Heat treatment system selection method based on machine learning and particle swarm intelligent optimization

Abstract

The invention relates to the technical field of heat treatment processes, and discloses a heat treatment system selection method based on machine learning and particle swarm intelligent optimization, and relates to the technical field of heat treatment process.The method comprises the steps that a heat treatment process feasible region is determined according to material characteristics, small samples are prepared through orthogonal experiment design, the hardness is tested, and a data set is constructed; training a Gaussian process regression or support vector machine regression model, establishing a mapping relation between process parameters and hardness, adopting a particle swarm algorithm to carry out reverse search by taking a target hardness value as an optimization target, generating a candidate heat treatment system, carrying out pre-estimation sorting on an empirical relation of plasticity based on tempering temperature and time, according to the method, the number of tensile tests is remarkably reduced, the research and development cost is reduced, and the research and development period is shortened.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of heat treatment process, in particular to a heat treatment process selection method based on machine learning and particle swarm intelligent optimization. BACKGROUND

[0002] The heat treatment of metal materials is a key process for changing the microstructure of materials by controlling the heating, holding and cooling processes to obtain the required mechanical properties. For example, annealing and tempering, the heat treatment system mainly includes parameters such as temperature, time and cooling method, and its setting has a decisive influence on the final performance of the material. In actual industrial research and development, it is often difficult to directly use the existing heat treatment system for different material systems or different preparation processes, and it is necessary to explore appropriate process parameter combinations.

[0003] At present, the common heat treatment system optimization method mainly relies on experience summary or traditional experimental design methods based on single factor test, orthogonal test, etc. However, the existing methods have the following significant shortcomings: first, the test cost is high and the processing cycle is long. Usually, the samples treated under each system are processed into standard tensile samples, and after screening through mechanical property testing, the next test scheme is designed, which needs to be iterated repeatedly, resulting in a substantial increase in material, energy consumption and time cost; second, it is difficult to realize the fine optimization of heat treatment process parameters. Traditional methods generally set process parameters at fixed temperature intervals, and only collect data at discrete test points, which cannot completely capture the continuous law of performance change with temperature, thus limiting the accurate identification of process window and optimization potential; in addition, when facing differentiated performance targets, the existing methods lack flexible reconstruction ability. For example, for different service requirements (such as high strength and medium plasticity, and medium strength and high plasticity), a new heat treatment scheme often needs to be developed and verified, which is difficult to quickly respond to diversified performance requirements by fine-tuning the original system, resulting in low research and development efficiency.

[0004] Therefore, a heat treatment system selection method based on machine learning and particle swarm intelligent optimization is proposed to solve the above problems. SUMMARY

[0005] The purpose of the present application is to provide a heat treatment system selection method based on machine learning and particle swarm intelligent optimization to solve the problems raised in the background.

[0006] In order to solve the above technical problems, the present application provides the following technical solutions: a heat treatment system selection method based on machine learning and particle swarm intelligent optimization, using a trained machine learning model to obtain a heat treatment system, the input of the machine learning model is the annealing temperature, annealing time, cooling method, tempering temperature and tempering time of the metal material heat treatment process, a plurality of heat treatment system schemes are generated by using an orthogonal experimental design method, and the output is a measured hardness value, the machine learning model is a Gaussian process regression GPR model or a support vector machine SVR model, and the Gaussian process regression GPR model or the support vector machine SVR model is optimized, and the model is verified by global reverse search through a particle swarm algorithm, and the process of selecting the heat treatment system by using the machine learning model and the particle swarm algorithm comprises: Step S100, applying a machine learning model, after the model verification and reverse search step, inputting the target strength value corresponding to the engineering requirement, obtaining the target hardness value and the allowable deviation according to the conversion relationship between strength and hardness, using the verified heat treatment system-hardness prediction model as a predictor, using the particle swarm algorithm to perform a one-time batch reverse search in the feasible region of the process parameters, and generating a plurality of candidate heat treatment systems; Step S200, difference screening is performed on the plurality of candidate treatment combinations generated in step S100, and combinations with a process parameter difference greater than a preset threshold are preferentially retained, and then the candidate heat treatment systems are sorted in order from high to low based on the tempering temperature and from long to short based on the tempering time; Step S300, according to the sorting result of step S200, only a predetermined number of candidate heat treatment systems at the front of the sorting are prepared for mechanical property testing to obtain their yield strength, tensile strength and elongation; Step S400, according to the tensile test result, selecting the heat treatment system with the optimal plastic property as the final scheme in the small block sample meeting the target strength.

[0007] According to the above technical solutions, the machine learning model training comprises: setting the heat treatment system scheme as the model input, setting the hardness H as the model output, training the regression model, the regression model is a Gaussian process regression GPR model or a support vector machine SVR model, and the prediction uncertainty of the model for the prediction result is obtained.

[0008] According to the above technical solutions, the model verification and reverse search comprise: converting the target strength value corresponding to the engineering requirement into a plurality of target hardness values, using the heat treatment system-hardness prediction model and its prediction uncertainty as the evaluation basis, using the particle swarm algorithm to perform global reverse search within the upper and lower limits of the heat treatment process parameters, searching out the corresponding heat treatment system prediction scheme for each target hardness value, preparing a small block sample and performing heat treatment and hardness test according to the prediction scheme.

[0009] According to the technical solution, in the orthogonal experiment design step, the temperature step and the time step are set, and the time step is set with priority according to the equipment resolution.

[0010] According to the technical solution, small material samples are prepared according to different heat treatment system schemes, the surfaces of the small samples are uniformly sanded to P1500, the heating rate, temperature, holding time and cooling rate are executed according to the design scheme, when the hardness is tested, a unified load and scale are used for testing, at least 5 points of each sample are tested, and the average value is calculated as the hardness value of the sample.

