A component design method for a high-strength material system containing nickel based on transfer learning and barrel theory optimization

Abstract

This invention discloses a method for designing the composition of nickel-containing high-strength material systems based on transfer learning and the barrel theory optimization. The method includes: first, using a recursive feature elimination algorithm to screen key features across source domain benchmark data and target domain experimental data containing sparse components; second, constructing a deep neural network for pre-training on the source domain dataset, extracting nonlinear feature representations between components and performance through hidden layers; third, freezing the weights of the feature extraction layers of the pre-trained model, and for sparse samples in the target domain, introducing Bayesian ridge regression to construct a residual correction model to achieve cross-domain knowledge transfer; and finally, combining multiple metallurgical constraint criteria to perform an evolutionary search within a limited composition space. This invention solves the problem of effectively modeling sparse data in new material systems. By combining deep feature extraction with Bayesian residual correction, it significantly improves the robustness of high-strength material performance prediction and enables precise optimization of industrial-grade composition formulations.

Description

Technical Field

[0001] This invention relates to the interdisciplinary fields of materials genome engineering and artificial intelligence, and in particular to a method for designing the composition of nickel-containing high-strength material systems based on transfer learning and the barrel theory optimization. Background Technology

[0002] Nickel-containing high-strength materials, as key structural materials in modern industrial applications, occupy a core position in high-end fields such as aerospace, automotive manufacturing, precision machinery, and energy equipment due to their excellent mechanical properties, corrosion resistance, and processing adaptability. In practical engineering applications, modifying the matrix by introducing key strengthening elements such as nickel (Ni) and designing ultra-high-strength material systems using microalloying or multi-component synergistic effects has become an important direction in advanced materials research and development. However, the mechanical properties of such materials are determined by multiple factors, including their elemental composition, content ratio, microstructure, and preparation process. In the high-dimensional composition space, there is often a strong nonlinear coupling effect between key additive elements, the matrix, and other trace elements. This makes the traditional "formulation-trial production-verification" design model, which relies on expert experience and experimental trial and error, inefficient, with long development cycles and high trial and error costs, making it difficult to meet the technical requirements for rapid response of new material systems under complex working conditions.

[0003] In recent years, data-driven machine learning (Materials Informatics) has provided a new technical path for predicting the performance and optimizing the composition of new materials. However, existing technologies still face severe challenges when modeling novel high-strength material systems containing specific reinforcing elements (such as nickel). First, there is a serious "domain shift" problem. Existing material databases often accumulate massive amounts of data on conventional basic materials (source domain), while data on high-performance novel materials containing specific reinforcing components (target domain) is extremely scarce. The source domain and target domain differ significantly in feature space distribution, making it difficult for traditional machine learning models to effectively inherit the general physical laws of the source domain. Direct transfer often leads to "negative transfer" or "catastrophic forgetting," resulting in prediction failure. Second, small sample data leads to discontinuous feature manifolds. Due to the high cost of preparation and testing, high-quality data points for the target material system are often discretely distributed, making it difficult to form a continuous feature manifold. Conventional deep learning models are prone to overfitting when trained on sparse data, resulting in insufficient generalization ability of the model to regions with unknown compositions.

[0004] Furthermore, in the component back-calculation and performance optimization stages after obtaining the predictive model, swarm intelligence algorithms are a key tool for solving high-dimensional nonlinear optimization problems. While traditional genetic algorithms (GA) or particle swarm optimization (PSO) are widely used, they often fall into local optima due to premature convergence when dealing with complex material systems with multiple physicochemical constraints, failing to find the truly globally optimal composition. In 2025, Van Tai Tran et al. published a paper titled "BTO: A BARREL THEORY-BASED OPTIMIZER FOR ENGINEERING DESIGN PROBLEMS" in the journal *Applied Engineering Letters*, proposing for the first time a novel optimization algorithm based on the "cannikin effect"—the Cannikin Theory Optimizer (BTO). This algorithm simulates the limiting mechanism of the "weakest link" in a system on overall performance, focusing on repairing the weakest individuals in the population to break evolutionary stagnation, demonstrating superior global search capabilities compared to traditional algorithms in solving complex engineering design problems. However, as a cutting-edge algorithm, there is currently no existing technology to apply the BTO algorithm to the field of composition design of complex material systems, especially for optimization problems of high-dimensional alloy systems with strict metallurgical taboos. Existing BTO algorithms still need further targeted improvements to adapt to the special characteristics of material design.

