A die heating rod arrangement optimization method

Abstract

The present application relates to a kind of die heating rod arrangement optimization methods, comprising the following steps:1), based on die heating temperature parameterization simulation model, generate the original data of die parameter and its heating rod parameter;2), original data is preprocessed, and the training data set of simulation model input parameter and output result is made;3), Gaussian process regression model training is carried out, and the mapping relationship of input parameter and output result is established;4), using genetic algorithm to establish multi-objective optimization model, generate offspring population;5), select Pareto front solution in new generation population as simulation model input parameter and carry out simulation, compared with Gaussian process regression model, retrain Gaussian process regression model with high error sample;6), repeat step 4-5, so that model reaches convergence condition, and the arrangement rule of heating rod is obtained.The present application can realize the uniform distribution of melt temperature in die, effectively reduce the total energy consumption of heating rod, and greatly shorten heating time.

Description

Technical Field

[0001] This invention relates to a method for arranging heating rods in a mold head, specifically to an optimization method for arranging heating rods in a mold head, and belongs to the field of digital design technology. Background Technology

[0002] In industries such as plastics processing and textile fiber manufacturing, the state of the melt inside the die head has a significant impact on product quality; therefore, the arrangement of heating rods is crucial.

[0003] Traditional die heating rod arrangement relies on manual experience. In plastic extrusion molding, manually determined heating rod parameters lack quantitative analysis, making it difficult to consider the complex die structure, melt characteristics, and thermal interactions. In spunbond nonwoven fabric production, this can lead to uneven fiber thickness, decreased strength and uniformity, and increased defect rates.

[0004] Existing optimization techniques also have many shortcomings. Most only target a single objective, such as increasing the number of heating rods to improve temperature uniformity, which significantly increases energy consumption. Moreover, the inside of the mold head is a complex multiphysics coupled system, and existing algorithms struggle to handle the complex coupling relationships between parameters. Traditional rule-based optimization methods, for example, cannot adapt to new mold head structures or process requirements and find it difficult to quickly find the optimal arrangement scheme.

[0005] Therefore, in order to solve the above problems, it is indeed necessary to provide an innovative method for optimizing the arrangement of the mold head heating rods to overcome the defects in the prior art. Summary of the Invention

[0006] The purpose of this invention is to provide a method for optimizing the arrangement of heating rods in a mold head, which solves the problems of uneven temperature distribution, high energy consumption of heating rods, and long heating time caused by the reliance on manual experience in the traditional design of heating rod arrangement.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: a method for optimizing the arrangement of heating rods in a mold head, comprising the following process steps:

[0008] 1) Based on the parameterized simulation model of the mold head heating temperature, generate the original data of the mold head parameters and its heating rod parameters;

[0009] 2) Preprocess the raw data obtained in step 1) to create a training dataset for the input parameters and output results of the simulation model;

[0010] 3) Train the Gaussian process regression model to establish the mapping relationship between input parameters and output results;

[0011] 4) A multi-objective optimization model is established using a genetic algorithm to generate a progeny population;

[0012] 5) Select the Pareto front solution in the new generation population as the input parameter of the simulation model and perform simulation. Compare the results with the Gaussian process regression model, add the high error samples to the training dataset and retrain the Gaussian process regression model.

[0013] 6) Repeat steps 4) to 5) until the multi-objective optimization model reaches the convergence condition, and finally obtain the arrangement pattern of the heating rods.

[0014] The method for optimizing the arrangement of heating rods in the mold head according to the present invention further comprises: in step 1), the mold head parameters include geometric parameters and fluid parameters, wherein the geometric parameters include the mold head half-width B, slit gap H, non-Newtonian exponent n, manifold height y, and manifold tilt angle. The parameters include: relaxation zone height L, feed pipe height h, and feed pipe radius r; fluid parameters include melt inlet velocity v and inlet volumetric flow rate. Inlet pressure p, inlet temperature T, fluid consistency K;

[0015] Heating rod parameters include heating rod position (x, y) and heating rod power. Number of heating rods (m).

[0016] The method for optimizing the arrangement of heating rods in the die head according to the present invention further comprises: in step 1), the optimization objective of the simulation model includes the standard deviation of melt temperature. Total power of heating rod Heating time t for the heating rod;

[0017] Objective function of the simulation model:

[0018] In the formula: Indicates the standard deviation of the melt temperature inside the die head; Indicates the total power of the heating rod; Indicates the heating time of the heating rod; , as well as These represent the weight coefficients of the objective function;

[0019] Standard deviation of melt temperature inside the die head The formula is:

[0020] In the formula: This is the total number of temperature points inside the die head; It is the first Temperature value at the point; It is the average temperature of all temperature points inside the die head;

[0021] The constraints include the heating rod position (xy) and the heating rod length. Heating rod spacing d, heating rod power The number of heating rods, m.

