A method for optimizing spray quenching process parameters

Abstract

The present invention discloses a method for optimizing spray quenching process parameters, comprising the following steps: Step 1: Establishing a three-dimensional spray quenching finite element model; Step 2: Embedding an improved quenching factor method into the finite element model; Step 3: Processing the simulation results; Step 4: Establishing a multi-objective optimization model; Step 5: Establishing a single-objective optimization model; Step 6: Solving the multi-objective and single-objective optimization models using a non-dominated genetic algorithm and a dung beetle algorithm, respectively. This method for optimizing spray quenching process parameters is an efficient research method based on existing experimental data, providing methodological and theoretical support for the selection of quenching process parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of quenching heat treatment process selection, and in particular to a method for optimizing spray quenching process parameters. Background Art

[0002] During the quenching process of heat-treatable and hardened aluminum alloys, when a sufficiently fast cooling rate is ensured, the uniform low-strength supersaturated solid solution formed can precipitate strengthening phases during the subsequent aging process, achieving a significant improvement in properties such as yield strength. However, the rapid cooling process is accompanied by a high temperature gradient field, which causes uneven plastic deformation of the aluminum alloy thick plate and produces residual stress, and this situation becomes more obvious as the thickness increases. Although relevant companies are now able to maturely use pre-stretching methods to effectively reduce the level of residual stress, it is impossible to completely eliminate it. Aviation integral structural parts have low stiffness due to their large size and material removal rate of over 90%. The residual stress level retained in the aluminum thick plate still easily causes the parts to deform. Therefore, reducing the workpiece deformation problem caused by the residual stress formed during the quenching of the aluminum thick plate and improving the hardenability are still one of the difficult problems in the aviation manufacturing industry. Summary of the Invention

[0003] In order to solve the above technical problems, the present invention proposes a method for optimizing spray quenching process parameters.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] The present invention provides a method for optimizing spray quenching process parameters, comprising the following steps:

[0006] Step 1: Establish a three-dimensional spray quenching finite element model;

[0007] Step 2: embed the improved quenching factor method into the finite element model;

[0008] Step 3: Process the simulation results;

[0009] Step 4: Establish a multi-objective optimization model;

[0010] Step 5: Establish a single-objective optimization model;

[0011] Step 6: Use non-dominated genetic algorithm and dung beetle algorithm to solve the multi-objective and single-objective optimization models respectively.

[0012] Furthermore, in step 1, a three-dimensional spray quenching finite element model is established, including the following steps:

[0013] S01: Build a model of target size;

[0014] S02: Assign material properties to the dimension;

[0015] S03: Set the analysis step to thermal-mechanical coupling and set the quenching time;

[0016] S04: Apply symmetry constraints to the symmetric boundary surfaces;

[0017] S05: Set the initial temperature field conditions;

[0018] S06: Set the heat transfer coefficient boundary condition of the spray end surface;

[0019] S07: Setting the heat transfer coefficient boundary condition of the air-cooled end surface;

[0020] S08: Divide the grid and set the grid type.

[0021] Furthermore, in step 2, the improved quenching factor method is embedded in the finite element model, and the USDFLD module is used to write the QFA into the finite element model, which includes the following steps:

[0022] S01: Get the maximum value σ of the aluminum alloy performance max ;

[0023] S02: Obtaining coefficients of the C curve equation and minimum performance equation coefficients of the aluminum alloy;

[0024] S03: Assuming the current moment is t and the time increment is dt, calculate the equivalent time C of [t, t+Δt] t ;

[0025] S04: Calculate the minimum performance value of [t, t+Δt];

[0026] S05: Calculate the performance loss of [t, t+dt];

[0027] S06: Let t=t+dt, and determine whether time t is the end time of quenching. If not, jump to S03, and end if it is.

[0028] Furthermore, in step three, a BP neural network prediction model of process parameters and target parameters is established, including the following steps:

[0029] S01: performing step 1 and step 2 using different process parameters;

[0030] S02: Extract the data set at the studied point from the simulation result files of different process parameters;

[0031] S03: Give the number of hidden layers as 1, 2 or 3 according to the number of neurons in the input and output layers;

[0032] S04: Establish a BP neural network prediction model with process parameters as input and research variables as output;

[0033] S05: Set the learning rate, back propagation algorithm, the percentage of the training set, validation set and test set in the total data set, and finally obtain the BP neural network prediction model.