[0011] According to the technical solution, the hyperparameter optimization of the support vector regression machine SVR model is performed by using a genetic algorithm, and specifically includes: Step S501, the hardness obtained by the test and the corresponding heat treatment scheme are arranged as sample data, and are divided into a training set and a test set according to a preset ratio; Step S502, a binary code is used to represent the kernel function type, kernel related parameters and penalty coefficient of the support vector machine SVR regression model, and an initial population is randomly generated on the training set; Step S503, the heat treatment system scheme is used as input and the hardness value H is used as output to establish a support vector machine SVR regression model, for each hyperparameter individual in the initial population, the model is trained and verified on the training set by using K-fold cross validation, and the average value of the mean absolute error MAE or the root mean square error RMSE of the K-fold cross validation is used as the fitness of the individual; Step S504, selection, crossover and mutation operations are sequentially performed on the initial population to generate a new generation population, until the fitness of the best individual reaches or exceeds a second preset threshold, and the optimal kernel parameter combination is output; Step S505, the support vector regression machine model is trained by using the optimal kernel parameter combination to obtain a primary heat treatment system-performance prediction model; Step S506, the test set is input into the primary heat treatment system-performance prediction model to calculate the prediction fitting degree; Step S507, it is judged whether the fitting degree is not lower than a first preset threshold, and the first preset threshold is R²≥0.90; If yes, a final heat treatment system-hardness prediction model is obtained; If no, return to step S502, adjust the parameters of the genetic algorithm and repeat the evaluation process of steps S502 to S507.

[0012] According to the technical solution, the model verification and reverse search include the following steps: Step S601, converting the target strength value corresponding to the engineering requirement into a plurality of target hardness values within the hardness range covered by the heat treatment system-hardness prediction model, and setting an allowable error window for each target hardness value; Step S602, constructing a particle swarm optimization algorithm evaluation function based on the feasible upper and lower limits of the annealing and tempering parameters, wherein the core term of the particle swarm optimization algorithm evaluation function is the deviation between the model predicted hardness and the target hardness, and the prediction uncertainty output by the prediction model when applicable can be used as an optimization term; Step S603, randomly generating a plurality of parameter vectors within the parameter feasible region defined by the feasible upper and lower limits of the annealing and tempering parameters to initialize the population of the particle swarm optimization algorithm, iteratively updating the population according to a predetermined rule, and after each iteration, performing constraint processing on the parameter vectors that exceed the parameter feasible region to return them to the parameter feasible region; Step S604, after the search converges, retaining 2-3 sets of differentiated heat treatment system combinations for each target hardness value; Step S605, preparing small block samples according to the heat treatment system combinations obtained in step S604 and performing heat treatment, and then testing their actual hardness values; Step S606, based on the measured hardness values and the target hardness values, calculating the overall prediction error and the hit rate, wherein the overall prediction error is the mean absolute error (MAE) or the root mean square error (RMSE), and the hit rate is defined as the proportion of measured hardness values falling within the allowable error window corresponding to the target hardness value; Step S607, determining whether the overall prediction error and the hit rate meet the standards simultaneously, and checking whether the predictions for low, medium, and high hardness segments are balanced; If the overall prediction error and the hit rate meet the standards, and the predictions for each hardness segment are balanced, it is determined that the prediction model and the reverse search method are reliable, and the current model and search parameters are recorded; If the overall prediction error is found to be too large or the hit rate is insufficient in a certain hardness segment, the new measured data corresponding to that hardness segment is backfilled to the training set, the machine learning model training step is re-executed to train and update the prediction model, and the search verification process of steps S601 to S607 is re-executed only for that hardness segment.

[0013] According to the above technical solution, in the model verification and reverse search, when verifying the accuracy of the model, the hit rate of the measured hardness falling within the target hardness ±10HV window is calculated, and when the hit rate is greater than or equal to 80%, the model is determined to be reliable.

[0014] According to the technical solution, in step S300, the top-ranking heat treatment system is the top 5-10 groups, and in step S400, if the plasticity of multiple candidate heat treatment systems is equivalent, the system with the shortest total heat treatment time, the lowest energy consumption, or the smallest size change of the small test sample is preferentially selected as the final solution.

[0015] Compared with the prior art, the present application has the following advantages: (1) The present application adopts a strategy of small test sample hardness testing + machine learning model + particle swarm intelligent algorithm reverse search. First, small test samples are used for rapid hardness testing to construct a data set and verify the model, avoiding the need to prepare and test the high-cost and long-cycle tensile samples each time. Finally, in the actual application stage, only a small number (such as the top 5-10 groups) of optimal candidate solutions screened by the intelligent algorithm need to be finally verified by tensile testing, which greatly reduces the number of expensive and time-consuming tensile tests, thereby significantly reducing the test cost and the cycle of the entire process exploration. (2) The present application uses a machine learning model to establish a mapping relationship between the heat treatment process parameters and the hardness. These models can learn and predict the continuous performance-process relationship in the entire process parameter feasible region from limited discrete experimental data, rather than being limited to discrete points set by experiments. This enables the model to capture the subtle effects of parameter changes on performance. Combined with intelligent optimization algorithms such as particle swarm algorithms, global and fine searches can be performed in the continuous parameter space, thereby finding the best process parameter combination that is difficult to find by traditional methods. (3) The present application establishes a general and reliable process-performance prediction model and reverse search process. Once the model is trained and verified, when facing a new performance target, only the new target strength needs to be converted to hardness and input into the system. The system can automatically and quickly search for multiple groups of candidate heat treatment systems that meet the new requirements in the feasible region using the verified model and particle swarm algorithm. This method saves the tedious process of redesigning a large number of experiments for each new target, realizes the rapid and intelligent reconstruction of the heat treatment system, and flexibly responds to diversified engineering needs. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 A schematic diagram of the electric arc additive low-alloy high-strength steel heat treatment test sample of the present application.

[0017] Figure 2 A schematic diagram of the machine learning model training result of the present application. DETAILED DESCRIPTION

