This paper develops an optimized prediction method based on machine learning for optimal process parameters for vacuum carburizing. The critical point is data expansion through machine learning based on a few parameters and data, which leads to optimizing parameters for vacuum carburization in heat treatment. This method extends the data volume by constructing a neural network with data augmentation in the presence of small data samples. In this paper, the database of 213 data is expanded to a database of 2,116,800 data by optimizing the prediction. Finally, we found the optimal vacuum carburizing process parameters through the vast database. The relative error of the three targets is less than that of the target obtained by the simulation of the corresponding parameters. The relative error is less than 5.6%, 1%, and 0.02%, respectively. Compared to simulations and actual experiments, the optimized prediction method in this paper saves much computational time. It provides a large amount of referable process parameter data while ensuring a certain level of accuracy.
Various heat treatment techniques, including hardening, carburizing, and tempering, are often used in material processing to provide critical components for aerospace, highspeed railroads, and automobiles with sufficient high strength and high resistance to friction and wear. However, deformation in the heat treatment process has been challenging to predict and control^{[1 2]}. In particular, the usual carburizing and hardening processes often result in significant and irregular deformations, making it difficult to predict how much machining allowance to leave for subsequent machining of these critical parts and creating difficulties in ensuring high performance and accuracy of the details. Recently, vacuum carburizing and quenching technology have been developed to solve this problem. In particular, the gas quenching method is adopted after vacuum carburization. This method can significantly reduce the deformation caused by quenching and play a good role in improving the performance and precision of parts^{[3]}. However, controlling a vacuum carburizing furnace is more complicated than the standard carburizing technology. It is still basically through many experimental methods to seek to meet the requirements of various materials and parts shapes and performance of the vacuum carburizing process. Therefore, efficiently finding out the best approach to vacuum carburizing and quenching is essential in vacuum carburizing technology.
In vacuum carburizing, steel parts are heated under a vacuum, a "carburizing phase" in which hydrocarbon gases are introduced at low pressure and held in a vacuum to allow the carbon to diffuse into the steel, and this "diffusion phase" results in a uniform hardness of the carburized layer and reduced part deformation^{[4]}. The process of vacuum carburizing is outlined as follows: The carburizing furnace is heated to the required temperature for carburizing under a particular heating process, kept stable, and then forced carburizing and diffusion are performed sequentially. After the diffusion time, reduces the furnace temperature. However, conditions such as heating temperature and carburization time in a vacuum, diffusion temperature and time, as well as gas pressure, have a significant influence on the concentration and depth of the carburized layer on the surface of the carburized part and should be optimally determined according to the steel properties and the part application^{[5]}.
As early as 1992, some scholars proposed a thermalphasechangemechanical theory and simulation method for heat treatment simulation^{[69]}, and this theory and calculation method have been used to simulate and verify the heat treatment process of many typical parts. Mechanisms and computational methods that consider the diffusion of carbon inside the steel during carburization have also been proposed and experimentally verified before^{[10]}. Recently, with the development of vacuum carburizing technology, the simulation method has also received attention and research^{[11]}.
The simulation technique can indeed describe the changes in the temperature field, diffusion field, phase change, and stressstrain field during heat treatment and reveal the relationship and mechanism of multifield coupling. However, finding the best process in the heat treatment process is still tough. Although a large amount of data can be obtained through many simulations such as software, the calculations take much time and work to get the process parameters from the target values. To solve this topic, with the development of artificial intelligence techniques, neural networks, and machine learning techniques, machine learning methods have started to find the optimal process for carburizing and quenching^{[12]}. In this paper, we also use neural networks and machine learning methods to propose a linear regression of trained teacher signals and expand the set of teacher signals for a small sample multiobjective vacuum carburization process. The vacuum carburizing process controls and reduces essential parts' thermal deformation and improves surface hardness. It has also received increasing attention in the heat treatment of crucial components such as gears and bearings. It is currently a more effective technology for energy conservation and emission reduction in heat treatment. However, what kind of vacuum carburizing process should be adopted for various shapes and materials to achieve the best effect has always been an urgent issue in applications. In the past, it was predicted through multiple heat treatment simulations to determine the carbon concentration, phase transformation, structure, and hardness changes within parts after vacuum carburizing. Although this simulation has a solid theoretical background, it requires long calculation times and often requires many iterations to find the best process conditions. This paper uses a heat treatment simulation to establish a small sample of teacher signal sets. Through neural networks and machine learning models, it optimizes the design of the vacuum carburizing process. This not only improves the efficiency of process optimization but, more importantly, proposes an efficient and lowcost solution for the process design of vacuum carburizing by combining heat treatment simulation with deep learning technology. Compared with the previous research^{[13]}, the innovation of this paper is that the vacuum carburizing data of small samples can be expanded according to the corresponding physical laws within a specific range of error, and the derivation from the demand target to the optimal process parameters can be completed. After the continuous expansion of the data set and deep learning, we find the vacuum carburizing process parameters closest to the target values of carburizing layer depth, surface carbon concentration, and hardness. At the same time, the obtained optimized process parameters are then validated by simulation, and the validation results are confirmed to be superior to the initially empirically adopted process parameters, thus verifying the reliability of the smallsample multiobjective optimization search method proposed in this paper.