[0034] Furthermore, in step six, the multi-objective model is solved by the NSGA-II algorithm, including the following steps:

[0035] S01: Initialize the population as the parent group, gen=1;

[0036] S02: non-dominated sorting and congestion calculation;

[0037] S03: selection, crossover, mutation;

[0038] S04: Generate the gen generation subgroup;

[0039] S05: The parent group and child group of the gen generation are merged;

[0040] S06: Perform fast non-dominated sorting and congestion calculation on the merged group;

[0041] S07: Select suitable individuals from the merged group as the gen+1 generation parent group;

[0042] S08: gen = gen + 1;

[0043] S09: Determine whether gen exceeds the maximum population iteration number. If so, exit to obtain the Pareto solution; if not, return to S03 for selection, crossover, and mutation.

[0044] Furthermore, the single-objective optimization model is solved by the dung beetle algorithm, which includes the following steps:

[0045] S01: Initialize the population size n, use the location information as an individual, and use the objective function to judge the quality of the location information. The current iteration number is k = 1.

[0046] S02: The number of rolling ball dung beetles is n1;

[0047] S03: Determine whether an obstacle is encountered. If so, adjust the direction by dancing; if not, update the position according to the sun, environmental influences and the current position direction;

[0048] S04: Select the best spawning location and the best foraging location at the moment;

[0049] S05: Lay the brooding ball in the spawning area and update the position of the brooding ball;

[0050] S06: The dung beetle n3 is foraging in the foraging area, and the position of the dung beetle is updated;

[0051] S07: Stealing dung beetle n4 competes for food and updates the thief's position;

[0052] S08: k=k+1;

[0053] S09: Determine whether k exceeds the maximum number of iterations. If so, exit to obtain the optimal solution; if not, return to S02 of this step.

[0054] In summary, the beneficial effects of the present invention are:

[0055] The present invention provides an optimization method for spray quenching process parameters. Once the parameters within the model are known, spray quenching process parameters can be selected in a standardized manner without the need for additional experiments. The process is based on a finite element model and can obtain temperature and stress fields. An improved quenching factor method is then used as a supplement to the finite element method for predicting properties after quenching and aging. A neural network of process parameters and target parameters is established through numerous simulation experiments. An objective function is given based on engineering requirements, and a multi-objective or single-objective optimization model is established. Based on the established neural network, an NSGA-II or dung beetle algorithm is used to solve the Pareto or optimal solution for the optimization model.

[0056] The present invention is directed to a method for optimizing spray quenching process parameters, with process parameters as independent variables, residual stress and mechanical properties as dependent variables, and a multi-objective or single-objective optimization model is established based on the objective function constructed based on the dependent variables. A certain mapping relationship between the process parameter independent variables, residual stress and mechanical properties is constructed, and the BP neural network can very effectively construct the mapping of this nonlinear relationship. When constructing the neural network, a large amount of data is required, so time-consuming experiments can be replaced by simulation experiments. The simulation experiment obtains residual stress results through three-dimensional thermomechanical coupling model analysis, and the quenching factor method is embedded in the finite element to obtain mechanical property results. The present invention provides an efficient research method based on existing experimental data, which provides methodological and theoretical support for the selection of quenching process parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a schematic diagram of the model in the present invention;

[0058] Figure 2 It is the heat transfer coefficient curve of air cooling in the present invention;

[0059] Figure 3A The water flux density in the present invention is 48 (L·m -2 ·s -1 ), the heat transfer coefficient curves when the pressures are 10, 50, 100, 200, and 300 (kPa);

[0060] Figure 3B The water flux density in the present invention is 70 (L·m -2 ·s-1 ), the heat transfer coefficient curves when the pressures are 10, 50, 100, 200, and 300 (kPa);

[0061] Figure 3C The water flux density in the present invention is 90 (L·m -2 ·s -1 ), the heat transfer coefficient curves when the pressures are 10, 50, 100, 200, and 300 (kPa);

[0062] Figure 3D The water flux density in the present invention is 108 (L·m -2 ·s -1 ), the heat transfer coefficient curves when the pressures are 10, 50, 100, 200, and 300 (kPa);

[0063] Figure 3E 1 is a heat transfer coefficient curve diagram of the present invention when the water flux density is 130 and the pressures are 10, 50, 100, 200, and 300 (kPa) respectively;

[0064] Figure 4A The water flux densities in the present invention are 48, 70, 90, 108, 130 (L·m -2 ·s -1 ), S11 curves when the pressures are 10, 50, 100, 200, and 300 (kPa);