[0018] With reference to the drawings of the embodiments of the present application, the technical solutions in the embodiments of the present application will be described below. The embodiments described below are only some of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0019] Please refer to Figure 1 and Figure 2 The present application provides a technical solution: a heat treatment system selection method based on machine learning and particle swarm intelligent optimization, using a trained machine learning model to obtain a heat treatment system, the input of training the machine learning model is the heat treatment process parameters of annealing temperature, annealing time, cooling mode, tempering temperature and tempering time of metal material, a plurality of heat treatment system schemes are generated by using an orthogonal experimental design method, and the output is a measured hardness value, the machine learning model is a Gaussian process regression GPR model or a support vector machine SVR model, and the Gaussian process regression GPR model or the support vector machine SVR model is optimized, and the model is verified by global reverse search through a particle swarm algorithm, and the process of selecting the heat treatment system by using the machine learning model and the particle swarm algorithm includes: Step S100, applying a machine learning model, after the model verification and reverse search step, inputting the target strength value corresponding to the engineering requirement, obtaining the target hardness value and the allowable deviation according to the conversion relationship between strength and hardness, taking the verified heat treatment system-hardness prediction model as a predictor, using a particle swarm algorithm to perform a one-time batch reverse search in the feasible region of the process parameters, and generating a plurality of candidate heat treatment systems; Step S200, difference screening is performed on the plurality of candidate heat treatment combinations generated in step S100, and combinations with process parameter differences greater than a preset threshold are preferentially retained, and the candidate heat treatment systems are sorted based on the order from high to low of the tempering temperature and from long to short of the tempering time; Step S300, according to the sorting result of step S200, only the predetermined number of candidate heat treatment systems at the front of the sorting are prepared for mechanical property testing to obtain their yield strength, tensile strength and elongation; Step S400, according to the tensile test results, selecting the heat treatment system with the best plastic performance among the small block samples meeting the target strength as the final scheme.

[0020] Gaussian process regression (GPR) and support vector machine (SVR) are two commonly used regression prediction models used to establish a nonlinear mapping relationship between heat treatment process parameters and hardness. This enables accurate prediction of hardness under unknown process conditions, avoiding the data gaps inherent in traditional discrete experiments and achieving performance prediction across continuous process spaces. Orthogonal experimental design is a multi-factor, multi-level experimental design method that covers the entire parameter space through a limited number of experimental combinations. During model training, it systematically generates representative heat treatment regime samples, ensuring comprehensive model training, improving model generalization ability, and reducing the number of experiments. Particle swarm optimization (PSO) is a global optimization algorithm based on swarm intelligence, simulating bird flock foraging behavior. It searches for optimal solutions through the collaborative search of individual and group experience. In this method, it is used for back-search, i.e., starting from the target hardness, it searches for multiple heat treatment regime combinations in the process parameter space that satisfy that hardness. This achieves global optimal solution search under multiple objectives and constraints, avoiding local optima and improving the diversity and reliability of recommended solutions. Unlike traditional forward modeling from process parameters to performance targets, reverse design refers to the inverse reasoning process from performance targets to process parameters. It uses engineering requirements (such as target hardness) as input and optimizes algorithms to deduce feasible heat treatment regimes, achieving a direct mapping from performance requirements to process solutions. This significantly improves the targeting and efficiency of process design. Candidate heat treatment regimes are ranked based on tempering temperature from high to low and tempering time from long to short. With minimal or no tensile testing, preliminary screening of candidate schemes is performed, prioritizing those with high plasticity potential, reducing the number of subsequent experiments and shortening the R&D cycle. This invention achieves rapid, low-cost, and high-performance targeted design of heat treatment regimes through a combined strategy of machine learning modeling, particle swarm optimization, empirical rule-based ranking, and precise experimental verification. It is particularly suitable for complex engineering scenarios with multiple objectives and constraints, and has significant industrial application value.

[0021] According to the above technical solution, the machine learning model training includes: setting the heat treatment regime scheme as the model input, taking the hardness H as the model output, training a regression model, wherein the regression model is a Gaussian process regression (GPR) model or a support vector machine (SVR) model, and obtaining the model's prediction uncertainty for the prediction results.

[0022] Model Input: The heat treatment regime scheme refers to a complete combination of heat treatment process parameters, typically including five key variables: annealing temperature, annealing time, cooling method, tempering temperature, and tempering time. These serve as input features for the machine learning model, establishing a mapping relationship from the process space to the performance space. This digitizes and models the complex knowledge of material heat treatment, enabling the computer to learn and understand the inherent laws between process parameters and performance. Model Output: Hardness H is a measure of a material's resistance to localized plastic deformation (such as indentation), using Vickers hardness (e.g., HV0.5). It serves as the target variable for model prediction. Choosing hardness over tensile strength as the initial model output is based on its significant advantages: rapid testing, low cost, and simple sample preparation (requiring only small samples). This greatly reduces the cost and time required for initial data collection. By constructing a "heat treatment regime → hardness" prediction model, it is possible to avoid conducting numerous expensive and time-consuming tensile tests during the exploration phase, thus allowing for the selection of potential candidate schemes for subsequent optimization. Gaussian process regression (GPR) is a probabilistic nonparametric Bayesian model. Its core feature is that it not only provides a predicted value but also naturally provides a measure of the uncertainty of that predicted value. Support vector machine regression (SVR) is a powerful regression algorithm suitable for small sample sizes and nonlinear problems. Standard SVR does not directly provide probability outputs, but its prediction uncertainty can be estimated through subsequent calculations. Both models are suitable for learning complex nonlinear relationships from limited experimental data, accurately predicting material hardness under unknown process conditions, and providing high-precision forward prediction capabilities. They are the technological cornerstone that enables the entire reverse search process. Prediction uncertainty refers to the quantification of a model's confidence level in its own predictions. For GPR, this is an inherent property; for SVR, it is an indicator that needs to be calculated additionally. It quantifies the possible error range of the model when making predictions at a certain input point (i.e., a specific set of heat treatment parameters). The main role of obtaining uncertainty is in the model validation stage. When validating schemes obtained from back-search, if a scheme's predicted hardness is close to the target but its prediction uncertainty is high, it indicates that the prediction result is unreliable, and this area may be a blind spot in the model's cognition. By focusing on uncertainty, process areas with high model confidence can be prioritized, thereby improving the success rate and reproducibility of the final recommended scheme and reducing application risks. If the prediction uncertainty of certain hardness ranges or process areas remains high, it can indicate the need to supplement new experimental data in these areas for retraining the model and achieving iterative optimization of the model. This upgrades the entire heat treatment regime selection method from a simple prediction-search system to an intelligent system with self-diagnosis and continuous optimization capabilities, ensuring that the final output heat treatment scheme is not only performance-compliant but also reliable and robust.

[0023] According to the above technical solution, the model verification and reverse search include: converting the target strength value corresponding to the engineering requirements into multiple target hardness values; using the heat treatment regime-hardness prediction model and its prediction uncertainty as the evaluation basis; using the particle swarm optimization algorithm to perform a global reverse search within the upper and lower limits of the heat treatment process parameters; searching for the corresponding heat treatment regime prediction scheme for each target hardness value; preparing small sample pieces and performing heat treatment and hardness testing according to the prediction scheme. This verification process is a closed-loop system. If an inaccurate hardness range is found, new data will be backfilled into the training set and the model will be retrained to improve the model performance in a targeted manner.

