Injection molding process parameter multi-objective optimization method based on high-precision prediction model

Abstract

The invention discloses an injection molding process parameter multi-objective optimization method based on a high-precision prediction model, and the method comprises the steps: carrying out the enhancement of data through MIC and GAN based on a simulation test result, so as to improve the quality of simulation data; then carrying out hyper-parameter tuning by using a KOA and IVYA mixed framework; then, an SHAP method is adopted to enhance the interpretability of the XGBoost model, and an optimized process parameter search range is provided; and finally, searching a Pareto leading edge of a quality target by applying MOCGO, and determining an optimal process parameter combination. Test results show that the buckling deformation and the volume shrinkage are respectively reduced by 35.7% and 10.1% by using the technological parameter combination optimized by the method disclosed by the invention, the buckling deformation and the volume shrinkage of the molded plastic part can be effectively reduced, so that a high-quality plastic part product is obtained, and the product quality is improved. And a theoretical basis and data support can be provided for obtaining an optimal process parameter combination of injection molding.

Description

Technical Field

[0001] The present invention relates to a multi-objective optimization method for injection molding process parameters based on a high-precision prediction model, specifically a multi-objective optimization method for injection molding process parameters based on the MIC-GAN-KOA-IVYA-XGBoost and MOCGO high-precision prediction models, belonging to the technical field of injection molding processing. Background Technique

[0002] In the technical field of injection molding processing in modern manufacturing, the optimization of process parameters is crucial for improving product quality, reducing the scrap rate, and enhancing production efficiency. Warping deformation and volume shrinkage are two of the most common and critical quality problems in the injection molding process. Warping deformation can cause deviations in the product shape, while volume shrinkage affects dimensional accuracy. The control of these two directly relates to the reliability and service life of the product. Therefore, how to achieve multi-objective optimization under complex process conditions and balance the minimization of these two defects has become a widely concerned research hotspot.

[0003] Simulation technologies such as finite element analysis and Moldflow analysis are widely used in injection molding process simulation to help predict warping deformation and volume shrinkage. Generally, first, the injection molding process of thin-walled plastic parts is simulated and analyzed by Moldflow software to analyze the cooling effect and flow performance. Then, a mathematical model is constructed based on the simulation data to establish the relationship between the quality target and process parameters. Finally, the optimal combination of process parameters is obtained through search-based optimization algorithms. For example, Cao Y et al. constructed an adaptive network fuzzy inference system (ANFIS) between the warping deformation amount and process parameters and obtained the optimal process parameter solution using a genetic algorithm (GA); Sun Zheng et al. constructed a mathematical surrogate model between the warping deformation amount, volume shrinkage rate, and process parameters based on the gradient-enhanced Kriging (GEK) model, and used the multi-objective differential evolution (MODE) algorithm to search for the Pareto solution set, and determined the optimal process parameter solution according to the weighting coefficient; Liu X et al. constructed a mathematical surrogate model between the warping deformation amount, volume shrinkage rate, and process parameters with the help of an extreme learning machine (ELM) model optimized by GA, and applied the multi-objective firefly algorithm combined with the GRA-TOPSIS multi-objective decision-making method to determine the final optimal process parameter solution.

[0004] In the study of actual injection molding problems, how to extract key process parameters from simulation data remains a challenge, and multiple interrelated objectives and constraints usually need to be comprehensively considered and balanced. For example, warpage deformation and volume shrinkage defects. When reducing the cooling rate to minimize warpage deformation, the volume shrinkage will also increase due to the extension of the cooling time. As a method to solve optimization problems involving multiple conflicting objectives, multi-objective optimization aims to find a reasonable balance among multiple objectives and generate a Pareto front of a set of multi-objective optimal values. Currently, the research on multi-objective optimization usually transforms the multi-objective problem into a single-objective problem through the idea of weighted combination. Common methods include Grey Relational Analysis (GRA), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Entropy Weight and Fuzzy Comprehensive Evaluation (FCE). However, from the perspective of multiple objectives, all objectives are usually mutually restrictive, and the improvement of one objective often comes at the expense of other objectives. Therefore, for a multi-objective optimization problem, a large number of non-dominated solutions (Pareto solutions) are usually generated. Currently, in the research on multi-objective optimization of injection molding process parameters, researchers often determine the final Pareto optimal solution based on engineering experience and repeated experiments. How to determine the optimal trade-off scheme to achieve the best comprehensive purpose is still a difficult problem in the industry. Summary of the Invention

[0005] Aiming at the above problems, the present invention provides a multi-objective optimization method for injection molding process parameters based on a high-precision prediction model, which can effectively reduce the warpage deformation amount and volume shrinkage rate of the molded plastic parts, and then obtain high-quality plastic part products, and can provide a theoretical basis and data support for obtaining the optimal process parameter combination of injection molding.

[0006] To achieve the above object, the multi-objective optimization method for injection molding process parameters based on a high-precision prediction model specifically includes the following steps:

[0007] Step1, taking the warpage deformation amount and volume shrinkage rate as quality optimization objectives, selecting the process parameters that affect these two objectives as optimization design variables, determining the value range of the process parameters according to the recommended values of the process parameters, and taking the value range of the process parameters as the experimental design space. Based on Moldflow, injection molding simulation is carried out to obtain the experimental results of the quality optimization objectives;

[0008] Step2, based on the simulation test results, preprocess the process parameter data through MIC and GAN;

[0009] Step3, use the KOA-IVYA hybrid optimization algorithm to optimize the hyperparameters of the XGBoost model, and construct the MIC-GAN-KOA-IVYA-XGBoost injection molding quality prediction model;

[0010] Step 4. Analyze the MIC-GAN-KOA-IVYA-XGBoost injection molding quality prediction model through the SHAP interpretation method. By generating a feature importance map, clarify the influence degree of each process parameter on the prediction result, and provide the search range of the optimized process parameters.