[0005] In summary, there is an urgent need to develop an intelligent material system composition design method that can deeply integrate implicit features of the source domain to solve the domain offset problem, overcome the sparsity defect of small sample data through manifold regularization, and break through the local optimum limitation by using an improved barrel theory algorithm, so as to achieve rapid and accurate development of nickel-containing high-strength materials. Summary of the Invention

[0006] The technical problem to be solved by this invention is to address the shortcomings in alloy design, such as feature loss, data sparsity, discontinuous feature manifolds in small samples, and the tendency of traditional optimization algorithms to get trapped in local optima. This invention provides a composition design method for nickel-containing high-strength material systems based on transfer learning and the barrel theory optimization.

[0007] To achieve the above objectives, the present invention provides the following solution: A method for designing the composition of nickel-containing high-strength material systems using a hybrid transfer learning and barrel theory optimization approach includes: S1. Construct the original material dataset, perform data cleaning and feature engineering on the original material dataset to obtain the preprocessed feature matrix; wherein, the original material dataset includes: a source domain benchmark set and a target domain experimental set, the source domain benchmark set includes: high-strength alloy composition and sparse composition alloys containing trace amounts of nickel strengthening elements and corresponding mechanical property data, the target domain experimental set includes: experimental data of sparse composition alloys containing most nickel strengthening elements; S2. A recursive feature elimination algorithm is adopted, using a random forest regressor as a base learner to perform recursive feature elimination filtering on the preprocessed source domain reference set and target domain transfer set, and to achieve alignment of the feature spaces of the source domain and the target domain. S3. Construct a deep neural network model, pre-train the deep neural network model using the aligned source domain benchmark set, extract the nonlinear characterization features between material composition and performance through the hidden layers of the deep neural network model, and save the weights of the pre-trained feature extraction layer. S4. Construct a residual correction prediction model based on transfer learning, freeze the weights of the feature extraction layer, use the aligned target domain experimental set as input, introduce the Bayesian ridge regression algorithm as the regression layer, and perform probability modeling and residual prediction correction on sparse component samples in the target domain. S5. Construct a component optimization algorithm based on the barrel principle, establish a constraint set including multiple metallurgical criteria, use the residual correction prediction model as the objective function, and perform evolutionary search within the limited component space; the component optimization algorithm based on the barrel principle verifies the weakest link of the candidate formulations in the search space, retains only the industrially feasible candidate set that simultaneously satisfies all metallurgical criteria, and selects the component formulation with the best performance prediction value from it.

[0008] Optionally, the preprocessing in S1 includes removing duplicate samples, identifying outliers, and automatically performing quality balance completion for missing matrix element components.

[0009] Optionally, the recursive feature elimination screening of the source domain in S2 for the source domain reference set and the target domain transfer set includes: The cross-validation determination coefficient of the source domain data is used as the evaluation index for feature retention; A whitelist is set up that includes trace elements such as nickel and titanium, as well as casting process parameters. During the recursive elimination process, when the feature score in the whitelist is lower than the elimination threshold, a hard constraint mechanism is triggered to force the feature to be retained, ensuring that the model has the physical basis to process specific dimensions of the target domain. The screening results are obtained by calculating the coefficient of determination; the formula for calculating the coefficient of determination is as follows: ; in, The coefficient of determination is represented by ; n represents the number of samples of each preprocessed feature value input into the model. Indicates the first Tensile strength after pretreatment; Indicates the first Ultimate tensile strength; This represents the average tensile strength after each pretreatment.

[0010] Optionally, the deep neural network model constructed in S3 includes: an input layer, three fully connected hidden layers, and an output layer; wherein the second fully connected hidden layer is set as a bottleneck layer to extract highly concentrated nonlinear feature vectors of material components.

[0011] Optionally, in S3, the deep neural network model uses mean squared error (MSE) as the loss function during pre-training, and its calculation formula is as follows: ; Where MSE represents the mean squared error loss; n represents the number of samples of each preprocessed feature value input into the model; Indicates the i-th ultimate tensile hardness; During training, an adaptive moment estimation (Adam) optimizer is used, and a learning rate decay strategy is introduced to ensure the stability of weight updates.