The carburizing and quenching process allows the phase transformation structure of the material to be changed. Mechanical components, such as gears, bearings, and rollers, which place high demands on the surface in terms of resistance to friction and wear, can be substantially hardened and improved by the carburizing process. However, the carburizing and quenching involves a complex continuous medium thermodynamic theory. It requires considering the coupling between the carbon concentration diffusion field, temperature field, phase transformation kinetics, tissue distribution, and the inelastic stress/strain field. In this theory, the coupling effects of the following aspects are considered. The first is carefully considering the impact on material properties and phase transformation kinetics due to the diffusion of carbon ions in the steel and the creation of a gradient distribution. The second considers the effect of temperature changes on the nucleation and growth of phase distortion and the temperature field due to the generation of latent heat from the phase transformation. The development of the phase transformation affects the stress and strain fields as the phase transformation brings about local expansion or contraction.
Conversely, the stress/strain fields can also inhibit or induce the nucleation and growth of the phase transformation. The third aspect is that changes in the temperature field inevitably lead to the expansion or contraction of the material, i.e., thermal strain. When significant distortions occur within the material because of processing and heat treatment, heat generation also occurs, affecting the temperature field change. This is the phenomenon of multifield coupling in the heat treatment process. Heat treatment simulation software (e.g., COSMAP  Computer Simulation of Manufacturing Process) has been used to simulate the coupled diffusion analysis, temperature analysis, phase transformation, and deformation/stress distribution during carburizing and quenching processes^{[13]}.
COSMAP simulation calculations have been validated many times and are consistent with the corresponding physical laws. Therefore, the data obtained from COSMAP simulations can be used as a teacher signal for vacuum carburizing optimization. However, calculations must be made using a large amount of data and time to determine the optimum conditions for the carburizing process. This needs to fit the immediate development needs of new energy vehicles. In developing new energy vehicles, the precision and time required for carburizing and quenching automobile parts are relatively high. Optimization or artificial intelligence technology is expected to propose a method to predict the optimal vacuum carburizing process conditions.
Basic theoretical diagram.
Based on the basic principles of heat treatment and COSMAP, a virtual heat treatment system (VHT) is proposed. The diagram of the heat treatment virtual manufacturing system is shown in
Overview of the heat treatment optimization process; A: Stressstrain analysis of materials; B: Quenching process; C: Vacuum Carburizing Process; D: Gear deformation; E: Part organization diagram; F:carbon concentration distribution; G: Hardness distribution.
This paper presents a method of process optimization based on machine learning and heat treatment simulation techniques and performance characteristics in the context of a specific database size with materialrelated information already available, which ultimately serves the heat treatment simulation system. Firstly, some of the vacuum carburization simulation data required for the study was used as the initial database. Secondly, the neural network structure is established and trained, and results are tested based on the total number of samples in the database and the target number. If the test results are poor or do not meet the criteria, the neural network is retrained by modifying it or the number of training sessions, for example. Then, once the training results pass the test criteria, data is expanded by data augmentation to keep it at a reasonable range and the correct total number. The expanded data is then optimally predicted by the optimization system in this paper to obtain the closest data to the desired target value. The data parameters obtained from the optimization are then simulated, and various comparison methods evaluate the effectiveness of the optimization. When a certain optimization level has been achieved, the final validation is carried out using experimental results. Finally, the validated data can be used as training samples in the database to improve the training results.