[0011] Step 5. Use MOCGO and the MIC-GAN-KOA-IVYA-AGBoost prediction model to perform multi-objective optimization on the range of the optimized process parameters to obtain the Pareto front of the quality optimization objective.

[0012] Step 6. Calculate the comprehensive score of each solution in the obtained Pareto front of the quality optimization objective through the AHP-EW-GM method and sort them to determine the optimal combination of process parameters.

[0013] Furthermore, in Step 2, when preprocessing the process parameter data through MIC, the specific steps are as follows:

[0014] ① Generate a variable scatter plot and divide the grid: Represent the values of the process parameters (x) and the quality target (y) in a two-dimensional space through a scatter plot, and divide the data into grids.

[0015] ② Calculate the mutual information of each grid: When calculating the mutual information under the given grid division, replace the probability distribution of the variables with the frequency of the scatter distribution in the grid, and measure the dependence relationship between the process parameter (x) and the quality target (y) through the mutual information.

[0016] ③ Obtain the maximum value of the mutual information: Calculate the mutual information values under all grid divisions and select the maximum value among them.

[0017] ④ Calculate MIC: Under multiple combinations of different numbers of rows x and columns y, calculate the maximum mutual information value using the following formula:

[0018]

[0019] In the formula: I(x,y) is the mutual information; log(min{|x|,|y|}) is the normalized adjustment of the grid division.

[0020] ⑤ Screen important process parameters: After calculating the MIC values of all process parameters for the quality target, compare the MIC values with a preset threshold, and select the process parameters with MIC values greater than or equal to the threshold as those with strong correlation.

[0021] Furthermore, in Step 2, when preprocessing the process parameter data through GAN, the specific steps are as follows:

[0022] ① Initialize the generator and discriminator networks: Set the initial parameters of the generator G and discriminator D;

[0023] ② Set the training parameters: Set the dimension of the random noise z input to the generator G, batch size, total number of training epochs, learning rate, optimizer, and momentum parameter;

[0024] ③ Define the overall optimization objective: The overall optimization objective expression is as follows:

[0025]

[0026] In the formula: D(x) represents the probability that the discriminator D determines that the real data x is real; G(z) represents the forged sample generated by the generator G according to the random noise z;

[0027] ④ Training loop: Generate initial synthetic data by inputting the random noise z into the generator G, and input it together with the real data into the discriminator D for classification. The discriminator D optimizes its own parameters by calculating the loss function to enhance the ability to distinguish real data and generated data. At the same time, the generator G optimizes its own parameters according to the feedback of the discriminator D to make the generated data gradually approach the real data until the discriminator D cannot effectively distinguish real data and generated data, and finally output the synthetic data;

[0028] ⑤ When the discriminator D cannot distinguish the generated data, use the k-means clustering algorithm to perform clustering analysis on the original data and the generated data, and use the t-SNE method to reduce the dimension of the data for visualization analysis.

[0029] Furthermore, in Step 3, the KOA-IVYA hybrid optimization algorithm is used as follows:

[0030] ① KOA global search:

[0031] The individual position update formula of KOA is as follows:

[0032]

[0033] In the formula: X i (t + 1) is the updated position after the (t + 1)-th iteration; X i (t) is the position after the t-th iteration; f is the flag to change the search direction; V i (t) is the velocity required for celestial body i to reach the new position; is the gravitational function between the current position and the position of the best solution; |r| is a number randomly generated based on the normal distribution; X s (t) is the position of the current best solution;

[0034] ② IVYA local exploitation:

[0035] The individual position update formula of IVYA is as follows:

[0036] X i (t + 1) = X i (t) + β 1 |X i+1 (t) - X i (t)| + G i (t)

[0037] Where: G i (t) is the gain vector, which is used to increase randomness;

[0038] ③ Dynamic population adjustment:

[0039] The formula for the change in population size through the number of iterations is as follows:

[0040]

[0041] IVYA_PopSize = SearchAgen ts_no - KOA_PopSize

[0042] Where: KOA_PopSize is the KOA population size; IVYA_PopSize is the IVYA population size; SearchAgents_no is the initial total number of individuals; t is the current number of iterations; Max_iteration is the maximum number of iterations.

[0043] Furthermore, in Step5, when using MOCGO for multi-objective optimization, candidate solution positions are generated in 4 different ways: based on the optimal solution position, based on the optimal solution and the mean population, based on the mean population and the optimal solution, and completely randomly generated.

[0044] Generate a new candidate solution based on the current global optimal solution:

[0045] X i,new = a 1 · (I 1 · X best - I 2 · X mean )

[0046] Generate a new solution around the average solution position:

[0047] X i,new = X best + a 2 · (I 3 · X mean - I 4 )

[0048] Generate a new solution around the optimal solution position:

[0049] X i,new = X mean + a 3 · (I 5 · X best - I 6 )

[0050] where: a i (i = 1, 2, 3) is a randomly generated scaling factor; I i (i = 1, 2, 3, 4, 5, 6) are randomly generated integers (1 or 2) that control the relative influence between the leader and the mean population; X best is the current optimal solution; X mean is the average position of the population;

[0051] Introduce random changes to the solution position, and the formula is:

[0052] X i,new = unifrnd(lb, ub)

[0053] where: unifrnd(lb, ub) is a uniform distribution random number generator that generates values between the upper and lower bounds lb and ub;

[0054] Evaluate the fitness of the generated potential solutions through the objective function, compare the dominance relationship with other solutions, and retain the non-dominated solutions. After the iteration ends, a Pareto front is formed.