[0012] Optionally, the construction logic of the residual correction prediction model in S4 is as follows: input the target domain experimental set into the pre-trained feature extraction layer to obtain high-dimensional feature mapping values. Introducing Bayesian Ridge regression, we assume that the regression coefficients w follow a Gaussian prior distribution. Iteratively update the regularization hyperparameters by maximizing the log-likelihood function. and We obtain the mean and variance of the performance predictions for the target domain samples.

[0013] Optionally, S4 also includes validation on the target domain experimental set using the leave-one-out method, and calculation of the mean absolute error (MAE) to evaluate the transfer effect: ; Where n is the number of samples; The actual value; These are predicted values.

[0014] Optionally, in S4, the prediction variance is used to construct the confidence interval for performance prediction, denoted as... ,in, To predict the mean, denoted as standard deviation and k as coverage factor; the confidence interval is used to quantify the reliability of the model in the sparse component region.

[0015] Optionally, in S5, the alloy composition atmosphere is limited by multiple metallurgical physical constraints, specifically set as follows: Magnesium element constraint: 0.01≤Mg≤0.08wt.%; Nickel element constraint: Ni≤2.0wt.%; Aluminum-copper ratio constraint: when Al<4.0wt.%, Cu≤1.5wt.%.

[0016] Optionally, the execution logic of the Bucket Optimization Algorithm (BTO) in S5 specifically includes: S51. Parameter space gridding: Generate a global component combination matrix within the value range of each key chemical component according to the preset element step size. S52. Shortcoming effect screening: For each component combination in the matrix, check whether it violates any metallurgical criteria in the constraint set. If it violates the criteria, it is considered to have a technical shortcoming and the combination is removed. S53. Performance Optimization: Use the model constructed in step S4 to predict the performance of the screening combinations and sort them in descending order according to the predicted mean.

[0017] Optionally, S53 may also include: Based on the preset performance threshold and confidence interval width, the top 50 industrially feasible candidate formulations are extracted from the ranking results as the final composition design recommendations for high-strength material systems.

[0018] The beneficial effects of this invention are as follows: This invention proposes a composition design method for nickel-containing high-strength material systems based on transfer learning and the barrel theory optimization. Compared with existing technologies, it has the following advantages: Through the synergistic effect of the cross-domain recursive feature elimination algorithm (RFECV) and the prior knowledge whitelist mechanism, the data distribution distance between the source domain and the target domain is narrowed at the physical level, ensuring the integrity of key physical dimensions of the model during cross-domain transfer; with the help of the ERC-Net deep representation network, the feature extraction capability is enhanced by using residual blocks and skip connections, realizing the deep fusion of general physical laws of the source domain and specific component information of the target domain, effectively avoiding negative transfer phenomenon. By employing a Bayesian residual correction model and utilizing explicit residual paths, the nonlinear performance fluctuations caused by trace amounts of nickel (Ni) are accurately captured, significantly improving the model's prediction accuracy in extremely sparse data regions. A Bayesian uncertainty perception mechanism is introduced, achieving high-performance prediction while quantifying the model's risk confidence in sparse regions through output prediction variance. This provides a reliable probability assessment for predicting alloy properties in small-sample environments, effectively overcoming the overfitting bottleneck of traditional machine learning models under sparse samples. Finally, the output composition of the barrel theory optimizer is used for precise reverse design. Through multiple metallurgical hard constraint filtering mechanisms and fitness scoring iterations, the technical drawback of traditional optimization algorithms easily falling into "mathematical optimality rather than physical feasibility" is fundamentally overcome, ensuring the synergistic strengthening effect and industrial fabrication feasibility of the optimized formulation in the multi-dimensional composition space. This invention provides a scientific design logic for overcoming the research and development bottlenecks of high-performance materials in sparse data environments, possessing significant practical value and broad application prospects. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention 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 the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of a method for designing the composition of a nickel-containing high-strength material system based on transfer learning and the barrel theory in an embodiment of the present invention. Figure 2 This is a statistical diagram showing the characteristic distribution of the source domain reference data in S1 of this embodiment of the invention. Figure 3 is a bar chart showing the ranking of the importance of source domain features in S2 according to an embodiment of the present invention; Figure 4 This is a schematic diagram showing the performance optimization curve and key feature number determination of the recursive feature elimination algorithm (RFECV) in the source domain in S2 of this embodiment of the invention. Figure 5This is a schematic diagram of the architecture of the pre-trained deep neural network model in S3 of this embodiment of the invention; Figure 6 This is a convergence plot of the Loss (error) curve of the deep neural network model in S3 of this embodiment of the invention as a function of Epochs (number of training rounds); Figure 7 This is a performance evaluation diagram of the transfer learning model that incorporates the Bayesian residual correction model in S4 of this embodiment of the invention. Figure 8 This is a schematic diagram of the component optimization evolution trajectory generated based on the BTO algorithm in S5 of this embodiment of the invention; Figure 9 This is a schematic diagram of the distribution of formulation components based on BTO output in S5 of this embodiment of the invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] like Figure 1 As shown, this embodiment proposes a composition design method for nickel-containing high-strength material systems based on transfer learning and the barrel theory, including: S1. Construct the original material dataset, perform data cleaning and feature engineering on the original material dataset to obtain the preprocessed feature matrix; the original material dataset includes: source domain benchmark set and target domain experimental set. The source domain benchmark set includes: high-strength alloy composition and sparse composition alloy containing trace amounts of nickel strengthening elements and corresponding mechanical property data. The target domain experimental set includes: experimental data of sparse composition alloy containing most nickel strengthening elements. S2. A recursive feature elimination algorithm is adopted, which uses a random forest regressor as a base learner to perform recursive feature elimination filtering of the source domain benchmark set and the target domain transfer set, and realizes the alignment of the feature spaces of the source domain and the target domain. S3. Construct a deep neural network model, pre-train the deep neural network model using the source domain benchmark set, extract the nonlinear characterization features between material composition and performance through the hidden layers of the deep neural network model, and save the weights of the pre-trained feature extraction layer. S4. Construct a residual correction prediction model based on transfer learning, freeze the weights of the feature extraction layer, use the target domain experimental set as input, introduce the Bayesian ridge regression algorithm as the regression layer, and perform probability modeling and residual prediction correction on sparse component samples in the target domain. S5. Construct a component optimization algorithm (BTO) based on the barrel principle, establish a constraint set containing multiple metallurgical criteria, use the residual correction prediction model as the objective function, and perform evolutionary search within the limited component space; the BTO algorithm performs "weakness" verification on the candidate formulations in the search space, retains only the industrially feasible candidate set that simultaneously satisfies all metallurgical criteria, and selects the component formulation with the best performance prediction value from it.

