Selective laser melting process parameter optimization method based on artificial neural network

By establishing a prediction model between the melting process parameters of laser selection areas and the forming density based on artificial neural network, the problem of difficult process parameters optimization in laser additive manufacturing is solved, and high-efficiency and low-cost high-quality forming is achieved.

CN119623242APending Publication Date: 2025-03-14SHENYANG LIMING AERO-ENGINE GROUP CORPORATION

Patent Information

Application Number
CN202411581070.0
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-07
Publication Date
2025-03-14

AI Technical Summary

Technical Problem

In laser additive manufacturing, it is difficult to optimize the melting process parameters of the laser selection area, resulting in forming defects and density problems, affecting product performance and production efficiency.

Method used

Using an artificial neural network-based method, a complex nonlinear relationship between the melting process parameters of the laser selection area and the forming density is established to achieve rapid iterative optimization of the process parameters.

Benefits of technology

It effectively reduces the waste of manpower and resources in the process parameter optimization process, improves the R&D efficiency of additive manufacturing processes, reduces production costs, and achieves high-quality formation.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention discloses a selective laser melting process parameter optimization method based on an artificial neural network. The method comprises the following steps: performing selective laser melting forming on metal powder; the influence rule of the selective laser melting process parameters on the metal forming density is determined through experimental testing, and a machine learning data set between the selective laser melting process parameters and the forming density is obtained; performing normalization and standardization processing on the machine learning data set; establishing an artificial neural network model; a nonlinear regression model is obtained; the nonlinear regression model is used as a forming density prediction model; determining the effectiveness and accuracy of the prediction model; and technological parameters of selective laser melting are optimized. The method has the advantages that rapid iterative optimization of the selective laser melting process parameters is achieved by building the forming density machine learning prediction model, the research and development efficiency of the additive manufacturing process is improved, and the method is reasonable in design, high in operability, simple, easy to implement and suitable for engineering application and popularization.
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Description

Technical Field

[0001] The present invention relates to the technical field of laser additive manufacturing, and in particular to a method for optimizing process parameters of laser selective melting based on artificial neural network. Background Art

[0002] In the field of laser additive manufacturing, laser selective melting technology has shown unique advantages and has received widespread attention in the high-precision preparation of high-performance complex components due to its advantages such as small laser focus spot, thin powder bed thickness, and rapid melting process characteristics. In the laser selective melting manufacturing process, forming defects such as powder unfusion, pores and holes will inevitably appear, affecting the density of the formed specimen, and then affecting the comprehensive performance of the additive manufacturing formed specimen. The laser selective melting process is a complex nonlinear process coupled with multiple factors. Process parameters such as laser power, scanning speed, scanning spacing, powder layer thickness and scanning strategy will directly affect the density of the formed specimen. At present, engineering still relies heavily on traditional trial and error methods to optimize laser selective melting process parameters, resulting in a large waste of manpower and resources, hindering the rapid preparation and iterative upgrading of additive manufacturing products, and thus seriously restricting the progress and widespread application of laser additive manufacturing technology.

[0003] Artificial neural network machine learning algorithm models can achieve modeling and prediction of complex nonlinear systems through data training, and have good technical advantages in describing multi-factor nonlinear coupling relationships. They have been successfully applied to the accurate prediction of material structure properties. Therefore, using artificial neural network training to fit the complex nonlinear relationship between laser selective melting process parameters and forming density, and establishing a forming density prediction model, it is expected to achieve rapid iterative optimization of laser selective melting process parameters, thereby guiding the laser additive manufacturing of high-performance complex components. Summary of the invention

[0004] The purpose of the present invention is to achieve rapid iterative optimization of laser selective melting process parameters through this method, so as to guide the laser additive manufacturing of high-performance complex components. A laser selective melting process parameter optimization method based on artificial neural network is particularly provided.

