Method for designing low-cost, high-strength and high-toughness nodular cast iron based on machine learning

Abstract

The invention discloses a method for designing low-cost, high-strength and high-toughness nodular cast iron based on machine learning, and belongs to the technical field of metal material preparation and the field of computer science. According to the method, nodular cast iron data are subjected to feature interaction operation and input into an MLP-GAN model, an alloy feature formula is obtained, reverse modeling is conducted based on the alloy feature formula to obtain a component scheme meeting the performance, and a final scheme is obtained through an alloy cooperation index formula. Meanwhile, on the basis of a Transform prediction tissue form, ultimate tensile strength and elongation solution formulas are finally constructed, and a result considering cost and performance is obtained in combination with the simulation cloud picture. The research and development period is shortened through the machine learning model; by means of the synergistic effect of intelligent model optimization elements, high strength and high toughness are achieved at the same time, and the teeterboard effect of the two in the traditional design is broken through; and the microstructure is predicted and accurately regulated through an intelligent model, so that the product performance consistency is improved by 30% or above, and the performance fluctuation is greatly reduced.

Description

Technical Field

[0001] This invention relates to the fields of metal material preparation technology and computer science, specifically to a method for designing low-cost, high-strength, and high-toughness ductile iron based on machine learning. Background Technology Ductile iron, as a cast iron material with excellent comprehensive properties, has been widely used in industrial fields due to its good strength, toughness, and casting performance. However, traditional ductile iron design methods often rely on experience accumulation and repeated experiments, resulting in problems such as long research and development cycles, high costs, and difficulty in achieving a balance between performance and cost.

[0002] With the continuous development of industry, the performance requirements for ductile iron are increasing. Not only must it possess high strength and toughness, but costs must also be controlled to enhance market competitiveness. Traditional methods struggle to precisely control alloy composition and process parameters, making it difficult to achieve an effective combination of low cost and high strength and toughness. Therefore, there is an urgent need for an advanced design method to optimize the composition and manufacturing process of ductile iron to meet the demands of modern industry.

[0003] The development of machine learning technology has provided new ideas for materials design. By analyzing and modeling large amounts of data, the complex relationships between material composition, process parameters, and performance can be uncovered, enabling precise material design and optimization. Based on this, this invention proposes a method for designing low-cost, high-strength, and high-toughness ductile iron based on machine learning, to address the shortcomings of traditional design methods. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for designing low-cost, high-strength, and high-toughness ductile iron based on machine learning.

[0005] To achieve the above technology, the specific steps include: S1. Collect ductile iron data and perform preprocessing operations on the collected data; Data for ductile iron includes: composition, process parameters, and mechanical properties; The composition includes: carbon (C) 3.1 - 4.0%, silicon (Si) 2.1 - 2.9%, manganese (Mn) 0.05 - 0.3%, phosphorus (P) ≤0.07%, sulfur (S) ≤0.025%, magnesium (Mg) 0.028 - 0.045%, rare earth (RE) 0.01 - 0.03%, bismuth (Bi) 0.0008-0.004%, titanium (Ti) 0.008-0.025%, boron (B) 0.0003-0.0015%, trace amounts of graphene derivatives (GRD) 0.0001-0.0005%, with the balance being iron (Fe); Preprocessing methods include: Outlier Removal: The interquartile range (IQR) method is used to identify and remove outliers in the component and performance data. Outliers are identified by calculating the middle 50% range of the data. First, the data is sorted in ascending order. Then, the first quartile (Q1) and third quartile (Q3) are determined. The first quartile (Q1) is the value at the 25th percentile, and the third quartile (Q3) is the value at the 75th percentile. The interquartile range is calculated using the following formula: Located in Q1 Data points outside the ranges of 1.5×IQR and Q3+1.5×IQR are considered outliers and are removed. Missing value imputation: Based on the K-nearest neighbor algorithm, imputation is performed using samples with similar components; Normalization: The component data is normalized to map the content of each element to the [0, 1] interval, which facilitates model training. The formula is as follows: In the formula, Represents the original data. and These represent the minimum and maximum values ​​in the dataset, respectively. This represents the normalized data.

[0006] S2. Based on the preprocessed data, perform feature engineering interactive operations to obtain comprehensive features; Feature engineering interactive operations include: Constructing interaction features: Create binary and ternary interaction features between elements, such as [C]×[Si] and [Mn]×[Bi]×[Ti]; Constructing domain characteristics: Calculating classical thermodynamic formulas, such as carbon equivalent CE=[C]+1 / 3 [Si], while introducing empirical characteristics based on historical experimental data statistics, such as the graphite spheroidization coefficient of specific element combinations; The method for obtaining the comprehensive features is to concatenate the preprocessed data, interaction features, and domain features into a comprehensive feature vector. x .