[0022] The method for optimizing the arrangement of heating rods in the mold head according to the present invention further comprises: in step 2), the input parameter is the mold head parameter: ;

[0023] The output includes the heating rod parameters and optimization objectives: .

[0024] The method for optimizing the arrangement of heating rods in the mold head according to the present invention further comprises: in step 3), a surrogate model is constructed using a Gaussian process regression model.

[0025] In the formula: It is the mean function; It is a kernel function;

[0026]

[0027] In the formula: It is a length scale; It is the signal variance;

[0028] ;

[0029] .

[0030] The method for optimizing the arrangement of heating rods in the mold head of the present invention is further described as follows: Step 4) specifically involves selecting several individuals with good fitness on a Gaussian process regression model to form an initial individual population; wherein, the initial population is set to 200 individuals;

[0031] The fitness function is as follows:

[0032] In the formula: Indicates the standard deviation of the melt temperature inside the die head; Indicates the total power of the heating rod; Indicates the heating time of the heating rod; , as well as These represent the weight coefficients of the objective function;

[0033] Selection operation: Select individuals with pre-arranged heating rods as parents based on fitness values ​​for genetic operations;

[0034] The genetic operations include crossover: performing crossover on the selected parent individuals to generate new individuals; and mutation: performing mutation on the newly generated individuals to introduce diversity and generate offspring populations.

[0035] The method for optimizing the arrangement of heating rods in the mold head of the present invention is further described as follows: Step 4) specifically involves: merging the parent and offspring populations to form a new generation population; performing a full simulation of the Pareto front solution of the new generation population; comparing the fitness values ​​of the simulation results with the fitness values ​​of the prediction results; adding high-error samples to the training set to form a new dataset; retraining the Gaussian process regression model using the new dataset; and optimizing the kernel function hyperparameters of the Gaussian process regression model by maximizing the marginal likelihood to form a new Gaussian process regression model.

[0036] The method for optimizing the arrangement of heating rods in the mold head of the present invention further comprises: using non-dominated sorting to stratify the Pareto front solutions obtained by the genetic algorithm according to their superiority or inferiority, prioritizing the selection of heating rod arrangement parameters with lower fitness values ​​to ensure the selection of better solutions; when the fitness values ​​are the same, the sparsity of the distribution of heating rod positions is measured, and individuals with sparse distribution are retained first to maintain diversity, thereby obtaining Pareto front solutions.

[0037] The method for optimizing the arrangement of heating rods in the mold head according to the present invention further comprises: a new Gaussian process regression model is used to ensure prediction accuracy through 10-fold cross-validation, the steps of which are as follows:

[0038] Data partitioning: The training dataset is randomly divided into 10 subsets to ensure that the data distribution of each subset is consistent with the overall dataset; Iterative training and validation: Ten independent training iterations are performed, each time using 90% of the dataset as the training set and the remaining 10% as the validation set; During each training iteration, the model is retrained using the training set data, and performance metrics are calculated on the validation set; The performance metrics include... And MSE, This indicates the degree of agreement between the model's predicted values ​​and the actual values; It measures the average squared error between the predicted and actual values; it records the results of each validation set. The average of the 10 results and the MSE results are used as the overall performance evaluation of the model.

[0039] in,

[0040]

[0041] In the formula: It is the first The actual value of each sample; It is the first Predicted values ​​for each sample; It is the average of the actual values; It refers to the number of samples.

[0042] The method for optimizing the arrangement of heating rods in the mold head according to the present invention can also be as follows: Step 6) specifically involves: selecting individuals with low fitness from the retrained GPR model to form a new population; performing genetic algorithm operations on the new population again, repeatedly selecting, crossing over, and mutating to generate a new population; performing full simulation on the new population; comparing the simulation results with the prediction results of the Gaussian process regression model; adding high-error samples back into the training set; retraining the Gaussian process regression model; and iterating repeatedly until convergence; finally, selecting the optimal heating rod arrangement result obtained by the genetic algorithm; wherein, the convergence condition is: This indicates that when the difference in optimal fitness values ​​between two consecutive generations of a population is less than 1, the population's fitness is 1.5%. When the algorithm has converged, the convergence threshold ε is set to 0.01.

