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

Abstract

The application discloses a kind of based on high-precision prediction model injection molding process parameter multi-objective optimization method, based on simulation test result, first by MIC and GAN to data is enhanced, to improve the quality of simulation data;Then utilize the mixed framework of KOA and IVYA to carry out hyperparameter tuning;Subsequently adopt SHAP method to enhance the explainability of XGBoost model, and provide the search range of optimized process parameter;Finally, application MOCGO finds the Pareto front of quality target, and determines optimal process parameter combination.Test results show that, using the process parameter combination optimized by the method of the application makes warping deformation and volume shrinkage rate reduce by 35.7% and 10.1% respectively, can realize effectively reduce the warping deformation and volume shrinkage rate of forming plastic part, and then obtain high-quality plastic product, can provide theoretical basis and data support for obtaining injection molding optimal process parameter combination.

Description

Technical Field

[0001] This 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 MIC-GAN-KOA-IVYA-XGBoost and MOCGO high-precision prediction models, belonging to the field of injection molding technology. Background Technology

[0002] In the field of injection molding technology in modern manufacturing, optimizing process parameters is crucial for improving product quality, reducing scrap rates, and increasing production efficiency. Warpage and shrinkage are two of the most common and critical quality issues in injection molding. Warpage leads to deviations in product shape, while shrinkage affects dimensional accuracy. Controlling these two directly impacts product reliability and lifespan. Therefore, achieving multi-objective optimization under complex process conditions and minimizing these two defects has become a widely studied research hotspot.

[0003] Simulation techniques such as finite element analysis and Moldflow analysis are widely used in injection molding process simulation to help predict warpage and volume shrinkage. Generally, the injection molding process of thin-walled plastic parts is first simulated and analyzed using Moldflow software to analyze cooling effects and flow properties. Then, a mathematical model is constructed based on the simulation data to establish the relationship between quality objectives and process parameters. Finally, a search-based optimization algorithm is used to obtain the optimal combination of process parameters. For example, Cao Y et al. constructed an Adaptive Network Fuzzy Inference System (ANFIS) for warpage deformation and process parameters, and used a Genetic Algorithm (GA) to obtain the optimal process parameter scheme; Sun Zheng et al. constructed a mathematical proxy model for warpage deformation, volume shrinkage rate, and process parameters based on a gradient-enhanced Kriging (GEK) model, used a multi-objective differential evolution (MODE) algorithm to search for Pareto solutions, and determined the optimal process parameter scheme based on weighted coefficients; Liu X et al. constructed a mathematical proxy model for warpage deformation, volume shrinkage rate, and process parameters using a GA-optimized Extreme Learning Machine (ELM) model, applied a multi-objective firefly algorithm combined with the GRA-TOPSIS multi-objective decision-making method to determine the final optimal process parameter scheme.

[0004] In the study of practical injection molding problems, extracting key process parameters from simulation data remains a challenge. Multiple interrelated objectives and constraints often require comprehensive consideration and trade-offs. For example, warpage and volume shrinkage defects: minimizing warpage by reducing the cooling rate will increase volume shrinkage due to prolonged cooling time. Multi-objective optimization, as a method for solving optimization problems involving multiple conflicting objectives, aims to find reasonable trade-offs among these objectives and generate a Pareto front of a set of multi-objective optimal values. Current research on multi-objective optimization often transforms multi-objective problems into single-objective problems using the idea of ​​weighted combination. Commonly used methods include Grey Relational Analysis (GRA), Top-Order Solution Approximation (TOPSIS), Entropy Weighting, and Fuzzy Comprehensive Evaluation (FCE). However, from the perspective of multiple objectives, all objectives are usually mutually restrictive; improving one objective often comes at the expense of others. Therefore, a multi-objective optimization problem typically generates a large number of non-dominated solutions (Pareto solutions). Currently, in multi-objective optimization research on 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 overall goal remains a challenge in the industry. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a multi-objective optimization method for injection molding process parameters based on a high-precision prediction model. This method can effectively reduce the warpage and volume shrinkage of molded plastic parts, thereby obtaining high-quality plastic products. It can provide theoretical basis and data support for obtaining the optimal combination of injection molding process parameters.

