Forging and heat synergistic material structure and performance integrated intelligent regulation and control method and system

Abstract

The invention discloses a forging heat synergistic material structure and performance integrated intelligent regulation and control method and system, and belongs to the technical field of material processing and intelligent manufacturing. The method comprises the following steps: 1) performing parameter calibration on a multi-module coupled physical model by using a small amount of real experimental data; 2) in the process parameter space, generating a large amount of virtual process combination parameter data by adopting a Latin hypercube sampling strategy, inputting the parameter data into a calibrated physical model for calculation to obtain output results, and screening the output results by taking physical constraints as conditions to obtain an enhanced data set meeting the physical constraints; 3, the enhanced data set is utilized to train a cascade prediction physical model.According to the cascade prediction physical model, integrated and high-precision prediction of multiple macroscopic performance and microstructure indexes of a material is achieved, the physical consistency of prediction results is ensured, physical derivative characteristics contribute to more than 70% of prediction capacity, and the interpretability of the model is ensured.

Description

Technical Field

[0001] This invention belongs to the field of materials processing and intelligent manufacturing technology, specifically relating to a method and system for collaborative process optimization and intelligent control of steel forging and heat treatment that combines physical mechanism models and data-driven models. This invention is particularly applicable to high-end manufacturing fields such as aerospace, automotive, and precision molds, enabling the optimization of process parameters and quality prediction for high-performance carburized steel parts. It can achieve high-precision collaborative prediction and refined control of material microstructure and properties under small industrial sample data conditions. Background Technology

[0002] Forging and heat treatment are key processes that determine the final service performance of high-end metal components (especially carburized steel parts used in aerospace, precision molds, and automotive transmission systems). Vacuum carburizing, as a new generation of advanced heat treatment process, significantly improves the surface hardness, wear resistance, and fatigue strength of parts by infiltrating carbon atoms into the surface of steel under low pressure to form a high-carbon hardened layer.

[0003] Traditional process parameter design relies heavily on expert experience and extensive trial-and-error experiments, resulting in long development cycles, high costs, and difficulty in ensuring the uniformity and consistency of the microstructure and properties of the final product across different batches and parts. With the ever-increasing demands for product quality in high-end manufacturing, there is an urgent need to establish intelligent models capable of accurately predicting the complex mapping relationships between "process parameters—microstructure—macroscopic properties."

[0004] Currently, the prediction and optimization of carburizing processes mainly adopt the following two technical approaches, but both have significant shortcomings: This method uses techniques such as finite element analysis to simulate the temperature field, carbon concentration field, and phase transition process during heat treatment. Its theoretical basis includes:

[0005] Carbon diffusion follows Fick's second law, and under semi-infinite boundary conditions, the carbon concentration distribution can be expressed as: .

[0006] Where Cs is the surface carbon content, D is the diffusion coefficient, t is the diffusion time, and x is the depth from the surface. The diffusion coefficient D follows the Arrhenius temperature dependence: .

[0007] However, this method has the following limitations: • Vacuum carburizing employs a pulsed "carburization-diffusion" cyclic process, under which the constant boundary condition assumption fails; • The diffusion coefficient is subject to complex influences from carbon concentration and alloying elements, and simplification introduces significant errors. • The model does not consider the effect of martensitic phase transformation during quenching on the final performance; • Under industrial conditions, the prediction error can reach 20%–40%, which is difficult to meet the requirements of fine control.

[0008] (ii) Data-driven machine learning methods This method uses machine learning algorithms to directly establish the mapping relationship between process parameters and performance, but it has the following core drawbacks: • Large data requirements: Hundreds to thousands of training samples are usually required, while a single carburizing experiment takes 4 to 8 hours and costs thousands to tens of thousands of yuan. • Small sample size leads to severe overfitting: When the sample size is insufficient (n<20), the model tends to memorize noise rather than the true pattern; • Lack of physical interpretability: Black box models cannot explain the prediction mechanism and are difficult for engineers to trust; • Physical consistency is not guaranteed: predictions may be produced that violate physical laws.

[0009] The core contradiction facing current technology is that, on the one hand, high-end manufacturing has increasingly higher requirements for the accuracy and reliability of process prediction; on the other hand, the current situation of small sample data (usually only 5-15 sets of experimental data), complex multi-physics coupling mechanisms, and the need for physical interpretability in industrial practice make it impossible for existing technical solutions to meet the requirements.

[0010] Therefore, there is an urgent need to develop an intelligent control method that can integrate the advantages of physical mechanisms and data-driven approaches, be suitable for small sample scenarios, maintain physical interpretability, and collaboratively predict multiple related targets. Summary of the Invention

[0011] (a) The technical problem to be solved by this invention The present invention aims to solve the technical problem that existing technologies, under conditions of small sample data, are unable to establish an accurate and reliable integrated prediction model of "forging and heating synergy process → microstructure → macro performance", thus making it impossible to finely and homogenously control the performance of the final product.

[0012] Specifically, the technical problems to be solved by the present invention include: 1. How to establish a reliable predictive model under typical industrial conditions with only 5-15 sets of experimental data; 2. How to simultaneously predict multiple continuous indicators such as surface carbon content, maximum hardness, and effective diffusion depth, as well as multiple sub-indices such as internal oxidation level and martensite level, and ensure that the prediction results are consistent with each other; 3. How to ensure that the prediction results conform to known metallurgical principles and thermodynamic constraints, and have physical interpretability; 4. How to achieve high prediction accuracy: Achieve generalization performance of R2>0.95 on augmented datasets and R2>0.85 on original small sample data.

[0013] To address the aforementioned technical problems, this invention discloses a physical-data fusion-driven intelligent control method for the integrated regulation of material microstructure and properties through forging and heating. The core idea is to use a physical model calibrated with a small amount of real data to guide the generation of large-scale, high-coverage, and evenly distributed virtual data, and then use this high-quality augmented dataset to train a multi-objective integrated prediction model.

[0014] The specific implementation steps of the method are as follows: 1) Perform parameter calibration on a multi-module coupled physical model using a small amount of real experimental data; 2) Within the process parameter space, a large amount of virtual process combination parameter data is generated using a Latin hypercube sampling strategy. The parameter data is then input into a calibrated physical model for calculation to obtain the output results. The output results are then filtered based on physical constraints to obtain an enhanced dataset that satisfies the physical constraints. 3) Use the augmented dataset to train a cascaded predictive physics model.

[0015] Specifically, the physical model in step 1) includes: Carbon diffusion model: Based on Fick's second law and the error function solution, the carbon concentration distribution curves on the surface of steel under different process parameters are calculated. The carbon concentration distribution is expressed as:

[0016] The diffusion coefficient D(T) follows the Arrhenius equation: For example, for 20Cr2Ni4 steel, the recommended parameters are D0 = 2.0 × 10⁻⁵ m² / s and Q = 148 kJ / mol; Carbon-Hardness Conversion Model: Based on the martensitic solid solution strengthening mechanism, the relationship between carbon content and Vickers hardness is established through linear regression. HV=H0+ H C ·C(5), where H0 is the matrix hardness, H C The hardening coefficient of carbon; Effective penetration depth model: Based on a calibrated Fick's law, the effective hardened layer depth is calculated (typically, the depth at which the hardness drops to 550 HV is taken as the standard): , Where α is the calibration factor and Ccrit is the critical carbon content; Step 1) utilizes a small amount of real experimental data collected on-site (usually 7-15 sets) to analyze the key unknown parameters (H0, H2, H3) in the physical model. C, etc., α) for optimization and calibration, and the least squares method and the Bootstrap method are used to evaluate parameter uncertainty, ensuring that the coefficient of variation CV of the calibrated parameters is less than 15%.