[0024] Furthermore, the alloy composition described in S1 includes: Data on material systems containing very little nickel are defined as the source domain reference set; A large amount of nickel alloy data is defined as the core target domain; The preprocessing includes removing duplicate samples, identifying outliers, and automatically performing quality balance to complete missing matrix element components.

[0025] Specifically, in this embodiment, to address the feature distortion problem of multi-source heterogeneous data, the following preprocessing strategy is implemented in step S1: First, to address the issue of missing matrix element Zn in the experimental records, a completion operation based on the mass balance principle is performed, using the formula... First, the physical closure of the feature dimensions is ensured. Second, the PowerTransformer operator is invoked to perform nonlinear mapping on the skewed component features, and the Yeo-Johnson transform is used to improve the model's sensitivity to small changes in the sparse interval. Finally, standard deviation is used to map each feature value to a standard normal space with a mean of 0 and a variance of 1, in order to eliminate the influence of dimensional differences on the feature extraction layer. An original material dataset was obtained and constructed using publicly available experimental databases, historical production records from enterprises, and high-throughput computational simulations. For example... Figure 2 As shown, the original material dataset includes: a source domain benchmark set, which contains conventional high-strength alloy compositions and sparse composition alloys containing trace amounts of nickel (Ni) strengthening elements, along with their corresponding mechanical property data (sample size). The dataset includes 7 data points for Ni-containing alloys; and a target domain experimental set containing experimental data for rare-composition alloys with most nickel (Ni) strengthening elements (sample size). (), of which there are 15 data points for alloys containing Ni.

[0026] Furthermore, in S2, the recursive feature elimination screening of the source domain for the source domain reference set and the target domain transfer set includes: The cross-validation determination coefficient of the source domain data is used as the evaluation index for feature retention; A whitelist is set up that includes trace elements such as nickel and titanium, as well as casting process parameters. During the recursive elimination process, when the feature score in the whitelist is lower than the elimination threshold, a hard constraint mechanism is triggered to force the feature to be retained, ensuring that the model has the physical basis to process specific dimensions of the target domain. The screening results are obtained by calculating the coefficient of determination; the formula for calculating the coefficient of determination is as follows: ; in, The coefficient of determination is represented by ; n represents the number of samples of each preprocessed feature value input into the model. Indicates the first Tensile strength after pretreatment; Indicates the first Ultimate tensile strength; This represents the average tensile strength after each pretreatment.