[0007] S3. Construct an MLP-GAN model, train the model based on comprehensive features to obtain a positive predictor generator, and obtain the alloy feature formula; Multilayer perceptron (MLP) is used as the generator of GAN to learn the mapping relationship between input data and target attributes; during training, the generator attempts to deceive the discriminator, making the discriminator mistakenly believe that the data it generates is real experimental data. In the generator, random noise z and the comprehensive feature vector are combined. x The generator takes concatenation as input and contains L hidden layers, with the first layer's input being h.(0) h (0) =[z;x], through the calculation of the hidden layer, the performance-related parameters of the prediction are obtained. ; The hidden layer is calculated as follows: h (l+1) =σ(W (l) h (l) +b (l) ), l =0, 1, ..., L 1, where σ(·) represents the activation function, W (l) Let b represent the weight matrix of the generator. (l) h represents the bias vector of the generator; (l) The generator's first... l The result of the layer; Performance parameters related to output layer prediction The method is as follows: =W (L) h (L) +b (L) , where h (L) This indicates the output of the last layer; A multilayer perceptron (MLP) is used as the discriminator in the GAN to determine whether the input data comes from real experimental data y or data generated by the generator. After receiving the data, the network layer extracts and analyzes the data features, and finally outputs a probability value D(·), which represents the probability that the input data is real data; In the discriminator, the input data is d, and after multiple layers of calculation, it outputs a probability value between [0,1]. The specific calculation process is as follows: Initial input: h1 (0) =d; Hidden layer calculation: h1 (m+1) =σ(W (m) h1 (m) +b (m) ), m=0,1,...,M 1, where M represents the number of hidden layers in the discriminator, σ(·) represents the activation function, and W (m) b represents the weight matrix of the discriminator. (m) h represents the bias vector of the discriminator. (m) This represents the result of the m-th layer of the discriminator; Output layer: D(d) = σ(W) (M) h (M) +b (M)), where D(d) represents the probability that data d is real data. When D(d) is close to 1, it means that the discriminator considers d to be real data; when D(d) is close to 0, it means that the discriminator considers d to be generated data. During the training of Generative Adversarial Networks (GANs), the performance of the generator and discriminator is measured by defining a loss function, and the network parameters are updated using optimization algorithms such as gradient descent. Generator loss function: In the formula, This represents the total loss of the generator; Let z represent the expectation of random noise z; Let z represent the distribution of random noise, from which random noise z is sampled; The generator is based on random noise z and the combined eigenvector. x The goal of the generator is to make the discriminator mistakenly identify the generated data as real data, i.e., to maximize D(G(z,x)). Therefore, the loss function of the generator is to maximize the logarithm of the probability that the discriminator judges the generated data as real. Discriminator loss function: In the formula, Represents the expectation about the experimental data y, where, This represents the distribution of the real data, from which the experimental data y is sampled; The first term of the discriminator loss function represents the discriminator's ability to judge real data, aiming to make the discriminator judge real data as true as possible (i.e., D(y) is close to 1); the second term represents the discriminator's ability to judge generated data, aiming to make the discriminator judge generated data as false as possible (i.e., D(G(z,x)) is close to 0). Extract nonlinear functions from the trained GAN to construct alloy feature formulas: In the formula, , , , The first, second, third, and fourth nonlinear functions, obtained through training with a generative adversarial network (GAN), are used to dynamically quantify the complex interactions between elements and achieve precise control of organizational performance.

[0008] S4. Based on the alloy characteristic formula, the composition is optimized using reverse modeling to obtain a composition scheme that meets the target performance. Reverse modeling methods include: With the target performance as a constraint, i.e., if the target tensile strength is ≥700MPa, the corresponding [performance value] is calculated using a function. The value needs to be ≥2000. Combined with the original interval [1800, 3200], determine the inverse modeling... The target range is [2000, 3200]; The element content in the alloy characteristic formula is solved by inversely using the gradient descent method, i.e., using the alloy characteristic formula. To achieve the goal, construct the loss function: In the formula, This indicates the result calculated based on the current element content. value; It is the value within the target interval; calculate the partial derivative of the loss function with respect to the content of each element, adjust the element content along the gradient descent direction, increasing the element content will... Increase, when < When necessary, increase the content of the element, adjusting the step size each time by 0.01%-0.1% of the element content range to avoid exceeding the boundary; repeat the calculation and update process until... and If the difference is less than a preset threshold, a set of preliminary conditions is obtained. Required element content; In the solution process, simulated annealing algorithm is introduced. The preliminary components obtained by gradient descent are used as the initial solution of simulated annealing, and their corresponding solutions are calculated. The values ​​and loss function values ​​are evaluated, and random perturbations are introduced with a perturbation amplitude of 0.05%-0.5% of the content range. Neighborhood solutions are generated to ensure that the element content after perturbation remains within a reasonable range. Inferior solutions are accepted according to the Metropolis criterion to escape local optima and perform a global search. The Metropolis criteria are expressed as follows: In the formula, The difference represents the loss function value; T represents the current annealing temperature. The initial annealing temperature T0 is set to 100, and the temperature is decreased by 5% every 100 iterations until it drops to 1. After a large number of iterations, a search is conducted globally to find the optimal annealing temperature. The combination of elements that falls within the target interval and minimizes the loss function is used to avoid gradient descent getting trapped in local optima. Finally, the optimized element content can be substituted into the element interaction verification experiment. , , , Functions were used to verify whether the output values ​​of each function conformed to the element interaction patterns during GAN training; orthogonal experiments were designed to fix the content of some elements and adjust the content of other elements, and observations were made. Does the change in value conform to the logic of the formula?

[0009] S5. Based on the optimized composition scheme, the final composition scheme is obtained by constructing an alloy synergy index formula to enhance synergy optimization. The formula for the alloy synergy index is as follows: In the formula, The reinforcement learning model function is a non-linear function obtained by training a deep Q-network. Methods for constructing the alloy synergy index formula include: (a) Perform data augmentation operations based on the data after preprocessing; (b) Processing the expanded dataset, including: Grayscale conversion, noise reduction, and feature dimensionality reduction; (c) Based on the expanded data in (a) and the organizational features obtained in (b), construct association features; The construction method is as follows: The correlation feature is defined as the correlation between an element and a tissue feature, such as the correlation coefficient between [C] and pearlite content; Design state characteristics to define the state of the learning process, including: the current combination of elemental contents, microstructure parameters, and mechanical performance indicators; Design motion features to define the adjustment step size for element content; (d) Based on the association features obtained in (c), train the RL model; A deep Q-network algorithm is employed, using state features as input. A multilayer perceptron outputs the Q-value corresponding to each action. The agent selects actions based on these Q-values, adjusts element content, and interacts with a simulated ductile iron composition-performance environment to obtain performance improvements. Through continuous iterative learning, the agent adaptively optimizes element synergy to enhance overall mechanical properties. If the adjusted... Positive rewards are given for objects that are close to the center of the target region [900, 1300] and have good mechanical properties; negative rewards are given for objects that deviate from the target region. Through iterative training, the agent gradually learns the optimal strategy of adjusting the element content to make YRL fall into the target region. (e) Based on the trained RL model, derive the alloy synergy index formula. ; (f) Based on the derived alloy synergy index formula The optimal ingredient formulation is obtained by performing strategy gradient algorithm and genetic algorithm. Inverse search is performed using the policy gradient algorithm: Define the state, which includes the current combination of elemental contents, microstructure parameters, and real-time mechanical performance indicators; Define the adjustment step size for element content, and the agent adjusts by changing the element content. The value of ; The policy gradient method updates the agent's policy by calculating the "reward gradient": increasing the probability of an action that brings a positive reward and decreasing it conversely. Through iteration, the agent learns "how to adjust its composition to achieve the desired reward." A reverse strategy of "falling into the target range"; Global optimization using a genetic algorithm: Initialization: Use the component scheme obtained by the policy gradient method as the initial population; Choose: With The fitness function is used to select individuals with high fitness as parents and retain the element content as genes. Crossover: Mixing genes (such as the content of [C] and [Si]) from parental component schemes to generate offspring; Mutation: Randomly altering the content of certain elements in offspring to simulate gene mutation and increase population diversity; Repeated iterations: The process of repeated selection, crossover, and mutation is repeated until the individual with the highest fitness is retained, thus satisfying the condition... The optimal formula is obtained by finding the combination of elements in the range [900, 1300] with the best mechanical properties.