[0017] Specifically, in step 2), within the reasonable physical range of the input process parameters, the Latin Hypercube Sampling (LHS) method is used to achieve more uniform and comprehensive coverage in the multi-dimensional parameter space with fewer sample points. The sampling parameter range is determined according to industrial practice and can be selected as follows: Table 1 Process Parameter Sampling Range

[0018] A large number of virtual process parameter combinations (usually more than 1000) generated by Latin Hypercube Sampling are used as inputs and batch-input into the calibrated physical model for calculation to generate a large-scale "process-structure-property" virtual dataset containing inherent physical correlations; Subsequently, screening is carried out based on physical constraints. That is, physical constraint conditions based on metallurgical principles are applied to eliminate abnormal samples that violate basic physical laws, and the remaining virtual dataset that conforms to physical laws is the enhanced data. The specific physical constraint conditions are as follows: • Carbon content constraint: 0.3wt% < C < 1.2wt% (austenite carbon solubility limit) • Hardness constraint: 500HV < HV < 900HV (martensite hardness range) • Case depth constraint: 0.5mm < x < 2.0mm (industrial application range) Further optionally, to solve the problem that the data generated by the physical model may have uneven distribution in classification metrics, an adaptive equalization algorithm is designed. By oversampling the minority-class samples and undersampling the majority-class samples, it is ensured that in the finally output enhanced dataset, the number of samples at each level of each classification metric is roughly equal. Specifically, (a) Distribution statistics: The number of samples at each level of each classification metric (such as internal oxidation levels 1-5, martensite levels 1-4, etc.) in the enhanced dataset is counted, and the proportion of samples at each level is calculated; (b) Imbalance degree evaluation: Calculate the class imbalance ratio IR (Imbalance Ratio) of each classification metric, which is defined as the ratio of the number of majority-class samples to the number of minority-class samples: IR = N_majority / N_minority. When IR > 3, it is determined to be severely imbalanced; (c) Determining the target number of samples: Set the target balanced number of samples N_target = (N_total × Balance coefficient) / number of categories, where the balance coefficient is 0.8-1.2, to ensure that the number of samples in each category is within ±20% of N_target; (d) Minority oversampling: For minority classes with fewer than N_target × 0.8 samples, the SMOTE (Synthetic Minority Over-sampling Technique) algorithm is used to generate synthetic samples. Specifically, for each minority class sample x_i, a sample x_j is randomly selected from its k nearest neighbors (k=5) to generate a new sample x_new = x_i + rand(0,1)× (x_j - x_i); (e) Majority class undersampling: For the majority class with more than N_target × 1.2 samples, a cluster-based undersampling method is used to cluster the majority class samples into N_target clusters using K-means, and each cluster retains the representative sample closest to the cluster center; (f) Multi-indicator joint equilibration: When a sample has multiple classification labels, a multi-label stratified sampling strategy is adopted to perform equilibration processing according to the joint distribution of each label combination to ensure that the coverage of the label combination is not less than 95%.

[0019] Specifically, in step 3), the cascaded prediction physical model is a three-stage cascaded prediction architecture established according to the physical causal chain of "carbon content → hardness → penetration depth," which specifically includes: The first stage—surface carbon content prediction—employs a four-model ensemble learning approach (gradient boosting regression, random forest, extreme random tree, and ridge regression). The input is a combination vector of process parameters and physically derived features, and the output is the predicted surface carbon content value C(ˆ). ; The second stage—maximum hardness prediction—employs a "physical baseline + residual learning" architecture. The physical baseline is provided by the carbon-hardness equation: The machine learning model learns the residual correction term: HˆV = HV physics +∆HV ML ; The third stage—effective infiltration depth prediction—employs a "calibrated Fick's law + residual learning" architecture. The physical baseline is provided by the calibrated depth model: x physics = α· 2√Dt· erfc-1(Ccrit / Cs), final predicted value: ; This cascaded design ensures the physical consistency of the prediction results—upstream predictions directly influence downstream predictions, avoiding contradictory results that might arise from independent models.

[0020] Specifically, step 3) further includes training a physical model architecture for predicting classification targets using the augmented dataset. Specifically, for classification targets such as internal oxidation level, martensite level, retained austenite level, carbide level, and core tissue level, a multi-task learning architecture is adopted, sharing the feature extraction backbone network and differentiating multiple classification prediction heads at the end.

[0021] The physical model architecture for multi-task classification target prediction specifically includes: (1) Shared feature extraction backbone network: A 3-layer fully connected neural network is used as the shared backbone, with the number of neurons in each layer being 128-64-32 respectively. The activation function is ReLU, and the input is a combination vector of process parameters and physical derived features (dimension is 16+12=28). (2) Classification prediction head design: Five independent classification prediction heads are differentiated at the end of the shared backbone. Each prediction head contains one fully connected layer + a Softmax output layer. The specific configuration is as follows: Classification target Number of categories Output layer structure Evaluation criteria Internal oxidation level Level 5 (Levels 1-5) 32→5+Softmax GB / T 25744 Martensitic level Level 4 (Levels 1-4) 32→4+Softmax JB / T 6141 Residual austenite level Level 4 (Levels 1-4) 32→4+Softmax ≤25% is considered acceptable Carbide level Level 5 (Levels 1-5) 32→5+Softmax GB / T 25744 Heart tissue level Level 4 (Levels 1-4) 32→4+Softmax JB / T 6141 Specifically, in step 3), training using the augmented dataset involves using the augmented dataset as the training set and defining the joint loss function: L MSE For mean squared error loss (used in regression tasks), L CE For cross-entropy loss (used in classification tasks), w i and λ j These are the weighting coefficients for each task.

[0022] For training the cascaded regression prediction model: only the regression part of the loss function is used, i.e., L = Σw_i·L_MSE^(i), where i=1,2,3 correspond to the three regression targets of surface carbon content, maximum hardness, and effective infiltration depth, respectively, and the weight coefficients are set to w_1=1.0, w_2=0.01, w_3=1.0 (normalized and adjusted according to the numerical scale of each target). For training the multi-class head prediction model: only the classification part of the loss function is used, i.e., L = Σλ_j·L_CE^(j), where j=1,2,...,5 correspond to 5 classification targets respectively, and the weight coefficients are set according to the difficulty and importance of each classification task, with the default being λ_j=1.0; Alternatively, when it is necessary to train regression and classification tasks simultaneously, the complete joint loss function L_total = Σw_i·L_MSE^(i) + Σλ_j·L_CE^(j) can be used to achieve feature sharing and knowledge transfer through multi-task learning.

[0023] Alternatively, physical derivative feature data can be constructed based on the augmented data. Specifically, starting from the original process parameters, derivative feature data with clear physical meaning can be constructed based on the physical mechanism as follows: Table 2 Definitions of Physically Derived Features

[0024] Further optional steps include step 4), model validation, specifically employing a two-stage cross-validation method to ensure model reliability, including: 5-fold cross-validation (augmented data): used for hyperparameter optimization and model selection; • Leave-one-out cross-validation (LOOCV) on raw data: Evaluates generalization ability on small real samples.