[0055] Furthermore, Step6 is specifically as follows:

[0056] ①Construct a pairwise comparison matrix between indicators according to expert judgment through AHP, and give the subjective weight ratio W AHP ;

[0057] ②Calculate the objective weight ratio W EW through EW using data distribution information to quantify the importance of each indicator;

[0058] ③Fuse the subjective weight and the objective weight through GM, integrate the advantages of both, and generate the final weight ratio W GM ;

[0059] ④Based on the final weight, score each solution in the solution set, sort the solutions on the Pareto front, and select the process parameter combination with the best comprehensive performance.

[0060] Compared with the prior art, the multi-objective optimization method for injection molding process parameters based on a high-precision prediction model is based on the results of simulation tests. First, the data is enhanced through the maximum information coefficient (MIC) and the generative adversarial network (GAN) to improve the quality of the simulation data. Then, a hybrid framework of the Kepler optimization algorithm (KOA) and the ivy optimization algorithm (IVYA) is used for hyperparameter tuning. Subsequently, the Shapley additive explanation (SHAP) method is adopted to enhance the interpretability of the extreme gradient boosting (XGBoost) model and provide the search range of the optimized process parameters. Finally, the multi-objective chaotic game optimization (MOCGO) is applied to find the Pareto front of the quality objectives and determine the optimal process parameter combination. The test results show that the optimized process parameter combination reduces the warpage deformation and volume shrinkage rate by 35.7% and 10.1% respectively, which can effectively reduce the warpage deformation and volume shrinkage rate of the molded plastic parts, and thus obtain high-quality plastic part products, providing a theoretical basis and data support for obtaining the optimal process parameter combination of injection molding. Description of the Drawings

[0061] Figure 1 is a three-dimensional model diagram of a sensor housing plastic part for ABS plastic injection molding, where (a) is the front view of the sensor housing plastic part and (b) is the back view of the sensor housing plastic part;

[0062] Figure 2 is a mold flow simulation analysis model diagram, where (a) is the front view of the mold flow simulation analysis model and (b) is the back view of the mold flow simulation analysis model;

[0063] Figure 3 is a view of the warpage deformation and volume shrinkage rate obtained by simulating based on the process parameter combination recommended by Moldflow software before optimization, where (a) is the simulation view of the warpage deformation and (b) is the simulation view of the volume shrinkage rate;

[0064] Figure 4 is a diagram showing the comparison of the MIC values of all process parameters with respect to the quality objectives with a preset threshold of 0.3, where (a) is the diagram showing the comparison of the MIC values of the warpage deformation and (b) is the diagram showing the comparison of the MIC values of the volume shrinkage rate;

[0065] Figure 5 is a flowchart of GAN data augmentation;

[0066] Figure 6 is a diagram showing the visualization of synthetic data, where (a) is the original data diagram and (b) is the generated data diagram;

[0067] Figure 7 is a comparison diagram of XGBoost models with different data processing, where (a) is the diagram of the warpage deformation and (b) is the diagram of the volume shrinkage rate;

[0068] Figure 8 It is a diagram showing the iterative convergence of the optimization algorithm. Among them, (a) is the diagram showing the iterative convergence of the warping deformation prediction model, and (b) is the diagram showing the iterative convergence of the volume shrinkage prediction model;

[0069] Figure 9 It is a diagram for comparing model accuracies. Among them, (a) is the diagram for comparing the accuracies of the warping deformation prediction model, and (b) is the diagram for comparing the accuracies of the volume shrinkage prediction model;

[0070] Figure 10 It is a SHAP summary diagram. Among them, (a) is the SHAP summary diagram of the warping deformation, and (b) is the SHAP summary diagram of the volume shrinkage;

[0071] Figure 11 It is a diagram of the Pareto front; among them, (a) is the diagram of the Pareto front before SHAP optimization, and (b) is the diagram of the Pareto front after SHAP optimization;

[0072] Figure 12 It is a diagram of the simulation values of the optimal process parameter combination; among them, (a) is the diagram of the warping deformation amount, and (b) is the diagram of the volume shrinkage rate. Specific implementation manners

[0073] This multi-objective optimization method for injection molding process parameters based on a high-precision prediction model first enhances the data through the maximum information coefficient (MIC) and the generative adversarial network (GAN) to improve the quality of the simulation data; then uses the hybrid framework of the Kepler optimization algorithm (KOA) and the ivy optimization algorithm (IVYA) for hyperparameter tuning; subsequently, adopts the Shapley additive explanation (SHAP) method to enhance the interpretability of the extreme gradient boosting (XGBoost) model and provide the search range of the optimized process parameters; finally, applies the multi-objective chaotic game optimization (MOCGO) to find the Pareto front of the quality objectives and determine the optimal process parameter combination.

[0074] The following takes the plastic part of the sensor housing formed by injection molding as an example to specifically illustrate the present invention.

