A low-cost high-strength high-wear-resistance nodular cast iron design method based on small sample machine learning

Abstract

This invention discloses a low-cost, high-strength, and high-wear-resistant ductile iron design method based on few-sample machine learning, belonging to the fields of metal material preparation technology and computer science. This invention constructs an enhanced dataset by collecting the composition and mechanical properties of annealed ductile iron and extracting and screening alloy features to obtain key alloy features. Then, a multi-objective optimization function is constructed, and feature space optimization is performed using an improved NSGA-II algorithm to obtain the Pareto solution set, which is then mapped to features and experimentally verified. This invention overcomes the risk of overfitting with few samples through a hybrid enhancement strategy; it constructs an adaptive multi-scale recurrent convolutional network and a dual attention mechanism to accurately screen key alloy features; it uses an improved NSGA-II algorithm for multi-objective optimization, introducing a dynamic sharing mechanism and local search to make the Pareto front distribution more uniform; and it establishes a random forest mapping model and a closed-loop automatic retraining system to achieve accurate feature-component mapping and continuous optimization.

Description

Technical Field

[0001] This invention relates to the fields of metal material preparation technology and computer science, specifically to a low-cost, high-strength, and high-wear-resistant ductile iron design method based on small-sample machine learning. Background Technology

[0002] Ductile iron, with its excellent mechanical properties, casting performance, and cost advantages, is widely used in automotive parts, construction machinery, wind power equipment, and other fields. As modern industry increasingly demands lightweight, high reliability, and long service life for equipment, high-strength and high-wear-resistant ductile iron has become a research hotspot. At the same time, the manufacturing industry's need for cost reduction and efficiency improvement also places stringent requirements on the research and development cycle and material costs of ductile iron.

[0003] Traditional ductile iron research and development primarily relies on a trial-and-error approach, adjusting alloy composition and processes through numerous orthogonal experiments. This method not only consumes significant human and material resources but also suffers from obvious bottlenecks: firstly, it is highly dependent on sample size, making it difficult to establish reliable correlations between composition, process, and performance under small sample conditions; secondly, it has weak multi-performance synergistic optimization capabilities and struggles to incorporate material costs into the optimization system. High-performance products often result in increased costs due to the addition of precious metals, limiting their application scope.

[0004] Machine learning technology offers a new approach to intelligent materials design. Existing research employs algorithms such as support vector regression and random forests to build predictive models, which are then optimized using genetic algorithms. However, these methods still have limitations: the feature extraction stage relies on traditional statistical methods, which are insufficient for deep correlation mining of high-dimensional alloy features, and key information is easily lost in small sample scenarios; furthermore, there is a lack of targeted optimization design for low-cost element ratios, making it difficult to balance performance and economy. In contrast, multi-scale convolution and attention mechanisms have significant advantages in high-dimensional data feature mining. Combining the two can effectively improve the feature extraction accuracy in small sample scenarios, providing a feasible solution for the precise design of low-cost, high-performance ductile iron. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a low-cost, high-strength, and high-wear-resistant ductile iron design method based on small-sample machine learning.

[0006] To achieve the above technology, the specific details are as follows: S1. Collect the composition and mechanical properties of ductile iron in the annealed state to construct an enhanced dataset; The mechanical properties include: tensile strength (UTS) and wear rate (WR); S2. Based on the enhanced dataset of S1, alloy features are extracted and screened to obtain key alloy features; S3. Based on the key features selected in S2, construct a multi-objective optimization function; The multi-objective optimization function consists of the tensile strength UTS prediction model f1(x) and the wear rate prediction model f2(x) of the improved support vector regression (SVR). S4. Based on the multi-objective optimization function constructed in S3, the Pareto solution set is obtained by performing feature space optimization through improved NSGA-II. S5. Based on the Pareto solution set obtained in S4, perform feature-component mapping and experimental verification to complete the closed-loop design of the method.