[0024] Backward search utilizes the particle swarm optimization algorithm to find feasible process solutions by working backward from the performance target—hardness. Model validation verifies the accuracy of these solutions recommended by the model and algorithm through physical experiments, thereby verifying the reliability of the entire intelligent system. Connecting pure computer simulation with the real physical world forms a virtual-reality verification loop, ensuring the reliability of the model and search process relied upon in subsequent practical applications. This significantly reduces the risk of deploying unreliable virtual solutions in actual production. Multiple target values ​​(e.g., 10) are uniformly selected within the hardness range covered by the model, covering low, medium, and high hardness levels. Stress testing is then performed on the model to verify its universality across the entire performance output range, rather than its effectiveness at only a specific point. This avoids the model being accurate only in localized areas, thus proving it to be a globally effective and robust model capable of handling diverse performance requirements. Using the heat treatment regime-hardness prediction model and its prediction uncertainty as the evaluation basis, this paper clarifies how the evaluation function (fitness function) of the particle swarm optimization algorithm (PSO) is constructed during the back-search. It not only focuses on the deviation between the predicted hardness and the target hardness but also incorporates prediction uncertainty as an important consideration. This guides the search algorithm not only to find solutions that meet the predicted values ​​but also to seek solutions that the model considers sufficiently certain and with low risk, significantly improving the robustness and reliability of the search results. The final candidate solutions are not only theoretically compliant but also originate from familiar regions with clear model understanding, resulting in a higher success rate of reproduction in actual production. The upper and lower limits of the heat treatment process parameters defined in claim 1, such as annealing temperatures of 650-1050℃, are used by the PSO algorithm and global back-search to efficiently and automatically explore the vast process parameter space, identifying all potential heat treatment solutions that meet specific hardness requirements and have significant parameter differences. This solves the problem that traditional methods cannot perform refined and global optimization, and can discover excellent process windows that are difficult to find through human experience or discrete experiments. Preparing small sample pieces and performing heat treatment and hardness testing according to the predicted scheme (the sample size can be 100×40×10mm) involves conducting actual, small-scale heat treatment experiments on the predicted heat treatment regime scheme obtained from the reverse search. The actual hardness is measured using the same hardness testing standard as in the model training phase. This process serves as the final arbiter in the entire verification process. By comparing the hardness predicted by the model with the actual tested hardness, quantitative indicators such as hit rate and mean absolute error (MAE) can be calculated. This provides indisputable experimental data support for the reliability of the model + search system. Only systems that pass this verification are qualified to be used in final practical engineering applications, thus ensuring the practical value of the entire method.

[0025] According to the above technical solution, in the orthogonal experimental design steps, a temperature step and a time step are set, and the time step is prioritized according to the device resolution.

[0026] Temperature and time steps together define the specific level of each process parameter in the orthogonal experiment. They are key to discretizing the continuous heat treatment process space into a series of finite, executable, and testable specific schemes. A reasonable step size is a prerequisite for overcoming the difficulty in finely optimizing heat treatment schemes. It ensures that the entire process space can be effectively explored within a controllable number of experiments. A scientifically set step size ensures that the initial data is reasonably distributed and representative within the process space, laying a solid foundation for training a machine learning model that can accurately characterize the continuous change of performance with temperature. By forcing the time step to prioritize matching the equipment resolution, process schemes that the equipment cannot precisely execute are fundamentally prevented. For example, if the designed holding time is 1.25 hours, but the minimum timing unit of the equipment is 0.5 hours, this ensures that all experimental data are obtained under the premise that the set process is faithfully executed, thus guaranteeing the authenticity and reliability of the data. The orthogonal experimental design generates more than 40 heat treatment schemes to cover the corners, intermediate points, and transition points of the feasible region.

[0027] According to the above technical solution, small material samples were prepared according to different heat treatment regimes. The surface of the small sample was uniformly sanded to P1500. The heating rate, temperature, holding time and cooling rate were implemented according to the design scheme. When testing the hardness, the test was conducted with a uniform load and scale. At least 5 points were tested for each sample, and the average value was calculated as the hardness value of the sample.

[0028] P1500 represents the fineness of the sandpaper. Grinding to P1500 means the sample surface has been treated to a specific and consistent smoothness. Hardness testing, especially Vickers hardness (HV) or Rockwell hardness (HRC), is extremely sensitive to the surface smoothness of the test points. Uniform fine polishing can minimize the random and systematic errors caused by surface roughness, oxide layers, or decarburized layers in indentation measurements, ensuring clear, regular indentations and accurate readings, thus directly improving the accuracy of individual hardness test data. The heating rate, temperature, holding time, and cooling rate are executed according to the design scheme, emphasizing the faithful reproducibility of the heat treatment process. It requires that the actual heat treatment operation must strictly adhere to the scheme established by the orthogonal experimental design. The machine learning model learns the mapping relationship between process parameters and performance. If the actual executed process parameters (input) do not match the design scheme, then the measured performance data (output) is invalid. Only by ensuring that each set of heat treatment regimes is executed precisely can the final measured hardness value be uniquely and reliably attributed to that specific set of process parameters. This is the most fundamental requirement for building a high-quality dataset. HV0.5 / HV1 or HRC is preferred, and only one scale should be used within the same batch. The hardness value is directly related to the test load and scale type. Uniform testing conditions eliminate systematic errors caused by different test parameters, ensuring that the hardness data of all samples are under the same dimension and standard, allowing for direct comparison and model training. If different loads or scales are used, the data will lose consistency, and the model cannot learn effectively. The microstructure of materials exhibits a certain degree of inhomogeneity; single-point testing may fall on hard or soft points and cannot represent the overall average hardness of the sample. Multi-point testing (center + four corners) effectively smooths out the random fluctuations caused by this micro-inhomogeneity. Taking the average value as the final hardness value of the sample yields a more robust characteristic that represents the overall performance of the material under this heat treatment regime. This provides the model with a more stable and reliable learning target, helping to improve the model's generalization ability and predictive stability.