[0005] The present invention provides a method for optimizing process parameters of laser selective melting based on an artificial neural network, comprising the following steps:

[0006] (1) Metal powder laser selective melting forming is performed in the following steps:

[0007] ① Keep the metal powder warm and dry in a vacuum drying oven;

[0008] ② Start the laser selective melting forming equipment, import the sliced ​​printed model into the computer operating system, and set the laser selective melting process parameters, including laser power, scanning speed, powder layer thickness, scanning spacing and inter-layer rotation angle;

[0009] ③Use a cleaning agent to ultrasonically clean the surface of the substrate, and use anhydrous ethanol to wipe and dry the surface of the substrate;

[0010] ④ Install the substrate in the forming chamber of the laser selective melting forming equipment, and load the metal powder into the powder chamber of the forming equipment;

[0011] ⑤Evacuate the molding chamber and introduce argon gas for purge, maintain the argon atmosphere in the molding chamber, and blow the argon gas parallel to the surface of the substrate;

[0012] ⑥ Preheat the substrate to reduce the temperature difference between the metal powder and the substrate;

[0013] ⑦ Use a scraper to spread the metal powder on the substrate to form a uniform powder layer;

[0014] ⑧ The forming equipment performs metal powder printing and forming according to the imported model and set program;

[0015] ⑨After printing is completed, maintain the argon atmosphere in the molding chamber, release the pressure after the temperature in the molding chamber cools down, open the chamber door, and take out the molded sample.

[0016] (2) Determine the influence of laser selective melting process parameters on metal forming density through experimental testing, and obtain a machine learning data set between laser selective melting process parameters and forming density;

[0017] (3) Normalize and standardize the machine learning dataset;

[0018] (4) An artificial neural network model is established. The model includes three layers: input layer, hidden layer and output layer. The input layer is used to receive input signals, and its variables are laser power, scanning speed, powder layer thickness, scanning spacing and inter-layer rotation angle; the output layer is used to output signals, and its variable is forming density; the number of neural nodes in the hidden layer is calculated according to the formula Determine, where m represents the number of neurons in the input layer, n represents the number of neurons in the output layer, and a represents a constant between [1, 10];

[0019] (5) Dividing the input and output machine learning data sets into a training set, a validation set, and a test set, using the training set to train the artificial neural network, the training algorithms include the Levenberg-Marquardt method, the Bayesian-regularization method, and the Scaled Conjugate Gradient method, and stopping the training when the output error meets the set requirements, and obtaining a nonlinear regression model;

[0020] (6) using the validation set and the test set to perform validation tests on the nonlinear regression model to obtain a validation test error. When the validation test error is within a preset error range, the obtained nonlinear regression model is used as a forming density prediction model.

[0021] (7) randomly setting a set of laser selective melting process parameters, performing the same normalization process as step (3) on the laser selective melting process parameters, and inputting the parameters into the forming density prediction model obtained in step (6) to obtain a forming density prediction value, printing a sample according to the randomly set laser selective melting process parameters, and measuring the density of the formed sample, and comparing the forming density prediction value with the actual measured value to determine the effectiveness and accuracy of the forming density prediction model;

[0022] (8) The laser selective melting process parameters are quickly iterated and optimized through the forming density prediction model, and the sample is printed according to the adjusted laser selective melting process parameters, thereby achieving high-quality forming by additive manufacturing.

[0023] Furthermore, the above-mentioned method for optimizing process parameters of laser selective melting based on artificial neural network is characterized in that, in step (1), the temperature of the vacuum drying oven is 80-150° C., and the drying time is 1-4 hours.

[0024] Furthermore, the above-mentioned method for optimizing process parameters of laser selective melting based on artificial neural network is characterized in that, in step (1), the laser power range is 250-300 W, the scanning speed range is 800-1200 mm / s, the powder layer thickness range is 0.04-0.06 mm, the scanning spacing range is 0.05-0.15 mm, and the interlayer rotation angle range is 0-90°.

[0025] Furthermore, the above-mentioned method for optimizing process parameters of laser selective melting based on artificial neural network is characterized in that, in step (1), the oxygen content of the molding chamber is ≤200ppm after vacuuming, and the argon flow rate ranges from 2 to 4m / s.

[0026] Furthermore, the above-mentioned method for optimizing process parameters of laser selective melting based on artificial neural network is characterized in that, in step (1), the preheating temperature range of the printed substrate is 50-100°C.

[0027] Furthermore, the above-mentioned method for optimizing process parameters of laser selective melting based on artificial neural network is characterized in that, in step (2), the experimental test method is metallographic method or drainage method.