[0043] Compared with the prior art, the present invention has the following beneficial effects: The die head heating rod arrangement optimization method of the present invention matches the optimal heating rod arrangement for different die head parameters and effectively improves the uniformity of melt temperature in the die head, reduces the total energy consumption of heating rods and shortens the heating time, providing an efficient and precise solution for the optimization of die head heating systems in industries such as plastic processing and textile fiber manufacturing, and has significant industrial application value. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the internal flow channel of a clothes hanger-type mold head.

[0045] Figure 2 This is a cross-sectional view of the internal flow channel of the hanger-type mold head.

[0046] Figure 3 This is a diagram showing the arrangement of the heating rods in a clothes hanger-shaped mold head.

[0047] Figure 4 This is an overall flowchart of the method for optimizing the arrangement of heating rods in the mold head according to the present invention.

[0048] Figure 5 This is a flowchart of step 4) of the genetic algorithm in this invention.

[0049] Figure 6 This is a simulation result diagram of the optimized arrangement method of the mold head heating rods of the present invention. Detailed Implementation

[0050] Please refer to the instruction manual appendix. Figure 4 As shown, the present invention is a method for optimizing the arrangement of heating rods in a mold head, which includes the following process steps:

[0051] 1) Based on the parameterized simulation model of the mold head heating temperature, generate the original data of the mold head parameters and its heating rod parameters.

[0052] As per the instruction manual Figure 1 and 2As shown in the figure, a coat hanger-type die head is revealed. It can be seen from the figure that the die head parameters mainly include geometric parameters and fluid parameters. Among them, the geometric parameters include the die head half-width B, slit gap H, non-Newtonian exponent n, manifold height y, and manifold tilt angle. The parameters include: relaxation zone height L, feed pipe height h, and feed pipe radius r; fluid parameters include melt inlet velocity v and inlet volumetric flow rate. Inlet pressure p, inlet temperature T, fluid consistency K.

[0053] As per the instruction manual Figure 3 As shown in the figure, the arrangement of the heating rods in the hanger-type mold head is revealed. It can be seen from the figure that the heating rod parameters include the heating rod position (xy) and the heating rod power. Number of heating rods (m).

[0054] The parameterized simulation model for the die head heating temperature was established using ANSYS Fluent simulation software to create a three-dimensional geometric model of the die head. Actual simulations were performed based on the actual values ​​of geometric parameters, fluid parameters, and heating rod parameters. The simulation results, i.e., the optimization objectives, include the standard deviation of the melt temperature. Total power of heating rod , heating time t of the heating rod.

[0055] The objective function used in the simulation model is:

[0056] In the formula: Indicates the standard deviation of the melt temperature inside the die head; Indicates the total power of the heating rod; Indicates the heating time of the heating rod; , as well as This represents the weighting coefficients of the objective function. The weighting coefficients are objectively assigned to the three optimization objectives using the entropy weighting method, quantifying the importance of each objective. Subsequently, fine-tuning is performed based on the specific needs of the industrial scenario (e.g., whether temperature uniformity or energy consumption is more important), ultimately determining a fixed set of weighting coefficients.

[0057] Furthermore, the standard deviation of the melt temperature inside the die head The formula is:

[0058] In the formula: This is the total number of temperature points inside the die head; It is the first Temperature value at the point; It is the average temperature of all points inside the mold head.

[0059] The constraints include the heating rod position (xy) and the heating rod length. Heating rod spacing d, heating rod power The number of heating rods is m. Each heating rod is assumed to have a fixed length. Because placing two heating rods too close together can cause localized temperature increases, the distance d between adjacent heating rods must be greater than the specified minimum distance. The number of heating rods is also within a certain range and is determined based on actual industrial conditions.

[0060] Due to the complex internal shape of the mold head, how to reasonably distribute the heating rod parameters and mold head parameters is a key issue. To address this, the present invention employs Latin hypercube sampling (LHS) to randomly combine the heating rod parameters and mold head parameters to form a complete unit.

[0061] The main steps of Latin hypercube sampling (LHS) are as follows:

[0062] Define the range of heating rod parameters and mold head parameters.

[0063] The parameters of the heating rod and the mold head are divided into equal-width intervals.

[0064] Randomly select a value within each interval of each parameter to ensure that the value of each parameter appears only once in its corresponding interval.