[0007] Furthermore, in S1, the methods for constructing the augmented dataset include: The SMOTE algorithm is used to perform linear interpolation on the original samples to augment the dataset, resulting in an augmented dataset. A conditional generative network cGAN is constructed, and the expanded dataset is used as the training condition to select sample data with a discriminator score ≥ 0.8 in order to obtain a high-confidence sample set. Metallurgical rules are introduced, and reasonable ranges for each element are set based on the Fe-C-Si ternary phase diagram and thermodynamic database to eliminate abnormal samples that exceed the range in the high-confidence sample set; The augmented dataset is obtained by merging the high-confidence sample set (after removing outliers) with the original sample set.

[0008] Furthermore, the augmented dataset is divided into training and testing sets according to a preset ratio, and 10-fold cross-validation is used to evaluate the model performance, with MAPE as the evaluation metric.

[0009] Furthermore, step S2 is as follows: S2.1 Based on the augmented dataset obtained in S1, extract 31 physicochemical features of each element in the dataset to construct an initial feature matrix; and calculate the mean and variance of each feature. S2.2. Using the Pearson correlation coefficient, redundant features with an absolute value greater than 0.95 are removed. Then, using support vector regression (SVR) as the base model, radial basis function is used to remove features that contribute the least to the model until the cross-validation error no longer decreases, thus completing the screening operation. S2.3. Construct a multi-scale, multi-layer recurrent convolutional network, introduce an adaptive kernel scale selection mechanism, and calculate the number of recurrent layers for the selected features, as shown below: In the formula, Indicates feature dimension; Indicates the candidate convolution kernel scale. b ∈{3, 5, 7}; Indicates the loop depth; S2.4, Based on the first layer input h(l- ¹ ) Residual connections and gating mechanisms are introduced into each recurrent convolutional layer to enhance gradient flow and nonlinear expression capabilities, as expressed in the following expression: In the formula, Indicates the level index; Represents standard convolution; Indicates gated convolution; This indicates element-wise multiplication; This represents the Sigmoid activation function; S2.5. Apply SENet-style attention weighting in the channel dimension and self-attention weighting in the spatial dimension to the convolutional feature map respectively. After generating the weighted feature map, perform residual fusion with the original feature map to obtain the enhanced feature representation. The operation performed by channel attention is: for h (k) After global flat pooling, the channel weights are obtained through two fully connected layers and Sigmoid activation, and then compared with h. (k) Multiply each channel sequentially to obtain the channel-weighted feature map; The spatial attention operation is as follows: the average and maximum values ​​of the channel weighted feature maps are taken along the channel dimension, concatenated and then passed through a convolutional layer to generate a spatial weight map, and the spatial weight map is multiplied element by element with the feature map to obtain the spatial weighted feature map; The residual fusion operation is as follows: the spatially weighted feature map is combined with h (k) The residuals are summed to obtain the enhanced feature map; S2.6 Perform principal component analysis (PCA) on the feature map after residual fusion, calculate the variance contribution rate of each principal component, and obtain the key alloy characteristics of mechanical properties.

[0010] Furthermore, step S3 is as follows: S3.1 Based on the key alloy features output by S2, for the tensile strength prediction task, a preset number of the most critical features are selected and denoted as vectors. For the wear rate prediction task, a predetermined number of the most critical features are selected and denoted as vectors. ; S3.2 Construct a tensile strength prediction model f1(x); The construction methods include: based on Support Vector Regression (SVR), a hybrid kernel function is constructed using a multi-kernel learning mechanism that integrates Radial Basis Function (RBF), Polynomial kernel (Poly), and Sigmoid kernel function. The expression is as follows: In the formula, This represents different kernel learning mechanisms, among which, Radial basement membrane (RBF) For polynomial kernel Poly, For the Sigmoid kernel function; Indicates the first The weights of each kernel function; Represents the input vector; Indicates the first training set Key feature vectors of each sample; Introducing an exponential collaborative term for element interactions, the complete model expression is: In the formula, Represents the first kind of Lagrange multipliers; Represents the model bias term; Indicates the synergistic effect coefficient; This represents the total number of key features. Indicates feature index; Indicates the first The numerical values ​​of the key features; Indicates the first The sample mean of each key feature; Indicates the first The collaborative sensitivity index of each element; S3.3 Construct the wear rate prediction model f2(x), with the following expression: In the formula, Indicates the wear resistance correction factor; Indicates the number of support vectors; Indicates the second kind of Lagrange multiplier; Indicates and A hybrid kernel function that is compatible with each other; Represents the model bias term; Indicates the wear inhibition coefficient; Indicates the first Attention weights for key features; Indicates the synergistic wear factor; Indicates the first Sensitivity index of each element; Wear mechanism classification embedding: Based on the wear rate value, the samples are divided into three categories: slight wear (WR < 0.06 mg / m), moderate wear (0.06 ≤ WR ≤ 0.10 mg / m), and severe wear (WR > 0.10 mg / m). Three sub-models are trained for each category, and the final output is weighted and fused. S3.4 Combine f1(x) and f2(x) into a multi-objective optimization function F(x) = [f1(x), f2(x)], with the optimization objective being to maximize f1(x) and minimize f2(x) to obtain the predicted values ​​of UTS and WR.