[0010] S6. Based on the final composition scheme, a multimodal phase transition prediction model with a Transformer architecture is used to control tissue formation; The prediction process includes: Data acquisition: Collect temperature sensor data during the smelting process, infrared thermal imager data during the cooling process, spectral data from ultrasonic vibration equipment, intensity waveform data from magnetic field generator, and phase structure data obtained using X-ray diffractometer; Data preprocessing: Moving average filtering is applied to time series data to remove high-frequency noise; multimodal data is aligned according to timestamps and normalized for different modes; phase structure data is encoded, converting phase types and contents into vector form; time-domain and frequency-domain features of multimodal data are extracted, such as the slope of temperature curves and the dominant frequency of vibration spectra; intermodal fusion features are constructed, such as the product of temperature change rate and ultrasonic vibration intensity; the contribution weights of different features to phase transitions are calculated using an attention mechanism. Transformer prediction: The Transformer architecture and multi-head attention mechanism are used to process multimodal input features in parallel and capture long-distance dependencies between different features. Feature transformation and prediction are performed through a feedforward neural network, and the output includes prediction results including the dynamic ratio change of pearlite-ferrite, the real-time growth trajectory of graphite spheres, and the distribution of nanoscale second phase precipitation. Reverse process control: Guided by the target microstructure parameters, the model parameters are adjusted through the backpropagation algorithm to calculate the adjustment amount of process parameters that makes the predicted results meet the requirements, thus realizing the control of process parameters through model feedback; the specific process includes: defining the objective function L1 as the deviation between the predicted microstructure parameters and the target parameters, the expression of which is as follows: In the formula, Indicates the total number of micro-organisms. Indexes representing microstructures; Indicates the weighting coefficient; Represents microstructure parameters, This represents the model's predicted value. Indicates the target value; Indicates Euclidean distance; The process parameters are adjusted by inverse gradient descent, where the gradient function expression is as follows: In the formula, The loss function is expressed as a function of process parameters. The gradient; This represents the model's predicted output; The expression for adjusting the process parameters is as follows: In the formula, express Process parameters under the next iteration; Indicates the first The process parameters for the next iteration; This represents the learning rate, used to adjust the range of process parameter adjustments.

[0011] S7. Combining all the results from S1 to S6, construct the formulas for solving the ultimate tensile strength and elongation of ductile iron. By combining the alloying elements, microstructure, grayscale values ​​of microscopic images, dynamic changes in the pearlite-ferrite ratio, real-time growth trajectory of graphite spheroids, and nanoscale second-phase precipitation with the mechanical properties of ductile iron, formulas for calculating the ultimate tensile strength and elongation of ductile iron are constructed, as follows: In the formula, Formula for ultimate tensile strength; The power function representing the pearlite-ferrite ratio, where, The power-law exponent is one of the core organizational parameters that are primarily predicted and controlled through the Transformer multimodal model. This indicates the attenuation effect of internal stress. Indicates stress, This represents the first characteristic attenuation length parameter; The power function representing the density of the nanoscale second phase precipitation is given by, where, Indicates the impact index; This represents the average gray value of a microscopic image; Indicates the standard deviation of the graphite sphere diameter; Indicates the graphite size sensitivity parameter; This represents the temperature change during the cooling process. It originates from temperature sensor data in multimodal data acquisition and serves as the input to the Transformer model, used to predict the phase transition process. This represents the second characteristic attenuation length parameter; Indicates the alloy characteristic index; Indicates the alloy synergy index; This represents the model bias correction term; , , This represents the first, second, and third basic weighting coefficients of each item; and These represent the first regularization parameter and the second regularization parameter, respectively. This indicates the average roundness of the graphite spheres. Logarithmic sensitivity to the roundness of graphite spheres; The ratio is pearlite to ferrite; This represents the standard deviation of the graphite sphere size. Indicates the grayscale contrast of a microscopic image; Saturation parameters that represent grayscale contrast; This indicates the density of the nanoscale second phase precipitation; and They represent The first Gaussian distribution parameter and the second Gaussian distribution parameter; This represents the model bias correction term; , and These represent the fourth, fifth, and sixth basic weighting coefficients for each item, respectively. , and These represent the third, fourth, and fifth regularization parameters, respectively.

[0012] S8. A machine learning-driven topology gradient alloying process is used. The stress cloud map of the casting is analyzed by deep learning image algorithm. With the goal of comprehensive optimization of cost and performance, the scheme is optimized globally by combining particle swarm optimization algorithm.