[0025] The present invention also provides an intelligent control system applying the aforementioned integrated intelligent control method, the system comprising: Data processing module: used to receive and preprocess the initial small amount of process data; Physical Model Module: Contains a built-in original physical model for calibration and performs step 1). Data Augmentation Module: Performs step 2) to generate virtual data and obtain augmented data; Proxy model module: Execute step 3) to obtain the trained multi-objective prediction model.

[0026] Based on the trained multi-objective prediction model, the intelligent control system of the present invention can perform positive prediction, that is, when a set of process parameters are input, the system can quickly predict the corresponding multiple performance indicators within milliseconds.

[0027] In a further preferred embodiment, the intelligent control system of the present invention also includes a cross-validation module for performing a two-level cross-validation step.

[0028] In a further preferred embodiment, the present invention also includes a process optimization module: receiving the target performance set by the user, calling the proxy model, and combining it with a global optimization algorithm to perform reverse solving, and outputting recommended optimal process parameters.

[0029] Thus, in addition to forward prediction, the present invention can also achieve reverse optimization. That is, by inputting the desired performance index range, the system uses global optimization algorithms such as differential evolution and genetic algorithms to search in the process parameter space and solve one or more sets of optimal process parameter combinations that can meet the performance requirements.

[0030] Beneficial effects Compared with the prior art, the present invention has the following significant advantages: I. Effectively solved the problem of small sample data in industrial applications This invention uses a data augmentation method of "calibrating physical models + intelligent sampling" to successfully expand a small amount of high-value real data (7-15 sets) into large-scale, high-quality training data (more than 1000 sets), effectively overcoming the data scarcity bottleneck caused by high experimental costs in the high-end manufacturing field.

[0031] II. Significantly improved prediction accuracy and generalization ability This method deeply integrates prior knowledge of physical mechanisms with the powerful nonlinear fitting capabilities of data-driven models. The final model exhibits extremely high prediction accuracy on the test set. Compared to existing technologies: • Compared to the purely physical model: the infiltration depth R2 increased from 0.82 to 0.999, an improvement of 21%; • Compared to pure machine learning: the surface carbon content R2 increased from 0.85 to 0.968, an improvement of 14%; • Compared to independent prediction models: it avoids the problem of contradictory prediction results.

[0032] Table 3 Model Prediction Performance Indicators

[0033] Third, it has strong physical interpretability. Feature importance analysis results indicate that physically derived features dominate model predictions (see...). Figure 5 ): Table 4. Ranking of Feature Importance

[0034] Physically derived features contribute more than 70% of the predictive power, indicating that the model's predictive mechanism is highly consistent with the physical mechanism of carbon diffusion, enhancing engineers' confidence in the model.

[0035] IV. Achieving integrated and synergistic regulation of organization and performance Through a multi-task learning architecture and cascaded prediction design, the model can simultaneously predict multiple interrelated performance and organizational metrics, making process optimization no longer a "one-sided" approach targeting a single objective, but rather a global collaborative optimization for overall performance.

[0036] V. Strong industrial applicability and significant economic benefits • Wide range of applicable materials: The methods developed for 20Cr2Ni4 gear steel can be directly transferred to similar Cr-Ni carburizing steels (such as 20CrNi2Mo, 18CrNiMo7-6, etc.). • Reduced testing costs: Traditional process development requires 20-50 sets of tests, while this invention only requires 5-10 sets, reducing testing costs by 60%-80%; • Shorten the development cycle: from the traditional 3-6 months to 2-4 weeks; • Real-time prediction capability: The trained model can complete predictions in milliseconds and supports online process optimization. Attached Figure Description

[0037] Figure 1 The diagram illustrates a three-stage cascaded model architecture. The left side shows the process parameter input module (including carburizing temperature, strong carburizing time, diffusion time, quenching temperature, and quenching pressure); the middle left shows the physical derived feature construction module (including diffusion coefficient, diffusion length, diffusion ratio, and temperature integral); the middle section represents three cascaded prediction stages: the first stage uses a four-model ensemble learning approach (random forest, kriging, multinomial, and radial basis function) to predict surface carbon content; the second stage uses a physical baseline (hardness = 521.4 + 498.2 × carbon content) plus residual learning to predict maximum hardness; the third stage uses a calibrated Fick's law plus residual correction to predict the effective carburized layer depth; the right side shows the prediction output. Dashed arrows indicate cascaded transmission, and solid arrows indicate data flow.

[0038] Figure 2 The scatter plots comparing predicted and actual values ​​show the predicted performance of surface carbon content, maximum hardness, and effective infiltration depth in three subplots. In each subplot: the horizontal axis represents the actual measured value, the vertical axis represents the model's predicted value, and the diagonal dashed line represents the ideal prediction (y=x). The red dashed line is the ideal prediction line, and the blue / green / orange data points are closely distributed near the diagonal line, indicating that the model has extremely high prediction accuracy (coefficients of determination are 0.968, 0.963, and 0.999, respectively).

[0039] Figure 3 This graph shows the calibration and verification results of the physical model, illustrating the carbon-hardness physical relationship. Blue dots represent experimental data points, and the solid red line represents the calibrated physical baseline (hardness = 521.4 + 498.2 × carbon content). The red shaded area represents the 95% confidence interval. Calibration parameters: baseline hardness = 521.4 Vickers, carbon coefficient = 498.2 Vickers / wt%, coefficient of determination = 0.94. The data points are evenly distributed on both sides of the fitted line, validating the effectiveness of the physical model.

[0040] Figure 4 The feature correlation heatmap shows the correlation analysis results between various input features and between features and target variables. It includes input features such as carburizing temperature, diffusion time, strong carburizing time, quenching temperature, and quenching pressure, as well as output targets such as surface carbon content, maximum hardness, and carburized layer depth, and their correlation coefficients. Red represents positive correlation, blue represents negative correlation, and darker colors indicate stronger correlations. This heatmap reveals the intrinsic influence mechanism of process parameters on carburizing results.

[0041] Figure 5The bar chart ranking features by importance shows the ranking of features from largest to smallest contribution to prediction. The results show that physically derived features (especially feature diffusion length √Dt 42.2%) contribute more than 70% of the predictive power, verifying the physical interpretability of the model.

[0042] Figure 6 The residual diagnostic plot shows that the first row is a histogram of the residual distribution for surface carbon content, maximum hardness, and penetration depth, indicating that the residuals are normally distributed, with the red curve representing a normal fit. The second row is a scatter plot of the residuals versus predicted values, showing that the residuals are randomly distributed around the zero line (red dashed line), with the orange dashed line representing the boundary of two standard deviations. This indicates that the model has no systematic bias and the fit is good.

[0043] Figure 7 The bar chart compares the performance of different models, showing the coefficients of determination (COPs) of the pure physical model, the pure machine learning model, and the physical information fusion machine learning model of this invention on three target variables (surface carbon content, maximum hardness, and penetration depth). The red dashed line represents the baseline of COP = 0.9. The method of this invention (highlighted in green) performs best on all prediction targets, with COPs reaching 0.97, 0.96, and 0.999, respectively, significantly outperforming existing methods.

[0044] Figure 8 Kernel density estimation (KDE) distribution plots, with multiple subplots showing the probability density distribution of the enhanced data across key process parameters (carburizing temperature, diffusion time, strong carburizing time, quenching temperature, and quenching pressure). The red dashed line represents the mean, and the orange dashed line represents the median. This verifies that the virtual samples generated through Latin hypercube sampling can effectively fill the entire process parameter space, achieving a coverage rate exceeding 95%, thus ensuring the model's generalization ability. Detailed Implementation

[0045] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Equivalent substitutions or improvements made by those skilled in the art based on the technical solutions of the present invention should all fall within the protection scope of the present invention.