[0011] Furthermore, in S4, the improvement strategy includes: Dynamic fitness sharing strategy: The sharing radius is dynamically adjusted according to the population density in each generation. ,initial Reduce when the average congestion distance is less than the threshold. Conversely, it increases to maintain a uniform distribution of the Pareto front. Local search strategy: every interval In this step, a particle swarm local search is performed on the current Pareto solution set to improve the convergence speed; Diversity preservation mechanism: A pruning strategy based on angular distance is adopted, which prioritizes the retention of solutions with the largest angular distance from other individuals during environmental selection.

[0012] Furthermore, in S5, the random forest mapping model includes the following mechanisms: Feature importance feedback mechanism: The feature importance ranking of the random forest output is fed back to S2 to dynamically adjust the feature selection threshold; Uncertainty quantification mechanism: Monte Carlo dropout is introduced into the model to output the uncertainty interval of component predictions, which guides the priority of experimental verification; Closed-loop automatic retraining mechanism: When experimental performance fails to meet the standard, new samples are automatically added to the dataset, triggering model retraining and adaptive parameter updates, forming a closed-loop optimization system of "data-model-experiment".

[0013] The beneficial effects of this invention are: This invention utilizes a SMOTE-cGAN hybrid enhancement strategy to generate high-confidence synthetic samples based on 30 sets of original samples, overcoming the risk of overfitting with small samples. It constructs an adaptive multi-scale recurrent convolutional network and a dual attention mechanism to accurately screen key alloy features from 62-dimensional features. It employs an improved NSGA-II algorithm for multi-objective optimization, introducing a dynamic sharing mechanism and local search to make the Pareto front distribution more uniform. Finally, it establishes a random forest mapping model and a closed-loop automatic retraining system to achieve accurate feature-component mapping and continuous optimization. Attached Figure Description

[0014] Figure 1 This is a flowchart of the steps of the present invention; Figure 2 This is a schematic diagram of the screening process in an embodiment of the present invention, wherein, Figure 2 (a) is the screening process for tensile strength UTS. Figure 2 (b) is the screening process for wear rate (WR). Detailed Implementation

[0015] The present invention will be further described in detail below with reference to specific embodiments.

[0016] like Figure 1 As shown, a low-cost, high-strength, and high-wear-resistant ductile iron design method based on few-sample machine learning includes the following steps: S1. Construction and enhancement of small sample datasets; Taking a certain enterprise as an example, the composition and mechanical properties of annealed (850℃–950℃) ductile iron were collected from historical data. The composition range was: C: 3.2%–3.8%, Si: 2.0%–2.8%, Mn: 0.3%–0.8%, Cu: 0.2%–0.6%, with the remainder being Fe. The corresponding mechanical properties included: tensile strength (UTS) 500–800 MPa and wear rate (WR) 0.05–0.15 mg / m. Initially, 30 valid samples were collected.