[0013] Beneficial effects of the present invention This invention uses machine learning models to conduct "virtual experiments," replacing time-consuming and costly physical trial and error, thus shortening the R&D cycle. By using intelligent models to optimize the synergistic effect of elements, it successfully achieves both high strength and high toughness simultaneously, breaking the "seesaw" effect where the two are mutually exclusive in traditional designs. Through intelligent model prediction and precise control of microstructure, the consistency of product performance is improved by more than 30%, greatly reducing performance fluctuations. Attached Figure Description

[0014] Figure 1 This is a flowchart of the steps of the present invention. 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 method for designing low-cost, high-strength, and high-toughness ductile iron based on machine learning includes the following steps: S1. Collect ductile iron data and perform preprocessing operations on the collected data; The data collection method involved collecting over 500,000 sets of ductile iron data from nearly 10 years of data from databases of more than 200 materials research institutions and more than 500 casting companies worldwide, as well as papers from well-known academic journals, to cover samples under different smelting equipment, casting processes and service scenarios. Data for ductile iron includes: composition, process parameters, and mechanical properties; The composition includes: carbon (C) 3.1 - 4.0%, silicon (Si) 2.1 - 2.9%, manganese (Mn) 0.05 - 0.3%, phosphorus (P) ≤0.07%, sulfur (S) ≤0.025%, magnesium (Mg) 0.028 - 0.045%, rare earth (RE) 0.01 - 0.03%, bismuth (Bi) 0.0008-0.004%, titanium (Ti) 0.008-0.025%, boron (B) 0.0003-0.0015%, trace amounts of graphene derivatives (GRD) 0.0001-0.0005%, with the balance being iron (Fe); Preprocessing methods include: Outlier Removal: The interquartile range (IQR) method is used to identify and remove outliers in the component and performance data. Outliers are identified by calculating the middle 50% range of the data. First, the data is sorted in ascending order. Then, the first quartile (Q1) and third quartile (Q3) are determined. The first quartile (Q1) is the value at the 25th percentile, and the third quartile (Q3) is the value at the 75th percentile. The interquartile range is calculated using the following formula: Located in Q1 Data points outside the ranges of 1.5×IQR and Q3+1.5×IQR are considered outliers and are removed. Missing value imputation: Based on the K-nearest neighbor algorithm, imputation is performed using samples with similar components; Normalization: The component data is normalized to map the content of each element to the [0, 1] interval, which facilitates model training. The formula is as follows: In the formula, Represents the original data. and These represent the minimum and maximum values ​​in the dataset, respectively. This represents the normalized data.

[0017] S2. Based on the preprocessed data, perform feature engineering interactive operations to obtain comprehensive features; Feature engineering interactive operations include: Constructing interaction features: Create binary and ternary interaction features between elements, such as [C]×[Si] and [Mn]×[Bi]×[Ti]; Constructing domain characteristics: Calculating classical thermodynamic formulas, such as carbon equivalent CE=[C]+1 / 3 [Si], while introducing empirical characteristics based on historical experimental data statistics, such as the graphite spheroidization coefficient of specific element combinations; The method for obtaining the comprehensive features is to concatenate the preprocessed data, interaction features, and domain features into a comprehensive feature vector. x .

[0018] S3. Construct an MLP-GAN model, train the model based on comprehensive features to obtain a positive predictor generator, and obtain the alloy feature formula; Multilayer perceptron (MLP) is used as the generator of GAN to learn the mapping relationship between input data and target attributes; during training, the generator attempts to deceive the discriminator, making the discriminator mistakenly believe that the data it generates is real experimental data. In the generator, random noise z and the comprehensive feature vector are combined. x The generator takes concatenation as input and contains L hidden layers, with the first layer's input being h.(0) h (0) =[z;x], through the calculation of the hidden layer, the performance-related parameters of the prediction are obtained. ; The hidden layer is calculated as follows: h (l+1) =σ(W (l) h (l) +b (l) ), l =0, 1, ..., L 1, where σ(·) represents the activation function, W (l) Let b represent the weight matrix of the generator. (l) h represents the bias vector of the generator; (l) The generator's first... l The result of the layer; Performance parameters related to output layer prediction The method is as follows: =W (L) h (L) +b (L) , where h (L) This indicates the output of the last layer; A multilayer perceptron (MLP) is used as the discriminator in the GAN to determine whether the input data comes from real experimental data y or data generated by the generator. After receiving the data, the network layer extracts and analyzes the data features, and finally outputs a probability value D(·), which represents the probability that the input data is real data; In the discriminator, the input data is d, and after multiple layers of calculation, it outputs a probability value between [0,1]. The specific calculation process is as follows: Initial input: h1 (0) =d; Hidden layer calculation: h1 (m+1) =σ(W (m) h1 (m) +b (m) ), m=0,1,...,M 1, where M represents the number of hidden layers in the discriminator, σ(·) represents the activation function, and W (m) b represents the weight matrix of the discriminator. (m) h represents the bias vector of the discriminator. (m) This represents the result of the m-th layer of the discriminator; Output layer: D(d) = σ(W) (M) h (M) +b (M)), where D(d) represents the probability that data d is real data. When D(d) is close to 1, it means that the discriminator considers d to be real data; when D(d) is close to 0, it means that the discriminator considers d to be generated data. During the training of Generative Adversarial Networks (GANs), the performance of the generator and discriminator is measured by defining a loss function, and the network parameters are updated using optimization algorithms such as gradient descent. Generator loss function: In the formula, This represents the total loss of the generator; Let z represent the expectation of random noise z; Let z represent the distribution of random noise, from which random noise z is sampled; The generator is based on random noise z and the combined eigenvector. x The goal of the generator is to make the discriminator mistakenly identify the generated data as real data, i.e., to maximize D(G(z,x)). Therefore, the loss function of the generator is to maximize the logarithm of the probability that the discriminator judges the generated data as real. Discriminator loss function: In the formula, Represents the expectation about the experimental data y, where, This represents the distribution of the real data, from which the experimental data y is sampled; The first term of the discriminator loss function represents the discriminator's ability to judge real data, aiming to make the discriminator judge real data as true as possible (i.e., D(y) is close to 1); the second term represents the discriminator's ability to judge generated data, aiming to make the discriminator judge generated data as false as possible (i.e., D(G(z,x)) is close to 0). Extract nonlinear functions from the trained GAN to construct alloy feature formulas: In the formula, , , , The first, second, third, and fourth nonlinear functions, obtained through training with a generative adversarial network (GAN), are used to dynamically quantify the complex interactions between elements and achieve precise control of organizational performance.