[0028] Furthermore, the above-mentioned method for optimizing process parameters of laser selective melting based on artificial neural network is characterized in that, in step (3), the data normalization and standardization processing method includes Min-Max normalization, Z-Score normalization and nonlinear normalization method.

[0029] Furthermore, the above-mentioned method for optimizing process parameters of laser selective melting based on artificial neural network is characterized in that, in step (3), the data normalization and standardization processing method is preferably Min-Max normalization, and the formula is:

[0030]

[0031] Where X is the original data, X max and X min are the maximum and minimum values ​​in the data set, respectively, norm The data are normalized.

[0032] Furthermore, the above-mentioned method for optimizing process parameters of laser selective melting based on artificial neural network is characterized in that, in step (4), the type of artificial neural network is a Back-Propagation artificial neural network, the number of input layer neurons m is 5, the number of output layer neurons n is 1, the number of hidden layer neurons ranges from [4, 13], the preferred number of hidden layer neurons is 8, the input layer and the output layer are expressed by purelin functions, and the hidden layer is expressed by sigmoid functions.

[0033] Furthermore, the above-mentioned method for optimizing process parameters of laser selective melting based on artificial neural network is characterized in that, in step (5), the proportions of training set, validation set and test set in the machine learning data set are 60-70%, 15-20% and 15-20% respectively, the training algorithm is preferably the Levenberg-Marquardt method, the learning rate is 0.01, the number of iterations is 1000, and the training accuracy requirement is 0.001.

[0034] Furthermore, the above-mentioned method for optimizing process parameters of laser selective melting based on artificial neural network is characterized in that, in step (6), the preset error of the verification test is 0.001.

[0035] Furthermore, the above-mentioned method for optimizing process parameters of laser selective melting based on artificial neural network is characterized in that, in step (7), the randomly set laser selective melting process parameters are within the process parameter range described in step (1), and laser selective melting additive manufacturing is performed according to the set process, and the density of the formed sample is determined by metallographic method or drainage method. When the error between the predicted value of the forming density prediction model and the actual measured value is within ±1%, the validity and accuracy of the prediction model are determined.

[0036] In the process of laser selective melting, forming defects such as unfused powder, pores and holes will inevitably appear, which will reduce the density of the formed sample and affect the comprehensive performance of the formed sample. The laser selective melting process is a complex nonlinear process coupled with multiple factors, and various process parameters will directly affect the density of the formed sample. The use of traditional trial and error methods to optimize the laser selective melting process parameters will inevitably cause a large waste of manpower and financial resources, hindering the rapid preparation and iterative upgrading of complex components in additive manufacturing.

[0037] With the rapid development of computer hardware and machine learning algorithm models, modeling and prediction of complex nonlinear systems can be achieved using machine learning methods. Artificial neural network machine learning models are widely used in materials science research due to their simple algorithms and clear structures. They have been successfully applied to the accurate prediction of material composition, organization, and performance. Therefore, by using artificial neural network training to fit the complex nonlinear relationship between laser selective melting process parameters and forming density, a forming density prediction model is established, which is expected to achieve rapid iterative optimization of laser selective melting process parameters, thereby guiding the laser additive manufacturing of high-performance complex components. The method of the present invention can reduce the time and cost of exploring process parameters, reduce the cost of additive manufacturing of precision components, and has important theoretical research significance and application value.

[0038] Advantages and beneficial effects of the present invention:

[0039] (1) The present invention is based on artificial neural network training to fit the complex nonlinear relationship between laser selective melting process parameters and forming density. By establishing a forming density machine learning prediction model, the rapid iterative optimization of laser selective melting process parameters is achieved, avoiding the waste of manpower and resources caused by the traditional trial and error method, effectively improving the research and development efficiency of the additive manufacturing process, and thus greatly reducing the production cost.