[0046] Example 1: Prediction of Vacuum Carburizing Process for 20Cr2Ni4 Gear Steel This embodiment uses 20Cr2Ni4 carburized steel for aerospace gears as the research object to describe in detail the complete implementation process of the method of the present invention. See also... Figure 1 The cascaded model architecture shown in this embodiment follows the process of "physical model construction → data augmentation → model training → application verification".

[0047] 1. Experimental Materials and Equipment 20Cr2Ni4 gear steel was used as the experimental material. This steel grade is the preferred material for high-load-bearing parts such as aerospace gears, automotive gearbox gears, and engineering machinery transmission gears, and has a wide range of industrial applications and is representative. The materials were procured and accepted in accordance with the GB / T3077-2015 standard "Alloy Structural Steel".

[0048] The preparation process of the experimental specimens is as follows: First, the raw material was forged into a round bar with a diameter of φ30mm × 100mm at a forging temperature of 1150°C and a final forging temperature of not less than 850°C; then, normalizing treatment was performed (holding at 880°C for 2 hours and air cooling) to eliminate forging stress and refine the grains; finally, it was machined into a cylindrical carburized specimen with a diameter of φ25mm × 15mm and a surface roughness Ra≤1.6μm.

[0049] The chemical composition of the material was analyzed using a direct-reading spectrometer (ARL4460). The nominal composition range and measured values ​​(mass fraction, wt%) are shown in the table below: Table 5 Chemical composition (wt%) of 20Cr2Ni4 steel

[0050] The metallurgical characteristics of this steel grade and its impact on the carburizing process are analyzed as follows: • Carbon content (0.17–0.23%): The low initial carbon content ensures that the core forms low-carbon martensite after quenching, which has good toughness and impact resistance, while providing sufficient carbon concentration gradient driving force for surface carburizing. • Chromium content (0.40–0.70%): Cr element improves the hardenability of steel, forms stable carbides (Cr7C3, Cr23C6), and improves wear resistance; at the same time, Cr will reduce the diffusion coefficient of carbon in austenite, which needs to be taken into account in the physical model; • Nickel content (1.25–1.65%): Ni significantly improves the hardenability and low-temperature toughness of steel, making the material suitable for cryogenic service environments such as aerospace (-40°C to -60°C); Ni also inhibits the tendency of internal oxidation during carburizing. • Silicon and manganese content: Si and Mn remain as deoxidizing elements. Si promotes internal oxidation, while Mn improves hardenability.

[0051] 1.2 Experimental Equipment and Process Capabilities: The vacuum carburizing equipment used was the Modul Therm single-chamber vacuum carburizing furnace manufactured by ALD GmbH, Germany. This equipment represents the current advanced level of industrial vacuum carburizing. The main technical parameters of the equipment are as follows: Table 6 Technical Parameters of Vacuum Carburizing Equipment

[0052] This embodiment employs a pulsed "carburization-diffusion" cyclic carburizing process. Unlike the constant carbon potential control of traditional gas carburizing, vacuum pulse carburizing controls carbon penetration and distribution by alternating between two stages: carburization (introducing acetylene) and diffusion (stopping carbon supply). In a single carburization stage, the acetylene flow rate is set to 20-30 L / min, lasting 2-5 minutes; in the diffusion stage, carbon supply is stopped, allowing the already penetrated carbon to diffuse further into the steel, lasting 10-30 minutes. By adjusting the carburization / diffusion time ratio and the number of cycles, the final carbon concentration distribution curve can be precisely controlled.

[0053] 2. Experimental Design and Data Acquisition 2.1 Experimental Factors and Level Design: Based on the metallurgical principles and industrial experience of carburizing processes, this embodiment selects the following five key process parameters as experimental factors, which have a decisive influence on carburizing quality:

[0054] • Carburizing temperature (930–970 °C): Temperature is the most critical factor affecting the carbon diffusion rate. According to the Arrhenius equation, the diffusion coefficient D has an exponential relationship with temperature. For every 50 °C increase in temperature, the diffusion coefficient increases by approximately 2–3 times. However, excessively high temperatures can lead to problems such as grain coarsening and accelerated internal oxidation.

[0055] • Diffusion time (100–140 min): Diffusion time determines the extent to which carbon migrates from the surface to the interior, directly affecting the diffusion layer depth and carbon concentration gradient. According to Fick's law, the diffusion layer depth is proportional to √Dt.

[0056] • Quenching temperature (830-840°C): The quenching temperature needs to be higher than the Ac3 critical point (about 810°C) to ensure complete austenitization, but it should not be too high to avoid grain coarsening and excessive retained austenite.

[0057] • Quenching pressure (6-10 MPa): The cooling rate of high-pressure gas quenching directly affects the completeness of martensitic transformation and the distribution of residual stress. The higher the pressure, the faster the cooling and the higher the hardness, but the risk of deformation and cracking also increases.

[0058] • Strong infiltration time (fixed at 45 min): The strong infiltration time is fixed in this embodiment to simplify the experimental design. 2.2 Experimental Design. Considering the high cost (approximately 5000-8000 RMB per experiment) and long cycle (approximately 6-10 hours per experiment) of carburizing experiments, this embodiment adopts a partially orthogonal experimental design to minimize the number of experiments while ensuring parameter space coverage. A total of 7 sets of experiments were designed, and the experimental design and measurement results are shown in the table below:

[0059] Table 7 Experimental Design and Measurement Results

[0060] 2.3 Performance testing methods: The carburized and quenched samples shall be tested for performance according to the following standard methods: • Surface carbon content determination: An ARL4460 direct-reading spectrometer (OES) was used for point analysis at a depth of 0.1 mm from the surface. Three points were measured for each sample, and the average value was taken. Measurement accuracy was ±0.02 wt%.

[0061] • Hardness distribution measurement: An FM-700 micro Vickers hardness tester was used, with a load of 500 gf (HV0.5) and a holding time of 15 s. Starting from the surface, measurements were taken at intervals of 0.1 mm along the depth direction until the hardness stabilized at the core hardness level. Three measurements were taken at each depth location, and the average value was taken.

[0062] • Determination of effective carburized layer depth: According to GB / T9450-2005 "Determination and verification of the depth of carburized and quenched hardened layer in steel parts", the effective hardened layer depth is defined as the vertical distance from the surface to a point where the hardness value equals 550 HV. This depth value is determined from the hardness-depth curve using linear interpolation.

[0063] • Metallographic observation: The microstructure of the infiltrated layer and the core was observed using a Zeiss Axio Observer metallographic microscope. The infiltrated layer should consist of fine acicular martensite + a small amount of retained austenite + diffusely distributed fine carbides; the core should consist of low-carbon lath martensite. 2.4 Experimental data analysis: The following patterns can be observed from the data in the table, and these patterns are consistent with the principles of metallurgy:

[0064] 1. As the carburizing temperature increases, the surface carbon content, hardness, and carburized layer depth all increase, demonstrating the promoting effect of temperature on diffusion; 2. The diffusion time is prolonged, and the infiltration layer depth increases significantly, which conforms to the diffusion law of x∝√t; 3. The surface carbon content is positively correlated with the maximum hardness, verifying the rationality of the assumption of a linear relationship between carbon and hardness; 4. The performance indicators of all samples are within the requirements of industrial applications (surface carbon 0.65-0.85wt%, hardness ≥800HV, diffusion layer 0.8-1.2mm).