[0065] Figure 4B The water flux densities in the present invention are 48, 70, 90, 108, 130 (L·m -2 ·s -1 ), the S33 curves at pressures of 10, 50, 100, 200, and 300 (kPa);

[0066] Figure 4C The water flux densities in the present invention are 48, 70, 90, 108, 130 (L·m -2 ·s -1 ) when the pressure is 10, 50, 100, 200, and 300 (kPa);

[0067] Figure 5 It is the regression diagram of the training, verification, testing and overall performance of the neural network in the present invention;

[0068] Figure 6A It is the process parameter coordinate point diagram after NSGA-II multi-objective optimization in the present invention;

[0069] Figure 6BIt is the coordinate point diagram of the objective function value after NSGA-II multi-objective optimization in the present invention. DETAILED DESCRIPTION

[0070] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention are clearly and completely described below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0071] The present invention provides a method for optimizing spray quenching process parameters, comprising the following steps:

[0072] Step 1: Establish a three-dimensional spray quenching finite element model;

[0073] Step 2: embed the improved quenching factor method into the finite element model;

[0074] Step 3: Process the simulation results, i.e., establish a BP neural network prediction model for process parameters and target parameters;

[0075] Step 4: Establish a multi-objective optimization model;

[0076] Step 5: Establish a single-objective optimization model;

[0077] Step 6: Use the non-dominated genetic algorithm (NSGA-II) and the dung beetle algorithm (DBO) to solve the multi-objective and single-objective optimization models respectively.

[0078] In one embodiment, in step 1, a three-dimensional spray quenching finite element model is established, taking a 1 / 4 aluminum alloy model with a size of l×d×h and single-side spraying as an example, including the following steps:

[0079] S01: Create a model with a size of 0.5l×d×0.5h;

[0080] S02: Assign material properties to the dimension;

[0081] S03: Set the analysis step to thermal-mechanical coupling and set the quenching time;

[0082] S04: Apply symmetry constraints to the symmetric boundary surfaces;

[0083] S05: Set the initial temperature field conditions;

[0084] S06: Set the heat transfer coefficient boundary condition of the spray end surface;

[0085] S07: Setting the heat transfer coefficient boundary condition of the air-cooled end surface;

[0086] S08: Divide the grid and set the grid type to C3D8RT.

[0087] In one embodiment, in step 2, the improved quenching factor method is embedded in the finite element model, and the QFA is written into the finite element model using the USDFLD module, which includes the following steps:

[0088] S01: Query the data to obtain the maximum value σ of the aluminum alloy performance max ;

[0089] S02: Query the data to obtain the coefficients of the C curve equation and the minimum performance equation coefficients k2, k3, k4, k5, k6, k7, k8, k9, k 10 ;

[0090] S03: Assuming the current moment is t and the time increment is dt, calculate the equivalent time C of [t, t+Δt] t :

[0091]

[0092] Where k1 is the natural logarithm of the transformation fraction, R is the molar gas constant, which is 8.314 J / (mol·K), and T is the temperature corresponding to the current moment. k2 is a constant related to the inverse number of nucleation sites (locations), k3 is a constant related to the energy required to form a nucleus, k4 is a constant related to the dissolution temperature, and k5 is a constant related to the diffusion activation energy.

[0093] S04: Calculate the minimum performance value of [t, t+Δt]:

[0094]

[0095] Where, T int is the temperature at the beginning of quenching;

[0096] S05: Unlike the additivity of isokinetic behavior assumed in the classical model, the non-isokinetic model is based on the assumption that the alloy loses its ability to develop properties incrementally at each individual time interval. Therefore, the amount of property loss at [t, t+dt] is:

[0097]

[0098] Where Δt j is the time increment, Δσ j is the loss of performance enhancement, At temperature T j The minimum yield strength of

[0099]

[0100] Get the performance prediction value at time t+Δt:

[0101]

[0102] S06: Determine whether time t is the end time of quenching, if not, jump to S03; if yes, end.

[0103] In one embodiment, in step three, establishing a BP neural network prediction model for process parameters and target parameters includes the following steps:

[0104] S01: performing steps 1 and 2 as described above using different process parameters;

[0105] S02: Extract the data set at the studied point from the simulation result files of different process parameters;

[0106] S03: Give the number of hidden layers as 1, 2 or 3 according to the number of neurons in the input and output layers;

[0107] S04: Establish a BP neural network prediction model with process parameters as input and the studied variables as output, where the number of neurons in the hidden layer is:

[0108]

[0109] Where n i and n o are the number of neurons in the input layer and the number of neurons in the output layer respectively;

[0110] S05: Set the learning rate, back propagation algorithm, the percentage of the training set, validation set, and test set in the total data set, and finally get the BP neural network prediction model:

[0111] f=sim(net,x) (7)

[0112] Where net is the result of a successfully trained neural network, x=[x1,x2,…,] T ,f=[f1,f2,…,] T .