[0017] To overcome the small sample size problem, the following data augmentation operations are performed: The present invention uses the SMOTE algorithm to perform linear interpolation between samples. By setting the number of nearest neighbors k=5 and the generation ratio=2, the present invention performs linear interpolation between samples of the same type for each original sample, generating 60 synthetic samples. A conditional generative network (cGAN) was constructed, using the original 30 sets of samples as training conditions. Both the generator and discriminator employed a three-layer fully connected network (with 128, 64, and 32 hidden nodes, respectively), and the training iterations were 200. After training, 60 samples generated by SMOTE were input into the discriminator to obtain a authenticity score, and samples with scores higher than the threshold θ=0.8 were retained; in this embodiment, 48 samples were retained. By introducing metallurgical rules and based on the Fe-C-Si ternary phase diagram and thermodynamic database, reasonable ranges for each element were set, abnormal samples that exceeded the range were eliminated, and finally 45 high-quality synthetic samples were retained. The original 30 sets of samples were merged to form 75 sets of samples. The training set (60 sets) and the test set (15 sets) were divided in an 8:2 ratio. The model performance was evaluated using 10-fold cross-validation, with MAPE as the evaluation metric.

[0018] S2. Based on the enhanced dataset of S1, perform alloy feature extraction and screening, including the following steps: S2.1 Initial Feature Construction: From the 75 samples obtained from S1, 31 physicochemical features of each element were extracted to construct an initial feature matrix; The 31 physicochemical characteristics include: atomic number, period number (counted from bottom left, left to right), period number (counted from top right, right to left), quantum number, atomic weight, electronegativity, absolute electronegativity, first ionization energy, second ionization energy, third ionization energy, chemical potential, group number, number of valence electrons, number of s orbital valence electrons, number of p orbital valence electrons, number of d orbital valence electrons, number of f orbital valence electrons, enthalpy of atomization, cohesive energy, Mendeleev number, pseudopotential radius, ionic radius, covalent radius, valence electron distance, nucleo-electron distance, atomic volume, total number of electron shells, polarizability, specific heat capacity, and enthalpy of oxide formation. Methods for constructing the initial feature matrix include: Calculate the mean and variance of each feature to obtain 62-dimensional features; S2.2 Preliminary Feature Screening: The Pearson correlation coefficients between each pair of the 62 features were calculated, and redundant features with an absolute correlation coefficient greater than 0.95 were removed. After screening, the feature dimension in this embodiment was reduced to 16. Using Support Vector Regression (SVR) as the base model, a radial basis function kernel is used to progressively eliminate features that contribute the least to the model until the cross-validation error no longer decreases. Ultimately, this embodiment retains 7 key features for UTS and 6 key features for WR. The selection process is as follows: Figure 2 middle Figure 2 (a) and Figure 2 As shown in (b); S2.3. Construct a multi-scale, multi-layer recurrent convolutional network, introducing an adaptive convolutional kernel scale selection mechanism and a channel-space dual attention module to extract deep alloy features. Specific methods include: Adaptive convolution kernel scale selection mechanism: Based on the selected features (UTS 7-dimensional / WR 6-dimensional), adjust the candidate convolution kernel scale and calculate the number of recurrent layers, as shown below: In the formula, Indicates feature dimension; Indicates the candidate convolution kernel scale. b ∈{3, 5, 7}; Indicates the loop depth; Different candidate convolutional kernel sizes were compared using cross-validation. Based on the model performance, select the candidate convolutional kernel scale that minimizes the validation error. ; In this embodiment, b=5 is chosen, which corresponds to k=5. Therefore, a 5-layer recurrent convolutional network is constructed, with each layer having a kernel size of 5, which yields the best extraction effect. S2.4, Residual Gated Recurrent Convolution Module: Based on the first layer inputh (l- ¹ ) (initial h (0) Taking a 13-dimensional feature vector (expanded to an appropriate size via embedding) as an example, residual connections and gating mechanisms are introduced in each recurrent convolutional layer to enhance gradient flow and nonlinear expressiveness. The expression is as follows: In the formula, Indicates the level index; Represents standard convolution; Indicates gated convolution; This indicates element-wise multiplication; This represents the Sigmoid activation function; The number of output channels is set to 64. After calculating layer by layer, the output h of the last layer is obtained. (5) The dimensions are 64-dimensional; S2.5, Dual Attention Fusion Module: The convolutional feature maps are subjected to SENet-style attention weighting in the channel dimension and self-attention weighting in the spatial dimension, respectively. After generating weighted feature maps, residual fusion is performed with the original feature maps to obtain enhanced feature representations. The specific method is as follows: Channel attention: for h (5) (64 channels) undergo global average pooling to obtain a 64-dimensional vector. This vector is then passed through two fully connected layers (first reduced to 16 dimensions and then restored to 64) and a sigmoid activation layer to obtain the channel weights, which are then compared with h. (5) Multiply each channel sequentially to obtain the channel-weighted feature map; Spatial attention: The average and maximum values ​​of the channel-weighted feature maps are taken along the channel dimension, concatenated, and then passed through a convolutional layer to generate a spatial weight map. The spatial weight map is then multiplied element-wise with the feature map to obtain the spatial weighted feature map. Residual fusion: combining spatially weighted feature maps with the original h (5) The residuals are summed to obtain an enhanced feature map, which still has a size of 64 dimensions; S2.6. Reducing Dimensions to Obtain Key Alloy Features: Principal component analysis (PCA) was performed on the 64-dimensional reinforcement features to calculate the variance contribution rate of each principal component. In this embodiment, 3 key features and 2 key features were retained for UTS and WR, respectively, for a total of 5 dimensions, as shown in Table 1.