[0075] The geometric model of the plastic part of the sensor housing formed by ABS plastic injection molding is as Figure 1 (a), Figure 1 (b) shown. The characteristics of the sensor housing require it to meet the requirements of sufficient heat dissipation and lightweight design. The external dimensions of this plastic part are 216 mm × 154 mm × 50 mm, and the volume is 239292 mm 3, the average wall thickness is 2.16 mm. A structural framework with ribs is adopted inside and at the edges of the plastic part to disperse external loads and reduce local stress concentration. At the same time, strict surface quality requirements are imposed on the mating posts and mating holes to ensure the mating accuracy and stability with other components. The requirements for the warpage deformation and volume shrinkage rate of this plastic part product are not greater than 0.584 mm and 7% respectively.

[0076] 1. Establishment of finite element model and simulation analysis

[0077] The 3D model of the plastic part is imported into Moldflow software for mesh generation. The mesh is divided into triangular elements. Since sharp changes in flow pressure, temperature, and velocity may occur during flow analysis, leading to analysis failure, long and thin elements should be avoided as much as possible. In the mesh statistics, the free edges and multiple edges of the plastic part are 0, the connected domain is 1, the misaligned elements are 0, and the aspect ratios are all less than 6.00. The generated mesh meets the requirements of the 3D model, and the surface mesh matching rate reaches 92% for flow analysis and 93% for warpage deformation analysis.

[0078] After mesh generation, a mold flow simulation analysis model including a gating system and a cooling system as shown in Figure 2 (a), Figure 2 (b) is established. The red pipeline is the gating system, which consists of a gate and a sprue and can fill the cavity with plastic melt smoothly to obtain a plastic product with clear external contour and excellent internal quality. The blue pipeline is the cooling system, which consists of straight-through water channels and circumferential water channels. During the molding cycle of the plastic part, the cooling time of the mold accounts for more than 2 / 3 of the entire cycle, significantly affecting the molding efficiency and quality.

[0079] The analysis sequence of Moldflow simulation is set as: cooling - filling - holding - warpage. The ABS material grade is PA - 757, and the process parameter combination recommended by Moldflow software is: melt temperature 210 °C, mold temperature 45 °C, holding pressure 80 MPa, and molding cycle time 30 s.

[0080] Moldflow uses multiple key formulas in warpage and volume shrinkage simulations for temperature and stress analysis.

[0081] Use the warpage deformation formula:

[0082] a. Temperature distribution analysis: First, calculate the temperature distribution in different regions during the cooling process through the heat conduction equation. This process needs to consider the influence of the initial melt temperature and mold temperature on each part of the plastic part to obtain an accurate temperature field.

[0083] b. Calculation of residual stress: Look up the coefficient of thermal expansion (β) and Young's modulus (E) of the ABS material, and calculate the residual stress (σ using the temperature changeres ) by using the following formula:

[0084] σ res = E·β·(T final - T initial )

[0085] Where: T final is the temperature after cooling; T initial is the melt temperature. Substitute the calculated temperature change into the formula to determine σ res .

[0086] c. Determination of the characteristic length (L) and calculation of the warpage deformation (W): L is usually defined as the average wall thickness of the plastic part. In this embodiment, L is 2.16 mm.

[0087]

[0088] As Figure 3 (a) the simulation results show, the maximum warpage deformation is 0.7645 mm, exceeding the design requirement of 0.6 mm for the plastic part.

[0089] The increase in the warpage deformation is mainly due to the temperature gradient and uneven shrinkage in different regions, resulting in stress concentration, which affects the final shape.

[0090] Use the volume shrinkage rate formula:

[0091] a. Determine the initial volume of the mold cavity (V mold ): Measure the geometry of the mold cavity and calculate V mold . In this embodiment, V mold is 239,292 mm 3 .

[0092] b. Simulate the cooling process: Use Moldflow to simulate the cooling process and obtain the final volume (V final ) of the plastic part after cooling to the ambient temperature. During this process, consider the volume change of the plastic due to temperature change during cooling.

[0093] c. Calculate the volume shrinkage:

[0094]

[0095] Where: V mold is the initial volume of the mold cavity; V final is the final volume after cooling. As Figure 3 (b) the simulation results show, the maximum volume shrinkage rate of the plastic part is 7.124%, exceeding the design requirement of 7% for the plastic part.

[0096] These results beyond the design scope indicate the necessity to further optimize the injection molding process to ensure that the quality and performance of plastic parts meet the expected requirements.

[0097] 2. Data preprocessing

[0098] Aiming at the problems of limited experimental data and unbalanced sample distribution in the simulation data set, the maximum information coefficient (MIC) and generative adversarial network (GAN) methods are used to preprocess the process parameters including melt temperature Tm, mold temperature Te, injection pressure Pi, holding pressure Pk, injection time ti, holding time tk, cooling time t c and quality targets (warpage deformation W, volume shrinkage rate V).

[0099] 2.1 MIC feature selection

[0100] The calculation of MIC value includes grid division, mutual information calculation and grid optimization, aiming to reveal the degree of mutual influence between process parameters and quality targets. In data preprocessing, first, the original data is divided by central composite design (CCD) to obtain 152 groups of process parameter combinations, and 152 groups of warpage deformation and volume shrinkage rate are obtained by using the Moldflow simulation model as quality targets. In the optimization of injection molding process, the steps of MIC are as follows:

[0101] a. Generate variable scatter plots and divide grids: Represent the values of process parameters (x) and quality targets (y) in a two-dimensional space through scatter plots, and divide the data into grids.