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

[0007] Step 1: Warpage deformation and volume shrinkage rate are taken as quality optimization targets. Process parameters that affect these two targets are selected as optimization design variables. The range of process parameters is determined according to the recommended values ​​of the process parameters. The range of process parameters is used as the experimental design space. Injection molding simulation is performed based on Moldflow to obtain the experimental results of quality optimization targets.

[0008] Step 2: Based on the simulation test results, the process parameter data are preprocessed using MIC and GAN.

[0009] Step 3: Use the KOA-IVYA hybrid optimization algorithm to fine-tune 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 using the SHAP interpretation method. By generating a feature importance map, clarify the degree of influence of each process parameter on the prediction results and provide the optimized process parameter search range.

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

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

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

[0014] ① Generate scatter plots of variables and divide the data into grids: Represent the values ​​of process parameters (x) and quality targets (y) in a two-dimensional space using scatter plots, and divide the data into grids;

[0015] ② Calculate the mutual information of each grid: Under a given grid division, when calculating the mutual information, the probability distribution of the variables is replaced by the frequency of the scattered points in the grid. The mutual information measures the dependency between the process parameters (x) and the quality target (y).

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

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

[0018]

[0019] In the formula: I(x,y) represents mutual information; log(min{x|,|y}) is the normalization adjustment for the mesh partitioning;

[0020] ⑤ Screening of important process parameters: After calculating the MIC values ​​of all process parameters for the quality target, compare the MIC values ​​with the preset thresholds. Select process parameters with MIC values ​​greater than or equal to the thresholds, which are considered to have strong correlation.

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

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

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

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

[0025]

[0026] In the formula: D(x) represents the probability that the discriminator D judges the real data x as real; G(z) represents the fake sample generated by the generator G based on random noise z;

[0027] ④ Training loop: Initial synthetic data is generated by inputting random noise z into generator G, and then input into discriminator D along with real data for classification. Discriminator D optimizes its own parameters by calculating the loss function to enhance its ability to distinguish between real data and generated data. At the same time, generator G optimizes its own parameters based on the feedback from discriminator D, so that the generated data gradually approaches the real data, until discriminator D can no longer effectively distinguish between real data and generated data, and finally outputs synthetic data.

[0028] ⑤ 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, and the t-SNE method is used to reduce the dimensionality of the data for visualization analysis.

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

[0030] ①KOA Global Search:

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

[0032]

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

[0034] ②Partial development of IVYA:

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

[0036] X i (t+1)=X i (t)+β1|X i+1 (t)-X i (t)|+G i (t)

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

[0038] ③ Dynamic population adjustment:

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

[0040]

[0041] IVYA_PopSize=SearchAgen ts_no-KOA_PopSize

[0042] In the formula: 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 iteration number; Max_iteration is the maximum number of iterations.

[0043] Furthermore, in Step 5, when using MOCGO for multi-objective optimization, candidate solution positions are generated in four different ways: based on the optimal solution location, based on the optimal solution and the mean population, based on the mean population and the optimal solution, and completely randomized generation.

[0044] Based on the current global optimal solution, generate new candidate solutions:

[0045] X i,new =a1·(I1·X best -I2·X mean )

[0046] Generate new solutions around the position of the average solution:

[0047] X i,new =X best +a2·(I3·X mean -I4)

[0048] Generate new solutions around the location of the optimal solution:

[0049] X i,new =X mean +a3·(I5·X best -I6)

[0050] In the formula: a i (i = 1, 2, 3) is a randomly generated scaling factor; I i (i = 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 It is the current optimal solution; X mean It is the average position of the population;

[0051] Introducing random variations at the solution location, the formula is:

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

[0053] In the formula: unifrnd(lb,ub) is a uniformly distributed random number generator that generates values ​​between the upper and lower bounds lb and ub;

[0054] The fitness of the generated potential solutions is evaluated using the objective function, and their dominance is compared with other solutions. Non-dominated solutions are retained, and the Pareto front is formed after the iteration is completed.

[0055] Furthermore, Step 6 is detailed below:

[0056] ① Using AHP (Analytical Hierarchy Process) to construct pairwise comparison matrices between indicators based on expert judgment, the subjective weight ratio W of each indicator is given. AHP ;

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

[0058] ③ By using GM to integrate subjective and objective weights, the advantages of both are combined to generate the final weight ratio W. GM ;

[0059] ④ Based on the final weights, each solution in the solution set is scored, and the solutions on the Pareto front are sorted to select the combination of process parameters with the best overall performance.