[0027] Specifically, in step S2 of this embodiment, recursive feature elimination (RFECV) within the source domain is performed on the preprocessed data. For example... Figure 3 As shown, the importance of each feature in the source domain random forest model is first calculated. It can be seen that the scores of major added elements such as Zn (0.64), Cu (0.11), and Al (0.09) are significantly higher than those of trace elements such as Ni and Ti. If only statistical scores are used for elimination, trace elements specific to the target domain are easily removed. Therefore, this invention introduces a "hard constraint mechanism." Figure 4 As shown, during the feature recursive elimination process (horizontal axis increases from 1 to 12), the algorithm filters based on the source domain cross-validation accuracy (red solid line, CVSourceR2). The graph shows that as the number of features increases, the source domain training accuracy increases upwards, reaching a peak (approximately 0.74) at 12 features; the green dashed line represents the features after preservation. The curve, after reaching this point... The scoring plateau demonstrates the effectiveness of dimensionality reduction in eliminating redundant noise and improving model generalization. During this process, to address the issue of low initial statistical scores due to the sparse distribution of Ni elements in the source domain, this embodiment introduces a prior knowledge whitelist mechanism (such as...). Figure 3 (As shown by the green dashed line, N=7). This mechanism ensures that features with significant metallurgical physical meaning are not eliminated by the algorithm by forcibly locking core trace element composition features, including Ni, Ti, and Mg. "Permanent type" and "casting" are classification / process features. In the algorithm's calculations, they are treated as the same set of process variables, or one of them is used as a baseline value and does not participate in the dimensionality reduction calculation. Therefore, the mathematically selected screening points (red line) remain at 12, while the actual physical tensor dimension fed into the neural network is 13.

[0028] Furthermore, the deep neural network model constructed in S3 includes: an input layer, three fully connected hidden layers, and an output layer; wherein, the second fully connected hidden layer is set as a bottleneck layer to extract highly concentrated nonlinear feature vectors of material components. Furthermore, in S3, the deep neural network model uses mean squared error (MSE) as the loss function during pre-training, and its calculation formula is as follows: ; Where MSE represents the mean squared error loss; n represents the number of samples of each preprocessed feature value input into the model; Indicates the i-th ultimate tensile hardness; During training, an adaptive moment estimation (Adam) optimizer is used, and a learning rate decay strategy is introduced to ensure the stability of weight updates.

[0029] Specifically, in step S3 of this embodiment, the present invention constructs an ERC-Net (Explicit Residual Correction Network) architecture, taking the key features determined in step S2 as input and the ultimate tensile strength (UTS) of the alloy as output. Figure 5 As shown, the pre-trained deep neural network model architecture constructed in this embodiment performs the following base model pre-training sub-steps: S31. Construction of ResNet Enhanced Feature Extraction Path: The model input layer receives the key feature vectors determined in step S2. The features first enter the projection layer, which maps them to a high-dimensional feature space through a densely connected layer with 128 neurons, a batch normalization (BN) layer, and a ReLU activation function. Subsequently, the model is connected in series to two structurally consistent residual blocks (Residual Block 1 & Residual Block 2). Each residual block adopts a dual-path design: the main path executes the Dense(128)-BN-ReLU-Dropout-Dense(128)-BN operation sequence in sequence to capture the deep nonlinear coupling relationship between components; the side path directly passes the initial input of the block across layers to the final output for summation and superposition through skip connections. This structure effectively mitigates the risk of gradient vanishing in 300 deep iterations and ensures the integrity of the model's extraction of material physical mechanism features.

[0030] S32. Bottleneck Layer Representation Compression and Source Domain Pre-training Convergence: After high-dimensional feature extraction from the residual blocks, the model is connected to the bottleneck layer (Dense(64)+RELU). This layer performs non-linear compression of the feature space by shrinking the number of neurons from 128 to 64 in a stepwise manner, generating highly condensed high-dimensional implicit logical features F. The architecture is pre-trained using the source domain benchmark set, and the Adam optimizer and early stopping mechanism are used for weight evolution. The loss curve of the deep neural network model with the number of training rounds is shown in the figure. Figure 6 As shown, the loss function values ​​of the training set and the validation set converged synchronously to a lower order of magnitude without significant oscillation, proving that the bottleneck layer has successfully precipitated the general knowledge representation of the evolution of high-strength zinc alloy components in the source domain big data.