[0113] In one embodiment, in step 4, establishing a multi-objective optimization model includes the following steps:

[0114] S01: Considering actual needs, establish a multi-objective optimization model:

[0115]

[0116] In one embodiment, in step five, establishing a single-objective optimization model includes the following steps:

[0117] S01: Considering actual needs, establish a single-objective optimization model:

[0118]

[0119] In one embodiment, in step six, a non-dominated genetic algorithm (NSGA-II) is used to solve the multi-objective and single-objective optimization models. Solving the multi-objective model equation (8) by the NSGA-II algorithm includes the following steps:

[0120] S01: Initialize the population as the parent group, gen=1;

[0121] S02: non-dominated sorting and congestion calculation;

[0122] S03: selection, crossover, mutation;

[0123] S04: Generate the gen generation subgroup;

[0124] S05: The parent group and child group of the gen generation are merged;

[0125] S06: Perform fast non-dominated sorting and congestion calculation on the merged group;

[0126] S07: Select suitable individuals from the merged group as the gen+1 generation parent group;

[0127] S08: gen = gen + 1;

[0128] S09: Determine whether gen exceeds the maximum population iteration number. If so, exit to obtain the Pareto solution; if not, go to S03.

[0129] In one embodiment, in step seven, the Dung Beetle Algorithm (DBO) solves the multi-objective and single-objective optimization models. Solving the single-objective model equation (9) by the DBO algorithm includes the following steps:

[0130] S01: Initialize the population size n, use the location information as an individual, and use the objective function to judge the quality of the location information. The current iteration number is k = 1.

[0131] S02: The number of rolling ball dung beetles is n1;

[0132] S03: Determine whether an obstacle is encountered. If so, adjust the direction according to formula (10); if not, update the position according to the sun, environmental influence and current position direction according to formula (11);

[0133] f i j (k+1)=f i j (k)+tan(θ)|fi j (k)-f i j (k-1)| (10)

[0134]

[0135] In the formula, k represents the current iteration number, f i j (k) represents the position information of the jth dung beetle i at the kth iteration. The position information represents the independent variable information. k0∈[0,0.2] represents the deflection coefficient. b represents a constant in the range of [0,1]. α represents the coefficient considering natural factors, which is 1 or -1. F i w represents the global worst position, Δf represents the light intensity change;

[0136] S04: Select the best spawning location at the moment, according to formula (11), and the best foraging location, according to formula (12);

[0137]

[0138] Where, F i * represents the current local optimal position (selected from the positions of the brooding ball, small dung beetle, and thief dung beetle at the end of the k-1th iteration and the position of the rolling ball dung beetle at the kth iteration). Lb i * and Ub i * Respectively represent the upper and lower limits of the spawning area;

[0139]

[0140] Where, F i b Indicates the global optimal position, which represents the global optimal value at the end of k-1 iteration steps, Lb i b and Ub i b Represent the upper and lower limits of the optimal foraging area respectively.

[0141] S05: Lay the brooding ball in the spawning area and update the position of the brooding ball;

[0142]

[0143] Where B i j (k) represents the position information of the j-th brooding ball i at the k-th iteration, b1 and b2 represent random numbers between 0 and 1;

[0144] S06: The dung beetle n3 is foraging in the foraging area, and the position of the dung beetle is updated;

[0145]

[0146] Where C i j (k) represents the position information of the jth dung beetle i at the kth iteration, c1 and c2 are random numbers obeying the normal distribution and random numbers between 0 and 1, respectively;

[0147] S07: Stealing dung beetle n4 competes for food and updates the thief's position;

[0148]

[0149] Where D i j (k) represents the position information of the j-th stealing dung beetle i at the k-th iteration, S is a constant, and g represents a random number between 0 and 1.

[0150] S08: k=k+1;

[0151] S09: Determine whether k exceeds the maximum number of iterations. If so, exit to obtain the optimal solution; if not, go to S02.