[0019] Table 1: Key Features S3. Based on the key features selected in S2, construct a multi-objective optimization function; Based on the 5 key features selected in S2, a UTS prediction model f1(x) and a wear rate prediction model f2(x) based on improved support vector regression (SVR) are constructed respectively. The two are then combined into a multi-objective optimization function F(x) = [f1(x), f2(x)], which provides the objective function for the feature space calculation in S4, as follows: S3.1, 5-dimensional key feature vector based on the output of S2 For the task of predicting tensile strength, three key features were selected and denoted as vectors. For the wear rate prediction task, two key features were selected and denoted as vectors. .

[0020] S3.2 Construct a tensile strength prediction model f1(x); Based on Support Vector Regression (SVR), a hybrid kernel function is constructed using a multi-kernel learning mechanism that integrates the radial basis function (RBF), polynomial kernel, and sigmoid kernel function. The expression is as follows: In the formula, This represents different kernel learning mechanisms, among which, It is a radial basis core (RBF). It is a polynomial kernel. For the Sigmoid kernel function; Indicates the first The weights of each kernel function are determined through cross-validation. ; Represents the input vector; Indicates the first training set Key feature vectors of each sample; Nonlinear extension of the synergistic term: Introducing an exponential synergistic term for element interactions, the complete model expression is: In the formula, Represents the first kind of Lagrange multipliers; Represents the model bias term; Indicates the synergistic effect coefficient; This represents the total number of key features. Indicates feature index; Indicates the first The numerical values ​​of the key features; Indicates the first The sample mean of each key feature; Indicates the first The collaborative sensitivity index of each element; In this embodiment, the test sample The mean vector is calculated. , , Number of support vectors in the SVR model Lagrange multipliers and bias Obtained from training; the output value of SVR is 720 MPa (calculated from the trained SVR model), and the co-sensitivity index is... Synergistic effect coefficient Calculations yielded .

[0021] S3.3 Construct the wear rate prediction model f2(x), with the following expression: In the formula, Indicates the wear resistance correction factor; Indicates the number of support vectors; Indicates the second kind of Lagrange multiplier; Indicates and A hybrid kernel function that is compatible with each other; Represents the model bias term; Indicates the wear inhibition coefficient; Indicates the first Attention weights for key features; Indicates the synergistic wear factor; Indicates the first Sensitivity index of each element; Wear mechanism classification embedding: Based on the wear rate value, the samples are divided into three categories: slight wear (WR < 0.06 mg / m), moderate wear (0.06 ≤ WR ≤ 0.10 mg / m), and severe wear (WR > 0.10 mg / m). Three sub-models are trained for each category, and the final output is a weighted fusion. In this embodiment, the test sample The mean of the training set was calculated. , , , (Output from the S2 dual attention module), sensitivity index , Other parameters: , , The SVR output is assumed to be 0.08, with an offset of... Calculations yielded ; S3.4 Combine f1(x) and f2(x) into a multi-objective optimization function F(x) = [f1(x), f2(x)], with the optimization objective being to maximize f1(x) and minimize f2(x) to obtain the predicted values ​​of UTS and WR.