[0040] (2) The method of the present invention is reasonably designed and highly operable, and can provide method guidance for optimizing the process parameters of additive manufacturing of other metal materials. At the same time, the method of the present invention is simple and easy to implement, and is suitable for engineering application and promotion. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1This is a structural diagram of the Back-Propagation artificial neural network model in an embodiment of the present invention;

[0042] Figure 2 It is a training set fitting regression graph in an embodiment of the present invention;

[0043] Figure 3 It is a validation set fitting regression graph in an embodiment of the present invention;

[0044] Figure 4 A regression graph for fitting the test set in an embodiment of the present invention;

[0045] Figure 5 Print the metallographic structure of the sample for a set of randomly set laser selective melting process parameters;

[0046] Figure 6 To print the metallographic structure of the sample using optimized laser selective melting process parameters. DETAILED DESCRIPTION

[0047] In the specific implementation process, the method of the present invention first determines the influence of laser selective melting process parameters such as laser power, scanning speed, powder layer thickness, scanning spacing and inter-layer rotation angle on the forming density through experimental tests, and obtains a machine learning data set between input and output; then, the multi-factor nonlinear coupling relationship between input and output is statistically analyzed through an artificial neural network machine learning algorithm, and a forming density prediction model based on an artificial neural network is established, and the artificial neural network structure and algorithm such as the number of neural network layers and the number of neurons are further optimized to improve the prediction accuracy of the forming density prediction model; finally, the laser selective melting process parameters are iteratively optimized using the optimized forming density prediction model, thereby achieving high-quality additive manufacturing.

[0048] In order to make the purpose, technical scheme and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. The scheme flow of a method for optimizing process parameters of laser selective melting based on artificial neural network is as follows:

[0049] (1) Laser selective melting of GH5188 high temperature alloy powder is performed in the following steps:

[0050] ① Dry the GH5188 high temperature alloy powder in a vacuum drying oven at 150°C for 1 hour;

[0051] ② Start the laser selective melting forming equipment, import the sliced ​​printed model into the computer operating system, and set the laser selective melting process parameters, including laser power, scanning speed, powder layer thickness, scanning spacing and interlayer rotation angle. The laser power range is 250-300W, the scanning speed range is 800-1200mm / s, the powder layer thickness range is 0.04-0.06mm, the scanning spacing range is 0.05-0.15mm, and the interlayer rotation angle range is 0-90°;

[0052] ③Use a cleaning agent to ultrasonically clean the surface of the substrate, and use anhydrous ethanol to wipe and dry the surface of the substrate;

[0053] ④Install the substrate in the forming chamber of the laser selective melting forming equipment, and load the GH5188 high-temperature alloy powder into the powder chamber of the forming equipment;

[0054] ⑤ The molding chamber is vacuumed, and the oxygen content is 180ppm after vacuuming, and argon gas is introduced for purge, and the argon atmosphere in the molding chamber is maintained, so that the argon gas is blown parallel to the surface of the substrate at a flow rate of 2m / s;

[0055] ⑥ Preheat the substrate at 80°C to reduce the temperature difference between the GH5188 high temperature alloy powder and the substrate;

[0056] ⑦ Use a scraper to spread the GH5188 high-temperature alloy powder on the substrate to form a uniform powder layer;

[0057] ⑧ The forming equipment prints and forms GH5188 high temperature alloy powder according to the imported model and set program;

[0058] ⑨After printing is completed, maintain the argon atmosphere in the molding chamber, release the pressure after the temperature in the molding chamber cools down, open the chamber door, and take out the GH5188 high-temperature alloy forming sample.

[0059] (2) The metallographic method was used to determine the influence of laser selective melting process parameters on the forming density of GH5188 high-temperature alloy, and a machine learning data set was obtained between laser selective melting process parameters and GH5188 forming density;

[0060] (3) Normalize and standardize the machine learning data set using Min-Max normalization, with the formula:

[0061]

[0062] Where X is the original data, X max and X min are the maximum and minimum values ​​in the data set, respectively, norm is the data after normalization;

[0063] (4) Establish an artificial neural network model, whose structure is as follows Figure 1 As shown in the figure, the model includes three layers of network: input layer, hidden layer and output layer. The input layer is used to receive input signals, the number of neurons is 5, and its variables are laser power, scanning speed, powder layer thickness, scanning spacing and inter-layer rotation angle; the output layer is used to output signals, the number of neurons is 1, and its variable is forming density; the number of neural nodes in the hidden layer is 8. The input and output layers are expressed by purelin function, and the hidden layer is expressed by sigmoid function;