[0019] S4. Based on the alloy characteristic formula, the composition is optimized using reverse modeling to obtain a composition scheme that meets the target performance. Reverse modeling methods include: With the target performance as a constraint, i.e., if the target tensile strength is ≥700MPa, the corresponding [performance value] is calculated using a function. The value needs to be ≥2000. Combined with the original interval [1800, 3200], determine the inverse modeling... The target range is [2000, 3200]; The element content in the alloy characteristic formula is solved by inversely using the gradient descent method, i.e., using the alloy characteristic formula. To achieve the goal, construct the loss function: In the formula, This indicates the result calculated based on the current element content. value; It is the value within the target interval; calculate the partial derivative of the loss function with respect to the content of each element, adjust the element content along the gradient descent direction, increasing the element content will... Increase, when < When necessary, increase the content of the element, adjusting the step size each time by 0.01%-0.1% of the element content range to avoid exceeding the boundary; repeat the calculation and update process until... and If the difference is less than a preset threshold, a set of preliminary conditions is obtained. Required element content; In the solution process, simulated annealing algorithm is introduced. The preliminary components obtained by gradient descent are used as the initial solution of simulated annealing, and their corresponding solutions are calculated. The values ​​and loss function values ​​are evaluated, and random perturbations are introduced with a perturbation amplitude of 0.05%-0.5% of the content range. Neighborhood solutions are generated to ensure that the element content after perturbation remains within a reasonable range. Inferior solutions are accepted according to the Metropolis criterion to escape local optima and perform a global search. The Metropolis criteria are expressed as follows: In the formula, The difference represents the loss function value; T represents the current annealing temperature. The initial annealing temperature T0 is set to 100, and the temperature is decreased by 5% every 100 iterations until it drops to 1. After a large number of iterations, a search is conducted globally to find the optimal annealing temperature. The combination of elements that falls within the target interval and minimizes the loss function is used to avoid gradient descent getting trapped in local optima. Finally, the optimized element content can be substituted into the element interaction verification experiment. , , , Functions were used to verify whether the output values ​​of each function conformed to the element interaction patterns during GAN training; orthogonal experiments were designed to fix the content of some elements and adjust the content of other elements, and observations were made. Does the change in value conform to the logic of the formula?

[0020] S5. Based on the optimized composition scheme, the final composition scheme is obtained by constructing an alloy synergy index formula to enhance synergy optimization. The formula for the alloy synergy index is as follows: In the formula, The reinforcement learning model function is a non-linear function obtained by training a deep Q-network. Methods for constructing the alloy synergy index formula include: (a) Data augmentation based on preprocessed data: Supplement the collection of microstructure data of ductile iron after different heat treatment processes, including the pearlite-ferrite ratio, graphite spheroid size distribution, and microstructure images obtained by electron microscopy imaging, and extract quantitative features by combining image analysis software. (b) Processing the expanded dataset, including: Grayscale conversion: Converts a color RGB image to a grayscale image. The expression is as follows: In the formula, R represents the red channel; G represents the green channel; B represents the blue channel; the calculated gray values ​​are mapped to the 0-255 range to generate a single-channel grayscale image, in which the contrast between dark graphite, bright pearlite, and gray ferrite is preserved; Noise reduction: Gaussian filtering and median filtering are used to remove noise from the image; an appropriate Gaussian kernel size is selected, the weighted average of each pixel with its surrounding pixels is calculated, and the image is convolved to reduce high-frequency noise; isolated bright or dark spots are replaced with the median of the pixel's neighborhood, and the average value of similar pixel blocks in the image is taken as the filtering result. Feature dimensionality reduction: Principal component analysis (PCA) is performed on the denoised features to retain more than 95% of the information and reduce data complexity; (c) Based on the expanded data in (a) and the organizational features obtained in (b), construct association features; The construction method is as follows: The correlation feature is defined as the correlation between an element and a tissue feature, such as the correlation coefficient between [C] and pearlite content; Design state characteristics to define the state of the learning process, including: the current combination of elemental contents, microstructure parameters, and mechanical performance indicators; Design motion features to define the adjustment step size for element content; (d) Based on the association features obtained in (c), train the RL model; A deep Q-network algorithm is employed, using state features as input. A multilayer perceptron outputs the Q-value corresponding to each action. The agent selects actions based on these Q-values, adjusts element content, and interacts with a simulated ductile iron composition-performance environment to obtain performance improvements. Through continuous iterative learning, the agent adaptively optimizes element synergy to enhance overall mechanical properties. If the adjusted... Positive rewards are given for objects that are close to the center of the target region [900, 1300] and have good mechanical properties; negative rewards are given for objects that deviate from the target region. Through iterative training, the agent gradually learns the optimal strategy of adjusting the element content to make YRL fall into the target region. (e) Based on the trained RL model, derive the alloy synergy index formula. ; (f) Based on the derived alloy synergy index formula The optimal ingredient formulation is obtained by performing strategy gradient algorithm and genetic algorithm. Inverse search is performed using the policy gradient algorithm: Define the state, which includes the current combination of elemental contents, microstructure parameters, and real-time mechanical performance indicators; Define the adjustment step size for element content, and the agent adjusts by changing the element content. The value of ; The policy gradient method updates the agent's policy by calculating the "reward gradient": increasing the probability of an action that brings a positive reward and decreasing it conversely. Through iteration, the agent learns "how to adjust its composition to achieve the desired reward." A reverse strategy of "falling into the target range"; Global optimization using a genetic algorithm: Initialization: Use the component scheme obtained by the policy gradient method as the initial population; Choose: With The fitness function is used to select individuals with high fitness as parents and retain the element content as genes. Crossover: Mixing genes (such as the content of [C] and [Si]) from parental component schemes to generate offspring; Mutation: Randomly altering the content of certain elements in offspring to simulate gene mutation and increase population diversity; Repeated iterations: The process of repeated selection, crossover, and mutation is repeated until the individual with the highest fitness is retained, thus satisfying the condition... The optimal formula is obtained by finding the combination of elements in the range [900, 1300] with the best mechanical properties.

