Data-driven multi-component composite coating cold spraying process optimization method

Abstract

The invention provides a data-driven multi-component composite coating cold spraying process optimization method, which relates to the field of cold spraying and comprises the following steps: establishing a metal / ceramic composite coating cold spraying process-performance database; constructing a metal / ceramic composite coating performance optimization objective function based on the adaptive neural network; optimizing the cold spraying process of the metal / ceramic composite coating based on a local search enhanced NSGA-II genetic algorithm; and according to the optimal cold spraying process parameter combination of the metal / ceramic composite coating obtained through optimization, a cold spraying test is carried out, and the effectiveness of an optimization result is verified. According to the optimization method, by combining tests and big data analysis, the optimal parameter combination of the cold spraying process can be rapidly and accurately determined, and the quality and performance of the composite coating are effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of cold spraying, and particularly relates to a data-driven optimization method for cold spraying process of multi-component composite coatings. Background Art

[0002] Metal / ceramic composite coatings are composite coating materials formed by combining metal materials and ceramic materials, which break through the performance limitations of single coatings and have characteristics such as high hardness and wear resistance, high temperature resistance, corrosion resistance, excellent electrical and thermal conductivity, etc. They provide effective solutions for solving complex material surface protection and performance improvement problems in many fields such as aerospace, ocean engineering, and automotive manufacturing. Cold spraying, also known as cold gas dynamic spraying or cold gas kinetic spraying, is based on aerodynamics. It uses a high-pressure gas source to drive solid particles to impact the substrate at extremely high speeds, thereby depositing and forming a coating. As a new type of material surface coating technology, it has advantages such as small thermal impact on the substrate and portable construction, and shows great potential in the preparation of metal / ceramic composite coatings. However, the cold spraying process is complex and is affected by many factors such as the pressure and temperature of the spraying gas, the particle size of the powder particles, the distance and angle between the spray gun and the substrate, and the surface state of the substrate. As a result, problems such as poor interfacial bonding of each component material, high porosity of the coating, low bonding strength between the coating and the substrate, and uneven thickness are likely to occur, resulting in unqualified coating performance and the inability to fully exert the synergistic effect of the metal / ceramic composite coating.

[0003] Currently, the optimization of the cold spraying process for metal / ceramic composite coatings mainly relies on empirical or trial-and-error methods, that is, a large number of experiments are carried out by changing process parameters, and the process is adjusted according to the observed changes in the coating quality and performance to obtain a relatively satisfactory coating effect. This empirical or trial-and-error type of process optimization method not only consumes a large amount of labor and time, but also is difficult to comprehensively consider the mutual influence relationship between various process parameters, and thus it is impossible to obtain the true globally optimal process parameter combination, making it difficult for the performance of the composite coating by cold spraying to reach the best level. At the same time, the empirical or trial-and-error type of process optimization method also has high requirements for the experience level of operators and large human influencing factors, thus affecting the accuracy of process optimization. Summary of the Invention

[0004] Aiming at the above problems existing in the prior art, the purpose of the present invention is to provide a data-driven optimization method for cold spraying process of multi-component composite coatings. This optimization method can quickly and accurately determine the best parameter combination of the cold spraying process by combining experiments and big data analysis, thereby effectively improving the quality and performance of the composite coating and solving problems such as low efficiency, poor accuracy, and large human influencing factors in the traditional cold spraying process optimization method.

[0005] The purpose of the present invention is achieved through the following technical solutions: A method for optimizing the cold spraying process of a data-driven multi-component composite coating, comprising: Step S1, establish a cold spraying process-performance database for metal / ceramic composite coatings; Step S2, construct an optimization objective function for the performance of metal / ceramic composite coatings based on an adaptive neural network; Step S3, optimize the cold spraying process of metal / ceramic composite coatings based on a local search enhanced NSGA-II genetic algorithm; Step S4, according to the optimal process parameter combination of the cold spraying of metal / ceramic composite coatings obtained by optimization, conduct cold spraying tests to verify the effectiveness of the optimization results.