[0065] 3. Physical model construction and parameter calibration Based on seven sets of experimental data, the parameters of the physical model were calibrated using the least squares method and the bootstrap method.

[0066] Specifically, the physical models mainly include: Carbon diffusion model: Based on Fick's second law and the error function solution, the concentration distribution curve of carbon on the surface layer of steel under different process parameters is calculated. The carbon concentration distribution is expressed as: , Among them, the diffusion coefficient D(T) follows the Arrhenius equation: For 20Cr2Ni4 steel, the recommended parameters are D0 = 2.0×10-5 m2 / s and Q = 148 kJ / mol; Carbon-hardness conversion model: Based on the martensite solid solution strengthening mechanism, the relationship between carbon content and Vickers hardness is established through linear regression: HV = H0 + H C ·C(5), where H0 is the matrix hardness and H C is the hardening coefficient of carbon; Effective case depth model: Based on the calibrated Fick's law, the effective hardened layer depth (the depth where the hardness drops to 550 HV) is calculated: , where α is the calibration factor and Ccrit is the critical carbon content; Using 7 groups of real experimental data collected on-site, the key unknown parameters (H0, H C , α, etc.) in the physical model are optimized and calibrated. The least squares method and the Bootstrap method are used to evaluate the parameter uncertainty, ensuring that the coefficient of variation CV of the calibrated parameters is less than 15% (see Figure 3 ).

[0067] Table 8 Calibration parameters of the physical model

[0068] The coefficient of variation of all parameters is less than 10%, indicating that the parameter estimation is stable and reliable.

[0069] 4. Data augmentation 1034 initial samples are generated by Latin hypercube sampling. The 1034 virtual process parameter combination samples generated by this Latin hypercube sampling are used as inputs and batch-input into the calibrated physical model for calculation to generate corresponding results;

[0070] Subsequently, screening is carried out based on physical constraints. That is, physical constraint conditions based on metallurgical principles are applied to eliminate abnormal samples that violate basic physical laws. The remaining virtual data set that conforms to physical laws is the enhanced data. The specific physical constraint conditions are as follows: • Carbon content constraint: 0.3 wt% < C < 1.2 wt% (austenite carbon solubility limit) • Hardness constraint: 500 HV < HV < 900 HV (martensite hardness range) • Penetration depth constraint: 0.5mm < x < 2.0mm (industrial application range), After screening, 1000 valid samples were retained (rejection rate 3.29%).

[0071] Subsequently, adaptive equalization processing was performed: to address the problem of uneven distribution of data that may be generated by the physical model in terms of classification metrics, the enhanced dataset was subjected to adaptive equalization processing. The specific process is as follows: Statistical analysis was conducted on the level distribution of each classification metric in the enhanced dataset:

[0072] Table 9-1 Level distribution of each classification metric before equalization Classification indicators Level 1 Level 2 Level 3 Level 4 Level 5 Imbalance Ratio IR Internal oxidation level 45 112 423 298 122 9.4 Martensitic level 67 156 512 265 - 7.6 Residual austenite level 89 234 445 232 - 5.0 Carbide level 38 98 456 287 121 12.0 Heart tissue level 112 289 378 221 - 3.4 It can be seen that there are varying degrees of class imbalance problems in each classification metric, among which the imbalance ratio of the carbide level is the highest (IR = 12.0).

[0073] Step 2: Determination of target sample number and sampling strategy Set the target sample number N_target = 200 (per class), and adopt the following strategy: (1) Minority class oversampling (SMOTE): For classes with a sample number less than 160, the SMOTE algorithm was used to generate synthetic samples. Taking internal oxidation level 1 (45 samples) as an example: For each sample x_i, find its 5 nearest neighbors in the feature space Randomly select a nearest neighbor x_j, and generate a new sample x_new = x_i + rand(0,1) × (x_j - x_i) Repeat until the sample number of this class reaches 200 (2) Majority class undersampling (cluster undersampling): For classes with a sample number greater than 240, K-means cluster undersampling was used. Taking internal oxidation level 3 (423 samples) as an example: Cluster the 423 samples into 200 clusters Retain 1 representative sample closest to the cluster center in each cluster Finally, 200 samples were retained Step 3: Equalization results Table 9-2 Level distribution of each classification metric after equalization

[0074] Classification indicators Level 1 Level 2 Level 3 Level 4 Level 5 Imbalance Ratio IR Internal oxidation level 198 202 200 201 199 1.02 Martensitic level 200 198 203 199 - 1.03 Residual austenite level 201 199 200 200 - 1.01 Carbide level 197 201 200 202 200 1.03 Heart tissue level 199 200 201 200 - 1.01 After adaptive equalization processing, the imbalance ratios of each classification metric were all reduced to the range of 1.0 - 1.03, meeting the data balance requirements for subsequent classification model training.

[0075] Figure 8This paper presents the kernel density estimation (KDE) distribution of the enhanced dataset generated by the Latin hypercube sampling (LHS) strategy of this invention across five key process parameters (carburizing temperature, diffusion time, strong carburizing time, quenching temperature, and quenching pressure). The subplots and annotations in the figure collectively demonstrate the following technical advantages: 1) Spatial coverage uniformity: The probability density curves of each parameter all show a flat and wide distribution within the preset industrial process range, and the mean (red dashed line) and median (orange dashed line) highly overlap, proving that the sampled data has excellent statistical symmetry. 2) High Coverage Validation: As shown in the [Sampling Validation Instructions] at the bottom right, LHS sampling ensures a uniform distribution of samples in the multidimensional parameter space, with a coverage rate exceeding 95%. This effectively overcomes the limitation of overly isolated sample points in traditional Design of Experiments (DOE). 3) Model generalization guarantee: This high-quality, unbiased augmented dataset provides a data guarantee for the high-precision fitting and strong generalization performance of the subsequent machine learning model in the full process parameter space. It is the core technical support for the invention to achieve reliable prediction under industrial small sample conditions.

[0076] The Kolmogorov-Smirnov test was used to verify the distributional consistency between the augmented data and the original data. The p-values ​​of all parameters were greater than 0.05, indicating that there was no significant difference.

[0077] In addition, physical derivative feature data is further constructed based on the augmented data to enable more accurate machine learning and training in the future. Specifically, derived feature data with clear physical meaning is constructed based on the physical mechanism, starting from the original process parameters, as shown in Table 2.

[0078] 5. Model Training A three-stage cascade model is established by constructing a physical causal chain of "carbon content → hardness → penetration depth," specifically including:

[0079] The first stage—surface carbon content prediction—employs a four-model ensemble learning approach with equal weights (gradient boosting regression 25%, random forest 25%, extreme random tree 25%, ridge regression 25%). The input is a vector combining process parameters and physical derived features, and the output is the predicted surface carbon content. ; The second stage—maximum hardness prediction—employs a "physical baseline + residual learning" architecture. The physical baseline is provided by the carbon-hardness equation: HV physics =H0+H C • C(ˆ), the residual correction term learned by the machine learning model: HˆV = HV physics +∆HV ML ; The third stage—effective infiltration depth prediction: Employing a "calibrated Fick's law + residual learning" architecture, the physical baseline is provided by the calibrated depth model: x physics = α· 2√Dt· erfc-1(Ccrit / Cs), final predicted value: ˆ(x) = x physics + ∆x ML ; This cascaded design ensures the physical consistency of the prediction results—upstream predictions directly influence downstream predictions, avoiding contradictory results that might arise from independent models.