In the initial phase of vacuum carburizing, after obtaining the required target values from the customer, a certain quantity of vacuum carburizing process conditions is first listed based on physical laws and experience to form the basis for the initial parameter data. Carburized quenching simulations are then carried out using software such as COSMAP. Suppose the results of the simulation experiments contain results that match the target values. In that case, the parameters for which the target values are obtained are set as the correct process parameter conditions. However, due to changes in the materials used for vacuum carburizing and accuracy requirements, it is almost impossible to obtain accurate data when setting the initial vacuum carburizing process conditions. Therefore, a more reasonable method is to use several vacuum carburizing process conditions, get the corresponding target values for each by carburizing and quenching simulation, and build a new database as a teacher signal. The advantage of the teacher signals conveyed by this method is that they fit the physical logic of carburized quenching and allow a large amount of data to be obtained relatively quickly. The disadvantage is that the data obtained from the simulation has a high degree of accuracy compared to the data from the actual experiment but needs to be fully representative of the existing experimental data. Based on the teacher signals obtained here, the optimization method of this paper yields one or more combinations of process parameters that are compatible with the target values, provided that specific errors are tolerated. The obtained parameters are calculated by carburized quenching simulation. If the error between the simulation results and the target values is within acceptable limits, actual operating experiments are conducted to determine whether these parameters are correct.
The artificial neural network initially used in this paper is a Multilayer Perceptron, and the specific structure is shown in
Neural network structure at the beginning of the experiment.
The Value range of training parameters and targets is shown in
Value range of training parameters and targets



Carburizing temperature (CC) (°C)  930/960  930 
Diffusion temperature (DC) (°C)  930/960  930 
Carburizing time (CT) (min)  (30~55,5)  35 
Diffusion time (DT) (min)  (135~160,5)  150 
Forced carburizing concentration (FCC) (%)  0.72~0.885  0.74 
Diffuse carbon concentration (DCC) (%)  0.67~0.835  0.69 
Carburizing layer depth (CLD)(mm)  0.698~1.43  0.76886 
Surface carbon concentration (SC) (%)  0.668~0.824  0.688 
Surface hardness (SH) (HV)  754.3783.6  764.50897 
The meaning of (30~55, 5) in the table is to set the value range from 30 to 55 and obtain samples at five intervals. All other identical formats in the table have the same meaning as above. The two brackets after the parameter are the abbreviation and the parameter unit. In this paper, such abbreviations and branches are used after that.
In addition to the above parameters, there are other conditions for vacuum carburizing, such as pressure, material, model construction, and the pulsing process used for carburizing. The model's material and structure are consistent in the simulation using corresponding calculation files; the simulation is carried out at the same pressure (the pressure used in the experiment) by default. Finally, the carburizing concentration parameters are adjusted in the file to match the pulsing process.
To overcome the difficulty of machine learning algorithms to obtain robust prediction results and excellent prediction accuracy with small samples, megatrenddiffusion (MTD) is used to estimate the acceptable range of attributes for small data sets, to fill the information interval and to calculate the virtual sample value and the affiliation function value (the probability of occurrence of that sample value). This paper uses a multidistribution megatrenddiffusion (MDMTD) technique based on the basic MTD, as shown in
Given a sample set X = {
Diagram of MDMTD.
Among them,
In Equation
The rollout regions of the sample set X are [L, min] and [max, U], and the directly observed part is [min, max]. Since the data distribution is unknown in the rollout regions [L, min] and [max, U], a uniform distribution is used to generate virtual sample points, represented as triangular hollow points in
Through the MDMTD process, the original sample set X, in terms of training, effectively increases the sample capacity. The MDMTD process expands the information of the original sample set X. The MDMTD process is discussed in the following section.
In this paper, the activation function used for the neural network is the ReLU activation function^{[15]}.