[0031] S33. Knowledge Transfer-Guided Weight Freezing: After completing source domain pre-training, the representation network weights, consisting of projection layers, residual blocks, and bottleneck layers, are extracted. During the target domain transfer modeling phase, these pre-trained weights are fully loaded into the front end of the target model, and a "Freeze" weight freezing operation is performed. For example... Figure 4 As indicated by the “Part 3 Feature Output” label, this step ensures that the model can maintain the stability of the front-end representation base in the subsequent training with only 58 sparse samples in the target domain, and directly outputs robust implicit logical features F as input for the residual correction in the subsequent step S4, fundamentally solving the overfitting problem in a small sample environment.

[0032] Based on this, in step S4 of this embodiment, in order to solve the problem that traditional neural networks have low prediction accuracy and cannot measure confidence in sparse samples in the target domain, this embodiment introduces a Bayesian probability modeling mechanism and constructs a residual correction model based on transfer learning.

[0033] Specifically, in S4 of this embodiment, the following residual correction and transfer learning model construction sub-steps are performed: S41. Explicit Residual Mapping Construction: Using the representation network with frozen weights from step S33 as the front end, the component features of the target domain experimental set are mapped into high-dimensional implicit logical features. Based on this, a residual learning path consisting of two densely connected layers is connected to fit the systematic deviation between the actual performance of the target domain and the output value of the pre-trained model in the source domain.

[0034] S42. Bayesian Ridge Regression Parameter Estimation: The Bayesian Ridge regression algorithm is introduced at the output of the residual path. This algorithm assumes that the regression coefficients follow a Gaussian prior distribution and dynamically adjusts the regularization parameter by performing maximum a posteriori probability estimation on sparse data in the target domain. For example... Figure 7The figure shown is a performance evaluation graph of the transfer learning model combined with the Bayesian residual correction model in this embodiment. The predicted value curve closely follows the true value curve, which indicates that through Bayesian residual correction, the model can effectively capture the nonlinear reinforcement contribution of Ni element in the sparse region and significantly reduce the mean absolute error (MAE).

[0035] S43. Quantification of Prediction Uncertainty: In addition to outputting the mean of performance predictions, the Bayesian residual correction model also outputs the prediction variance for each component point. In regions with extremely sparse data distribution, the variance value output by the model increases significantly, thus providing a risk assessment basis for subsequent component optimization. This uncertainty perception mechanism effectively avoids the model generating blindly optimistic prediction results in the "data vacuum zone," ensuring the reliability of high-strength alloy design.

[0036] Furthermore, in S5, multiple metallurgical physical constraints are used to limit the alloy composition atmosphere, specifically set as follows: magnesium element constraint: 0.01≤Mg≤0.08wt.%; nickel element constraint: Ni≤2.0wt.%; aluminum-copper ratio constraint: when Al<4.0wt.%, Cu≤1.5wt.%; When the target material system is a zinc alloy system, the metallurgical taboo criteria include: aluminum-copper microstructure stability constraints, magnesium content hot brittleness constraints, nickel solubility constraints, and zinc matrix balance constraints.

[0037] Furthermore, the execution logic of the Bucket Optimization (BTO) algorithm in S5 specifically includes: S51. Parameter space gridding: Generate a global component combination matrix within the value range of each key chemical component according to the preset element step size. S52. Shortcoming effect screening: For each component combination in the matrix, check whether it violates any metallurgical criteria in the constraint set. If it violates the criteria, it is considered to have a technical shortcoming and the combination is removed. S53. Performance Optimization: Use the model constructed in step S4 to predict the performance of the screening combinations and sort them in descending order according to the predicted mean.

[0038] Furthermore, S53 also includes: Based on the preset performance threshold and confidence interval width, the top 50 industrially feasible candidate formulations are extracted from the ranking results as the final composition design recommendations for high-strength material systems.