[0064] (5) The input and output machine learning data sets are divided into training set, validation set and test set, with the ratios of 70%, 15% and 15% respectively. The training set is used to train the artificial neural network. The training algorithm adopts the Levenberg-Marquardt method, the learning rate is set to 0.01, the number of iterations is set to 1000, and the training accuracy requirement is set to 0.001. The training is stopped when the output error meets the set requirements. The training set fitting regression graph is shown in the figure below. Figure 2 As shown, a nonlinear regression model is obtained;

[0065] (6) The validation set and test set were used to verify the nonlinear regression model. It was found that the validation test error was less than 0.001. The validation set fitting regression graph and the test set fitting regression graph were as follows: Figure 3 , 4 As shown, the obtained nonlinear regression model is used as a forming density prediction model;

[0066] (7) A set of laser selective melting process parameters is randomly set. After the laser selective melting process parameters are normalized in the same way as in step (3), they are input into the forming density prediction model obtained in step (6). The forming density prediction value is 99.12%. The GH5188 high temperature alloy sample is printed according to the randomly set laser selective melting process parameters. The metallographic structure of the formed sample is as follows: Figure 5 As shown, the density of the formed sample was measured by metallographic method and Image-pro software to be 99.87%, and the difference between the predicted value and the actual measured value of the formed density was found to be 0.75%, thus confirming the validity and accuracy of the formed density prediction model;

[0067] (8) The forming density prediction model is used to quickly iterate and optimize the laser selective melting process parameters of GH5188 high-temperature alloy. The GH5188 high-temperature alloy specimen is printed according to the optimized laser selective melting process parameters. The metallographic structure of the formed specimen is as follows: Figure 6 As shown in the figure, the density of the formed sample was statistically analyzed by metallographic method and Image-pro software, and it was found that the density of the formed sample after optimizing the process parameters was 99.96%, thus achieving high-quality forming of GH5188 high-temperature alloy by additive manufacturing.

[0068] Based on the above results, it can be seen that the present invention can achieve rapid iterative optimization of additive process parameters by establishing an artificial neural network model to train and fit the complex nonlinear relationship between laser selective melting process parameters and forming density, verifying the feasibility of the technical solution of the present invention, thereby providing methodological guidance for laser additive manufacturing of high-performance complex components.

[0069] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features therein may be replaced by equivalents. However, these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing process parameters of laser selective melting based on artificial neural network, characterized in that: The method for optimizing process parameters of laser selective melting based on artificial neural network comprises the following steps: (1) Metal powder laser selective melting forming is performed in the following steps: ① Keep the metal powder warm and dry in a vacuum drying oven; ② Start the laser selective melting forming equipment, import the sliced ​​printed model into the computer operating system, and set the laser selective melting process parameters, including laser power, scanning speed, powder layer thickness, scanning spacing and inter-layer rotation angle; ③Use a cleaning agent to ultrasonically clean the surface of the substrate, and use anhydrous ethanol to wipe and dry the surface of the substrate; ④ Install the substrate in the forming chamber of the laser selective melting forming equipment, and load the metal powder into the powder chamber of the forming equipment; ⑤Evacuate the molding chamber and introduce argon gas for purge, maintain the argon atmosphere in the molding chamber, and blow the argon gas parallel to the surface of the substrate; ⑥ Preheat the substrate to reduce the temperature difference between the metal powder and the substrate; ⑦ Use a scraper to spread the metal powder on the substrate to form a uniform powder layer; ⑧ The forming equipment performs metal powder printing and forming according to the imported model and set program; ⑨After printing is completed, maintain the argon atmosphere in the molding chamber, release the pressure after the temperature in the molding chamber cools down, open the chamber door, and take out the molded sample. (2) Determine the influence of laser selective melting process parameters on metal forming density through experimental testing, and obtain a machine learning data set between laser selective melting process parameters and forming density; (3) Normalize and standardize the machine learning dataset; (4) An artificial neural network model is established. The model includes three layers: input layer, hidden layer and output layer. The input layer is used to receive input signals, and its variables are laser power, scanning speed, powder layer thickness, scanning spacing and inter-layer rotation angle; the output layer is used to output signals, and its variable is forming density; the number of neural nodes in the hidden layer is calculated according to the formula Determine, where m represents the number of neurons in the input layer, n represents the number of neurons in the output layer, and a represents a constant between [1, 10]; (5) Dividing the input and output machine learning data sets into a training set, a validation set, and a test set, using the training set to train the artificial neural network, the training algorithms include the Levenberg-Marquardt method, the Bayesian-regularization method, and the Scaled Conjugate Gradient method, and stopping the training when the output error meets the set requirements, and obtaining a nonlinear regression model; (6) using the validation set and the test set to perform validation tests on the nonlinear regression model to obtain a validation test error. When the validation test error is within a preset error range, the obtained nonlinear regression model is used as a forming density prediction model. (7) randomly setting a set of laser selective melting process parameters, performing the same normalization process as step (3) on the laser selective melting process parameters, and inputting the parameters into the forming density prediction model obtained in step (6) to obtain a forming density prediction value, printing a sample according to the randomly set laser selective melting process parameters, and measuring the density of the formed sample, and comparing the forming density prediction value with the actual measured value to determine the effectiveness and accuracy of the forming density prediction model; (8) The laser selective melting process parameters are quickly iterated and optimized through the forming density prediction model, and the sample is printed according to the adjusted laser selective melting process parameters, thereby achieving high-quality forming by additive manufacturing.