[0029] Based on the above technical solution, please refer to Figure 2 The hyperparameter optimization of the Support Vector Regression (SVR) model is performed using a genetic algorithm, specifically including: Step S501: Organize the hardness obtained from the test and its corresponding heat treatment scheme into sample data, and divide it into training set and test set according to a preset ratio. Step S502: The kernel function type, kernel correlation parameters and penalty coefficient of the support vector machine SVR regression model are encoded using binary encoding, and an initial population is randomly generated on the training set. Step S503: Using the heat treatment regime scheme as input and the hardness value H as output, establish a support vector machine SVR regression model. For each group of hyperparameter individuals in the initial population, K-fold cross-validation is used to train and validate the model on the training set, and the average of the mean absolute error (MAE) or root mean square error (RMSE) of K-fold cross-validation is used as the fitness of the individual. Step S504: Select, crossover and mutation operations are performed sequentially on the initial population to iteratively generate a new generation of population until the fitness of the best individual reaches or exceeds the second preset threshold, and the optimal combination of kernel parameters is output. Step S505: Train the support vector regression machine model using the optimal kernel parameter combination to obtain the primary heat treatment regime-performance prediction model; Step S506: Input the test set into the primary heat treatment regime-performance prediction model and calculate its prediction fit. Step S507: Determine whether the fitting degree is not lower than a first preset threshold, wherein the first preset threshold is R²≥0.90; If so, then confirm that the final heat treatment regime-hardness prediction model has been obtained; If not, return to step S502, adjust the parameters of the genetic algorithm, and repeat the evaluation process from steps S502 to S507.

[0030] The performance of SVR models heavily relies on hyperparameters, such as the choice of kernel function type and kernel parameters. Genetic algorithms, simulating natural evolution, are used to perform global optimization in a complex hyperparameter space, automatically finding the optimal parameter combination that maximizes the model's prediction accuracy. This avoids the tedious, time-consuming, and expert-experience-dependent problems of traditional manual parameter tuning, automating the hyperparameter optimization process and significantly improving efficiency. Genetic algorithms can effectively escape local optima and, compared to traditional methods like grid search, are more likely to find globally optimal or near-global optimal hyperparameter combinations, thus training SVR models with superior performance. Mean Absolute Error (MAE) or Root Mean Square Error (RMSE) are objective, quantitative standards for quantifying the prediction error of regression models. They are used in genetic algorithms to calculate the fitness of each set of hyperparameters. MAE measures the average absolute difference between predicted and true values, is insensitive to outliers, and directly reflects the average prediction error. RMSE is more sensitive to larger errors because the error is squared before averaging, which makes the optimization process more inclined to penalize individual samples with larger prediction biases. By optimizing these metrics, the model is directly driven to evolve towards higher prediction accuracy and smaller errors.

[0031] The training set is randomly divided into K parts. K-1 parts are used for training and 1 part for validation in turn, repeated K times. The average of the K validation results is then used as the model performance estimate for that set of hyperparameters. By training and validating under different partitions, the volatility of model evaluation results caused by different random partitions of the training and test sets is effectively reduced. The resulting performance evaluation results better represent the model's true generalization ability on unknown data, avoiding the selection of hyperparameters that only perform well under specific data partitions. The goodness of fit is then determined to be no less than a first preset threshold, where R² ≥ 0.90. This first preset threshold is the final entry threshold and quantification standard for model performance. The coefficient of determination R² measures the model's ability to explain data variability. Setting a high threshold of R² ≥ 0.90 mandates that the final SVR model must achieve extremely high prediction accuracy, providing a hard guarantee for the reliability of subsequent backpropagation and practical applications. The second preset threshold is set based on the model prediction error (MAE or RMSE). The fully automated, closed-loop, and high-standard quality control and optimization system for SVR models uses a combination of genetic algorithms, K-fold cross-validation, MAE / RMSE, and R² thresholding to ensure that the final heat treatment regime-hardness prediction SVR model is fully evolved, rigorously evaluated, and of excellent performance.

[0032] Based on the above technical solution, please refer to Figure 2 The model validation and reverse search include the following steps: Step S601: Convert the target strength value corresponding to the engineering requirements into multiple target hardness values ​​within the hardness range that the heat treatment regime-hardness prediction model can cover, and set an allowable error window for each target hardness value. Within the effective prediction range of the model (e.g., 300-500 HV), multiple target hardness values ​​(e.g., 10) should be selected at equal intervals, and a reasonable acceptable range (i.e., allowable error window, ±10 HV) should be set for each target.

[0033] Step S602: Based on the feasible upper and lower limits of annealing and tempering parameters, construct the evaluation function of particle swarm optimization algorithm. The core term of the evaluation function of particle swarm optimization algorithm is the deviation between the model's predicted hardness and the target hardness, and the prediction uncertainty output by the prediction model can be used as an optimization term when applicable. The optimization objective of the particle swarm optimization algorithm is defined, requiring that the predicted hardness of the process solution found by the algorithm should be as close as possible to the target hardness. The evaluation function can also incorporate the prediction uncertainty of the model output as an auxiliary optimization term.

[0034] Step S603: Within the feasible domain of parameters defined by the feasible upper and lower limits of the annealing and tempering parameters, multiple parameter vectors are randomly generated to initialize the population of the particle swarm optimization algorithm. The population is iteratively updated according to preset rules. After each iteration, parameter vectors that exceed the feasible domain of parameters are constrained to return to the feasible domain of parameters. The algorithm initializes the particle swarm (i.e., candidate solutions) within a pre-defined feasible region (i.e., the legal range of all heat treatment parameters, such as annealing temperature 650-1050℃) and simulates swarm intelligence for iterative search. The constraint handling mechanism ensures that any invalid parameters generated during the search process (such as temperatures outside the range) are automatically corrected to return them to the feasible region.

[0035] Step S604: After the search converges, retain 2-3 sets of differentiated heat treatment regime combinations for each target hardness value. When no significantly better solution can be found and a stable state is reached, retain 2-3 sets of heat treatment regimes with significantly different combinations of process parameters for each target hardness.