Reasons to use ReLU are^{[16]}: 1: Network training can be faster because compared to Sigmoid and tanh, derivatives are easier to obtain, backpropagation constantly updates parameters, and its products are simple in uncomplicated form; 2: The ReLU function is a segmented linear function. Classifying a neural network can be regarded as a multistage small linear regression process, effectively improving the classification effect; 3: Prevent gradient loss. Suppose the values are too large or too small. In that case, the derivatives of sigmoid and tanh approach zero, and the phenomenon of ReLU being a nonsaturated activation function does not exist; 4: To reduce overfitting, make the mesh sparse, with parts smaller than 0 and values larger than 0.
Parameter normalization is carried out once before the training and expansion data. The normalization method uses the MinmaxScaler method uniformly, with the following Eqation (8):
In model training, the three target values are trained independently and used in the MSE loss function to reduce the mutual influence between the target values. The gradient is adjusted by backpropagation. The loss function is shown in Equation:
L is the mean of the sum of squares of the errors,
∂L/∂w and ∂L/∂b are the gradients of the weights (w) and biases (b), n is the total number of data,
Calculate the gradient of the ttime steps.
First, the exponential moving average number of gradients is calculated and m0 is initialized to 0. As in the Momentum algorithm, the gradient dynamics of previous time steps are considered comprehensively.
The β_{1} coefficient is an exponential decay rate, which controls the weight assignment (moving mass and current gradient). It usually takes a value close to 1. The default value is 0.9.
Second, the exponential moving average number of gradient squares is calculated and
Calculate the gradient for each time step as time accumulates.
Third, since m0 is initialized to 0,
Fourth, when
Fifth, update parameters, multiplying the ratio of the initial learning rate α gradient mean to the square root of the gradient variance. Default learning rate α = 0.001. ε = 10^{8}, avoiding a divisor of 0. The equation shows that the calculation of updated step length is not directly determined by the current gradient but can be adaptively adjusted from two angles: the gradient means and the gradient square.
The error rates of the three target values are output after each training session to intuitively determine whether the gradient optimization of the current training is standard. The model creation flowchart is shown in
Model Creation Flowchart.
The neural network for the three targets is then introduced through the NET part of the program, introducing three models each; the MSE loss function, Adam optimization algorithm, and error backpropagation are used to optimize the gradients of the models.
After the optimization is completed, the current model is saved. The model is evaluated in the TEST part of the program by the goodness of fit of the data in the test set comparison chart.
If the errors are within acceptable limits, the current model extends the parameter range and generates new data for data loading in the central program part.
In this paper, to determine how often the training is most appropriate under the current neural network structure, the training results are shown in
Training results at 3500 training sessions.
Training results at 5000 training sessions.
We analyze
The process flow of vacuum carburizing optimization is as follows: First, each process condition is determined, and carburizing and quenching simulations are performed under each process condition using the heat treatment simulation program COSMAP to obtain initial vacuum carburizing process conditions and teacher signals. As the simulated process is theoretically representative of vacuum carburization's physical and chemical phenomena, these teacher signals are introduced into the neural network for learning and training. The appropriate parameter values for each cell in the neural network are determined. On the other hand, if there are few teacher signals, the results obtained in training do not match the demanded target values, so the database must be expanded. However, since the vacuum carburization simulation uses partial differential equations and finite element methods to represent physical and chemical phenomena, expanding the teacher signals by coupled analysis is pretty computationally timeconsuming. Therefore, for optimal training, this paper first performs initial training using the initial database (215 pairs) obtained from the simulation, and then the process conditions of vacuum carburization given to the teacher signal are expanded by the rules of linear expansion to including the carburization temperature, diffusion temperature, time interval of each process, and carburization effects (results) are extended, and the training is performed again.