[0039] Specifically, in step S5 of this embodiment, a composition optimization algorithm based on the barrel principle (BTO) is established, aiming to search for the globally optimal alloy composition ratio in a multi-dimensional composition space. This step introduces the BTO algorithm proposed in 2025 for the first time, and directly calls the high-precision deep learning model trained in step S4 as the algorithm's fitness evaluation function. Figure 8 As shown, the convergence curve of the BTO algorithm exhibits a typical "step-like rise" characteristic. It can be seen that as the number of iterations increases, the algorithm eliminates individuals with "physical weaknesses" (i.e., the barrel effect filtering), causing the average fitness of the population to rapidly increase and converge within 50 generations, and finally stabilize at above 478. This proves that the algorithm has a very strong ability to capture the global optimal solution under multiple hard constraints.

[0040] To ensure the practical engineering feasibility of the alloy formulations generated by the algorithm, this embodiment introduces strict metallurgical expert constraints to limit the search space during the BTO optimization process. These constraints specifically include: Al (4.0-7.5 wt.%), Cu (1.0-3.0 wt.%), Mg (0.01-0.10 wt.%), Ni (0.01-1.5 wt.%), and other trace elements. Within this space, Cartesian product operations are performed with a physical discrete step size of 0.05 wt.%, generating over 100,000 candidate formulation matrices to be evaluated. The gridding of the search space ensures that the algorithm can cover complex "composition-performance" manifold distributions in subsequent iterations. In the Bayesian residual correction model constructed in step S4, which inputs feasible formulations filtered by constraints, the algorithm is guided by maximizing the predicted strength and incorporates the predicted variance output by the Bayesian model. The results are weighted by confidence level, and unstable formulations that are in a data vacuum or have large prediction fluctuations are eliminated.

[0041] like Figure 9 As shown in the analysis, the high-performance formulation exhibits a significant multi-peak distribution: Ni content forms a bicentric cluster around 0.0 wt.% and around 1.5 wt.%; Al content forms a dense synergistic strengthening cluster with Cu in the 20.0 wt.%–28.0 wt.% range; while Mg content is concentrated in the discrete range of 0.01 wt.%–0.03 wt.%. This distribution pattern identifies several "compositional islands" with high strength potential, providing accurate multi-component reference data for subsequent experiments.

[0042] To verify the accuracy of the design method of this invention, this embodiment selected actual experimental formulations not included in the database for physical experimental verification. The alloy sample was prepared using vacuum induction melting and gravity casting processes, and its actual ultimate tensile strength was measured to be 279.8 MPa after tensile testing. The relative error between this actual measured value and the model predicted value (282.23 MPa) is extremely small, strongly demonstrating that the design method proposed in this invention, based on transfer learning and the barrel theory optimization, possesses extremely high predictive accuracy and engineering practical value when dealing with complex multi-component alloy systems. This realizes a paradigm shift in alloy design from traditional "experience-based trial and error" to "intelligent computing."

[0043] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for designing the composition of a nickel-containing high-strength material system based on transfer learning and the barrel theory, characterized in that, include: S1. Construct the original material dataset, perform data cleaning and feature engineering on the original material dataset to obtain the preprocessed feature matrix; wherein, the original material dataset includes: a source domain benchmark set and a target domain experimental set, the source domain benchmark set includes: high-strength alloy composition and sparse composition alloys containing trace amounts of nickel strengthening elements and corresponding mechanical property data, the target domain experimental set includes: experimental data of sparse composition alloys containing most nickel strengthening elements; S2. A recursive feature elimination algorithm is adopted, using a random forest regressor as a base learner to perform recursive feature elimination filtering on the preprocessed source domain reference set and target domain transfer set, and to achieve alignment of the feature spaces of the source domain and the target domain. S3. Construct a deep neural network model, pre-train the deep neural network model using the aligned source domain benchmark set, extract the nonlinear characterization features between material composition and performance through the hidden layers of the deep neural network model, and save the weights of the pre-trained feature extraction layer. S4. Construct a residual correction prediction model based on transfer learning, freeze the weights of the feature extraction layer, use the aligned target domain experimental set as input, introduce the Bayesian ridge regression algorithm as the regression layer, and perform probability modeling and residual prediction correction on sparse component samples in the target domain. S5. Construct a component optimization algorithm based on the barrel principle, establish a constraint set including multiple metallurgical criteria, use the residual correction prediction model as the objective function, and perform evolutionary search within the limited component space; the component optimization algorithm based on the barrel principle verifies the weakest link of the candidate formulations in the search space, retains only the industrially feasible candidate set that simultaneously satisfies all metallurgical criteria, and selects the component formulation with the best performance prediction value from it.