[0036] Step S605: Prepare small sample blocks according to the heat treatment regime combination obtained in step S604 and perform heat treatment, and then test their actual hardness values. Step S606: Based on the measured hardness value and the target hardness value, calculate the overall prediction error and hit rate. The overall prediction error is the mean absolute error (MAE) or the root mean square error (RMSE). The hit rate is defined as the proportion of the measured hardness value falling within the allowable error window of the corresponding target hardness value. The virtual scheme obtained in step S604 is put into physical experimentation by preparing small sample pieces, heat-treating them and measuring their actual hardness values. Then, the measured values ​​are compared with the target values ​​to calculate the overall prediction error and hit rate.

[0037] Step S607: Determine whether the overall prediction error and hit rate meet the standard at the same time, and check whether the predictions for low, medium and high hardness segments are balanced. If the overall prediction error and hit rate meet the standards, and the predictions for each hardness segment are balanced, then the prediction model and the reverse search method are considered reliable, and the current model and search parameters are recorded. If the overall prediction error is found to be too large or the hit rate is insufficient in a certain hardness range, the new measured data corresponding to that hardness range will be backfilled into the training set, the machine learning model training steps will be re-executed to train and update the prediction model, and the search and verification process of steps S601 to S607 will be re-executed only for that hardness range.

[0038] The system assesses whether the overall error and hit rate meet the standards and checks the balance of model performance across low, medium, and high hardness ranges. If all standards are met, the system is certified as reliable. If poor performance is found in a particular hardness range, a self-optimization mechanism is activated, incorporating new experimental data for that range into the training set to retrain the model and specifically address its weaknesses. Validation is then performed only in this weak area. A complete, closed-loop, adaptive model validation and back-search process is provided, going beyond simply testing model accuracy to a dynamic system optimization process integrating an active learning mechanism. This process ensures high reliability and robustness of the final model-search system used in practical applications through systematic testing across the entire hardness range, introducing uncertainty to guide the search, and automatically feeding back validation results to model retraining.

[0039] According to the above technical solution, in the model verification and reverse search, when verifying the accuracy of the model, the hit rate of the measured hardness falling within the target hardness ±10HV window is statistically analyzed. When the hit rate is greater than or equal to 80%, the model is considered reliable.

[0040] The target hardness ±10HV window defines an engineering-acceptable performance deviation range. ±10HV is a reasonable tolerance. In step S100, the corresponding allowable deviation value required by engineering is also ±10HV. For example, if the target hardness is 400HV, measured values ​​between 390HV and 410HV are considered to be hit or meet the standard. This provides a clear and unambiguous judgment rule for calculating the hit rate, ensuring consistency and comparability of subsequent statistical results. The minimum entry threshold for the overall performance of the model-search system requires that, in verification experiments targeting multiple target hardnesses, at least 80% of the measured results fall within the expected tolerance window. This threshold is widely considered a standard of good performance in statistical and industrial applications.

[0041] According to the above technical solution, in step S200 and step S300, the top-ranked heat treatment regimes are the top 5-10 groups. In step S400, if there are multiple candidate heat treatment regimes with similar plasticity, the regime with the shortest total heat treatment time, the lowest energy consumption, or the smallest change in the size of the small sample is selected as the final regime.

[0042] Further quantification and refinement of independent claim 1 reveals that selecting 5-10 groups is a well-considered optimization decision. Fewer than 5 groups may result in missing the truly optimal solution due to insufficient sample size, posing a high risk. More than 10 groups significantly increase the cost and time of tensile testing, contradicting the invention's initial intention of reducing the number of tests. When plasticity is comparable, prioritizing the option with the best overall performance avoids meaningless deliberation between solutions with insignificant performance differences, shifting the decision-making focus from finding the absolute optimum to finding the comprehensive optimum. This approach, on the one hand, ensures the method's economy and reliability through quantitative verification of 5-10 groups; on the other hand, by introducing multi-dimensional selection criteria, such as time, energy consumption, and dimensional stability, it ensures the overall superiority of the final solution.

[0043] Example: Using low-alloy ultra-high strength steel T150TG thin-walled components manufactured by arc additive manufacturing as the application object, this invention aims to demonstrate how the method can quickly determine the optimal heat treatment process for two different engineering requirements.

[0044] Sample size and preparation as follows Figure 1 As shown, a T150TG thin-walled component sample with dimensions of 100mm × 40mm × 10mm was prepared. This embodiment sets two target schemes: Target Option 1: Meet the requirements of a certain ultra-high strength steel armor, with a strength ≥1500 MPa and an elongation ≥8%; Option 2: For use as an aerospace component, the tensile strength must be ≥1000MPa and the elongation must be ≥15%.

[0045] Based on the above technical solution, the feasible region of heat treatment process parameters is determined according to the material composition and phase diagram. The specific design is as follows: Annealing temperature: 650℃ to 1050℃, in 100℃ increments.

[0046] Annealing time: 1 to 4 hours, with 1-hour intervals.

[0047] Cooling method: water cooling or air cooling.

[0048] Tempering temperature: 250℃ to 550℃, in 100℃ increments.

[0049] Tempering time: 1 to 4 hours, with a 1-hour interval.

[0050] A five-variable orthogonal experimental design was used to randomly generate 40 heat treatment schemes. These schemes fully covered the corner points, intermediate points, and transition points of the feasible region, ensuring the representativeness and breadth of the sample data.

[0051] Subsequently, the samples were heat-treated using an electric furnace in strict accordance with the 40 heat treatment regimes set. At least 5 points (center and four corners) were measured for each sample, and the average value was calculated to finally obtain a dataset of "heat treatment regime → hardness" containing 40 sets of data.

[0052] Based on the above technical solution, please refer to Figure 2 The 40 sets of data were divided into training and test sets according to a set ratio. This embodiment uses a Support Vector Regression (SVR) model as the machine learning model and optimizes its hyperparameters using a Genetic Algorithm (GA) combined with K-fold cross-validation. The specific steps are as follows: Step S501: Organize the sample data and divide it into training and test sets.

[0053] Step S502: Use binary encoding to encode the kernel function type, kernel-related parameters and penalty coefficient of the SVR model, and randomly generate an initial population on the training set.

[0054] Step S503: Using the heat treatment regime as input and hardness value as output, establish an SVR regression model, use K-fold cross-validation for performance evaluation, and calculate the mean absolute error (MAE) or root mean square error (RMSE) of K validations as the fitness value of the hyperparameter individuals in this group.