The extension of data is considered based on the following points. 1:The training data contains only two carburizing temperatures, 930°C and 960°C, and the diffusion temperature is the same as the carburizing temperature. Practically all combinations of temperatures between these two temperatures can be obtained based on these two temperatures, and the error is within the range allowed by machine learning; 2:To make the training results more convincing and to make the objective of the data extension clearer, three sets of experimental data with the same material and model as the training data were included in this paper so that the parameters had to be extended to include the corresponding values of the experimental data when the data was developed; 3:Because the data expansion is a complete permutation, each additional parameter value adds a large amount of total data. More total data can seriously affect the speed of data expansion and optimization of predictions. Therefore, we only partially perform the same interval data expansion in this paper. The specific expansion results are shown in
Results of data expansion



Carburizing temperature (CC)  (930960,5)  7 
Diffusion temperature (DC)  (930960,5)  7 
Carburizing time (CT)  3055  8 
Diffusion time (DT)  100160  8 
Forced carburizing concentration (FCC)  0.721.48  27 
Diffuse carbon concentration (DCC)  0.670.835  25 
After the range expansion of the parameter values, an array of 6 parameter value ranges is combined to obtain the new database. Therefore, the maximum number of new data is 7*7*8*8*27*25, 2,116,800 pairs. To ensure that the new data generated is reasonable, restrictions are added to the expansion process: the forced carburizing temperature is greater than or equal to the diffusion temperature; and the forced carburizing concentration is greater than the diffusion concentration. The predictions of the process parameters will be determined based on an extended database. Therefore, the experiments will reasonably extend the range of parameter values in the database.
This paper uses C# as the front end to call the Python program running on the back end. See Appendix A for the interface of the optimization prediction system. In this optimization result evaluation, the demand target values were set as follows: carburization layer depth 0.95, surface carbon concentration 0.69, and surface hardness 833. One set of experimental data from BMEI is consistent with the currently set requirements; therefore, data relating to a 1/4 cylinder of the same material and size were used in the COSMAP simulations, and the parameters for the simulations were obtained by optimization.
The results of COSMAP simulations are read as shown in
A: Selection of surface hardness; B: surface carbon; C: Martensitic phase transition.
Example of manual image conversion.
The results of the four sets of parameters resulting from the optimization carried out by this system, compared with the target values calculated from simulations with the same parameters, are shown in
Relative error of optimization results to simulation results and to experimental data











Assumptions  930  930  42  140  1.35  0.69  0.95  0.69  833  Demand 
Experimental  930  930  42  140  1.35  0.69  0.95  0.69  833  result 
Optimization1  935  935  49  100  1.22  0.76  0.94902  0.73557  833.0437  Optimization 
Result  935  935  49  100  1.22  0.76  0.103%  6.604%  0.005%  Relative error 
Simulation1  935  935  49  100  1.22  0.76  0.75  0.76  775.47  Simulation 
Result  935  935  49  100  1.22  0.76  21.053%  10.145%  6.906%  Relative error 
Optimization2  940  940  50  100  1.22  0.76  0.95795  0.743  833.0293  Optimization 
Result  940  940  50  100  1.22  0.76  0.837%  7.681%  0.004%  Relative error 
Simulation2  940  940  50  100  1.22  0.76  0.707  0.76  775.51  Simulation 
Result  940  940  50  100  1.22  0.76  15.263%  10.145%  6.902%  Relative error 
Optimization3  950  950  50  100  1.22  0.74  0.94334  0.73048  832.95538  Optimization 
Result  950  950  50  100  1.22  0.74  0.701%  5.867%  0.005%  Relative error 
Simulation3  950  950  50  100  1.22  0.74  0.783  0.765  776.68  Simulation 
Result  950  950  50  100  1.22  0.74  17.579%  10.870%  6.761%  Relative error 
Optimization4  950  950  42  100  1.26  0.765  0.97569  0.75537  832.99841  Optimization 
Relative error  950  950  42  100  1.26  0.765  2.704%  9.474%  0.0002%  Relative error 
Simulation4  950  950  42  100  1.26  0.765  0.783  0.74  773.26  Simulation 
Relative error  950  950  42  100  1.26  0.765  17.579%  7.246%  7.172%  Relative error 
The relative errors can be obtained from the three data sets in blue. The relative errors of the target values of the optimization results are smaller than the corresponding simulation results. However, the problem is that the relative error of the surface carbon concentration values in the current case is very large, which theoretically does not play a role in optimization.