[0060] Compared with existing technologies, this multi-objective optimization method for injection molding process parameters based on a high-precision prediction model is grounded in simulation results. First, it enhances the data by using maximum mutual information coefficient (MIC) and generative adversarial networks (GANs) to improve the quality of the simulation data. Then, it performs hyperparameter tuning using a hybrid framework of Kepler optimization algorithm (KOA) and Ivy League optimization algorithm (IVYA). Subsequently, it employs the Shapley additive interpretation (SHAP) method to enhance the interpretability of the extreme gradient boosting (XGBoost) model and provides the search range for the optimized process parameters. Finally, it applies multi-objective chaotic game optimization (MOCGO) to find the Pareto front of the quality objective and determine the optimal combination of process parameters. Experimental results show that the optimized combination of process parameters reduces warpage and volume shrinkage by 35.7% and 10.1%, respectively, effectively reducing warpage and volume shrinkage in molded parts, thus obtaining high-quality products. This provides a theoretical basis and data support for obtaining the optimal combination of injection molding process parameters. Attached Figure Description

[0061] Figure 1 This is a 3D model of a sensor housing made of ABS plastic injection molding, where (a) is a front view of the sensor housing and (b) is a back view of the sensor housing.

[0062] Figure 2 These are diagrams of the model flow simulation analysis model, where (a) is the front view of the model flow simulation analysis model and (b) is the back view of the model flow simulation analysis model.

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

[0064] Figure 4 The graphs show the comparison of the calculated MIC values ​​of all process parameters for the quality target with the preset threshold of 0.3, where (a) is a comparison graph of the MIC values ​​of warpage deformation and (b) is a comparison graph of the MIC values ​​of volume shrinkage rate.

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

[0066] Figure 6 These are visualizations of the synthesized data, where (a) is the original data graph and (b) is the generated data graph;

[0067] Figure 7 These are comparison charts of XGBoost models with different data processing methods, where (a) is the warping deformation chart and (b) is the volume shrinkage rate chart.

[0068] Figure 8 These are diagrams illustrating the iterative convergence of the optimization algorithm, where (a) is a diagram illustrating the iterative convergence of the warping deformation prediction model and (b) is a diagram illustrating the iterative convergence of the volume shrinkage prediction model.

[0069] Figure 9 These are model accuracy comparison charts, where (a) is a comparison chart of warping deformation prediction model accuracy and (b) is a comparison chart of volume shrinkage prediction model accuracy.

[0070] Figure 10 These are SHAP summary diagrams, where (a) is a SHAP summary diagram with warped deformation and (b) is a SHAP summary diagram with volume shrinkage.

[0071] Figure 11 These are Pareto front plots; where (a) is the Pareto front plot before SHAP optimization and (b) is the Pareto front plot after SHAP optimization.

[0072] Figure 12 The diagram shows the simulation values ​​of the optimal combination of process parameters; (a) is a diagram showing the warping deformation and (b) is a diagram showing the volume shrinkage rate. Detailed Implementation

[0073] This multi-objective optimization method for injection molding process parameters based on a high-precision prediction model first enhances the data by using maximum mutual information coefficient (MIC) and generative adversarial network (GAN) to improve the quality of simulation data. Then, it uses a hybrid framework of Kepler optimization algorithm (KOA) and Ivy optimization algorithm (IVYA) for hyperparameter tuning. Subsequently, the Shapley additive interpretation (SHAP) method is used to enhance the interpretability of the extreme gradient boosting (XGBoost) model and provide the search range of optimized process parameters. Finally, multi-objective chaotic game optimization (MOCGO) is applied to find the Pareto front of the quality objective and determine the optimal combination of process parameters.

[0074] The present invention will be specifically described below using an injection-molded sensor housing as an example.

