001, 1000] (logarithmically uniform distribution over 50 points), kernel function coefficient γ ∈ [0.0001, 10] (logarithmically uniform distribution over 40 points), insensitivity ϵ ∈ [0.001, 10] (logarithmically uniform distribution over 20 points). Five-fold cross-validation is used, with mean relative error (MRE) as the primary evaluation metric and coefficient of determination R0. 2 To assist in the evaluation of indicators, the optimal combination of hyperparameters for each model was determined.

[0088] Step 7: Use KernelSHAP to calculate the marginal contribution of each feature to the four performance prediction values. Perform global feature importance analysis to identify the key features that have the greatest impact on tensile strength, elongation after fracture, ignition delay time, and combustion rate; perform partial dependency graph analysis to reveal the nonlinear influence of composition and process on mechanical and combustion properties and the optimal range.

[0089] Step 8: NSGA-II multi-objective optimization, setting the population size to 200, the number of iterations to 500, the crossover probability to 0.9, and the mutation probability to 0.1. The optimization objectives are to maximize tensile strength and minimize |elongation after fracture - δ target| (deviation from the target plasticity value), minimize ignition delay time, maximize combustion rate, where δ target The target elongation after fracture is set within the range of 1%-5% based on specific application requirements. Energetic structural materials require a suitable elongation after fracture (typically 1-5%) to ensure that brittle fracture does not occur during the action, while also enabling sufficient fragmentation after the action. Constraints include: composition conservation ∑c i =100%, elemental content range 10%≤Ti≤70%, 10%≤Zr≤60%, 0%≤V≤15%, 5%≤Nb≤25%, 0%≤Al≤10%, 0%≤W≤10%, tungsten particle volume fraction 0%≤c W_particle ≤80%, process parameters range: laser power 500-2000 W, scanning speed 300-1000 mm / min, heat treatment temperature 500-1500℃, matrix BCC phase stability ΔH mix ∈[-15,5]kJ / mol, δ≤6.6%, 4.5≤VEC≤6.5. The Pareto optimal solution set was obtained, providing guidance for composition-process design in experimental preparation.

[0090] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 9 As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and databases. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a method for the synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys.

[0091] Those skilled in the art will understand that Figure 9The structures shown are merely block diagrams of some structures related to the present application and do not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than shown in the figures, or combine certain components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0092] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0093] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0094] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties. Moreover, the collection, use and processing of the relevant data are carried out in compliance with the relevant data protection laws and policies of the country where the location is located, and with the authorization granted by the owner of the corresponding device.

[0095] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0096] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0097] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0098] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys, characterized in that, include: Obtain the matrix chemical composition, tungsten particle volume fraction, and preparation process parameters of the tungsten-energetic high-entropy alloy to be optimized; Based on the matrix chemical composition and the tungsten particle volume fraction, the combustion activity index, d-electron concentration, and oxygen affinity difference of the tungsten-energetic high-entropy alloy to be optimized are calculated. The combustion activity index, the d-electron concentration, the oxygen affinity difference of the system, the matrix chemical composition, the tungsten particle volume fraction, and the preparation process parameters are used to form an input feature vector. The combustion activity index is used to characterize the relative content of active elements and refractory elements to reflect the chemical activity of the alloy, the d-electron concentration is used to characterize the valence electron structure strength, and the oxygen affinity difference of the system is used to characterize the thermodynamic driving force of the oxidation reaction. The input feature vectors are respectively input into four models in the pre-trained support vector regression model group to simultaneously obtain predicted values ​​of tensile strength, elongation after fracture, ignition delay time, and combustion rate. The support vector regression model group includes four independent support vector regression models. The four independent support vector regression models are used to predict tensile strength, elongation after fracture, ignition delay time, and combustion rate, respectively. Each support vector regression model shares the same input feature space and uses a radial basis function as the kernel function. Using the predicted value as the objective function value for multi-objective optimization, a multi-objective evolutionary algorithm is used to search within the design space defined by the matrix chemical composition, tungsten particle volume fraction, and preparation process parameters. The multi-objective optimization aims to maximize tensile strength, minimize the deviation of elongation after fracture from the target value, minimize ignition delay time, and maximize combustion rate. The output is a Pareto optimal solution set for balancing mechanical properties and combustion performance.

2. The method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys according to claim 1, characterized in that, The formula for calculating the combustion activity index is as follows: In the formula, Indicates the combustion activity index, , , , These represent the atomic percentages of Ti, Zr, V, Al, W, and Nb in the matrix of the tungsten-energetic high-entropy alloy to be optimized. This represents the equivalent atomic percentage of tungsten particles; The formula for calculating the d-electron concentration is: In the formula, Indicates d-electron concentration. Let represent the atomic percentage of the i-th element in the matrix of the tungsten-energetic high-entropy alloy to be optimized. Let d be the number of d electrons of the i-th element. The number of d electrons in tungsten; The formula for calculating the oxygen affinity difference of the system is as follows: In the formula, This indicates that the system has poor oxygen affinity. The average oxygen affinity of the active components in the system. The average oxygen affinity of the refractory components in the system. , , , , and The Pauling electronegativity difference between Ti, Zr, V, Al, W, and Nb and oxygen is considered.