[0065] By randomly combining sampled values ​​of different parameters, a complete individual is formed.

[0066]

[0067] Individuals that do not meet the constraints are excluded, and additional sampling is performed until the preset population size is reached.

[0068] Finally, a full simulation was performed on the obtained model, and the resulting raw data are the data of the mold head parameters, heating rod parameters, and optimization targets obtained after multiple simulations.

[0069] 2) Preprocess the raw data obtained in step 1) to create a training dataset for the input parameters and output results of the simulation model.

[0070] The preprocessing involves imputing missing values, cleaning data, and normalizing the original data. Imputing missing values ​​uses the mean imputation method to remove missing values ​​from the simulation data. Cleaning removes or corrects outlier simulation data points to ensure data accuracy. Normalization normalizes the data so that its value range is between [0, 1], eliminating the influence of different data units.

[0071] The input parameters are the mold head parameters: The output includes the heating rod parameters and optimization objectives. .

[0072] 3) Train the Gaussian process regression model (GPR) to establish the mapping relationship between input parameters and output results.

[0073] The Gaussian process regression (GPR) model accelerates iterative convergence and reduces the number of simulations. The surrogate model it constructs is as follows:

[0074] In the formula: It is the mean function; It is a kernel function;

[0075]

[0076] In the formula: It is a length scale; It is the signal variance;

[0077] ;

[0078] .

[0079] This step uses the preprocessed training dataset from step 2) to train a Gaussian process regression model (GPR). During training, a radial basis function (RBF) kernel is preferentially used as the kernel function. RBF is suitable for simulating smoothly changing processes. To obtain the optimal model, maximum likelihood estimation is employed, aiming to maximize the marginal likelihood of the model and automatically searching for the optimal combination of hyperparameters. , To balance the goodness of fit and model complexity, overfitting is avoided, and a mapping relationship is established between the mold head parameters, heating rod parameters, and optimization objectives. The optimization objectives are the criteria for judging the quality of the heating rod arrangement, namely, the smaller the standard deviation of the melt temperature inside the mold head, the smaller the total power of the heating rods, and the shorter the heating time of the heating rods, the better the heating rod arrangement.

[0080] 4) Please refer to the instruction manual appendix. Figure 5 As shown, a multi-objective optimization model is established using a genetic algorithm to generate a progeny population. The genetic algorithm automatically searches for the optimal heating rod arrangement under different die parameters to improve the uniformity of melt temperature within the die, reduce the total energy consumption of the heating rods, and shorten the heating time of the heating rods.

[0081] Specifically, this step involves selecting several individuals with good fitness from the Gaussian process regression (GPR) model to form an initial population; in this embodiment, the initial population is set to 200 individuals.

[0082] The fitness function of the model is as follows: It calculates the fitness value of each individual, and the smaller the fitness value, the better the arrangement of the heating rods.

[0083] In the formula: Indicates the standard deviation of the melt temperature inside the die head; Indicates the total power of the heating rod; Indicates the heating time of the heating rod; , as well as These represent the weighting coefficients of the objective function.

[0084] Next, a selection operation is performed: individuals with the heating rods arranged according to their fitness values ​​are selected as parents for genetic operations. The genetic operations include a crossover operation: crossover of the selected parent individuals with different parameters is performed to generate new individuals; and a mutation operation: mutation of the newly generated individuals with different parameters is performed to introduce diversity and generate a progeny population.

[0085] 5) Select the Pareto front solution from the new generation population as the input parameter of the simulation model and perform simulation. Compare the results with the Gaussian process regression model, add the high error samples to the training dataset and retrain the Gaussian process regression model.

[0086] Specifically, this step involves: merging the parent and offspring populations to form a new generation population; performing a full simulation of the Pareto front solution of the new generation population; comparing the fitness values ​​of the simulation results with the fitness values ​​of the predicted results; adding high-error samples to the training set to form a new dataset; retraining the Gaussian process regression model using the new dataset; and optimizing the kernel function hyperparameters of the Gaussian process regression model by maximizing the marginal likelihood to form a new Gaussian process regression model.

[0087] Among them, the Pareto front solution is a set of solutions with good fitness, selected according to the principles of non-dominated sorting and crowding calculation. The input parameters are the model parameters with good fitness.