[0021] S6. Based on the final composition scheme, a multimodal phase transition prediction model with a Transformer architecture is used to control tissue formation; The prediction process includes: Data acquisition: Collect temperature sensor data during the smelting process, infrared thermal imager data during the cooling process, spectral data from ultrasonic vibration equipment, intensity waveform data from magnetic field generator, and phase structure data obtained using X-ray diffractometer; Data preprocessing: Moving average filtering is applied to time series data to remove high-frequency noise; multimodal data is aligned according to timestamps and normalized for different modes; phase structure data is encoded, converting phase types and contents into vector form; time-domain and frequency-domain features of multimodal data are extracted, such as the slope of temperature curves and the dominant frequency of vibration spectra; intermodal fusion features are constructed, such as the product of temperature change rate and ultrasonic vibration intensity; the contribution weights of different features to phase transitions are calculated using an attention mechanism. Transformer prediction: The Transformer architecture and multi-head attention mechanism are used to process multimodal input features in parallel and capture long-distance dependencies between different features. Feature transformation and prediction are performed through a feedforward neural network, and the output includes prediction results including the dynamic ratio change of pearlite-ferrite, the real-time growth trajectory of graphite spheres, and the distribution of nanoscale second phase precipitation. Reverse process control: Guided by the target microstructure parameters, the model parameters are adjusted through the backpropagation algorithm to calculate the adjustment amount of process parameters that makes the predicted results meet the requirements, thus realizing the control of process parameters through model feedback; the specific process includes: defining the objective function L1 as the deviation between the predicted microstructure parameters and the target parameters, the expression of which is as follows: In the formula, Indicates the total number of micro-organisms. Indexes representing microstructures; Indicates the weighting coefficient; Represents microstructure parameters, This represents the model's predicted value. Indicates the target value; Indicates Euclidean distance; The process parameters are adjusted by inverse gradient descent, where the gradient function expression is as follows: In the formula, The loss function is expressed as a function of process parameters. The gradient; This represents the model's predicted output; The expression for adjusting the process parameters is as follows: In the formula, express Process parameters under the next iteration; Indicates the first The process parameters for the next iteration; This represents the learning rate, used to adjust the range of process parameter adjustments.

[0022] S7. Combining all the results from S1 to S6, construct the formulas for solving the ultimate tensile strength and elongation of ductile iron. By combining the alloying elements, microstructure, grayscale values ​​of microscopic images, dynamic changes in the pearlite-ferrite ratio, real-time growth trajectory of graphite spheroids, and nanoscale second-phase precipitation with the mechanical properties of ductile iron, formulas for calculating the ultimate tensile strength and elongation of ductile iron are constructed, as follows: In the formula, Formula for ultimate tensile strength; The power function representing the pearlite-ferrite ratio, where, The power-law exponent is one of the core organizational parameters that are primarily predicted and controlled through the Transformer multimodal model. This indicates the attenuation effect of internal stress. Indicates stress, This represents the first characteristic attenuation length parameter; The power function representing the density of the nanoscale second phase precipitation is given by, where, Indicates the impact index; This represents the average gray value of a microscopic image; Indicates the standard deviation of the graphite sphere diameter; Indicates the graphite size sensitivity parameter; This represents the temperature change during the cooling process. It originates from temperature sensor data in multimodal data acquisition and serves as the input to the Transformer model, used to predict the phase transition process. This represents the second characteristic attenuation length parameter; Indicates the alloy characteristic index; Indicates the alloy synergy index; This represents the model bias correction term; , , This represents the first, second, and third basic weighting coefficients of each item; and These represent the first regularization parameter and the second regularization parameter, respectively. This indicates the average roundness of the graphite spheres. Logarithmic sensitivity to the roundness of graphite spheres; The ratio is pearlite to ferrite; This represents the standard deviation of the graphite sphere size. Indicates the grayscale contrast of a microscopic image; Saturation parameters that represent grayscale contrast; This indicates the density of the nanoscale second phase precipitation; and They represent The first Gaussian distribution parameter and the second Gaussian distribution parameter; This represents the model bias correction term; , , These represent the fourth, fifth, and sixth basic weighting coefficients for each item, respectively. , , These represent the third, fourth, and fifth regularization parameters, respectively.

[0023] S8. A machine learning-driven topology gradient alloying process is used. The stress cloud map of the casting is analyzed by deep learning image algorithm. With the goal of comprehensive optimization of cost and performance, the scheme is optimized globally by combining particle swarm optimization algorithm. Specifically, stress cloud maps of castings under different shapes and load conditions are simulated using finite element analysis software, generating 100,000 sets of stress data for different working conditions. Combined with stress test data from actual castings, a stress-composition-performance dataset is constructed. Geometric features of the stress cloud maps, such as the area and perimeter of stress concentration regions, are extracted. Stress gradient features are calculated to reflect the severity of stress changes. Correlation features between stress and composition are constructed, such as the strengthening effect coefficient of elements corresponding to specific stress regions. The U-Net deep learning image segmentation algorithm is used, taking the stress cloud map as input, to output a binarized segmented image of the stress concentration region. Based on the segmentation results, a decision tree algorithm is used to establish a mapping relationship between stress regions and gradient component distribution, automatically generating component addition schemes. With the goal of comprehensive cost and performance optimization, the required stress distribution is deduced from the target mechanical property distribution using reverse engineering methods. Then, based on the stress-composition mapping relationship, the component adjustment scheme for each region is solved in reverse, and the scheme is globally optimized using a particle swarm optimization algorithm. By automatically generating a gradient composition distribution scheme in the stress concentration area, 0.03-0.12% vanadium (V) and 0.01-0.05% niobium (Nb) are added to the surface layer to form a nano-precipitation reinforcement layer. The sub-surface layer uses the pre-treated basic composition, and the content of alloying elements in the internal region is reduced by 10-20%, so that the mechanical properties are distributed as needed. Compared with traditional uniform alloying, the cost is reduced by more than 40% and the performance is improved by 25%.