2. The method for designing the composition of nickel-containing high-strength material systems based on transfer learning and the barrel theory optimization as described in claim 1, characterized in that, The preprocessing in S1 includes removing duplicate samples, identifying outliers, and automatically performing quality balance to complete missing matrix element components.

3. The method for designing the composition of nickel-containing high-strength material systems based on transfer learning and the barrel theory optimization as described in claim 1, characterized in that, S2 involves performing recursive feature elimination filtering of the source domain into the source domain reference set and the target domain transfer set, including: The cross-validation determination coefficient of the source domain data is used as the evaluation index for feature retention; A whitelist is set up that includes trace elements such as nickel and titanium, as well as casting process parameters. During the recursive elimination process, when the feature score in the whitelist is lower than the elimination threshold, a hard constraint mechanism is triggered to force the feature to be retained, ensuring that the model has the physical basis to process specific dimensions of the target domain. The screening results are obtained by calculating the coefficient of determination; the formula for calculating the coefficient of determination is as follows: ； in, The coefficient of determination is represented by ; n represents the number of samples of each preprocessed feature value input into the model. Indicates the first Tensile strength after pretreatment; Indicates the first Ultimate tensile strength; This represents the average tensile strength after each pretreatment.

4. The method for designing the composition of nickel-containing high-strength material systems based on transfer learning and the barrel theory optimization as described in claim 1, characterized in that, The deep neural network model built in S3 includes an input layer, three fully connected hidden layers, and an output layer; the second fully connected hidden layer is set as a bottleneck layer to extract highly concentrated nonlinear feature vectors of material components.

5. The method for designing the composition of nickel-containing high-strength material systems based on transfer learning and the barrel theory optimization as described in claim 1, characterized in that, In S3, the deep neural network model uses mean squared error as the loss function during pre-training, and its calculation formula is as follows: ； Where MSE represents the mean squared error loss; n represents the number of samples of each preprocessed feature value input into the model; Indicates the i-th ultimate tensile hardness; An adaptive moment estimation optimizer is used during model training, and a learning rate decay strategy is introduced to ensure the stability of weight updates.

6. The method for designing the composition of nickel-containing high-strength material systems based on transfer learning and the barrel theory optimization as described in claim 1, characterized in that, The methods for constructing residual correction prediction models in S4 include: The aligned target domain experimental set is input into the pre-trained feature extraction layer to obtain high-dimensional feature mapping values. We introduce Bayesian ridge regression, assuming that the regression coefficients follow a Gaussian prior distribution; By iteratively updating the regularization hyperparameter by maximizing the log-likelihood function, the mean and variance of the performance predictions for the target domain samples are obtained.

7. The method for designing the composition of nickel-containing high-strength material systems based on transfer learning and the barrel theory optimization as described in claim 6, characterized in that, S4 also includes: validating the target domain experimental set after leaving one-out alignment, and calculating the mean absolute error to evaluate the transfer effect. ； Where n is the number of samples; The actual value; These are predicted values.

8. The method for designing the composition of nickel-containing high-strength material systems based on transfer learning and the barrel theory optimization as described in claim 6, characterized in that, In S4, the prediction variance is used to construct the confidence interval for performance prediction, denoted as... ,in, To predict the mean, denoted as standard deviation and k as coverage factor; the confidence interval is used to quantify the reliability of the model in the sparse component region.

9. The method for designing the composition of nickel-containing high-strength material systems based on transfer learning and the barrel theory optimization as described in claim 1, characterized in that, In S5, the constraint set is used to define the alloy composition atmosphere, and the constraint set includes: magnesium element constraint: 0.01≤Mg≤0.08wt.%; nickel element constraint: Ni≤2.0wt.%; aluminum-copper ratio constraint: when Al<4.0wt.%, Cu≤1.5wt.%.

10. The method for designing the composition of nickel-containing high-strength material systems based on transfer learning and the barrel theory optimization according to claim 1, characterized in that, The execution steps of the component optimization algorithm based on the barrel principle described in S5 include: S51. Parameter space gridding: Generate a global component combination matrix within the value range of each key chemical component according to the preset element step size. S52. Shortcoming effect screening: For each component combination in the matrix, check whether it violates any metallurgical criteria in the constraint set. If it violates the criteria, it is considered to have a technical shortcoming and the combination is removed. S53. Performance Optimization: Use the residual correction prediction model constructed in step S4 to predict the performance of the screening combinations and sort them in descending order according to the predicted mean.

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