[0088] In this embodiment, the Pareto front solution is obtained in the following way: the Pareto front solutions obtained by the genetic algorithm are stratified according to their superiority and inferiority using non-dominated sorting, and the heating rod arrangement parameters with smaller fitness values ​​are selected first to ensure the selection of better solutions; when the fitness values ​​are the same, the sparsity of the heating rod position distribution is measured, and individuals with sparse distribution are retained first to maintain diversity, thereby obtaining the Pareto front solution.

[0089] Furthermore, the high-error samples refer to samples whose fitness values ​​from simulation results differ significantly from those predicted by the Gaussian process regression model (GPR).

[0090] The new Gaussian process regression model ensures prediction accuracy through 10-fold cross-validation. The specific validation steps are as follows: Data partitioning: The training dataset is randomly divided into 10 subsets, ensuring that the data distribution of each subset is consistent with the overall dataset; Iterative training and validation: Ten independent training iterations are performed, each time selecting 9 folds as the training set and the remaining 1 fold as the validation set; During each training iteration, the model is retrained using the training set data, and performance metrics are calculated on the validation set; among these performance metrics are... And MSE, This indicates the degree of agreement between the model's predicted values ​​and the actual values; It measures the average squared error between the predicted and actual values; it records the results of each validation set. The average of the 10 results and the MSE results are used as the overall performance evaluation of the model.

[0091] in,

[0092]

[0093] In the formula: It is the first The actual value of each sample; It is the first Predicted values ​​for each sample; It is the average of the actual values; It refers to the number of samples.

[0094] 6) Repeat steps 4) to 5) until the multi-objective optimization model reaches the convergence condition, and finally obtain the arrangement pattern of the heating rods.

[0095] Specifically, in the retrained GPR model, individuals with low fitness are selected to form a new population. This new population is then subjected to a genetic algorithm, with repeated selection, crossover, and mutation to generate another new population. A full simulation is performed on this new population, and the simulation results are compared with the predictions of the Gaussian Process Regression (GPR) model. High-error samples are re-added to the training set, and the GPR model is retrained. This process is iterated until convergence. Finally, the optimal heating rod arrangement obtained by the genetic algorithm is selected. The convergence condition is: This indicates that when the difference in optimal fitness values ​​between two consecutive generations of a population is less than 1, the population's fitness is 1.5%. When the algorithm has converged, the convergence threshold ε is set to 0.01.

[0096] Figure 6 This is a simulation model result diagram of one of the layouts, with a width B=530mm, slit gap H=3, non-Newtonian exponent n=0.79, manifold height y=190mm, and manifold tilt angle. =5°, relaxation zone height L=60mm, feed pipe height h=20mm, feed pipe radius r=10mm; fluid parameters include melt inlet velocity v=0.25m / s, inlet mass flow rate =900kg / h, inlet temperature T=230℃, fluid consistency K=1370Pa·sn, the temperature standard deviation is 2.8℃, while the actual industrial temperature is about 0~10℃, which greatly improves the temperature uniformity, indicating that the method is real and effective.

[0097] The above-described specific embodiments are merely preferred embodiments of this invention and are not intended to limit this invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the protection scope of this invention.

Claims

1. A method for optimizing the arrangement of heating rods in a mold head, characterized in that: The process includes the following steps: 1) Based on the parameterized simulation model of the mold head heating temperature, generate the original data of the mold head parameters and its heating rod parameters; The die parameters include geometric parameters and fluid parameters. The geometric parameters include the die half-width B, slit gap H, non-Newtonian exponent n, manifold height y, and manifold tilt angle. The parameters include: relaxation zone height L, feed pipe height h, and feed pipe radius r; fluid parameters include melt inlet velocity v and inlet volumetric flow rate. Inlet pressure p, inlet temperature T, fluid consistency K; Heating rod parameters include heating rod position (x, y) and heating rod power. Number of heating rods (m); The optimization objectives of the simulation model include the standard deviation of melt temperature. Total power of heating rod Heating time t for the heating rod; Objective function of the simulation model: In the formula: Indicates the standard deviation of the melt temperature inside the die head; Indicates the total power of the heating rod; Indicates the heating time of the heating rod; , as well as These represent the weight coefficients of the objective function; Standard deviation of melt temperature inside the die head The formula is: In the formula: This is the total number of temperature points inside the die head; It is the first Temperature value at the point; It is the average temperature of all temperature points inside the die head; The constraints include the heating rod position (xy) and the heating rod length. Heating rod spacing d, heating rod power The number of heating rods, m; 2) Preprocess the raw data obtained in step 1) to create a training dataset for the input parameters and output results of the simulation model; 3) Train the Gaussian process regression model to establish the mapping relationship between input parameters and output results; 4) A multi-objective optimization model is established using a genetic algorithm to generate a progeny population; 5) Select the Pareto front solution in the new generation population as the input parameter of the simulation model and perform simulation. Compare the results with the Gaussian process regression model, add the high error samples to the training dataset and retrain the Gaussian process regression model. 6) Repeat steps 4) to 5) until the multi-objective optimization model reaches the convergence condition, and finally obtain the arrangement pattern of the heating rods.