[0006] For further optimization based on the above scheme, the specific content of step S1 is: Step S11, determine the key process parameters affecting the coating quality and performance according to the coating performance indicators; Step S12, determine the initial value range of the key process parameters of cold spraying, and use Latin hypercube sampling to select multiple groups of combinations of key process parameters of cold spraying in the initial value range to ensure the uniformity and representativeness of the parameter space; Step S13, conduct experiments on the preparation of metal / ceramic composite coatings according to the selected combination of key process parameters by using cold spraying equipment; during the preparation process, record the set of test combination parameters in real time, that is, the set of key process parameters of the i th group of tests is Q i ; and after the experiment, test and record the performance of the prepared composite coating in real time to obtain the coating performance set, and the coating performance set corresponding to the i th group of tests is R i ; finally, organize the key process parameters adopted in each group of tests and the corresponding coating performance data, and enter them into the database to complete the construction of the cold spraying process-performance database.

[0007] For further optimization based on the above scheme, the key process parameters include cold spraying gas pressure, spraying temperature, spraying distance, metal / ceramic powder particle size, proportion of metal / ceramic powder, etc.

[0008] For further optimization based on the above scheme, the composite coating performance includes coating porosity, coating deposition rate, bonding strength between the coating and the substrate, coating hardness, etc.

[0009] For further optimization based on the above scheme, the specific content of step S2 is: Step S21, preprocess the cold spraying process-performance data to eliminate the influence of dimensions between different data, improve the data quality and usability, specifically:

[0010] In the formula: x * represents the i th data after preprocessing; x i represents the x th original data in the variable i ; Step S22: Use the hierarchical partitioning method to partition the preprocessed process-performance data into a training set, a validation set, and a test set; and determine the number of neurons in the input layer, hidden layer, and output layer, as well as the number of hidden layers and the activation function according to the process parameters and target performance parameters, and construct a neural network; Step S23: First, input the training set into the constructed neural network, calculate the output through forward propagation, and obtain the model output value; After that, use the mean squared error loss function MSE to calculate the difference between the model output value and the target value:

[0011] In the formula: N represents the number of samples, M represents the number of neurons in the output layer; for the i th sample, represents the j th true value of the output, that is, the model output value, represents the j th predicted value of the output, that is, the target value; Then, define an adaptive learning optimizer:

[0012] In the formula: w t represents the parameters of the t th iteration of the neural network; represents the learning rate; , respectively represent the decay coefficients; m t , v t respectively represent the first moment and the second moment of the estimated gradient of the t th iteration:

[0013] In the formula: g t represents the gradient of the parameters at the t th iteration; Update the weights and biases of the neural network according to the loss backpropagation; Finally, during the training process, the loss of the validation set is monitored in real time. When the loss of the validation set no longer decreases, the training is stopped to obtain a trained neural network model; Meanwhile, the mean squared error loss function is used MSE The threshold is used to determine whether the trained neural network model can predict the coating performance based on the process parameters. If not, the number of neurons in the hidden layer is adjusted and the model is retrained.

[0014] Based on the further optimization of the above solution, the mean squared error loss function MSE The threshold is 0.1. When the mean squared error loss function MSE is not less than the mean squared error loss function MSE threshold, it is considered that the trained neural network model can predict the coating performance based on the process parameters.

[0015] Based on the further optimization of the above solution, the specific steps of step S3 are as follows: Step S31: Taking the cold spraying process parameters of the metal / ceramic composite coating as the optimization variables, and taking minimizing the coating porosity, maximizing the coating deposition rate, and meeting the requirements of the coating bonding strength as the optimization objectives, a cold spraying process optimization model is established:

[0016] Constraints:

[0017] In the formula: F(X) represents the set of optimization objectives; represents minimizing the coating porosity, represents the porosity; represents maximizing the coating deposition rate, represents the deposition rate; S represents the bonding strength, S c represents the bonding strength threshold, and the bonding strength threshold is obtained according to the actual composite coating material, substrate material to be optimized, and test data; X represents the corresponding cold spraying process parameters, X max , X min respectively represent the upper and lower limits of the process parameters; Step S32: Using real number coding, each cold spraying process parameter is represented by a real number, and an initial population of a certain scale (set as N 0 ) is randomly generated G 0 , and the parameter values of each individual are randomly generated within their corresponding value ranges; Step S33: For each individual in the population, substitute the decoded process parameter values into the trained neural network model to replace the actual test process and obtain the objective function value of each individual; Step S34: First, G 0 sort all individuals in the initial population i and j calculate the crowding degree according to the non-dominated relationship. For any two individuals CI in the population,