[0075] The geometric model of the sensor housing made of ABS plastic injection molding is as follows: Figure 1 (a) Figure 1 As shown in (b), the sensor housing requires adequate heat dissipation and a lightweight design. The dimensions of the plastic part are 216mm × 154mm × 50mm, and its volume is 239292mm². 3The average wall thickness is 2.16 mm. The interior and edges of the plastic part utilize a reinforcing rib structure to distribute external loads and reduce localized stress concentration. Simultaneously, strict surface quality requirements are imposed on the mating posts and holes to ensure the precision and stability of mating with other components. This plastic part is required to have a warpage deformation and volume shrinkage rate not exceeding 0.584 mm and 7%, respectively.

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

[0077] The 3D model of the plastic part was imported into Moldflow software for mesh generation. The mesh was created using triangular elements. Since flow analysis may result in drastic changes in flow pressure, temperature, and velocity, potentially leading to analysis failure, long and thin elements should be avoided as much as possible. Mesh statistics show that the free edges and multi-edges of the plastic part are 0, connected components are 1, misaligned elements are 0, and the aspect ratio is less than 6.00. The generated mesh meets the requirements of the 3D model, with a surface mesh matching rate of 92% for flow analysis and 93% for warpage deformation analysis.

[0078] After the mesh is generated, establish as follows: Figure 2 (a) Figure 2 (b) shows the mold flow simulation analysis model including the gating system and the cooling system. The red pipes represent the gating system, which consists of the gate and the main runner. It can smoothly fill the mold cavity with the plastic melt, resulting in a plastic product with a clear outline and excellent internal quality. The blue pipes represent the cooling system, which consists of straight-through channels and circumferential channels. In the molding cycle of plastic parts, the cooling time of the mold accounts for more than 2 / 3 of the entire cycle, significantly affecting molding efficiency and quality.

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

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

[0081] Using the formula for warpage deformation:

[0082] a. Temperature Distribution Analysis: First, the temperature distribution in different regions during the cooling process is calculated using the heat conduction equation. This process needs to consider the influence of the initial melt temperature and mold temperature on various parts of the plastic part in order to obtain an accurate temperature field.

[0083] b. Calculation of residual stress: Find the coefficient of thermal expansion (β) and Young's modulus (E) of ABS material, and calculate the residual stress (σ) using temperature changes.res The following formula is used:

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

[0085] In the formula: T final The temperature after cooling; T initial Let be the melt temperature. Substitute the calculated temperature change into the formula to determine σ in different regions. res .

[0086] c. Determination of characteristic length (L) and calculation of 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] like Figure 3 (a) The simulation results show that the maximum warpage deformation is 0.7645 mm, which exceeds the design requirement of 0.6 mm for the plastic part.

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

[0090] Using the formula for volume shrinkage:

[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 239,292mm 3 .

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

[0093] c. Calculate volume shrinkage:

[0094]

[0095] In the formula: V mold V represents the initial volume of the mold cavity; final This is the final volume after cooling. For example... Figure 3 (b) The simulation results show that the maximum volume shrinkage rate of the plastic part is 7.124%, which exceeds the design requirement of 7%.

[0096] These results, which exceed the design scope, indicate the need for further optimization of the injection molding process to ensure that the quality and performance of the molded parts meet the expected requirements.

[0097] 2. Data Preprocessing

[0098] To address the issues of limited experimental data and imbalanced sample distribution in simulation datasets, the Maximum Information Coefficient (MIC) and Generative Adversarial Network (GAN) methods are employed to optimize process parameters such as melt temperature Tm, mold temperature Te, injection pressure Pi, holding pressure Pk, injection time ti, holding time tk, and cooling time t. c Preprocessing is performed to meet quality targets (warpage W, volume shrinkage V).

[0099] 2.1 MIC Feature Selection

[0100] The calculation of MIC (Mutual Influence Limit) includes mesh generation, mutual information calculation, and mesh optimization, aiming to reveal the degree of interaction between process parameters and quality objectives. In data preprocessing, the raw data is first divided into experimental arrangements using a central composite design (CCD), resulting in 152 combinations of process parameters. Then, the warpage and volume shrinkage rates of these 152 combinations are obtained using the Moldflow simulation model as quality objectives. The steps for optimizing the injection molding process are as follows:

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

[0102] b. Calculate mutual information for each grid cell: Given a grid division, when calculating mutual information, the probability distribution of the variables is replaced by the frequency of scattered points distributed in the grid, i.e., the number of scattered points in each grid cell is counted. Mutual information measures the dependency between process parameters (x) and quality objectives (y).