2. The method for optimizing the arrangement of heating rods in the mold head as described in claim 1, characterized in that: In step 2), the input parameter is the mold head parameter: ; The output includes the heating rod parameters and optimization objectives: .

3. The method for optimizing the arrangement of heating rods in the mold head as described in claim 1, characterized in that: In step 3), the Gaussian process regression model constructs a surrogate model: In the formula: It is the mean function; It is a kernel function; In the formula: It is a length scale; It is the signal variance; ; 。 4. The method for optimizing the arrangement of heating rods in the mold head as described in claim 1, characterized in that: Step 4) specifically involves: selecting several individuals with good fitness from the Gaussian process regression model to form an initial population; wherein, the initial population is set to 200 individuals; The fitness function is as follows: In the formula: Indicates the standard deviation of the melt temperature inside the die head; Indicates the total power of the heating rod; Indicates the heating time of the heating rod; , as well as These represent the weight coefficients of the objective function; Selection operation: Select individuals with the heating rods arranged according to their fitness values ​​as parents for genetic operations; The genetic operations include crossover: performing crossover on the selected parent individuals to generate new individuals; and mutation: performing mutation on the newly generated individuals to introduce diversity and generate offspring populations.

5. The method for optimizing the arrangement of heating rods in the mold head as described in claim 1, characterized in that: Step 5) specifically involves: merging the parent and offspring populations to form a new generation population; performing a full simulation of the Pareto front solution of the new generation population; comparing the fitness values ​​of the simulation results with the fitness values ​​of the predicted results; adding high-error samples to the training set to form a new dataset; retraining the Gaussian process regression model using the new dataset; and optimizing the kernel function hyperparameters of the Gaussian process regression model by maximizing the marginal likelihood to form a new Gaussian process regression model.

6. The method for optimizing the arrangement of heating rods in the mold head as described in claim 5, characterized in that: The Pareto front solutions obtained by the genetic algorithm are stratified according to their quality using non-dominated sorting. The heating rod arrangement parameters with lower fitness values ​​are selected first to ensure the selection of better solutions. When the fitness values ​​are the same, the sparsity of the heating rod position distribution is measured, and individuals with sparse distribution are retained first to maintain diversity, thus obtaining the Pareto front solutions.

7. The method for optimizing the arrangement of heating rods in the mold head as described in claim 5, characterized in that: The new Gaussian process regression model ensures prediction accuracy through 10-fold cross-validation, as follows: Data partitioning: The training dataset is randomly divided into 10 subsets to ensure that the data distribution of each subset is consistent with the overall dataset; Iterative training and validation: Ten independent training iterations are performed, each time using 90% of the dataset as the training set and the remaining 10% as the validation set; During each training iteration, the model is retrained using the training set data, and performance metrics are calculated on the validation set; The performance metrics include... And MSE, This indicates the degree of agreement between the model's predicted values ​​and the actual values; It measures the squared average error between the predicted and actual values; Record each validation set The average of the 10 results and the MSE results are used as the overall performance evaluation of the model. in, In the formula: It is the first The actual value of each sample; It is the first Predicted values ​​for each sample; It is the average of the actual values; It refers to the number of samples.

8. The method for optimizing the arrangement of heating rods in the mold head as described in claim 1, characterized in that: Step 6) specifically involves: selecting individuals with low fitness from the retrained GPR model to form a new population; performing genetic algorithm operations on the new population again, repeatedly selecting, crossing over, and mutating to generate a new population; performing a full simulation on the new population; comparing the simulation results with the prediction results of the Gaussian process regression model; adding high-error samples back into the training set; retraining the Gaussian process regression model; and iterating repeatedly until convergence. Finally, selecting the optimal heating rod arrangement obtained by the genetic algorithm; where the convergence condition is: This indicates that when the difference in optimal fitness values ​​between two consecutive generations of a population is less than 1, the population's fitness is 1.5%. When the algorithm has converged, the convergence threshold ε is set to 0.01.

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