[0080] Meanwhile, the physical model architecture for predicting classification targets is trained using augmented datasets. Specifically, for classification targets such as internal oxidation level, martensite level, retained austenite level, carbide level, and core tissue level, a multi-task learning architecture is adopted, sharing the feature extraction backbone network and differentiating multiple classification prediction heads at the end. A three-layer fully connected neural network is used as a shared backbone, with 128, 64, and 32 neurons in each layer. The activation function is ReLU, and the input is a combination vector of process parameters and physical derived features (16+12=28 dimensions).

[0081] (2) Classification prediction head design: Five independent classification prediction heads are differentiated at the end of the shared backbone. Each prediction head contains one fully connected layer + a Softmax output layer. The specific configuration is as follows: Classification target Number of categories Output layer structure Evaluation criteria Internal oxidation level Level 5 (Levels 1-5) 32→5+Softmax GB / T 25744 Martensitic level Level 4 (Levels 1-4) 32→4+Softmax JB / T 6141 Residual austenite level Level 4 (Levels 1-4) 32→4+Softmax ≤25% is considered acceptable Carbide level Level 5 (Levels 1-5) 32→5+Softmax GB / T 25744 Heart tissue level Level 4 (Levels 1-4) 32→4+Softmax JB / T 6141 (3) Classification prediction performance: After training and verification, the prediction accuracy of each classification target is as follows: Classification target Training set accuracy Test set accuracy Macro average F1 Diagonal proportion of the confusion matrix Internal oxidation level 94.2% 91.5% 0.89 91.5% Martensitic level 96.8% 94.3% 0.93 94.3% Residual austenite level 95.1% 92.8% 0.91 92.8% Carbide level 93.5% 90.2% 0.88 90.2% Heart tissue level 97.2% 95.6% 0.94 95.6% The prediction accuracy for each classification target reached over 90%, with the highest prediction accuracy (>94%) for martensitic and core tissue levels. This is related to their clearer physical mechanisms and stronger correlation with process parameters.

[0082] For the above training, specifically using the augmented dataset as the training set, the joint loss function is defined as follows: L MSE For mean squared error loss (used in regression tasks), L CE For cross-entropy loss (used in classification tasks), w i and λ j These are the weighting coefficients for each task.

[0083] Explanation of the applicable scope of the loss function: The joint loss function is applicable to the training of both cascaded regression prediction models and multi-class head prediction models, but their specific applications differ: (1) Training of cascaded regression prediction model: Only the regression part of the loss function is used, i.e., L = Σw_i·L_MSE^(i), where i=1,2,3 correspond to the three regression targets of surface carbon content, maximum hardness, and effective infiltration depth, respectively. The weight coefficients are set as w_1=1.0, w_2=0.01, w_3=1.0 (normalized according to the numerical scale of each target). (2) Training of multi-class head prediction model: Only the classification part of the loss function is used, i.e., L = Σλ_j·L_CE^(j), where j=1,2,...,5 correspond to 5 classification targets respectively. The weight coefficients are set according to the difficulty and importance of each classification task, and the default is λ_j=1.0; (3) Joint training mode (optional): When it is necessary to train regression and classification tasks at the same time, the complete joint loss function L_total = Σw_i·L_MSE^(i) + Σλ_j·L_CE^(j) is adopted to achieve feature sharing and knowledge transfer through multi-task learning.

[0084] Figure 4 This figure displays a Pearson correlation thermodynamic matrix showing the relationships between various process parameters (carburizing temperature, strong carburizing time, diffusion time, strong carburizing / diffusion ratio, quenching temperature, quenching pressure) and the final performance indicators (surface carbon concentration, hardness, carburized layer depth). The values ​​in the figure represent correlation coefficients, and the color intensity reflects the strength of the correlation. This figure reveals the following key technical information: 1) Physical consistency verification: Carburizing temperature showed a very high positive correlation with surface carbon concentration, hardness and carburized layer depth (correlation coefficient was 0.86 for all of them), which strongly verified the decisive influence of temperature on carbon diffusion rate described by the Arrhenius equation from a data perspective. 2) Cascaded architecture support: There is a very strong linear correlation between surface carbon concentration and hardness and carburized layer depth (correlation coefficients reach 1.00 and 0.94, respectively), which provides a solid statistical basis for the physical causal chain cascade prediction architecture of "carbon content → hardness → carburized layer depth" described in the claims of this invention; 3) Feature decoupling analysis: The strong carburizing / diffusion ratio, quenching temperature and quenching pressure have extremely low correlation with carbon concentration distribution, indicating the relative independence of the carburizing kinetics process and the subsequent quenching phase transformation process in terms of feature dimensions, which supports the rationality of the feature classification and extraction in this invention.

[0085] 6. Model Validation Results An 80 / 20 training / test set split was performed on 1000 augmented data samples, using 5-fold cross-validation for hyperparameter optimization and model selection (see [link]). Figure 2Meanwhile, leave-one-out cross-validation was performed on 7 sets of original data to evaluate the generalization ability on real small samples: Table 10 Model Validation Results 7. Comparison with existing methods Table 11 Comparison of prediction performance of different methods

[0086]

[0087] The method of this invention significantly outperforms existing methods on all objectives, with an average R² improvement of 15–49 percentage points (see [link]). Figure 7 ).

[0088] Example 2: Application of process parameter optimization This embodiment details how to use a trained cascaded prediction model combined with a global optimization algorithm to achieve reverse process parameter optimization, that is, to solve for the optimal combination of process parameters that meets the requirements based on the target performance index set by the user.

[0089] Inverse optimization of process parameters is essentially a constrained multi-objective optimization problem. Let the process parameter vector be x = [Tc, td, Tq, Pq]T, representing carburizing temperature, diffusion time, quenching temperature, and quenching pressure, respectively. The optimization problem can be formally expressed as: ,in For the target surface carbon content and diffusion depth, HV min For the minimum hardness requirement, w1 and w2 are weighting coefficients, x L x U These are the upper and lower bounds of the parameter.

[0090] (1.2) Definition of search space Based on industrial practices and equipment capabilities, a feasible search space for process parameters is defined: Table 12 Search Space for Process Parameter Optimization

[0091] 2. Principles and Implementation of Differential Evolution Algorithm

[0092] This embodiment selects the Differential Evolution (DE) algorithm as the global optimizer, mainly based on the following considerations: • Strong global search capability: The DE algorithm can effectively avoid getting trapped in local optima through population evolution mechanism; • Fewer parameters and better robustness: Only three control parameters need to be set: population size, scaling factor and crossover probability; • High adaptability: It has no special requirements for the continuity and differentiability of the objective function, making it suitable for handling black-box optimization problems; • High computational efficiency: Compared with genetic algorithms, DE's mutation operation is more efficient and converges faster.

[0093] (2.2) Core operations of the algorithm The core of the differential evolution algorithm includes three operations: mutation, crossover, and selection. Mutation operation: For each individual xi(G) in the current generation, generate mutated individuals using the difference vector: vi(G)= xr1(G)+ F·(xr2(G)—xr3(G)) (9) Where r1, r2, r3 are randomly selected distinct individual indices, and F∈[0.4, 1.0] is the scaling factor.

[0094] Crossover operation: Crossover the mutated individual with the original individual to generate experimental individuals: , where CR∈[0.5, 1.0] is the crossover probability, and jrand ensures that at least one dimension comes from the mutated individual.

[0095] Selection operation: A greedy selection strategy is adopted to retain individuals with better fitness. .