For the sake of optimization rigor, the parameters obtained from the optimization are simulated in this paper, and the results are compared with the best results in the original training set. The results are shown in
Comparison of optimized parameter simulations with the original optimal data











Assumptions  930  930  42  140  1.35  0.69  0.95  0.69  833  Demand 
Experimental  930  930  42  140  1.35  0.69  0.95  0.69  833  result 
Simulation1  935  935  49  100  1.22  0.76  0.75  0.76  775.47  Simulation 
result  935  935  49  100  1.22  0.76  21.053%  10.145%  6.906%  Relative error 
Simulation 2  940  940  50  100  1.22  0.76  0.707  0.76  775.51  Simulation 
result  940  940  50  100  1.22  0.76  15.263%  10.145%  6.902%  Relative error 
Simulation 3  950  950  50  100  1.22  0.74  0.783  0.765  776.68  Simulation 
result  950  950  50  100  1.22  0.74  17.579%  10.870%  6.761%  Relative error 
Simulation 4  950  950  42  100  1.26  0.765  0.783  0.74  773.26  Simulation 
result  950  950  42  100  1.26  0.765  17.579%  7.246%  7.172%  Relative error 
Training  960  960  40  160  0.81  0.76  95.23%  75.01%  773.64%  best 
result  960  960  40  160  0.81  0.76  0.238%  8.711%  7.126%  Relative error 
It is easy to see from the combined error rate that although the optimization results do not achieve the accuracy of the training data in terms of individual target values, they do have an overall optimization effect. However, according to
Therefore, in this paper, the structure of the neural network is modified, and a second optimization and simulation calculation is performed. The number of layers of the neural network has changed from 6 to 8, and the maximum number of nodes has increased to 30. Based on the new neural network, training, data expansion, optimization prediction, and simulation calculation are carried out again.
The optimization and simulation results after modifying the neural network with the optimal data of the training set are shown in
Comparison results of relative errors after modifying the neural network











Assumptions  930  930  42  140  1.35  0.69  0.95  0.69  833  Demand 
Experimental  930  930  42  140  1.35  0.69  0.95  0.69  833  result 
Optimization1  960  950  50  160  1.28  0.68  0.97854  0.68676  833.12805  Optimization 
Result  960  950  50  160  1.28  0.68  3.00%  0.47%  0.0154%  Relative error 
Simulation1  960  950  50  160  1.28  0.68  0.907  0.68  767.5  Simulation 
Result  960  950  50  160  1.28  0.68  4.526%  1.449%  7.863%  Relative error 
Optimization2  960  955  49  120  1.26  0.72  0.96749  0.72111  832.94519  Optimization 
Result  960  955  49  120  1.26  0.72  1.841%  4.509%  0.0066%  Relative error 
Simulation2  960  955  49  120  1.26  0.72  0.865  0.7  770.19  Simulation 
Result  960  955  49  120  1.26  0.72  8.947%  1.449%  7.54%  Relative error 
Optimization3  960  960  30  120  1.26  0.75  0.96773  0.74116  832.91785  Optimization 
Result  960  960  30  120  1.26  0.75  1.866%  7.414%  0.0099%  Relative error 
Simulation3  960  960  30  120  1.26  0.75  0.846  0.72  773.06  Simulation 
Result  960  960  30  120  1.26  0.75  10.947%  4.348%  7.196%  Relative error 
Optimization4  960  960  35  155  1.22  0.7  0.89685  0.69691  833.00464  Optimization 
Result  960  960  35  155  1.22  0.7  5.60%  1.00%  0.0006%  Relative error 
Simulation4  960  960  35  155  1.22  0.7  0.81  0.75  768  Simulation 
Result  960  960  35  155  1.22  0.7  14.737%  8.696%  7.80%  Relative error 
Comparison results of simulated data after modifying the neural network











Assumptions  930  930  42  140  1.35  0.69  0.95  0.69  833  Demand 
Experimental  930  930  42  140  1.35  0.69  0.95  0.69  833  result 
Simulation 1  960  950  50  160  1.28  0.68  0.907  0.68  767.5  Simulation 
result  960  950  50  160  1.28  0.68  4.526%  1.449%  7.863%  Relative error 
Simulation 2  960  955  49  120  1.26  0.72  0.865  0.7  770.19  Simulation 
result  960  955  49  120  1.26  0.72  8.947%  1.449%  7.54%  Relative error 
Simulation 3  960  960  30  120  1.26  0.75  0.846  0.72  773.06  Simulation 
result  960  960  30  120  1.26  0.75  10.947%  4.348%  7.196%  Relative error 
Simulation 4  960  960  35  155  1.22  0.7  0.81  0.75  768  Simulation 
result  960  960  35  155  1.22  0.7  14.737%  8.696%  7.80%  Relative error 
Training  960  960  40  160  0.81  0.76  0.95226  0.75010598  773.64301  best 
result  960  960  40  160  0.81  0.76  0.238%  8.711%  7.126%  Relative error 
Although the relative errors of each target value are smaller than the corresponding simulated data for only two sets of data after modifying the neural network, the relative errors of each target value are small enough to achieve the optimization effect. In some cases, substituting the parameters of the optimization results back into the simulation gives results with more minor errors than the training data. The combined error rate also becomes smaller compared to the training data and can justify this method of modifying the neural network.