[0152] Specifically, the present invention provides a method for optimizing spray quenching process parameters. The method is verified through specific examples and finally provides a Pareto solution and optimization parameters under multiple objectives. The method includes the following steps:

[0153] Step 1: First, establish a finite element model. Here, take Abaqus as an example and create a three-dimensional model with a size of 1440mm×240mm×60mm. Figure 1 As shown in the figure, given the symmetry between the model size and boundary conditions, a 1 / 4 model was used for modeling, and symmetry constraints were applied to the symmetry surfaces. Symmetry surface constraints were applied to surfaces ABDC and EACG respectively. This simulation is a one-way spray quenching simulation. To meet the requirements of the actual quenching experimental process, air cooling heat transfer coefficient boundary conditions were applied to surfaces EFHG and FBDH, as shown in the figure. Figure 2 , ABFE is the spray end face, and the applied heat transfer coefficient is shown in Figure 3 (including Figure 3A 、 Figure 3B 、 Figure 3C 、 Figure 3D 、 Figure 3E), the surface CDHG is an adiabatic boundary surface. The initial temperature is set to 470℃, and the spray medium temperature and ambient temperature are 25℃. The analysis step adopts temperature-displacement coupling, and the time is 180s. The initial step size, minimum step size, and maximum step size are set to 0.1, 0.00001, and 10, respectively. Since the model is relatively simple, the grid is divided by edge, and the grid size of length, width, and height are 6mm, 6mm, and 5mm respectively. The grid unit type is set to C3D8RT, and the number of grids is 28800. Figure 1 shown.

[0154] Step 2: The residual stress after quenching is obtained through simulation of the above model. For the performance after quenching and aging, secondary development of ABAQUS is required. The improved quenching factor method is embedded in ABAQUS using the USDFLD module to realize the prediction calculation of the performance after aging by combining the finite element method with the improved quenching factor method. The parameters in the model are shown in Table 1.

[0155] Table 1 Model parameters

[0156] k2 k3 k4 k5 k6 k7 k8 k9 k10 <![CDATA[σ max ]]> 2.91e-11 3547 881 115420 42.5 35.9 2410 5.18e14 21900 458

[0157] Step 3: The process parameters are pressure (kPa) p = [10, 50, 100, 200, 300] T , water flux density (L·m -2 ·s -1 )q=[48,70,90,108,130] T .by Figure 1 All nodes on the midline segment AC are the research objects, and the S11, S33 and FV1 values ​​of 25 groups of simulation results are derived as shown in Figure 4. Figure 4A 、 Figure 4B 、 Figure 4C ) data was used to establish a BP neural network model with water flux density, pressure, and position as input and S11, S33, and FV as output. The built-in neural network parameters of Matlab were used, with the number of hidden layers set to 2, the number of neurons in each hidden layer to 10, the neural network structure to "3-10-10-3", the learning rate and backpropagation algorithm to 0.01 and Levenberg-Marquardt respectively. The training set, validation set, and test set accounted for 0.7, 0.15, and 0.15 of the total data set respectively. The training regression diagram of the neural network is shown in Figure 5 .

[0158] Step 4: Establish a multi-objective optimization model. Position parameters are not optimized here, so we have:

[0159]

[0160] Taking into account the different objective functions given in actual engineering, generally, the lowest hardenability is required in the design stage. Therefore, the target must first be greater than a minimum threshold ξ, defined as:

[0161] ξ=κσ max (2)

[0162] Where κ is the specified minimum coefficient, which ranges from 0 to 1, and here ξ=0.965σ max Therefore, the objective function in the multi-objective optimization model becomes:

[0163]

[0164] Where, σ min is the minimum σ value on the line segment AC of a certain simulation result, where N represents the number of nodes on the line segment AC.

[0165] Step 5: Establish a single-objective optimization model:

[0166]

[0167] Among them, the objective function is defined as:

[0168]

[0169]

[0170] Step 6: Set the NSGA-II algorithm parameters as follows: Pareto solution accounts for 0.5 of the population, population size is 100, genetic generation is 100, and NSGA-II solves the multi-objective model (1). Figure 6A , the corresponding objective function is Figure 6B .

[0171] Step 7: Set the population size to 30, the four sizes are 6, 6, 7, and 11 respectively, set the maximum number of iterations to 100, and use DBO to solve the single-objective optimization model (4). The optimal solution is: [q, p] T =[130, 204] T .

[0172] The present invention provides an optimization method for spray quenching process parameters. Once the parameters within the model are known, spray quenching process parameters can be selected in a standardized manner without the need for additional experiments. The process is based on a finite element model and can obtain temperature and stress fields. An improved quenching factor method is then used as a supplement to the finite element method for predicting properties after quenching and aging. A neural network of process parameters and target parameters is established through numerous simulation experiments. An objective function is given based on engineering requirements, and a multi-objective or single-objective optimization model is established. Based on the established neural network, an NSGA-II or dung beetle algorithm is used to solve the Pareto or optimal solution for the optimization model.