[0055] Step S504: Perform selection, crossover, and mutation operations sequentially on the population to iteratively generate a new generation of population until the fitness (i.e., MAE or RMSE) of the best individual reaches or exceeds a second preset threshold. The second preset threshold is pre-set based on the material hardness range and historical experimental data. Finally, the globally optimal combination of kernel parameters is output. In this embodiment, after optimization by the genetic algorithm, the model achieves a performance of MAE ≤ 15 HV on the test set, meeting the preset model accuracy requirements.

[0056] Step S505: Train the SVR model using the optimal kernel parameter combination to obtain a primary "heat treatment regime-hardness" prediction model.

[0057] Steps S506-S507: Input the test set into the primary model to calculate the goodness of fit. If the goodness of fit is not lower than the first preset threshold, the final heat treatment regime-hardness prediction model is confirmed to be obtained. If the threshold is not met, the genetic algorithm parameters are adjusted and the training process is repeated.

[0058] The final model fitting result obtained from training is as follows Figure 2 As shown, Figure 2In the training set, the coefficient of determination R² = 0.923 and the mean absolute error (MAE) = 11.968, while in the test set, the coefficient of determination R² = 0.913 and the MAE = 12.824. The R² value is close to 1, indicating that the model can accurately depict the mapping relationship between heat treatment regime and hardness. The low MAE value indicates that the model's prediction error is controllable. All of the above indicators meet the first preset threshold requirement. Therefore, the final "heat treatment regime-hardness" prediction model has been obtained and can be used for subsequent model validation and backpropagation steps.

[0059] According to the above technical solution, after the model training is completed, model validation is performed to ensure its predictive reliability.

[0060] Step S601: To simulate real engineering requirements, set a set of virtual target strength values ​​covering low, medium and high levels, convert them into corresponding target hardness values, and set an allowable deviation window for each target, such as ±10 HV.

[0061] Steps S602-S604: Construct an evaluation function with the deviation between the model-predicted hardness and the target hardness as the core term. When applicable, the prediction uncertainty can be incorporated into the evaluation function as an optimization term. Use the particle swarm optimization algorithm to perform a global back-search within the feasible domain of the process parameters to find 2-3 sets of differentiated heat treatment combinations for each target hardness value.

[0062] Steps S605-S606: Prepare small sample blocks according to the heat treatment combination obtained from the search and perform heat treatment, test their actual hardness values, and statistically analyze the overall prediction error and hit rate, the proportion of the measured hardness falling within the target ±10 HV window. In this embodiment, the mean absolute error (MAE) is used for evaluation.

[0063] Step S607: It has been verified that the hit rate of this embodiment is greater than 80%, and the prediction of each hardness segment is balanced. Therefore, the "model + search" method is deemed reliable.

[0064] Based on the above technical solution, after the method has been verified to be reliable, it will be applied to specific engineering needs.

[0065] Step S100: Convert Target Scheme 1 (strength ≥ 1500 MPa) and Target Scheme 2 (strength ≥ 1000 MPa) into target hardness values ​​using empirical formulas, and set the allowable deviation to ±10 HV. Using a trained and validated heat treatment regime-hardness prediction model (in this embodiment, the trained SVR model) as the predictor, perform a one-time batch reverse search within the feasible region using particle swarm optimization to generate multiple sets (e.g., 10-15 sets) of candidate heat treatment regimes that meet the target hardness.

[0066] Step S200: First, the candidate combinations are screened for differences to avoid schemes that are too similar. Then, based on the empirical rule that "higher tempering temperature and longer tempering time are generally more beneficial to plasticity", the screened candidate schemes are ranked.

[0067] Step S300: Prepare tensile small block specimens only for the top-ranked predetermined number (e.g., the top 5 groups) of candidate heat treatment regimes, perform heat treatment and mechanical property tests, and obtain their tensile strength and elongation.

[0068] Step S400: Based on the tensile test results, select the heat treatment regime with the highest elongation (i.e., the best plasticity) from all the small specimens that meet the target strength requirements as the final solution.

[0069] Through the above process, the optimal heat treatment regime was found for the two target schemes in this embodiment. Some experimental results are shown in the table below: Based on the results: For target scheme 1 (strength ≥1500MPa, elongation ≥8%), both HT1 and HT3 meet the requirements, with HT1 having a better elongation and thus being the preferred scheme.

[0070] For target scheme two (strength ≥1000MPa, elongation ≥15%), HT5 fully meets the requirements and has excellent plasticity.

[0071] In summary, this invention has successfully determined the optimal heat treatment process quickly and accurately for two different application scenarios of arc additive manufacturing of T150TG steel, significantly reducing the large amount of experimental costs and time required by the traditional "trial and error method".

[0072] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for selecting a heat treatment regime based on machine learning and particle swarm intelligence optimization, characterized in that, The application relates to a method for obtaining a heat treatment system by using a trained machine learning model, wherein the input of the machine learning model is composed of annealing temperature, annealing time, cooling mode, tempering temperature and tempering time in a metal material heat treatment process, a plurality of heat treatment system schemes are generated by using an orthogonal experimental design method, and the output is a measured hardness value; the machine learning model is a Gaussian process regression (GPR) model or a support vector machine (SVR) model, and the GPR model or the SVR model is optimized; the model is verified by global reverse search through a particle swarm algorithm; and the process of selecting the heat treatment system by using the machine learning model and the particle swarm algorithm comprises the following steps. In step S100, the machine learning model is applied, the target strength value corresponding to the engineering requirement is inputted after the model verification and reverse search steps, the target hardness value and the allowable deviation are obtained according to the conversion relationship between the strength and the hardness, the verified heat treatment system-hardness prediction model is used as a predictor, a batch of reverse searches are performed in the feasible region of the process parameters by using the particle swarm algorithm, and a plurality of candidate heat treatment systems are generated. In step S200, the plurality of candidate treatment combinations generated in step S100 are subjected to differential screening, and combinations with process parameter differences greater than a preset threshold value are preferentially reserved, and then the candidate heat treatment systems are sorted in descending order of the tempering temperature and in descending order of the tempering time. In step S300, according to the sorting result in step S200, only a predetermined number of candidate heat treatment systems at the front of the sorting are used to prepare tensile small block samples for mechanical property testing, and the yield strength, the tensile strength and the elongation rate are obtained. In step S400, according to the tensile test result, the heat treatment system with the optimal plastic property is selected from the small block samples meeting the target strength as the final scheme.