[0018] where, N 0 represents the size of the population; x ik represents the i th k component of the feature vector of individual x jk represents the j th k component of the feature vector of individual select, crossover, and mutate the individuals on the non-dominated front or with a larger crowding degree; Then, return the newly generated process parameter combination to the neural network model to perform coating performance prediction, and comprehensively generate the offspring population g 0 and merge it with the parent population to generate a population N 0 with a capacity of 2 G 0 g 0 ; Step S35: Then, perform non-dominated sorting and crowding degree calculation on the population G 0 g 0 select N 0 individuals to form the new parent population G i according to the elitist strategy; perform selection, crossover, mutation operations and objective function evaluation on the new parent population G i and screen out the next-generation population G i+1 ; Step S36: Monitor the change of the objective function value of the individuals in the population. If the distance between the non-dominated solution set of the current population and the known optimal front is less than d , then start local search; set the neighborhood search range ± for the concerned cold spraying process parametersh %, starting from the selected initial individual, sequentially change the values of the decision variables within the given neighborhood search range; if the objective function value corresponding to the new individual is better than that of the current individual, accept the new individual as the current individual until no better solution can be found within this local area; Step S37, when the optimal solutions of several consecutive generations of the population do not change significantly or when the number of iterations reaches the preset value, stop the iteration and output the final population, that is, obtain the optimal process parameter combination within the value range of the process parameters.

[0019] The following are the effects of the technical means of the present invention: The present invention combines experimental design and big data analysis means, through data preprocessing, mean square error loss function and adaptive learning optimizer, establishes a mapping relationship between cold spraying process parameters and coating properties based on a neural network model, and realizes the prediction of coating properties through the input of process parameters, effectively solving the problems of many spraying process parameters, complex process and non-linear system of metal / ceramic composite coatings; at the same time, combined with the NSGA-II genetic algorithm to quickly search for the optimal process parameter combination, not only overcomes the limitations of traditional process optimization methods, but also effectively avoids the problem of insufficient local search ability of the traditional NSGA-II genetic algorithm, can accurately search for the optimal solution, improves the optimization efficiency and accuracy of the cold spraying process of metal / ceramic composite coatings, and thus prepares high-quality and high-performance composite coatings for the strict requirements of material surface properties in different fields. Brief Description of the Drawings

[0020] Figure 1 It is a flowchart of the data-driven multi-component composite coating cold spraying process optimization method in the embodiment of the present invention.

[0021] Figure 2 It is the morphology diagram of the Ni / Al 2 O 3 composite coating prepared by the traditional empirical optimization method.

[0022] Figure 3 It is the morphology diagram of the Ni / Al 2 O 3 composite coating prepared by the data-driven multi-component composite coating cold spraying process optimization method of the present invention. Detailed Embodiments

[0023] The technical solutions in the embodiments of the present invention will be clearly and completely described below. In the following description, specific details such as specific system structures and technologies are proposed for the purpose of illustration rather than limitation, so as to thoroughly understand the embodiments of the present invention.

[0024] In this embodiment, a method for optimizing the cold spraying process of a data-driven multi-component composite coating, the flowchart of which is as follows Figure 1 shown. Taking the optimization of the cold spraying process of a metal Ni and ceramic Al 2 O 3 composite coating as an example, it includes: Step S1. Establish a cold spraying process-performance database for metal / ceramic composite coatings: Step S11. According to the coating performance indexes, determine the key process parameters affecting the coating quality and performance; the key process parameters include cold spraying gas pressure, spraying temperature, spraying distance, metal / ceramic powder particle size, the proportion of metal / ceramic powder, etc.; specifically in this embodiment: the key process parameters include gas pressure P, spraying temperature T, the particle size D 1 of the metal powder Ni, the particle size D 2 of the ceramic powder Al 3 O 2 and the proportion φ of the ceramic powder Al 2 O 3 in the composite powder; Step S12. Determine the initial value range of the key process parameters of cold spraying (for example: in this embodiment, the range of spraying pressure is: 1 MPa ≤ P ≤ 3 MPa, the range of spraying temperature is: 200 °C ≤ T ≤ 500 °C, the particle size range of the metal powder Ni is: 5 μm ≤ D 1 ≤ 50 μm, the particle size range of the ceramic powder Al 2 O 3 is: 20 μm ≤ D 2 ≤ 100 μm, the proportion of the ceramic powder Al 2 O 3 in the composite powder is: 0 < φ ≤ 0.5), and use the Latin hypercube sampling to select multiple groups of combinations of cold spraying key process parameters in the initial value range (50 groups are selected in this embodiment) to ensure the uniformity and representativeness of the parameter space; Step S13. According to the selected combination of key process parameters, use the cold spraying equipment to conduct experiments on the preparation of metal / ceramic composite coatings; during the preparation process, record the set of experimental combination parameters in real time, that is, the set of key process parameters of the i th group of experiments is Q i ; and after the experiment, test and record the performance of the prepared composite coating in real time. The performance of the composite coating includes coating porosity, coating deposition rate, bonding strength between the coating and the substrate, coating hardness, etc., to obtain the coating performance set. The coating performance set corresponding to the i th group of experiments is R iFinally, organize the key process parameters and corresponding coating performance data used in each group of tests, and enter them into the database to complete the construction of the cold spraying process-performance database.