[0103] c. Obtain the maximum mutual information: For a specific number of rows and columns, calculate the mutual information values ​​under all possible grid partitions and select the maximum value. This maximum value is denoted as the maximum mutual information I. max (x,y).

[0104] d. Calculate MIC: Calculate the maximum mutual information value under multiple different combinations of row number x and column number y.

[0105]

[0106] In the formula: I(x,y) is mutual information, 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 the mesh to ensure the stability and comparability of MIC values.

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

[0108] 2.2 GAN Data Augmentation

[0109] A Generative Adversarial Network (GAN) consists of a generator and a discriminator. The generator G continuously attempts to generate new combinations of process parameters and quality targets by adjusting the input random noise z. The discriminator D judges the similarity between the generator's output and real data, prompting the generator to generate process parameter combinations that are more realistic. To achieve this process, the specific steps include:

[0110] a. Initialize the generator and discriminator networks: Set the initial parameters of the generator G and 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 training parameters: The input random noise z dimension of the generator G is set to 100, the batch size is set to 8, the total number of training rounds is set to 2000, the learning rate is set to 0.0001, the optimizer is 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, expressed as follows:

[0113]

[0114] In the formula: D(x) represents the probability that the discriminator D judges the real data x as real; G(z) represents the fake sample generated by the generator G based on random noise z.

[0115] d. Training cycle: such as Figure 5 As shown, during GAN training, initial synthetic data is first generated by inputting random noise z into the generator G, and then input into the discriminator D along with real data for classification. The discriminator D optimizes its parameters by calculating the loss function to enhance its ability to distinguish between real and generated data. At the same time, the generator G optimizes its parameters based on the feedback from the discriminator D, making the generated data gradually approach the real data. Through the alternating game training between the generator G and the discriminator D, the authenticity and quality of the generated data are continuously improved until the discriminator D can no longer effectively distinguish between real and generated data, and finally outputs 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 and generated data, dividing them into 6 classes. Then, the 7-dimensional data is reduced to 2 dimensions using the t-SNE method for visualization analysis. Figure 6 From the visualization results, out of 200 generated datasets, 48 ​​generated datasets effectively address the issues of uneven sample distribution and insufficient data volume in the original dataset. Furthermore, as... Figure 7 As shown, after MIC feature selection and GAN data augmentation, the initially 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 integrates multiple CART trees using Gradient Tree Boosting. To determine the optimal configuration of the XGBoost model, this invention employs a KOA-IVYA hybrid optimization algorithm to explore the hyperparameter space. This method aims to improve model accuracy, balance model complexity, and prevent over-optimization. The hyperparameters of the XGBoost model that need optimization are shown in Table 1 below.

[0119] Table 1. Hyperparameters to be optimized in the XGBoost model

[0120]

[0121] 3.1 Design of IVYA-KOA Hybrid Optimization Algorithm

[0122] The IVYA-KOA hybrid optimization algorithm combines KOA and IVYA to achieve an organic integration of global search and local exploitation. KOA simulates the gravitational effects of celestial bodies, using the gravitational function... Dynamic adjustments enhance global search capabilities; IVYA, on the other hand, simulates the growth behavior of ivy, relying on interactions between individuals to achieve local development. Specifically:

[0123] a.KOA Global Search:

[0124] In KOA, the gravitational function The dynamic adjustment of the gravity function gives KOA a stronger global search capability in the early stages, while as iterations progress, the gravity function... As the number of individuals decreases, they gradually concentrate near the current global optimum. The formula for updating the individual position in KOA is as follows:

[0125]

[0126] In the formula: X i (t+1) is the position updated after t+1 iterations; X i (t) is the position after t iterations; f is the flag indicating a change in the search direction; V i (t) is the velocity required for celestial body i to reach its new position; It is the gravitational function between the current position and the position of the optimal solution; |r| is a number randomly generated based on a normal distribution; X s (t) is the position of the current best solution.