3. The method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys according to claim 1, characterized in that, After inputting the input feature vectors into four models in a pre-trained support vector regression model group to simultaneously obtain predicted values ​​for tensile strength, elongation after fracture, ignition delay time, and combustion rate, the method further includes: Based on the pre-trained support vector regression model set, the KernelSHAP algorithm is used to calculate the SHAP value of each feature pair predicted in the input feature vector, and the SHAP value matrix of each feature on each sample to be optimized is obtained; the sample to be optimized is each sample corresponding to the input feature vector. Based on the SHAP value matrix, the average absolute SHAP value of each feature on all samples to be optimized is calculated and sorted in descending order of numerical value to obtain the feature importance ranking. From the feature importance ranking, the top k features that have the greatest impact on tensile strength, elongation after fracture, ignition delay time and combustion rate are identified as the key feature set. Based on the key feature set, typical samples are selected from the samples to be optimized, and based on the SHAP value matrix, the specific SHAP contribution value of each key feature to the four performance prediction values ​​of the typical samples is extracted, where a positive value indicates that the key feature drives the prediction value to increase, and a negative value indicates that it drives it to decrease, thus obtaining the local interpretation result of the typical samples; Based on the key feature set, for each key feature in the key feature set, several observation points are uniformly selected within its value range. Keeping other features in the input feature vector unchanged, the arithmetic mean of the predicted values ​​of all samples to be optimized at each observation point is calculated based on the corresponding support vector regression models in the pre-trained support vector regression model group. The observation points and their corresponding average predicted values ​​are connected sequentially to draw a partial dependency graph. The performance inflection point and saturation effect are identified by the change in the slope of the curve, and the nonlinear influence law and optimal range of each key feature on mechanical performance and combustion performance are obtained.

4. The method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys according to claim 1, characterized in that, The multi-objective evolutionary algorithm is the NSGA-II algorithm, and the target value of elongation after fracture is set in the range of 1%-5%. The constraints include: composition conservation, the content range of each element, the volume fraction range of tungsten particles, the range of process parameters, and the stability constraint of the matrix BCC phase.

5. The method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys according to claim 1, characterized in that, The training process for the support vector regression model group includes: A database of tungsten-energetic high-entropy alloys is constructed. The database includes the matrix chemical composition, tungsten particle volume fraction, preparation process parameters, and the corresponding tensile strength, elongation after fracture, ignition delay time, and combustion rate. Based on the matrix chemical composition and tungsten particle volume fraction in the database, the combustion activity index, d-electron concentration, and system oxygen affinity difference are calculated to obtain training calculation parameters. The matrix chemical composition, tungsten particle volume fraction, preparation process parameters, and training calculation parameters in the database are collectively composed of a training feature set. Using the training feature set as input, and tensile strength, elongation after fracture, ignition delay time, and combustion rate as outputs, and radial basis function as kernel function, four independent support vector regression networks are trained to obtain a support vector regression model group; wherein, the four support vector regression networks share the same input feature space.

6. The method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys according to claim 5, characterized in that, Using the aforementioned training feature set as input, and tensile strength, elongation at break, ignition delay time, and combustion rate as outputs, respectively, and radial basis functions as kernel functions, four independent support vector regression networks are trained to obtain a set of support vector regression models, specifically including: Using the training feature set as input, and tensile strength, elongation after fracture, ignition delay time, and combustion rate as outputs, with radial basis function as kernel function, the hyperparameters of four independent support vector regression networks are optimized using grid search combined with cross-validation to determine the optimal hyperparameter combination for each independent support vector regression network, thus obtaining a set of support vector regression models.

7. The method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys according to claim 5, characterized in that, The matrix chemical composition, tungsten particle volume fraction, preparation process parameters, and training calculation parameters in the database are collectively composed of a training feature set, specifically including: The matrix chemical composition, tungsten particle volume fraction, preparation process parameters, and training calculation parameters in the database are combined to form an initial training feature set. The Pearson correlation coefficient method is used to perform preliminary screening of the initial training feature set to remove redundant features, resulting in a screened feature set. The selected feature set is subjected to deep screening using the recursive feature elimination cross-validation method to obtain the training feature set. The recursive feature elimination cross-validation method uses the average relative error of the five-fold cross-validation of the support vector regression model as the evaluation index. In each iteration, the feature with the lowest SHAP importance is eliminated until the model performance no longer improves or the number of features is reduced to a preset number.

8. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that the processor executes the computer program to implement the method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys as described in any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys as described in any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the method for synergistic prediction and multi-objective optimization of the mechanical and combustion properties of tungsten-energetic high-entropy alloys as described in any one of claims 1-7.

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