[0022] S4. Based on the multi-objective optimization function constructed in S3, the Pareto solution set is obtained by performing feature space optimization through improved NSGA-II. The feature space optimization method is as follows: based on the improved NSGA-II feature space optimization, that is, setting the population size N and the maximum number of iterations G, adopting non-dominated sorting, crowding calculation, simulated binary crossover (SBX) and polynomial mutation, and introducing a dynamic fitness sharing mechanism and local search strategy, iterative optimization to obtain the Pareto optimal solution set that meets the multi-objective requirements; Improvement strategies include: Dynamic fitness sharing strategy: The sharing radius is dynamically adjusted according to the population density in each generation. ,initial Reduce when the average congestion distance is less than the threshold. Conversely, it increases to maintain a uniform distribution of the Pareto front. Local search strategy: every interval In this step, a particle swarm local search is performed on the current Pareto solution set to improve the convergence speed; Diversity preservation mechanism: A pruning strategy based on angular distance is adopted, which prioritizes the retention of solutions with the largest angular distance from other individuals during environmental selection.

[0023] In this embodiment, the decision variable is a 5-dimensional vector. The value range of each dimension is determined based on the minimum and maximum values ​​of the corresponding features in the training set; the optimization objective is to maximize... , minimize Set population size Maximum iteration algebra Genetic operation parameters: Simulated binary crossover (SBX) distribution index Crossover probability 0.9; multinomial variation distribution index Probability of mutation Local search strategy: every interval For each generation, a particle swarm optimization (PSO) is performed on the individuals in the current Pareto solution set, with a search step size of 0.01 and 10 iterations. After 200 generations of optimization, the Pareto front is obtained, containing approximately 50 non-dominated solutions, each corresponding to a set of key features. and the corresponding and .

[0024] S5. Based on the Pareto solution set obtained in S4, perform feature-component mapping and experimental verification; A random forest algorithm was used to construct a random forest mapping model from key alloy features to alloy composition, and samples were prepared for mechanical property testing. If the performance did not meet the standards, new samples were added to the dataset and an automatic retraining mechanism was triggered to form a closed-loop optimization system. Random forest mapping models include the following mechanisms: Feature importance feedback mechanism: The feature importance ranking of the random forest output is fed back to S2 to dynamically adjust the feature selection threshold; Uncertainty quantification mechanism: Monte Carlo dropout is introduced into the model to output the uncertainty interval of component predictions, which guides the priority of experimental verification; Closed-loop automatic retraining mechanism: When experimental performance fails to meet the standard, new samples are automatically added to the dataset, triggering model retraining and adaptive parameter updates, forming a closed-loop optimization system of "data-model-experiment".

[0025] The methods for conducting experimental verification include: Multi-batch validation strategy: Perform parallel experiments to validate multiple candidate components in the Pareto solution set, and select the one with the best performance as the output; Interpretability analysis in metallurgy: By combining the SHAP value analysis model output with the element content, an interpretable report is generated.

[0026] In this embodiment, the 5-dimensional key features x of all samples in S2 are used as input, and the original alloy composition is used as output to train a random forest regression model. The number of trees is set to 200, the maximum depth to 10, and the minimum number of leaf samples to 5. After training, the model can predict the corresponding composition for any new x. Monte Carlo dropout is enabled during random forest prediction, and the prediction is repeated 50 times to obtain the mean and standard deviation of the content of each element. The standard deviation is used as a measure of uncertainty, and candidate components with low uncertainty are selected for experimental verification. Three representative solutions are selected from the Pareto front, denoted as solution A, solution B, and solution C, and their key features are input into the random forest model to obtain the predicted components. Solution A: C 3.55%, Si 2.30%, Mn 0.55%, Cu 0.35% UTS = 748 MPa, W = 0.082 mg / m Solution B: C 3.65%, Si 2.10%, Mn 0.65%, Cu 0.40% UTS = 762 MPa, W = 0.079 mg / m Solution C: C 3.45%, Si 2.50%, Mn 0.45%, Cu 0.30% UTS = 735 MPa, W = 0.091 mg / m Ductile iron samples were prepared according to the above composition (annealed at 900℃ for 2 hours), and tensile strength and wear rate were tested. Test results: Solution A: UTS = 729 MPa, W = 0.084 mg / m Solution B: UTS = 778 MPa, W = 0.080 mg / m³ Solution C: UTS = 720 MPa, W = 0.093 mg / m³ The predicted values ​​had a very small error compared to the measured values, and ultimately achieved the design requirements of high strength and high wear resistance, with UTS ≥ 770 MPa and W ≤ 0.08 mg / m.