[0096] (2.3) Algorithm parameter settings The specific parameter configuration of the differential evolution algorithm in this embodiment is as follows: Table 13 Differential Evolution Algorithm Parameter Configuration

[0097] 3. Specific Optimization Cases 3.1 Optimize target setting The technical requirements for the carburized layer performance of a certain aerospace gear part are as follows: • Effective penetration depth: 1.0 ± 0.05 mm (target value 1.0 mm, allowable deviation ±5%) • Surface carbon content: 0.75 ± 0.03wt% (target value 0.75wt%, allowable deviation ±4%) • Maximum hardness: ≥ 835HV (rigid constraint) The weighting coefficients are set as w1 = 100 (carbon content weight, due to its small numerical range) and w2 = 1 (permeability depth weight). Hardness constraints are handled using a penalty function method: when HV < 835, the objective function value is increased by a penalty term λ · (835 — HV)², where λ = 1000.

[0098] 3.2 Optimization Process and Convergence Analysis The key information recorded during the optimization algorithm execution process is as follows: Table 14 Convergence Record of Optimization Process

[0099] The algorithm converged in generation 142 (with fitness improvement of less than 10⁻⁶ for 30 consecutive generations), with a total computation time of approximately 2.3 seconds (on an Intel i7-10700 processor), including approximately 7100 model inference calls.

[0100] 3.3 Optimal Process Parameter Output Table 15 shows the optimal process parameters output by the optimization team.

[0101] The corresponding predicted performance indicators are: surface carbon content 0.746wt% (0.5% deviation from the target), effective penetration depth 1.003mm (0.3% deviation from the target), and maximum hardness 838HV (meeting the ≥835HV constraint).

[0102] 4. Verification Experiment and Error Analysis

[0103] 4.1 Verification test plan: To verify the reliability of the optimization results, three sets of repeated verification experiments were conducted according to the optimized output process parameters (rounded down: carburizing temperature 955◦C, diffusion time 125min, quenching temperature 833◦C, quenching pressure 8MPa).

[0104] 4.2 Comparison of Verification Results Table 16 Results of the optimization verification experiment (see Table 16) Figure 6 )

[0105] 4.3 Error Source Analysis The main sources of the deviation between the experimental results and the model predictions are: 1) Fluctuations in process parameters: In actual production, the temperature control accuracy is ±3◦C, the time control accuracy is ±1min, and the pressure control accuracy is ±0.2MPa; 2) Material batch differences: The chemical composition of raw materials varies within an acceptable range between different batches; 3) Measurement errors: Surface carbon content measurement error ±0.02wt%, hardness measurement error ±5HV, depth measurement error ±0.02mm; 4) Inherent model error: The LOOCVR2 of the cascaded prediction model is 0.87-0.95, indicating a certain degree of prediction uncertainty.

[0106] In summary, the prediction errors of all performance indicators are less than 2%, and the experimental results are completely within the target allowable range, proving that the reverse optimization method of this invention has good engineering application value.

[0107] 5. Multi-objective trade-offs and Pareto front analysis In practical engineering applications, different performance indicators may also have mutually restrictive relationships. This embodiment also performs multi-objective Pareto optimization analysis to reveal the trade-offs between performance indicators.

[0108] The NSGA-II multi-objective optimization algorithm was used, with surface carbon content deviation, infiltration layer depth deviation, and production cost (positively correlated with temperature and time) as the three optimization objectives, to obtain the Pareto optimal solution set. Analysis shows that: • Increasing the carburizing temperature can shorten the diffusion time, but it will increase energy consumption costs by about 8% / 10◦C; • Under the premise of meeting performance requirements, there are two equivalent process paths: "high temperature for short time" and "low temperature for long time"; • The optimal solution selected in this embodiment is located in the middle region of the Pareto front, balancing performance accuracy and production cost.

[0109] Example 3: Migration applied to other steel grades This embodiment details how to transfer the prediction model developed based on 20Cr2Ni4 steel to other Cr-Ni carburizing steels, thereby achieving cross-material generalization of the model and reducing the time and cost of developing new material processes.

[0110] 1. Theoretical basis and strategies of transfer learning 1.1 Applicability Analysis of Transfer Learning The method of this invention has good transferability, mainly based on the commonality of the following physical mechanisms:

[0111] • Similar diffusion mechanisms: Carbon diffusion in Cr-Ni carburized steels follows Fick's law, and the Arrhenius temperature dependence of the diffusion coefficient is the same, with only slight differences in activation energy Q and pre-factor D0. • Same strengthening mechanism: Surface hardening relies on martensitic solid solution strengthening mechanism, and the linear relationship between carbon and hardness is generally applicable, with the coefficient slightly adjusted according to alloy composition; • Overlapping process parameter ranges: The process windows (temperature, time, pressure) of similar carburizing steels highly overlap, and the physical constraints are basically the same.

[0112] 1.2 Migration Strategy Design This invention employs a transfer learning strategy of "parameter fine-tuning + incremental learning", specifically including:

[0113] 1) Physical model parameter recalibration: Using a small amount of experimental data (3-5 sets) of the target steel grade, only the material-related parameters (H0, H2, ...) in the physical model are recalibrated. C Recalibrate (α, D0, Q) while keeping the model structure unchanged; 2) Feature space alignment: Verify the effectiveness of original features and physically derived features on new materials, and add material composition-related features if necessary; 3) Fine-tuning of machine learning models: Using the original model parameters as initial values, perform a limited number of rounds of fine-tuning training on newly generated augmented data to avoid overfitting.

[0114] 2. Target material selection and data preparation 2.1 Selection of target steel grade In this embodiment, 18CrNiMo7-6 wind turbine gear steel is selected as the migration target. This steel is the mainstream material for large wind turbine gearboxes. It belongs to the Cr-Ni-Mo carburizing steel system, the same as 20Cr2Ni4 steel, and has similar alloy design concepts but slightly different chemical compositions.

[0115] Table 17 Chemical composition (wt%) of target steel grade 18CrNiMo7-6

[0116] 2.2 Analysis of Metallurgical Differences Between the Two Types of Steel Compared to 20Cr2Ni4 steel, 18CrNiMo7-6 steel has the following characteristics: • Higher Cr content (1.5-1.8% vs 0.4-0.7%): Higher Cr content reduces the diffusion coefficient of carbon in austenite by about 10-15% and increases the tendency for carbide formation; • Contains Mo (0.25-0.35%): Mo significantly improves hardenability and tempering stability, but further reduces the carbon diffusion rate; • Comparable Ni content: Both have similar Ni content and contribute similarly to toughness and hardenability.

[0117] These differences necessitate careful adjustment of diffusion coefficient-related parameters during the migration process.

[0118] 2.3 Data Collection for Migration Experiments Five sets of carburizing experiments were conducted on 18CrNiMo7-6 steel using the same experimental equipment and testing methods as in Example 1: Table 18 Experimental data on migration of 18CrNiMo7-6 steel

[0119] 3. Physical model parameter recalibration 3.1 Parameter Calibration Method

[0120] The same least squares and bootstrap methods as the original model are used for parameter calibration, but prior constraints are added to utilize the knowledge from the original model: , where θj(prior) is the calibration parameter value of the original model (20Cr2Ni4 steel), and λ=0.1 is the regularization coefficient, which is used to maintain continuity with the original model while fitting new data.