2. The method for optimizing process parameters of laser selective melting based on artificial neural network according to claim 1, characterized in that: In the step (1), the temperature of the vacuum drying oven is 80-150°C, and the drying time is 1-4h; the laser power range is 250-300W, the scanning speed range is 800-1200mm / s, the powder layer thickness range is 0.04-0.06mm, the scanning spacing range is 0.05-0.15mm, and the interlayer rotation angle range is 0-90°; the oxygen content of the molding chamber after vacuuming is ≤200ppm, and the argon flow rate range is 2-4m / s.

3. The method for optimizing process parameters of laser selective melting based on artificial neural network according to claim 1, characterized in that: In the step (1), the preheating temperature of the printed substrate is in the range of 50-100°C.

4. The method for optimizing process parameters of laser selective melting based on artificial neural network according to claim 1, characterized in that: In the step (2), the experimental test method is metallographic method or drainage method.

5. The method for optimizing process parameters of laser selective melting based on artificial neural network according to claim 1, characterized in that: In the step (3), the data normalization and standardization processing methods include Min-Max normalization, Z-Score normalization and nonlinear normalization methods.

6. The method for optimizing process parameters of laser selective melting based on artificial neural network according to claim 1, characterized in that: In the step (3), the data normalization and standardization processing method is preferably Min-Max normalization, and the formula is: Where X is the original data, X max and X min are the maximum and minimum values ​​in the data set, respectively, norm The data are normalized.

7. The method for optimizing process parameters of laser selective melting based on artificial neural network according to claim 1, characterized in that: In the step (4), the artificial neural network type is a Back-Propagation artificial neural network, the number of input layer neurons m is 5, the number of output layer neurons n is 1, the number of hidden layer neurons ranges from [4, 13], the preferred number of hidden layer neurons is 8, the input layer and the output layer are expressed using purelin functions, and the hidden layer is expressed using sigmoid functions.

8. The method for optimizing process parameters of laser selective melting based on artificial neural network according to claim 1, characterized in that: In the step (5), the proportions of the training set, validation set and test set in the machine learning data set are 60-70%, 15-20% and 15-20% respectively, the training algorithm is preferably the Levenberg-Marquardt method, the learning rate is 0.01, the number of iterations is 1000, and the training accuracy requirement is 0.

001.

9. The method for optimizing process parameters of laser selective melting based on artificial neural network according to claim 1, characterized in that: In the step (6), the verification test preset error is 0.

001.

10. The method for optimizing process parameters of laser selective melting based on artificial neural network according to claim 1, characterized in that: In the step (7), the randomly set laser selective melting process parameters are within the process parameter range described in step (1), and laser selective melting additive manufacturing is performed according to the set process. The density of the formed sample is determined by metallographic method or drainage method. When the error between the predicted value of the forming density prediction model and the actual measured value is within ±1%, the validity and accuracy of the prediction model are determined.

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