2. The method for selecting heat treatment regime based on machine learning and particle swarm intelligence optimization according to claim 1, characterized in that, The machine learning model training comprises the following steps: the heat treatment system scheme is set as the model input, the hardness H is set as the model output, a regression model is trained, the regression model is a Gaussian process regression (GPR) model or a support vector machine (SVR) model, and the prediction uncertainty of the model for the prediction result is obtained. 3.The method of selecting heat treatment regime based on machine learning and particle swarm intelligence optimization according to claim 2, wherein, The model verification and reverse search comprise the following steps: the target strength value corresponding to the engineering requirement is converted into a plurality of target hardness values, the heat treatment system-hardness prediction model and the prediction uncertainty thereof are used as evaluation bases, the particle swarm algorithm is used for global reverse search in the upper and lower limit ranges of the heat treatment process parameters, the corresponding heat treatment system prediction scheme is searched for each target hardness value, small block samples are prepared, heat treatment and hardness testing are performed according to the prediction scheme. 4.The method of selecting heat treatment regime based on machine learning and particle swarm intelligence optimization according to claim 1, characterized in that: In the orthogonal experimental design step, the temperature step and the time step are set, and the time step is preferentially set according to the equipment resolution. 5.The method of selecting heat treatment regime based on machine learning and particle swarm intelligence optimization according to claim 1, characterized in that: The material small block samples are prepared according to different heat treatment system schemes, the surfaces of the small block samples are uniformly sanded to P1500, the heating rate, the temperature, the holding time and the cooling rate are executed according to the design scheme, the hardness is tested according to the unified load and the scale, at least 5 points of each sample are tested, and the average value is calculated as the hardness value of the sample. 6.The method of selecting heat treatment regime based on machine learning and particle swarm intelligence optimization according to claim 2, wherein, The hyperparameter optimization of the support vector regression machine SVR model is performed by using a genetic algorithm, and specifically includes the following steps: In step S501, the hardness obtained by the test and the corresponding heat treatment scheme are arranged as sample data, and are divided into a training set and a test set according to a preset proportion; In step S502, binary coding is used to represent the kernel function type, kernel related parameters and penalty coefficient of the support vector machine SVR regression model, and an initial population is randomly generated on the training set; In step S503, the heat treatment scheme is taken as the input and the hardness value H is taken as the output, and a support vector machine SVR regression model is established. For each hyperparameter individual in the initial population, the model is trained and verified on the training set by using K-fold cross-validation, and the average value of the mean absolute error MAE or the root mean square error RMSE of K-fold cross-validation is taken as the fitness of the individual; In step S504, selection, crossover and mutation operations are sequentially performed on the initial population to generate a new population, and the process is repeated until the fitness of the best individual reaches or exceeds a second preset threshold, and the optimal kernel parameter combination is output; In step S505, the support vector regression machine model is trained using the optimal kernel parameter combination to obtain a primary heat treatment scheme-performance prediction model; In step S506, the test set is input into the primary heat treatment scheme-performance prediction model to calculate the prediction fitting degree; In step S507, it is determined whether the fitting degree is not less than a first preset threshold, and the first preset threshold is R²≥0.90; If yes, a final heat treatment scheme-hardness prediction model is obtained; If no, the parameters of the genetic algorithm are adjusted and the evaluation process of steps S502 to S507 is repeated.

7. The method of selecting heat treatment regime based on machine learning and particle swarm intelligence optimization according to claim 3 or 6, characterized in that, The model verification and reverse search includes the following steps: In step S601, the target strength value corresponding to the engineering requirement is converted into a plurality of target hardness values within the hardness range covered by the heat treatment scheme-hardness prediction model, and an allowable error window is set for each target hardness value; In step S602, based on the feasible upper and lower limits of the annealing and tempering parameters, an evaluation function of a particle swarm algorithm is constructed, and the core term of the evaluation function of the particle swarm algorithm is the deviation between the model predicted hardness and the target hardness, and the prediction uncertainty output by the prediction model when applicable can be used as an optimization term; In step S603, a plurality of parameter vectors are randomly generated within the parameter feasible region defined by the feasible upper and lower limits of the annealing and tempering parameters to initialize the population of the particle swarm algorithm, the population is iteratively updated according to a preset rule, and after each iteration, the parameter vectors that exceed the parameter feasible region are constrained to return to the parameter feasible region; In step S604, after the search converges, 2-3 groups of differentiated heat treatment scheme combinations are reserved for each target hardness value; In step S605, small block samples are prepared and heat treated according to the heat treatment scheme combinations obtained in step S604, and then the actual hardness values are tested; Step S606, based on the measured hardness value and the target hardness value, the overall prediction error and the hit rate are calculated, the overall prediction error is the mean absolute error MAE or the root mean square error RMSE, and the hit rate is defined as the proportion of the measured hardness value falling within the allowable error window of the corresponding target hardness value; Step S607, it is judged whether the overall prediction error and the hit rate meet the standards at the same time, and it is checked whether the prediction of the low, medium and high hardness segments is balanced; If the overall prediction error and the hit rate meet the standards, and the prediction of each hardness segment is balanced, it is determined that the prediction model and the reverse search method are reliable, and the current model and search parameters are recorded; If it is found that the overall prediction error is large or the hit rate is insufficient in a certain hardness segment, the new measured data corresponding to the hardness segment is backfilled to the training set, the machine learning model training step is re-executed to train and update the prediction model, and the search verification process of steps S601 to S607 is re-executed only for the hardness segment.

8. The method for selecting heat treatment regime based on machine learning and particle swarm intelligence optimization according to claim 7, characterized in that, In the model verification and reverse search, when verifying the accuracy of the model, the hit rate of the measured hardness falling within the target hardness ± 10HV window is calculated, and when the hit rate is greater than or equal to 80%, it is determined that the model is reliable. 9.The method of selecting heat treatment regime based on machine learning and particle swarm intelligence optimization according to claim 1, wherein: In step S300, the top heat treatment systems are the top 5-10 groups, and in step S400, if there are multiple candidate heat treatment systems with similar plasticity, the scheme with the shortest total heat treatment time, the lowest energy consumption, or the smallest size change of the small block sample is preferentially selected as the final scheme.

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