[0102] b. Calculate the mutual information of each grid: Under the given grid division, when calculating the mutual information, replace the probability distribution of variables with the frequency of scatter points distributed in the grid, that is, count the number of scatter points in each grid cell. The mutual information measures the dependence between process parameters (x) and quality targets (y).

[0103] c. Obtain the maximum value of mutual information: For a specific row and column division, calculate the mutual information values under all possible grid divisions and select the maximum value among them. This maximum value is denoted as the maximum mutual information I max (x,y).

[0104] d. Calculate MIC: Calculate the maximum mutual information values under multiple different combinations of number of rows x and number of columns y.

[0105]

[0106] In the formula: I(x,y) is the mutual information, which is used to measure the dependence between process parameters and targets such as warpage deformation and volume shrinkage rate; log(min{|x|,|y|}) is the normalization adjustment of grid division to ensure the stability and comparability of MIC values.

[0107] e. Screen important process parameters: such as Figure 4 As shown, after calculating the MIC values of all process parameters for the quality target, compare the MIC values with the preset threshold of 0.3. Select the process parameters with MIC values greater than or equal to 0.3, which are considered to have a strong correlation. Such as Figure 4 As shown, 6 process parameters except Te are retained for warpage analysis, and 7 process parameters are retained for volume shrinkage analysis.

[0108] 2.2. GAN data augmentation

[0109] GAN consists of a generator and a discriminator. The generator G continuously tries to generate new combinations of process parameters and quality targets by adjusting the input random noise z. The discriminator D promotes the generator to generate more realistic combinations of process parameters by judging the similarity between the output of the generator and the real data. To achieve this process, it specifically includes the steps:

[0110] a. Initialize the generator and discriminator networks: Set the initial parameters of the generator G and the discriminator D. Since the number of samples (152) is small, the depth and width of the network are kept small to prevent overfitting.

[0111] b. Set the training parameters: The dimension of the input random noise z of the generator G is set to 100, the batch size is set to 8, the total number of training epochs is set to 2000, the learning rate is set to 0.0001, the optimizer uses Adam, and the momentum parameters are β1 = 0.5 and β2 = 0.999.

[0112] c. Define the overall optimization objective: The optimization objective of GAN is the adversarial loss between the generator G and the discriminator D, and the expression is as follows:

[0113]

[0114] In the formula: D(x) represents the probability that the discriminator D determines that the real data x is real; G(z) represents the forged sample generated by the generator G according to the random noise z.

[0115] d. Training loop: Such as Figure 5 As shown, during the GAN training process, first generate initial synthetic data through the input of random noise z to the generator G, and input it together with the real data into the discriminator D for classification; the discriminator D optimizes its own parameters by calculating the loss function to enhance the ability to distinguish real data and generated data. At the same time, the generator G optimizes its own parameters according to the feedback of the discriminator D, so that the generated data gradually approaches the real data; through the alternating game training of the generator G and the discriminator D, continuously improve the authenticity and quality of the generated data until the discriminator D cannot effectively distinguish real data and generated data, and finally output high-quality synthetic data.

[0116] e. When the discriminator D cannot distinguish the generated data, the k-means clustering algorithm is used to perform clustering analysis on the original data and the generated data, which are divided into 6 categories, and the 7-dimensional data is reduced to 2 dimensions by the t-SNE method for visual analysis. From Figure 6 the visualization results, among the 200 synthesized data, 48 groups of generated data can effectively solve the problems of uneven sample distribution and insufficient data volume in the original data. In addition, as Figure 7 shown, after MIC feature selection and GAN data augmentation processing, the preliminarily fitted model (MIC-GAN-XGBoost) can significantly improve the prediction accuracy, and the average RMSE of 50 predictions is reduced to 0.023 and 0.17 respectively.

[0117] 3. Construction of the quality target prediction model

[0118] The XGBoost model is a supervised learning algorithm that realizes the integration of multiple CART trees through a Gradient Tree Boosting. To determine the optimal configuration of the XGBoost model, the present invention uses the KOA-IVYA hybrid optimization algorithm to explore the hyperparameter space. This method aims to improve the model accuracy, balance the model complexity and prevent overfitting. The XGBoost model hyperparameters to be optimized are shown in Table 1 below.

[0119] Table 1 XGBoost model hyperparameters to be optimized

[0120]

[0121] 3.1 Design of the IVYA-KOA hybrid optimization algorithm

[0122] The IVYA-KOA hybrid optimization algorithm combines KOA and IVYA, which can realize the organic combination of global search and local development. KOA simulates the celestial gravitational effect and enhances the global search ability through the dynamic adjustment of the gravitational function ; IVYA realizes local development by simulating the growth behavior of ivy and relying on the interaction between individuals. Specifically as follows:

[0123] a. KOA global search:

[0124] In KOA, the dynamic adjustment of the gravitational function makes KOA have a stronger global search ability in the early stage. As the iteration progresses, the gravitational function decreases, and the individuals gradually concentrate near the current global optimal solution. The individual position update formula of KOA is as follows:

[0125]

[0126] Where: X i (t + 1) is the updated position after the (t + 1)-th iteration; X i (t) is the position after the t-th iteration; f is the flag for changing the search direction; V i (t) is the velocity required for celestial body i to reach the new position; is the gravitational function between the current position and the position of the best solution; |r| is a number randomly generated based on the normal distribution; X s (t) is the position of the current best solution.