[0121] 3.2 Recalibration Results Table 19 Calibration Parameters for the Physical Model of 18CrNiMo7-6 Steel

[0122] 3.3 Physical Explanation of Parameter Variation • H0 and H C Slightly increased: The higher Cr and Mo content in 18CrNiMo7-6 steel brings stronger solid solution strengthening and carbide precipitation strengthening effects; • α is slightly reduced: The lower carbon diffusion rate results in a slightly shallower diffusion layer depth under the same process conditions; • D0 correction factor < 1: This reflects the hindering effect of Cr and Mo on carbon diffusion, which is consistent with the expectations of metallurgical theory.

[0123] 4. Fine-tuning of machine learning models 4.1 Enhanced Data Generation Using the recalibrated physical model, 1000 virtual samples were generated as a fine-tuning training set, following the same Latin hypercube sampling strategy as in Example 1.

[0124] 4.2 Model Fine-tuning Strategy The following fine-tuning configuration is used to prevent overfitting: • Parameter initialization: Use the weights of the original model (trained with 20Cr2Ni4 steel) as initial values; • Learning rate decay: The initial learning rate is set to 1 / 10 of the original training rate (0.001→0.0001), and a cosine annealing strategy is used; • Early stopping mechanism: Training is stopped if the validation set loss shows no improvement for 20 consecutive rounds; • Fine-tuning rounds: Maximum 50 rounds (actually stopped early on round 32).

[0125] 4.3 Feature Space Validation Verify the applicability of the original physical derivative features to new materials: Table 20 Comparison of the Importance of Physical Derivative Characteristics in Two Types of Steel

[0126] The high consistency in the ranking of feature importance indicates that the physically derived features have good cross-material generalization ability.

[0127] 5. Transfer Model Validation 5.1 Cross-validation results

[0128] Leave-one-out cross-validation was performed on the 5 sets of original experimental data: Table 21 Validation results of the migration model

[0129] 5.2 Comparison with retrained models To verify the effectiveness of the migration strategy, the following three modeling schemes are compared: Table 22 Performance Comparison of Different Modeling Schemes

[0130] The migration method of this invention requires only 5 sets of experimental data and 2 days of development time to achieve prediction accuracy close to that of a complete redevelopment, improving development efficiency by about 20 times.

[0131] 6. Analysis of other transferable steel grades The method of this invention can be extended to the following Cr-Ni carburizing steels: Table 23 List of applicable steel grades

[0132] The difficulty assessment is based on the similarity of the chemical composition of the target steel and the degree of difference in carburizing characteristics between them.

Claims

1. A method for integrated intelligent control of material microstructure and properties through forging and heating synergy, characterized in that, Includes the following steps: 1) Perform parameter calibration on a multi-module coupled physical model using a small amount of real experimental data; 2) Within the process parameter space, a large amount of virtual process combination parameter data is generated using a Latin hypercube sampling strategy. The parameter data is then input into a calibrated physical model for calculation to obtain the output results. The output results are then filtered based on physical constraints to obtain an enhanced dataset that satisfies the physical constraints. 3) Use the augmented dataset to train a cascaded predictive physics model.

2. The method according to claim 1, characterized in that: In step 3), the cascaded prediction physical model is a three-stage cascaded prediction architecture established according to the physical causal chain of "carbon content → hardness → penetration depth". The training specifically includes the following three stages: The first stage—surface carbon content prediction—employs a four-model ensemble learning approach (gradient boosting regression, random forest, extreme random tree, and ridge regression). The input is a combined vector of process parameters and physically derived features, and the output is the predicted surface carbon content. ; The second stage—maximum hardness prediction—employs a "physical baseline + residual learning" architecture. The physical baseline is provided by the carbon-hardness equation: The machine learning model learns the residual correction term: HˆV = HV physics +∆HV ML ; The third stage—effective infiltration depth prediction—employs a "calibrated Fick's law + residual learning" architecture. The physical baseline is provided by the calibrated depth model: x physics = α· 2√Dt· erfc-1(Ccrit / Cs), final predicted value: ； The training cascaded prediction physics model uses an augmented dataset as the training set and defines a joint loss function: L MSE L represents the mean squared error loss, used for regression tasks. CE Cross-entropy loss is used for classification tasks, w i and λ j These are the weighting coefficients for each task; The training cascade prediction physical model uses only the regression part of the loss function, where i=1,2,3 correspond to the three regression targets: surface carbon content, maximum hardness, and effective infiltration depth, respectively, and the weight coefficients are set as w1=1.0, w2=0.01, and w3=1.

0.

3. The method according to claim 2, characterized in that: Step 3) further includes training a physical model architecture for predicting classification targets using the augmented dataset. Specifically, for the five classification targets, namely internal oxidation level, martensite level, retained austenite level, carbide level, and core tissue level, a multi-task learning architecture is adopted, sharing the feature extraction backbone network and differentiating multiple classification prediction heads at the end. Specifically, only the classification part of the loss function is used, where j=1,2,...,5 correspond to 5 classification targets, and the weight coefficients are set according to the difficulty and importance of each classification task, with a default value of λ_j=1.

0.

4. The method according to claim 1, characterized in that: The physical model in step 1) includes: Carbon diffusion model: Based on Fick's second law and the error function solution, the carbon concentration distribution curves on the surface of steel under different process parameters are calculated. The carbon concentration distribution is expressed as: The diffusion coefficient D(T) follows the Arrhenius equation: Carbon-hardness conversion model: Based on the martensitic solid solution strengthening mechanism, the relationship between carbon content and Vickers hardness is established through linear regression. HV=H0+H C Q(5) Where H0 is the matrix hardness, H C The hardening coefficient of carbon; Effective penetration depth model: Calculating the effective hardened layer depth based on a calibrated Fick's law. , where α is the calibration factor and Ccrit is the critical carbon content.

5. The method according to claim 1, characterized in that: The physical constraints include: Carbon content constraint: 0.3wt% <C<1.2wt%; Hardness constraint: 500 HV <HV<900HV; Permeation depth constraint: 0.5mm < x < 2.0mm.

6. The method according to claim 1, characterized in that: Physically derived feature data is constructed based on the augmented data. The physically derived features include feature diffusion length √Dt, logarithmic diffusion coefficient log10(D), and diffusion ratio tboost / tdiff.

7. The method according to claim 1, characterized in that: It also includes step 4) model validation, which uses a two-stage validation method of augmented data 5-fold cross-validation and leave-one-out cross-validation.

8. The method according to claim 1, characterized in that: This also includes step 5) model adjustment for adapting to the new material, which includes the following sub-steps: Physical model parameters are recalibrated using a small amount of experimental data of the target material, employing the same least squares method and bootstrap method as the original physical model, and adding prior constraints to utilize the knowledge of the original model. To enhance data generation, a large number of virtual samples are generated using the recalibrated physical model, following the same Latin hypercube sampling strategy as in step 2), to serve as a fine-tuning training set. The machine learning model is fine-tuned by using the original model parameters as initial values ​​and performing fine-tuning training on newly generated augmented data with a limited number of training epochs less than the original training in step 3), and combining it with an early stopping mechanism.

9. An intelligent control system applying the aforementioned integrated intelligent control method, the system comprising: Data processing module: used to receive and preprocess the initial small amount of process data; Physical Model Module: Contains a built-in original physical model for calibration and performs step 1). Data Augmentation Module: Performs step 2) to generate virtual data and obtain augmented data; Proxy model module: Execute step 3) to obtain the trained multi-objective prediction model.

10. The intelligent control system according to claim 9, further comprising: Process optimization module: Receives the target performance set by the user, calls the proxy model module, and combines it with the global optimization algorithm to perform reverse solving, and outputs the recommended optimal process parameters.

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