[0173] The present invention is directed to a method for optimizing spray quenching process parameters, with process parameters as independent variables, residual stress and mechanical properties as dependent variables, and a multi-objective or single-objective optimization model is established based on the objective function constructed based on the dependent variables. A certain mapping relationship between the process parameter independent variables, residual stress and mechanical properties is constructed, and the BP neural network can very effectively construct the mapping of this nonlinear relationship. When constructing the neural network, a large amount of data is required, so time-consuming experiments can be replaced by simulation experiments. The simulation experiment obtains residual stress results through three-dimensional thermomechanical coupling model analysis, and the quenching factor method is embedded in the finite element to obtain mechanical property results. The present invention provides an efficient research method based on existing experimental data, which provides methodological and theoretical support for the selection of quenching process parameters.

[0174] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the essence and scope of the technical solutions of the present invention.

Claims

1. A method for optimizing spray quenching process parameters, characterized in that: The following steps are involved: Step 1: Establish a three-dimensional spray quenching finite element model, including the following steps: S01: Build a model of target size; S02: Assign material properties to the dimension; S03: Set the analysis step to thermal-mechanical coupling and set the quenching time; S04: Apply symmetry constraints to the symmetric boundary surfaces; S05: Set the initial temperature field conditions; S06: Set the heat transfer coefficient boundary condition of the spray end surface; S07: Set the boundary condition of heat transfer coefficient of air-cooled end face; S08: Divide the grid and set the grid type; Step 2: Embed the improved quenching factor method into the finite element model. Use the USDFLD module to write the QFA into the finite element model, including the following steps: S01: Get the maximum value of aluminum alloy performance σ max ; S02: Obtaining coefficients of the C curve equation and minimum performance equation coefficients of the aluminum alloy; S03: Assume that the current moment is t , the time increment is d t， calculate[ t , t +Δ t ] equivalent time C t ; S04: Calculate the minimum performance value of [t, t+Δt]; S05: Calculation t , t +d t ]Amount of performance loss; S06: Command t=t +d t， Judgment time t Is it the quenching end time? If not, jump to S03. If yes, end. Step 3: Process the simulation results, including the following steps: S01: performing step 1 and step 2 using different process parameters; S02: Extract the data set at the studied point from the simulation result files of different process parameters; S03: Give the number of hidden layers as 1, 2 or 3 according to the number of neurons in the input and output layers; S04: Establish a BP neural network prediction model with process parameters as input and research variables as output; S05: Set the learning rate, back propagation algorithm, the percentage of the training set, validation set, and test set in the total data set, and finally obtain the BP neural network prediction model; Step 4: Establish a multi-objective optimization model; Step 5: Establish a single-objective optimization model; Step 6: Use non-dominated genetic algorithm and dung beetle algorithm to solve the multi-objective and single-objective optimization models respectively; Solving the multi-objective model using the NSGA-II algorithm includes the following steps: S01: Initialize the population as the parent group, gen=1; S02: non-dominated sorting and congestion calculation; S03: selection, crossover, mutation; S04: Generate the gen generation subgroup; S05: The parent group and child group of the gen generation are merged; S06: Perform fast non-dominated sorting and congestion calculation on the merged group; S07: Select suitable individuals from the merged group as the gen+1 generation parent group; S08: gen=gen+1; S09: Determine whether gen exceeds the maximum population iteration number. If so, exit to obtain the Pareto solution; if not, return to S03 of this step; Solving the single-objective optimization model using the dung beetle algorithm includes the following steps: S01: Initialize the population size n, use the location information as an individual, and use the objective function to judge the quality of the location information. The current iteration number is k=1. S02: The number of rolling ball dung beetles is n1; S03: Determine whether an obstacle is encountered. If so, adjust the direction by dancing; if not, update the position according to the sun, environmental influences and the current position direction; S04: Select the best spawning location and the best foraging location at the moment; S05: Lay the brooding ball in the spawning area and update the position of the brooding ball; S06: The dung beetle n3 is foraging in the foraging area, and the position of the dung beetle is updated; S07: Stealing dung beetle n4 competes for food and updates the thief's position; S08: k=k+1; S09: Determine whether k exceeds the maximum number of iterations. If so, exit to obtain the optimal solution; if not, return to S02 of this step.

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