[0127] b. IVYA local development:

[0128] The position update of IVYA is based on neighboring individuals and the global optimal solution. If the fitness of an individual is better than a certain multiple (controlled by β1) of the global optimal solution, the update of the individual depends more on the relationship with its neighbors. Otherwise, the individual moves closer to the global optimal solution. The individual position update formula of IVYA is as follows:

[0129] X i (t + 1) = X i (t) + β 1 |X i+1 (t) - X i (t)| + G i (t)

[0130] Where: G i (t) is the gain vector, which is used to increase randomness.

[0131] c. Dynamic population adjustment:

[0132] In order to make full use of the global search advantage of KOA and the local search advantage of IVYA, dynamic population adjustment is adopted. The formula for changing the population size according to the number of iterations is as follows:

[0133]

[0134] IVYA_PopSize = SearchAgen ts_no - KOA_PopSize

[0135] Where: KOA_PopSize is the KOA population size; IVYA_PopSize is the IVYA population size; SearchAgents_no is the initial total number of individuals; t is the current number of iterations; Max_iteration is the maximum number of iterations. As the number of iterations t increases, the KOA population size gradually decreases, while the IVYA population size increases accordingly.

[0136] In the KOA-IVYA optimization algorithm, SearchAgents_no is set to 100, which determines the number of initial individuals. The initial M 0 is 0.1, which controls the gravitational strength between individuals. The gravitational decay factor (lambda) is 15, which is used to adjust the decay of gravity over time. Max_iteration is set to 100, which limits the running time of the algorithm. To improve the accuracy of evaluation, the fitness value is evaluated by the normalized mean absolute error (MAE). As Figure 8 shown, in the warping deformation prediction model, the KOA-IVYA hybrid algorithm not only optimizes the parameters to 0.059 in the first iteration, which is much lower than those of the individual algorithms KOA (0.12) and IVYA (0.095), but also reaches the optimal hyperparameter configuration after 25 iterations, significantly faster than the 70 iterations required by KOA and the 40 iterations required by IVYA. A similar trend also appears in the volume shrinkage prediction model. In the first iteration, the optimal result is 0.081, which is much lower than the values of KOA (0.178) and IVYA (0.145). In addition, the optimal configuration is achieved after 22 iterations, significantly exceeding the 61 iterations of KOA and the 67 iterations of IVYA. The iteration curve shows that KOA performs better than IVYA in the initial stage of iteration, while IVYA performs better in local optimization, thus improving the accuracy of the solution. As Figure 9 shown, MIC-GAN-KOA-IVYA-XGBoost performs best among the five fitting models, with the lowest RMSE, MAE, and MAPE. In addition, as shown in Table 2 below, the optimal evaluation indexes of the warping prediction model are RMSE: 0.02, MAE: 0.0121, MAPE: 0.0212, R 2 : 0.9915; the optimal evaluation indexes of the volume shrinkage prediction model are RMSE: 0.0881, MAE: 0.048, MAPE: 0.008, R 2 : 0.9909.

[0137] Table 2 Model Evaluation Indexes

[0138]

[0139] Ensemble learning models perform well in many complex tasks, but their "black box" characteristics make it difficult to understand the internal mechanisms of the models. SHAP analysis provides a quantification of the contribution of each feature to the model prediction, helping to identify key process parameters. The present invention uses the SHAP library to calculate the SHAP values of the MIC-GAN-KOA-IVYA-XGBoost model, and by generating a feature importance map, clarifies the degree of influence of each process parameter on the prediction result.

[0140] In the injection molding process, temperature, time, and pressure play a crucial role in the molding quality and the performance of the final product. As Figure 10 shown, the melt temperature is the main influencing factor. A higher temperature helps to improve the material flowability, surface quality, and density of the product. However, the influence of the melt temperature on warping and volumetric shrinkage is different. A higher melt temperature can reduce warping but increase volumetric shrinkage. Therefore, when controlling warping, the melt temperature should be appropriately increased, while when reducing volumetric shrinkage, the temperature setting needs to be balanced. Increasing the mold temperature also helps to reduce warping and volumetric shrinkage and maintain molding uniformity. From the perspective of time, a longer injection time is beneficial for full filling of the mold cavity, thus reducing warping, while the cooling time is important for reducing volumetric shrinkage. Appropriately extending the cooling time helps to achieve uniform curing. The injection pressure has a significant impact on volumetric shrinkage. A higher injection pressure helps to reduce volumetric shrinkage, while the holding pressure has a relatively small impact on warping and volumetric shrinkage, but appropriate adjustment can improve the molding stability.

[0141] Therefore, when optimizing the injection molding process, the melt temperature and injection time should be preferentially controlled to reduce warping, while the injection pressure and cooling time should be adjusted to effectively reduce volume shrinkage. After analyzing the SHAP summary plot, the optimal ranges of each feature can be identified as shown in Table 3 below, providing a more precise feature range for multi-objective chaotic game optimization (MOCGO) and further guiding the optimization process.

[0142] Table 3 Optimization ranges of process parameters

[0143]

[0144]

[0145] 4. Multi-objective optimization

[0146] In the multi-objective optimization process of the injection molding process, the MOCGO and MIC-GAN-KOA-IVYA-AGBoost prediction models are used to further optimize the optimized process parameter ranges to find a set of optimal process parameter combinations that minimize both the warping deformation and the volume shrinkage rate simultaneously. MOCGO is a multi-objective optimization algorithm based on chaotic systems and game strategies, which can achieve an efficient search of the Pareto front through dynamic archiving and selection strategies. Its parameter settings include Max_iteration as 100, population size as 50, grid inflation parameter (alpha) as 0.1, optimal solution selection pressure (beta) as 4, and archive elimination pressure (gamma) as 2. In addition, candidate solution positions are generated in 4 different ways (based on the optimal solution position, based on the optimal solution and the mean population, based on the mean population and the optimal solution, and completely randomly generated).