[0025] Step S2: Construct an optimization objective function for the performance of metal / ceramic composite coatings based on an adaptive neural network: Step S21: Preprocess the cold spraying process-performance data to eliminate the influence of dimensions between different data, improve data quality and usability, specifically:

[0026] In the formula: x * represents the i th data after preprocessing; x i represents the x th i original data in the variable; Step S22: Use the hierarchical partitioning method to divide the preprocessed process-performance data into a training set, a validation set, and a test set (where the ratio of the training set, the validation set, and the test set is 7:2:1); and determine the number of neurons in the input layer, hidden layer, and output layer according to the process parameters and target performance parameters (in this embodiment, the number of neurons in the input layer, hidden layer, and output layer are 5, 10, and 4 respectively) and the number of hidden layers (in this embodiment, the number of hidden layers is 1), activation function (using the sigmod activation function), and construct a neural network; Step S23: First, input the training set into the constructed neural network, calculate the output through forward propagation, and obtain the model output value; After that, use the mean square error loss function MSE to calculate the difference between the model output value and the target value:

[0027] In the formula: N represents the number of samples, M represents the number of neurons in the output layer; for the i th sample, represents the j th true value of the output, that is, the model output value, represents the j th predicted value of the output, that is, the target value; Then, define an adaptive learning optimizer:

[0028] In the formula: w t represents the parameters of the t th iteration of the neural network; represents the learning rate; , respectively represent the attenuation coefficient (in this embodiment, , ); m t , v t respectively represent the first moment and the second moment of the estimated gradient at the t -th iteration:

[0029] In the formula: g t represents the gradient of the parameter at the t -th iteration; Update the weights and biases of the neural network according to the loss backpropagation; Finally, during the training process, monitor the loss of the validation set in real time. When the loss of the validation set no longer decreases, stop the training to obtain the trained neural network model; At the same time, use the mean square error loss function MSE threshold, that is, 0.1 to judge whether the trained neural network model can predict the coating performance according to the process parameters. When the mean square error loss function MSE ≥0.1, it is considered that the trained neural network model can predict the coating performance according to the process parameters; otherwise, it cannot. Adjust the number of neurons in the hidden layer and retrain the model.

[0030] Step S3. Optimize the cold spraying process of the metal / ceramic composite coating based on the local search enhanced NSGA-II genetic algorithm: Step S31. Take the cold spraying process parameters of the metal / ceramic composite coating as the optimization variables, and take minimizing the coating porosity, maximizing the coating deposition rate, and meeting the requirements of the coating bonding strength as the optimization objectives to establish a cold spraying process optimization model:

[0031] Constraint conditions:

[0032] In the formula: F(X) represents the set of optimization objectives; represents minimizing the coating porosity, represents the porosity; represents maximizing the coating deposition rate, represents the deposition rate; S represents the bonding strength, S c represents the bonding strength threshold (in this embodiment, S c= 40 MPa), and the bonding strength threshold is obtained according to the actually optimized composite coating material, substrate material, and test data; X represents the corresponding cold spraying process parameters, X max 、 X min respectively represent the upper and lower limits of the process parameters; Step S32: Use real number coding, represent each cold spraying process parameter with a real number, and randomly generate an initial population of a certain scale (set as N 0 , for example: N 0 is 20), G 0 , and the parameter values of each individual are randomly generated within their corresponding value ranges; the i th individual X i can be represented as ; Step S33: For each individual in the population, substitute the decoded process parameter values into the trained neural network model to replace the actual test process and obtain the objective function value of each individual, that is, obtain the coating porosity, deposition rate, and coating bonding strength; Step S34: First, sort and calculate the crowding degree of all individuals in the initial population G 0 according to the non-dominance relationship. For any two individuals i and j in the population, their crowding degree CI is:

[0033] where, N 0 represents the size of the population; x ik represents the i th component of the feature vector of individual k , x jk represents the j th component of the feature vector of individual k ; Select, cross, and mutate the individuals on the non-dominated front or with a larger crowding degree (in this embodiment, the crossover probability is 0.6 and the mutation probability is 0.1); Then, return the newly generated process parameter combination to the neural network model to perform coating performance prediction, and comprehensively generate a subpopulation g 0 , and at the same time merge it with the parent population to generate a capacity of 2 N0 a population with a size of 40 (i.e., capacity of 40) G 0 g 0 ; Step S35: Then, perform non - dominated sorting and crowding degree calculation on the population G 0 g 0 and select 20 individuals according to the elitist strategy to form a new parental population N 0 ; Perform selection, crossover, mutation operations and objective function evaluation on the new parental population G i ; and screen out the next - generation population G i ; G i+1 ; Step S36: Monitor the change of the objective function values of the individuals in the population. If the distance between the non - dominated solution set of the current population and the known optimal front is less than d (in this embodiment, d = 0.01), then start local search; set the neighborhood search range of ± h % (in this embodiment, h = 5) for the cold - spray process parameters of concern. Starting from the selected initial individual, sequentially change the values of the decision variables within the given neighborhood search range; if the objective function value corresponding to the new individual is better than that of the current individual, accept the new individual as the current individual until no better solution can be found in this local area; Step S37: When the optimal solution of the population has not changed significantly for several consecutive generations (e.g., 10 generations) or when the number of iterations reaches the preset value (e.g., the iteration preset value is 100 times), stop the iteration and output the final population, that is, obtain the optimal process parameter combination within the value range of the process parameters. For example: determine the optimal process parameter combination that satisfies minimizing the coating porosity, maximizing the coating deposition rate, and the coating bonding strength not less than 40 MPa as follows: the cold - spray pressure P is 1.3 MPa, the cold - spray temperature T is 345 °C, the normal distribution particle size of Ni metal powder is 18 μm, the normal distribution particle size of Al 2 O 3 ceramic powder is 45 μm, and the proportion of Al 2 O 3 in the composite powder is 18.5%.

[0034] Step S4: According to the optimized optimal process parameter combination of the cold - spray of the metal / ceramic composite coating, conduct cold - spray experiments to verify the effectiveness of the optimization results; the final obtained coating structure and performance characterization are as Figure 3As shown, the prepared coating has a porosity of 1.3%, a deposition efficiency of 35.2%, and a coating bonding strength of 42.3 MPa. Compared with the Ni / Al 2 O 3 composite coating prepared by the traditional empirical optimization method, the coating prepared in this example has a lower porosity, a higher deposition efficiency, and a higher bonding strength (which can be combined with the Figure 2 and Figure 3 morphology diagrams shown).

Claims

1. A data-driven multi-component composite coating cold spray process optimization method, characterized in that: include: Step S1, establishing a metal / ceramic composite coating cold spraying process-performance database; Step S2, constructing a metal / ceramic composite coating performance optimization objective function based on an adaptive neural network; Step S3, optimizing the cold spraying process of metal / ceramic composite coating based on local search enhanced NSGA-II genetic algorithm; Step S4: According to the optimized optimal process parameter combination for cold spraying of the metal / ceramic composite coating, a cold spraying test is performed to verify the effectiveness of the optimization result.

2. The data-driven multi-component composite coating cold spray process optimization method according to claim 1, characterized in that: The step S1 is specifically as follows: Step S11, determining key process parameters affecting coating quality and performance according to coating performance indicators; Step S12, determining the initial value range of the key process parameters of cold spraying, and using super Latin cube sampling to select multiple groups of combinations of key process parameters of cold spraying in the initial value range to ensure the uniformity and representativeness of the parameter space; Step S13, conducting a test of preparing a metal / ceramic composite coating using a cold spraying device according to the selected key process parameter combination; During the preparation process, each set of test combination parameters, i.e. i The key process parameter set for the group test is G i After the test, the performance of the prepared composite coating is tested and recorded in real time to obtain a coating performance set. i The coating performance set corresponding to the group test is R i ; Finally, the key process parameters used in each group of experiments and the corresponding coating performance data are sorted out and entered into the database to complete the construction of the cold spray process-performance database.

3. A data-driven multi-component composite coating cold spray process optimization method according to claim 1 or 2, characterized in that: The key process parameters include cold spraying gas pressure, spraying temperature, spraying distance, metal / ceramic powder particle size, and metal / ceramic powder ratio.