In this paper, a machine learningbased optimization method for the vacuum carburizing process is developed. The plan is based on the database provided by the heat treatment simulation and computation system. A multilayer perceptron neural network is used to build a vacuum carburizing optimization prediction system to train and extend the data of vacuum carburizing to obtain more training and optimization parameters with small samples. Currently, the optimization and prediction method proposed in this paper is based on 213 sets, which were expanded to 2,116,800 locations through neural network training and data expansion. The training results were tested with a comparison R2 of 0.928, 0.989, and 0.647 within an acceptable error range. Using the expanded database as a basis for predicting the optimal vacuum carburizing process parameters, the expected parameters for the three objectives had relative errors that were better than the corresponding simulated results, and the relative errors were all maintained below 5.6%, 7.414%, and 0.0154%, respectively. At the beginning of the study, the neural network used was six layers, which was gradually fixed to use a neural network with eight layers. After simulation and calculation, the maximum number of nodes was adjusted from 30 to 32 layers. It was finally possible to make the simulation results of the parameters obtained by the optimized system better than the optimal data in the initial database. Compared with the standard vacuum carburizing process parameters calculation, the method is characterized by the following. 1:Fast analysis and application of the vacuum carburizing simulation data; 2: The process parameter data obtained by optimization can be used as new data for the database within a specific error allowance.
After the data extension is completed, the extended data set is used as a database for process optimization. When numerical requirements are made for the vacuum carburizing process regarding the carburizing layer depth, surface carbon concentration, and hardness, the process parameters with the closest results to the needs can be obtained by this system. Finally, the obtained optimization results were simulated again, and the simulation results obtained were better than the results of the process conditions initially set by relying on experience. When research or experiments require a greater variety of parameters or more minor errors, the neural network can be tuned to meet the target requirements depending on the training set data.
Given the current metal vacuum carburization, the process parameters that meet the production requirements can be obtained by specific experiments or by setting parameters for simulation based on experience. The former may take several days to carry out each investigation, while the latter also needs dozens of hours to calculate when the part model used for simulation is complex. The results obtained in these two cases are highly authentic but may not achieve the original purpose. The limitation of the research in this paper lies in the training and data expansion based on a few experimental data and a few simulation data. The reliability of the obtained data is difficult to exceed the simulation, and it can reach the level of experimental data. But relatively, this research can obtain many parameters with certain reliability in relatively little time. The future research direction of this research is to solve the problem of reducing training accuracy when the types of process parameters and targets increase to better put into the carburizing and quenching process of automobile parts.
The authors thank Wenping Luo and Xusheng Li of the Saitama Institute of Technology for their support in algorithm implementation and specific data acquisition.The authors thank the Saitama Institute of Technology for permission to publish this paper.The authors thank anonymous and editorial reviewers for their valuable revision comments.
Conceptualization, methodology, software, validation, formal analysis, investigation, data curation, writing  original draft and visualization: Jia H
Performed data acquisition, made substantial contributions to the conception and design of the study, and performed data analysis and interpretation: Ju D
Provided administrative, technical, and material support: Cao J
The data supporting this study's findings are available from the corresponding author, Ju D, upon reasonable request.
None.
All authors declared that there are no conflicts of interest.
Not applicable.
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© The Author(s) 2023.
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