[0147] Generate new candidate solutions based on the current global optimal solution:

[0148] X i,new = a 1 ·(I 1 ·X best - I 2 ·X mean )

[0149] Generate a new solution around the average solution position:

[0150] X i,new = X best + a 2 ·(I 3 ·X mean - I 4 )

[0151] Generate a new solution around the optimal solution position:

[0152] X i,new = X mean + a 3 ·(I 5 ·X best - I 6 )

[0153] Where: a i (i = 1, 2, 3) is a randomly generated scaling factor; I i (i = 1, 2, 3, 4, 5, 6) are randomly generated integers (1 or 2) that control the relative influence between the leader and the mean population; X best is the current optimal solution; X mean is the average position of the population.

[0154] Introduce random variation at the solution position, the formula is:

[0155] X i,new = unifrnd(lb, ub)

[0156] Where: unifrnd(lb, ub) is a uniform distribution random number generator that generates values between the upper and lower bounds lb and ub.

[0157] Evaluate the fitness of the generated potential solutions through the objective function and compare their domination relationships with other solutions, so as to retain the non-dominated solutions and form the Pareto front after the iteration ends. As Figure 11As shown, compared with the situation before optimization, the parameter range optimized through SHAP analysis enables MOCGO to converge faster to the Pareto front in the region of warpage deformation less than 0.6 mm and volume shrinkage rate less than 7% under the same 100 iterations. This result indicates that accurately identifying key process parameters through SHAP analysis and adjusting their optimization range can not only improve the distribution density and quality of the solution set but also effectively shorten the convergence time of the multi-objective optimization algorithm.

[0158] 5. Experimental Verification

[0159] To comprehensively evaluate the Pareto front, a method combining the Analytic Hierarchy Process (AHP), Entropy Weight Method (EW), and Game Combination Method (GM) is used to calculate the comprehensive score of each solution. First, through AHP, a pairwise comparison matrix between indicators is constructed based on expert judgment to give the subjective weight ratio W AHP of (0.6771, 0.3229); then, through EW, the objective weight ratio W EW is (0.5419, 0.4581) to quantify the importance of each indicator. Finally, through GM, the subjective weight and objective weight are fused to combine the advantages of both and generate the final weight ratio W GM of (0.6095, 0.3905). Based on the final weight, each solution in the solution set is scored, and the solutions on the Pareto front are ranked to select the process parameter combination with the optimal comprehensive performance.

[0160] As shown in Table 4 below, the target simulation value of the original process parameter combination is (0.7645, 7.124), while the target predicted value of the optimal process parameter combination drops to (0.4913, 6.407), indicating that the warpage deformation and volume shrinkage rate are reduced by 35.7% and 10.1% respectively. As Figure 12 shown, through simulation verification, the target simulation value of the optimal process parameter combination is (0.5017, 6.4586), and the error rates compared with the predicted values are 2.13% and 0.81% respectively, verifying the accuracy and effectiveness of the multi-objective optimization process of the present invention.

[0161] Table 4 The top 5 groups of process parameter combination scores

[0162]

[0163] The test results show that the optimized process parameter combination obtained by using the multi-objective optimization method of injection molding process parameters based on the high-precision prediction model reduces the warpage deformation amount and the volume shrinkage rate by 35.7% and 10.1% respectively, can effectively reduce the warpage deformation amount and the volume shrinkage rate of the molded plastic parts, and further obtain high-quality plastic part products, which can provide a theoretical basis and data support for obtaining the optimal process parameter combination of injection molding.

Claims

1. A multi-objective optimization method for injection molding process parameters based on a high-precision prediction model, characterized in that: The specific steps include: Step 1: Take the warpage deformation and volume shrinkage as the quality optimization targets, select the process parameters that affect these two targets as the optimization design variables, determine the value range of the process parameters according to the recommended values ​​of the process parameters, and use the value range of the process parameters as the experimental design space. Perform injection molding simulation based on Moldflow to obtain the quality optimization target test results. Step 2, based on the simulation test results, the process parameter data is preprocessed through MIC and GAN; Step 3, use the KOA-IVYA hybrid optimization algorithm to tune the hyperparameters of the XGBoost model and build a MIC-GAN-KOA-IVYA-XGBoost injection molding quality prediction model; Step 4, analyze the MIC-GAN-KOA-IVYA-XGBoost injection molding quality prediction model through the SHAP interpretation method, clarify the influence of each process parameter on the prediction result by generating a feature importance diagram, and provide an optimized process parameter search range; Step 5, use MOCGO and MIC-GAN-KOA-IVYA-AGBoost prediction models to perform multi-objective optimization on the optimized process parameter range to obtain the Pareto frontier of the quality optimization target; Step 6, calculate the comprehensive score of each solution in the Pareto frontier of the obtained quality optimization target through the AHP-EW-GM method, sort them, and determine the optimal combination of process parameters.