[0127] b. Partial development of IVYA:

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

[0129] X i (t+1)=X i (t)+β1|X i+1 (t)-X i (t)|+G i (t)

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

[0131] c. Dynamic population adjustment:

[0132] To fully leverage the advantages of KOA global search and IVYA local search, dynamic population adjustment is employed. The formula for changing the population size based on the number of iterations is as follows:

[0133]

[0134] IVYA_PopSize=SearchAgen ts_no-KOA_PopSize

[0135] In the formula: 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 iteration number; Max_iteration is the maximum number of iterations. As the iteration number 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, determining the initial number of individuals. The initial M0 is 0.1, controlling the gravitational strength between individuals, and the gravitational decay factor (lambda) is 15 to adjust for the decay of gravity over time. Max_iteration is set to 100, limiting the algorithm's runtime. To improve evaluation accuracy, fitness values ​​are evaluated using normalized mean absolute error (MAE). Figure 8 As shown, in the warping deformation prediction model, the KOA-IVYA hybrid algorithm not only optimized the parameters to 0.059 in the first iteration, far lower than the individual algorithms KOA (0.12) and IVYA (0.095), but also reached 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 was observed in the volume shrinkage prediction model. In the first iteration, the optimal result was 0.081, far lower than the values ​​of KOA (0.178) and IVYA (0.145). Furthermore, the optimal configuration was achieved after 22 iterations, significantly exceeding the 61 iterations required by KOA and the 67 iterations required by IVYA. The iteration curves show that KOA performs better than IVYA in the early stages of iteration, while IVYA performs better in local optimization, thus improving the accuracy of the solution. Figure 9 As shown, MIC-GAN-KOA-IVYA-XGBoost performed best among the five fitting models, with the lowest RMSE, MAE, and MAPE. Furthermore, as shown in Table 2 below, the optimal evaluation metrics for the warpage prediction model were RMSE: 0.02, MAE: 0.0121, MAPE: 0.0212, and R0.02. 2 The optimal evaluation indexes for the body shrinkage prediction model are RMSE: 0.0881, MAE: 0.048, MAPE: 0.008, and R0.9915. 2 : 0.9909.

[0137] Table 2 Model Evaluation Indicators

[0138]

[0139] Ensemble learning models excel in many complex tasks, but their "black box" nature makes understanding their internal mechanisms difficult. SHAP analysis quantifies the contribution of each feature to the model's predictions, helping to identify key process parameters. This invention uses the SHAP library to calculate the SHAP value 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 results.

[0140] In injection molding, temperature, time, and pressure play crucial roles in molding quality and the performance of the final product. For example... Figure 10 As shown, melt temperature is the primary influencing factor; higher temperatures help improve material flowability and enhance product surface quality and density. However, melt temperature has different effects on warpage and shrinkage. Higher melt temperatures reduce warpage but increase shrinkage. Therefore, melt temperature should be appropriately increased to control warpage, while a trade-off must be struck when reducing shrinkage. Increasing mold temperature also helps reduce warpage and shrinkage, maintaining molding uniformity. From a time perspective, longer injection times facilitate full filling of the mold cavity, thus reducing warpage, while cooling time is more important in reducing shrinkage; appropriately extending the cooling time helps achieve uniform solidification. Injection pressure has a significant impact on shrinkage; higher injection pressure helps reduce shrinkage, while holding pressure has a relatively smaller impact on warpage and shrinkage, but proper adjustment can improve molding stability.

[0141] Therefore, when optimizing the injection molding process, priority should be given to controlling the melt temperature and injection time to reduce warpage, while adjusting the injection pressure and cooling time to effectively reduce volume shrinkage. After analyzing the SHAP summary diagram, the optimal ranges for each feature can be identified as shown in Table 3 below, thus providing a more accurate feature range for multi-objective chaotic game optimization (MOCGO) and further guiding the optimization process.

[0142] Table 3 Optimization Range of Process Parameters

[0143]

[0144]

[0145] 4. Multi-objective optimization

[0146] In the multi-objective optimization of injection molding processes, MOCGO and MIC-GAN-KOA-IVYA-AGBoost prediction models are used to further optimize the range of optimized process parameters to find a set of optimal process parameter combinations that simultaneously minimize warpage and volume shrinkage. MOCGO is a multi-objective optimization algorithm based on chaotic systems and game theory strategies, capable of efficient Pareto front search through dynamic archiving and selection strategies. Its parameter settings include Max_iteration of 100, population size of 50, grid expansion parameter (alpha) of 0.1, optimal solution selection pressure (beta) of 4, and archiving elimination pressure (gamma) of 2. Furthermore, candidate solution positions are generated in four different ways (based on optimal solution location, based on optimal solution and mean population, based on mean population and optimal solution, and completely randomly generated).