4. A data-driven multi-component composite coating cold spray process optimization method according to claim 1 or 2, characterized in that: The composite coating properties include coating porosity, coating deposition rate, and bonding strength between the coating and the substrate.

5. The data-driven multi-component composite coating cold spray process optimization method according to claim 1, characterized in that: The step S2 is specifically as follows: Step S21, preprocessing the cold spraying process-performance data to eliminate the dimension effect between different data and improve data quality and availability, specifically: Where: x * After preprocessing, i individual data; x i Representation variables x The i The original data; Step S22, using a hierarchical partitioning method to divide the pre-processed process-performance data into a training set, a validation set, and a test set; and according to the process parameters and the target performance parameters, determining the number of neurons in the input layer, hidden layer, and output layer, as well as the number of hidden layers and the activation function, to construct a neural network; Step S23: First, input the training set into the constructed neural network, calculate the output through forward propagation, and obtain the model output value; Afterwards, the mean square error loss function is used MSE Calculate the difference between the model output and the target value: Where: N represents the number of samples, M Represents the number of neurons in the output layer; For i samples, Indicates j The true value of the output, that is, the model output value, Indicates j The predicted value of the output, that is, the target value; Then, define the adaptive learning optimizer: Where: w t Represents the neural network t The parameters of the iterations; represents the learning rate; , It does not represent the attenuation coefficient; m t , v t Respectively represent t Iterate the estimated first and second moments of the gradient: Where: g t Indicates t The gradient of the parameters at iteration ; Update the weights and biases of the neural network based on the loss backpropagation; Finally, the loss of the validation set is monitored in real time during the training process. When the loss of the validation set no longer decreases, the training is stopped to obtain a trained neural network model. At the same time, using the mean square error loss function MSE The threshold determines whether the trained neural network model can predict the coating performance based on the process parameters. If not, the number of hidden layer neurons is adjusted and the model is retrained.

6. The data-driven multi-component composite coating cold spray process optimization method according to claim 1, characterized in that: The step S3 is specifically as follows: Step S31, using the cold spraying process parameters of the metal / ceramic composite coating as optimization variables, minimizing the coating porosity, maximizing the coating deposition rate, and ensuring that the coating bonding strength meets the requirements as optimization goals, and establishing a cold spraying process optimization model: Constraints: Where: F(X) represents the optimization target set; represents the minimization of coating porosity, represents the porosity; represents the maximum coating deposition rate, represents the deposition rate; S Indicates the bonding strength, S c represents a bonding strength threshold value, which is obtained according to the actually optimized composite coating material, substrate material and test data; X represents the corresponding cold spraying process parameters, X max , X min Respectively represent the upper and lower limits of process parameters; Step S32: Use real number coding to represent each cold spraying process parameter with a real number, and randomly generate an initial population of a certain size. G 0, the parameter values ​​of each individual are randomly generated within the corresponding value range; Step S33: for each individual in the population, substitute the decoded process parameter value into the trained neural network model, replace the actual test process, and obtain the objective function value of each individual; Step S34: First, the initial population G All individuals in 0 are sorted and the crowding degree is calculated according to the non-dominated relationship. For any two individuals in the population i and j , the degree of crowding between them CI for: in, N 0 indicates the size of the population; x ik Represents an individual i The eigenvector of k Quantity, x jk Represents an individual j The eigenvector of k Quantity; Perform selection, crossover, and mutation operations on non-dominated frontiers or individuals with high crowding; Then, the newly generated process parameter combination is returned to the neural network model to perform coating performance prediction and comprehensively generate the progeny population g 0, and the capacity is 2 when combined with the parent population N 0 population G 0 g 0; Step S35: G 0 g 0 Perform non-dominated sorting, crowding calculation, and select according to the elite strategy N 0 individuals form the new parent population G i ; For the new parent population G i Perform selection, crossover, mutation operations and objective function evaluation to screen the next generation population G i+1 ; Step S36: monitor the change of individual objective function values ​​in the population. If the distance between the current population non-dominated solution set and the known optimal frontier is less than d When , local search is started; set the neighborhood search range ± h %, starting from the selected initial individual, the value of the decision variable is changed in turn within the given neighborhood search range; if the objective function value corresponding to the new individual is better than the current individual, the new individual is accepted as the current individual until no better solution is found in the local area; Step S37: When the optimal solution of several consecutive generations of populations does not change significantly or when the number of iterations reaches a preset value, the iteration is stopped and the final population is output, that is, the optimal process parameter combination is obtained within the range of process parameter values.

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