[0024] In this embodiment, a GAN model is trained using 500,000 sets of data to obtain a stable generator and discriminator.

[0025] By reverse modeling, set The target range is [2150, 2400].

[0026] After global optimization using gradient descent and simulated annealing algorithms, the model outputs a set of recommended components as shown in Table 1: Table 1: Recommended components output by the model in Example 1 Based on the trained GAN model, simulation calculations were performed according to the above components, and the predicted performance is: ultimate tensile strength 718 MPa, elongation 11.5%.

[0027] Verification results: Subsequent laboratory smelting and casting of test bars yielded the following experimental results: tensile strength 731 MPa and elongation 11.1%. The deviation from the model prediction was within 5%, demonstrating the effectiveness of the method.

[0028] Based on the composition, the impact toughness is further optimized by adjusting the composition, and the alloy synergy index Y_RL is ensured to fall within the ideal range of [1050, 1150].

[0029] Execution process: 1. Use the components as the initial state of the reinforcement learning agent.

[0030] 2. The agent conducted multiple rounds of "virtual experiments" based on the deep Q-network, and the actions included fine-tuning the content of Mn, Ti and RE.

[0031] 3. After optimization using the policy gradient method and genetic algorithm, the optimized components are obtained: The main changes are: Mn: 0.10% (-0.02%), Ti: 0.018% (+0.003%), RE: 0.019% (-0.003%), and other elements remain basically unchanged.

[0032] 4. Calculate the optimized result = 1087, falling within the target range.

[0033] Verification results: The test bar prepared using the optimized composition showed an increase in impact toughness (unnotched) from 18 J to 22 J, while tensile strength (713 MPa) and elongation (11.2%) remained at a high level. This indicates that through... By optimizing the indices in a coordinated manner, the "seesaw" effect between performance metrics can be effectively broken.

[0034] In this embodiment, the Transformer multimodal model guides the heat treatment process as follows: Process objectives: Optimize the ideal pearlite-ferrite ratio of the casting (target 55:45) and predict the growth of graphite nodules.

[0035] Execution process: 1. During the casting cooling process, collect multimodal data such as temperature, ultrasonic vibration, and magnetic field strength, and input them into the trained Transformer model.

[0036] 2. The model predicts in real time that the current pearlite ratio is approximately 62%, which is higher than the target value.

[0037] 3. The model calculates and outputs suggestions for adjusting process parameters through backpropagation: The air-cooling intensity was increased by 15%, and ultrasonic vibration (frequency 28kHz, intensity 0.8kW / m²) was initiated at 700℃ for 120 seconds. Validation results: The process recommended by the model was executed. Post-processing metallographic analysis showed that the final pearlite content was precisely controlled at 57%, and the graphite spheroid size distribution was more uniform (more than 90% of the graphite spheroids had a diameter between 25-45 μm). Compared with the uncontrolled conventional process, the microstructure uniformity was improved by 30%.

[0038] In this embodiment, a standard multi-notch impact specimen was selected as the verification object. The geometry of this specimen can be stably reproduced under laboratory conditions, and its stress concentration region can be accurately predicted through finite element analysis. The experimental objective is to significantly improve the impact toughness of the specimen without increasing the total alloy cost by designing a gradient composition in the predicted stress concentration region.

[0039] Execution process: 1. Stress Simulation and Data Generation: Using finite element analysis software, a mechanical simulation was performed on a standard multi-notched impact specimen, generating a high-resolution stress contour map. The finite element model calculated that under a specific load, there is significant stress concentration at the root of the notch in the specimen, with a predicted maximum stress value of 385 MPa.

[0040] 2. Image Segmentation and Composition Scheme Generation: The stress cloud map output from the finite element analysis is input into the pre-trained U-Net deep learning image segmentation model. The model successfully and accurately identifies and segments the stress concentration region at the root of the notch.

[0041] 3. Based on the segmentation results, the decision tree algorithm automatically generates a gradient component distribution scheme: Surface reinforcement zone: In the segmented stress concentration area, an alloy powder containing 0.05% V and 0.02% Nb is selectively sprayed using a small laboratory spraying device to form a nano-precipitated reinforcement layer.

[0042] Core matrix region: The internal region of the sample adopts the basic composition of claim 1, but the Mn content is reduced from 0.12% to 0.09% and the Si content is reduced from 2.45% to 2.20% to save costs.

[0043] Verification results: (1) Mechanical properties: The two groups of specimens were tested on a pendulum impact testing machine in the laboratory. The results showed that the impact absorption energy of the gradient alloying experimental group reached 24 J, while that of the control group with uniform composition was 21 J, with a performance improvement of about 14.2%.

[0044] (2) Microstructure verification: Line scanning analysis was performed on the notch root of the sample using a scanning electron microscope and an energy dispersive spectroscopy analyzer. The results clearly showed the enrichment of V and Nb elements in the surface region, and finer grains and dispersed nanoscale carbonitride precipitates were observed in this region, which explained the performance improvement from a microscopic mechanism perspective.

[0045] (3) Cost analysis: The raw material cost of the two groups of samples was calculated. Since the experimental group reduced the content of elements such as Mn and Si in most volumes and enriched V and Nb only in a very small surface area, its total alloy cost was reduced by about 15% compared with the uniform alloying control group.

[0046] It should be noted that the above are merely preferred embodiments of this application and do not limit the scope of patent protection of this application. Any equivalent structural or procedural changes made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of this application.

Claims

1. A method for designing low-cost, high-strength, and high-toughness ductile iron based on machine learning, characterized in that, Includes the following steps: S1. Collect ductile iron data and perform preprocessing operations on the collected data; S2. Based on the preprocessed data, perform feature engineering interactive operations to obtain comprehensive features; S3. Construct an MLP-GAN model, train the model based on comprehensive features to obtain a positive predictor generator, and obtain the alloy feature formula; S4. Based on the alloy characteristic formula, the composition is optimized using reverse modeling to obtain a composition scheme that meets the target performance. S5. Based on the optimized composition scheme, the final composition scheme is obtained by constructing an alloy synergy index formula to enhance synergy optimization. S6. Based on the final composition scheme, a multimodal phase transition prediction model with a Transformer architecture is used to control tissue formation; S7. Combining S1~S6, construct the formulas for solving the ultimate tensile strength and elongation of ductile iron; S8. A machine learning-driven topology gradient alloying process is used. The stress cloud map of the casting is analyzed by deep learning image algorithm. With the goal of comprehensive optimization of cost and performance, the scheme is optimized globally by combining particle swarm optimization algorithm.