2. The multi-objective optimization method for injection molding process parameters based on a high-precision prediction model according to claim 1, characterized in that: In Step 2, when preprocessing the process parameter data through MIC, the specific steps are as follows: ① Generate variable scatter plot and divide the grid: The values ​​of process parameters (x) and quality targets (y) are represented in two-dimensional space through scatter plots, and the data are divided into grids; ② Calculate the mutual information of each grid: Under a given grid division, when calculating the mutual information, the probability distribution of the variable is replaced by the frequency of the scattered points in the grid, and the mutual information is used to measure the dependency between the process parameters (x) and the quality target (y); ③ Obtain the maximum value of mutual information: calculate the mutual information values ​​under all grid divisions and select the maximum value; ④ Calculate MIC: Under different combinations of row number x and column number y, use the following formula to calculate the maximum mutual information value: Where: I(x,y) is the mutual information; log(min{x|,|y}) is the normalized adjustment of the grid division; ⑤ Screening of important process parameters: After completing the calculation of the MIC values ​​of all process parameters for the quality target, compare the MIC value with the preset threshold, and select the process parameters with MIC values ​​greater than or equal to the threshold as having a strong correlation.

3. The multi-objective optimization method for injection molding process parameters based on a high-precision prediction model according to claim 2, characterized in that: In Step 2, when preprocessing the process parameter data through GAN, the specific steps are as follows: ① Initialize the generator and discriminator networks: set the initial parameters of the generator G and the discriminator D; ② Set training parameters: set the input random noise z dimension, batch size, total number of training rounds, learning rate, optimizer, and momentum parameters of the generator G; ③Define the overall optimization goal: The overall optimization goal expression is as follows: Where: D(x) represents the probability that the discriminator D judges the real data x as real; G(z) represents the forged sample generated by the generator G based on the random noise z; ④ Training cycle: Initial synthetic data is generated by inputting random noise z into the generator G, and inputting it into the discriminator D for classification together with the real data. The discriminator D optimizes its own parameters by calculating the loss function to enhance the ability to distinguish between real data and generated data. At the same time, the generator G optimizes its own parameters according to the feedback of the discriminator D, making the generated data gradually close to the real data, until the discriminator D can no longer effectively distinguish between real data and generated data, and finally outputs synthetic data; ⑤ When the discriminator D cannot distinguish the generated data, the k-means clustering algorithm is used to perform cluster analysis on the original data and the generated data, and the t-SNE method is used to reduce the dimension of the data for visual analysis.

4. The multi-objective optimization method for injection molding process parameters based on a high-precision prediction model according to claim 3 is characterized in that: In Step 3, the KOA-IVYA hybrid optimization algorithm is used as follows: ①KOA global search: The individual position update formula of KOA is as follows: Where: X i (t+1) is the updated position after t+1 iterations; X i (t) is the position after t iterations; f is a flag to change the search direction; V i (t) is the speed required for celestial body i to reach its new position; F gi (t) is the gravitational function between the current position and the position of the optimal solution; |r| is a randomly generated number based on the normal distribution; X s (t) is the position of the current best solution; ②IVYA local development: IVYA's individual position update formula is as follows: X i (t+1)=X i (t)+β1|X i+1 (t)-X i (t)|+G i (t) Where: G i (t) is the gain vector, used to increase randomness; ③Dynamic population adjustment: The formula for changing the population size through the number of iterations is as follows: IVYA_PopSize=SearchAgen ts_no-KOA_PopSize Where: KOA_PopSize is the KOA population size; IVYA_PopSize is the IVYA population size; SearchAgents_no is the total number of individuals at the beginning; t is the current number of iterations; Max_iteration is the maximum number of iterations.

5. The multi-objective optimization method for injection molding process parameters based on a high-precision prediction model according to claim 4, characterized in that: In Step 5, when using MOCGO for multi-objective optimization, candidate solution positions are generated in four different ways: based on the optimal solution position, based on the optimal solution and the mean group, based on the mean group and the optimal solution, and completely random generation. Generate new candidate solutions based on the current global optimal solution: X i,new =a1·(I1·X best -I2·X mean ) Generate new solutions around the average solution position: X i,new =X best +a2·(I3·X mean -I4) Generate new solutions around the optimal solution location: X i,new =X mean +a3·(I5·X best -I6) Where: a i (i is 1, 2, 3) is a randomly generated scaling factor; I i (i is 1, 2, 3, 4, 5, 6) is a randomly generated integer (1 or 2) that controls the relative influence between the leader and the mean group; X best is the current optimal solution; X mean is the mean position of the population; Introducing random changes in the solution position, the formula is: X i,new =unifrnd(lb,ub) Where: unifrnd(lb,ub) is a uniformly distributed random number generator, generating values ​​between the upper and lower bounds lb and ub; The generated potential solution is evaluated for its fitness through the objective function, and compared with other solutions for dominance, and non-dominated solutions are retained. After the iteration, the Pareto front is formed.

6. The multi-objective optimization method for injection molding process parameters based on a high-precision prediction model according to claim 5, characterized in that: Step 6 is as follows: ① Use AHP to construct a pairwise comparison matrix between indicators based on expert judgment, and give the subjective weight ratio W of each indicator. AHP ; ② Calculate the objective weight ratio W by using data distribution information through EW EW , quantify the importance of each indicator; ③ Through GM, subjective weight and objective weight are integrated, and the advantages of both are combined to generate the final weight ratio W GM ; ④ Based on the final weight, score each solution in the solution set, sort the solutions on the Pareto frontier, and select the process parameter combination with the best comprehensive performance.

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