[0027] The specific embodiments of the present invention have been described in detail above with reference to examples. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A low-cost, high-strength, and high-wear-resistant ductile iron design method based on few-sample machine learning, characterized in that, Includes the following steps: S1. Collect the composition and mechanical properties of ductile iron in the annealed state to construct an enhanced dataset; The mechanical properties include: tensile strength (UTS) and wear rate (WR); S2. Based on the enhanced dataset of S1, alloy features are extracted and screened to obtain key alloy features; S3. Based on the key features selected in S2, construct a multi-objective optimization function; The multi-objective optimization function consists of the tensile strength UTS prediction model f1(x) and the wear rate prediction model f2(x) of the improved support vector regression (SVR). S4. Based on the multi-objective optimization function constructed in S3, the Pareto solution set is obtained by performing feature space optimization through improved NSGA-II. S5. Based on the Pareto solution set obtained in S4, construct a random forest mapping model for feature-component mapping and experimental verification, and complete the closed-loop design of the method.

2. The low-cost, high-strength, and high-wear-resistant ductile iron design method based on small-sample machine learning according to claim 1, characterized in that, In S1, the methods for constructing the augmented dataset include: The SMOTE algorithm is used to perform linear interpolation on the original samples to augment the dataset, resulting in an augmented dataset. A conditional generative network cGAN is constructed, and the expanded dataset is used as the training condition to select sample data with a discriminator score ≥ 0.8 in order to obtain a high-confidence sample set. Metallurgical rules are introduced, and reasonable ranges for each element are set based on the Fe-C-Si ternary phase diagram and thermodynamic database to eliminate abnormal samples that exceed the range in the high-confidence sample set; The augmented dataset is obtained by merging the high-confidence sample set (after removing outliers) with the original sample set.

3. The low-cost, high-strength, and high-wear-resistant ductile iron design method based on small-sample machine learning according to claim 1, characterized in that, The augmented dataset is divided into training and testing sets according to a preset ratio, and 10-fold cross-validation is used to evaluate the model performance, with MAPE as the evaluation metric.

4. The low-cost, high-strength, and high-wear-resistant ductile iron design method based on small-sample machine learning according to claim 1, characterized in that, The steps in S2 are as follows: S2.1 Based on the augmented dataset obtained in S1, extract the physicochemical features of each element in the dataset to construct an initial feature matrix; and calculate the mean and variance of each feature. S2.

2. Using the Pearson correlation coefficient, redundant features with absolute values ​​greater than the threshold are removed. Then, using support vector regression (SVR) as the base model, radial basis function is used to remove features that contribute the least to the model until the cross-validation error no longer decreases, thus completing the screening operation. S2.

3. Construct a multi-scale, multi-layer recurrent convolutional network, introduce an adaptive kernel scale selection mechanism, and calculate the number of recurrent layers for the selected features, as shown below: In the formula, Indicates feature dimension; Indicates the candidate convolution kernel scale; Indicates the loop depth; S2.4, Based on the first layer input h (l- ¹ ) Residual connections and gating mechanisms are introduced into each recurrent convolutional layer to enhance gradient flow and nonlinear expression capabilities, as expressed in the following expression: In the formula, Indicates the level index; Represents standard convolution; Indicates gated convolution; This indicates element-wise multiplication; This represents the Sigmoid activation function; S2.

5. Apply SENet-style attention weighting in the channel dimension and self-attention weighting in the spatial dimension to the convolutional feature map respectively. After generating the weighted feature map, perform residual fusion with the original feature map to obtain the enhanced feature representation. The operation performed by channel attention is: for h (k) After global flat pooling, the channel weights are obtained through two fully connected layers and Sigmoid activation, and then compared with h. (k) Multiply each channel sequentially to obtain the channel-weighted feature map; The spatial attention operation is as follows: the average and maximum values ​​of the channel weighted feature maps are taken along the channel dimension, concatenated and then passed through a convolutional layer to generate a spatial weight map, and the spatial weight map is multiplied element by element with the feature map to obtain the spatial weighted feature map; The residual fusion operation is as follows: the spatially weighted feature map is combined with h (k) The residuals are summed to obtain the enhanced feature map; S2.6 Perform principal component analysis (PCA) on the feature map after residual fusion, calculate the variance contribution rate of each principal component, and obtain the key alloy characteristics of mechanical properties.