2. The method for designing low-cost, high-strength, and high-toughness ductile iron based on machine learning according to claim 1, characterized in that: The feature engineering interactive operations include: Constructing interaction features: Creating binary and ternary interaction features between elements; Domain characteristics: Calculating classical thermodynamic formulas; The method to obtain the comprehensive features is to concatenate the preprocessed data, interaction features, and domain features into a comprehensive feature vector.

3. The method for designing low-cost, high-strength, and high-toughness ductile iron based on machine learning according to claim 1, characterized in that: In the construction of the MLP-GAN model, the multilayer perceptron (MLP) is used as the generator and discriminator of the GAN, respectively. During the training of Generative Adversarial Networks (GANs), a loss function is defined to measure the performance of the generator and discriminator, and optimization algorithms such as gradient descent are used to update the network parameters. Extract nonlinear functions from the trained GAN to construct alloy feature formulas: In the formula, , , , These are the first, second, third, and fourth nonlinear functions obtained through training with a Generative Adversarial Network (GAN). Represents carbon; Indicates silicon; It represents manganese; It represents bismuth; It represents titanium; It represents boron; This indicates trace amounts of graphene derivatives.

4. The method for designing low-cost, high-strength, and high-toughness ductile iron based on machine learning according to claim 1, characterized in that: In the composition optimization based on alloy characteristic formulas using inverse modeling, the inverse modeling method involves: using the target performance as a constraint, solving for the element content in the alloy characteristic formula using gradient descent; during the solution process, a simulated annealing algorithm is introduced, using the preliminary composition obtained from gradient descent as the initial solution for simulated annealing, and calculating its corresponding... The element content and loss function values ​​are determined by introducing random perturbations with an amplitude of 0.05%-0.5% of the element content range. Neighborhood solutions are generated to ensure the perturbed element content remains within a reasonable range. Inferior solutions are accepted according to the Metropolis criterion to escape local optima and perform a global search. Finally, element interaction experiments are conducted to verify the optimized element content. , , , Functions were used to verify whether the output values ​​of each function conformed to the element interaction patterns during GAN training; orthogonal experiments were designed to fix the content of some elements and adjust the content of other elements, and observations were made. Does the change in value conform to the logic of the formula? 5. The method for designing low-cost, high-strength, and high-toughness ductile iron based on machine learning according to claim 1, characterized in that: The formula for the alloy synergy index is as follows: In the formula, This represents a reinforcement learning model function; Represents carbon; Indicates silicon; It represents manganese; Indicates phosphorus; Indicates magnesium; Indicates rare earth elements; It represents bismuth; It represents titanium; It represents boron; This indicates trace amounts of graphene derivatives.

6. The method for designing low-cost, high-strength, and high-toughness ductile iron based on machine learning according to claim 1, characterized in that: In the process of controlling microstructure formation using the multimodal phase transition prediction model with Transformer architecture, the prediction process is executed sequentially as follows: data acquisition operation, data preprocessing operation, Transformer prediction operation, and reverse process control operation. The Transformer prediction operation takes preprocessed features as input and outputs prediction results including the dynamic ratio change of pearlite-ferrite, the real-time growth trajectory of graphite spheres, and the distribution of nanoscale second phase precipitation. The reverse process control operation first defines the objective function L1 as the deviation between the predicted microstructure parameters and the target parameters, and its expression is as follows: In the formula, Indicates the total number of micro-organisms. Indexes representing microstructures; Indicates the weighting coefficient; Represents microstructure parameters, This represents the model's predicted value. Indicates the target value; Indicates Euclidean distance; The process parameters are adjusted by gradient inversion, where the gradient function expression is as follows: In the formula, The loss function is expressed as a function of process parameters. The gradient; This represents the model's predicted output; The expression for adjusting the process parameters is as follows: In the formula, express Process parameters under the next iteration; Indicates the first The process parameters for the next iteration; This represents the learning rate, used to adjust the range of process parameter adjustments.

7. The method for designing low-cost, high-strength, and high-toughness ductile iron based on machine learning according to claim 1, characterized in that: The formulas for determining the ultimate tensile strength and elongation of ductile iron are expressed as follows: In the formula, Formula for ultimate tensile strength; The power function representing the pearlite-ferrite ratio, where, Indicates the power-law exponent; This indicates the attenuation effect of internal stress. Indicates stress, This represents the first characteristic attenuation length parameter; The power function representing the density of the nanoscale second phase precipitation is given by, where, Indicates the impact index; This represents the average gray value of a microscopic image; Indicates the standard deviation of the graphite sphere diameter; Indicates the graphite size sensitivity parameter; This indicates the temperature change during the cooling process; This represents the second characteristic attenuation length parameter; Indicates the alloy characteristic index; Indicates the alloy synergy index; This represents the model bias correction term; , , This represents the first, second, and third basic weighting coefficients of each item; and These represent the first regularization parameter and the second regularization parameter, respectively. This indicates the average roundness of the graphite spheres. Logarithmic sensitivity to the roundness of graphite spheres; The ratio is pearlite to ferrite; This represents the standard deviation of the graphite sphere size. Indicates the grayscale contrast of a microscopic image; Saturation parameters that represent grayscale contrast; This indicates the density of the nanoscale second phase precipitation; and They represent The first Gaussian distribution parameter and the second Gaussian distribution parameter; This represents the model bias correction term; , , These represent the fourth, fifth, and sixth basic weighting coefficients for each item, respectively. , , These represent the third, fourth, and fifth regularization parameters, respectively.

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