5. The low-cost, high-strength, and high-wear-resistant ductile iron design method based on small-sample machine learning according to claim 1, characterized in that, The steps in S3 are as follows: S3.1 Based on the key alloy features output by S2, for the tensile strength prediction task, a preset number of the most critical features are selected and denoted as vectors. For the wear rate prediction task, a predetermined number of the most critical features are selected and denoted as vectors. ; S3.2 Construct a tensile strength prediction model f1(x); The construction methods include: based on Support Vector Regression (SVR), a hybrid kernel function is constructed using a multi-kernel learning mechanism that integrates Radial Basis Function (RBF), Polynomial kernel (Poly), and Sigmoid kernel function. The expression is as follows: In the formula, This represents different kernel learning mechanisms, among which, Radial basement membrane (RBF) For polynomial kernel Poly, For the Sigmoid kernel function; Indicates the first The weights of each kernel function; Represents the input vector; Indicates the first training set Key feature vectors of each sample; Introducing an exponential collaborative term for element interactions, the complete model expression is: In the formula, Represents the first kind of Lagrange multipliers; Represents the model bias term; Indicates the synergistic effect coefficient; This represents the total number of key features. Indicates feature index; Indicates the first The numerical values ​​of the key features; Indicates the first The sample mean of each key feature; Indicates the first The collaborative sensitivity index of each element; S3.3 Construct the wear rate prediction model f2(x), with the following expression: In the formula, Indicates the wear resistance correction factor; Indicates the number of support vectors; Indicates the second kind of Lagrange multiplier; Indicates and A hybrid kernel function that is compatible with each other; Represents the model bias term; Indicates the wear inhibition coefficient; Indicates the first Attention weights for key features; Indicates the synergistic wear factor; Indicates the first Sensitivity index of each element; Wear mechanism classification embedding: Based on the wear rate value, the samples are divided into three categories: slight wear (WR < 0.06 mg / m), moderate wear (0.06 ≤ WR ≤ 0.10 mg / m), and severe wear (WR > 0.10 mg / m). Three sub-models are trained for each category, and the final output is weighted and fused. S3.4 Combine f1(x) and f2(x) into a multi-objective optimization function F(x) = [f1(x), f2(x)], with the optimization objective being to maximize f1(x) and minimize f2(x) to obtain the predicted values ​​of UTS and WR.

6. The low-cost, high-strength, and high-wear-resistant ductile iron design method based on small-sample machine learning according to claim 1, characterized in that, In S4, the improvement strategy includes: Dynamic fitness sharing strategy: The sharing radius is dynamically adjusted according to the population density in each generation. ,initial Reduce when the average congestion distance is less than the threshold. Conversely, it increases to maintain a uniform distribution of the Pareto front. Local search strategy: every interval In this step, a particle swarm local search is performed on the current Pareto solution set to improve the convergence speed; Diversity preservation mechanism: A pruning strategy based on angular distance is adopted, which prioritizes the retention of solutions with the largest angular distance from other individuals during environmental selection.

7. The low-cost, high-strength, and high-wear-resistant ductile iron design method based on small-sample machine learning according to claim 1, characterized in that, In S5, the random forest mapping model includes the following mechanisms: Feature importance feedback mechanism: The feature importance ranking of the random forest output is fed back to S2 to dynamically adjust the feature selection threshold; Uncertainty quantification mechanism: Monte Carlo dropout is introduced into the model to output the uncertainty interval of component predictions, which guides the priority of experimental verification; Closed-loop automatic retraining mechanism: When experimental performance fails to meet the standard, new samples are automatically added to the dataset, triggering model retraining and adaptive parameter updates, forming a closed-loop optimization system of "data-model-experiment".

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