[0147] Based on the current global optimal solution, generate new candidate solutions:

[0148] X i,new=a1·(I1·X best -I2·X mean )

[0149] Generate new solutions around the position of the average solution:

[0150] X i,new =X best +a2·(I3·X mean -I4)

[0151] Generate new solutions around the location of the optimal solution:

[0152] X i,new =X mean +a3·(I5·X best -I6)

[0153] In the formula: a i (i = 1, 2, 3) is a randomly generated scaling factor; I i (i = 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 It is the current optimal solution; X mean It is the average position of the population.

[0154] Introducing random variations at the solution location, the formula is:

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

[0156] In the formula: unifrnd(lb,ub) is a uniformly distributed random number generator that generates values ​​between the upper and lower bounds lb and ub.

[0157] The generated latent solutions are evaluated for fitness using an objective function and compared with other solutions in terms of dominance, thus preserving non-dominated solutions. After iteration, a Pareto front is formed. Figure 11 As shown, compared to the unoptimized state, the parameter range optimized by SHAP analysis enabled MOCGO to converge to the Pareto front in the region with warpage deformation below 0.6 mm and volume shrinkage rate below 7% more quickly, even with the same 100 iterations. This result demonstrates that accurately identifying key process parameters and adjusting their optimization range through SHAP analysis can not only improve the distribution density and quality of the solution set but also effectively shorten the convergence time of multi-objective optimization algorithms.

[0158] 5. Experimental verification

[0159] To comprehensively evaluate the Pareto front, a combined approach using the Analytic Hierarchy Process (AHP), Entropy Weight Method (EW), and Game Theory Combinatorial Method (GM) is employed to calculate the comprehensive score for each solution. First, AHP is used to construct pairwise comparison matrices between indicators based on expert judgment, providing the subjective weight ratio W for each indicator. AHP The values ​​are (0.6771, 0.3229); then, the objective weight ratio W is calculated using data distribution information via EW. EW The weights are (0.5419, 0.4581), quantifying the importance of each indicator. Finally, the subjective and objective weights are integrated using GM to combine their advantages and generate the final weight ratio W. GM The values ​​are (0.6095, 0.3905). Based on the final weights, each solution in the solution set is scored, and the solutions on the Pareto front are ranked to select the combination of process parameters with the best overall performance.

[0160] As shown in Table 4 below, the target simulation values ​​for the original process parameter combination are (0.7645, 7.124), while the target predicted values ​​for the optimal process parameter combination decrease to (0.4913, 6.407), indicating that the warpage deformation and volume shrinkage rate are reduced by 35.7% and 10.1%, respectively. Figure 12 As 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, which verifies the accuracy and effectiveness of the multi-objective optimization process of the present invention.

[0161] Table 4: Top 5 combinations of process parameters scored

[0162]

[0163] Experimental results show that the optimized process parameter combination obtained by the multi-objective optimization method of injection molding process parameters based on the high-precision prediction model reduces the warpage deformation and volume shrinkage rate by 35.7% and 10.1%, respectively. This effectively reduces the warpage deformation and volume shrinkage rate of molded plastic parts, thereby obtaining high-quality plastic parts. This provides a theoretical basis and data support for obtaining the optimal combination of injection molding process parameters.

Claims

1. A multi-objective optimization method for injection molding process parameters based on a high-precision prediction model, characterized in that, Specifically, the following steps are included: Step 1: Warpage deformation and volume shrinkage rate are taken as quality optimization targets. Process parameters that affect these two targets are selected as optimization design variables. The range of process parameters is determined according to the recommended values ​​of the process parameters. The range of process parameters is used as the experimental design space. Injection molding simulation is performed based on Moldflow to obtain the experimental results of quality optimization targets. Step 2: Based on the simulation test results, the process parameter data are preprocessed using MIC and GAN. Step 3: Use the KOA-IVYA hybrid optimization algorithm to fine-tune the hyperparameters of the XGBoost model and construct the MIC-GAN-KOA-IVYA-XGBoost injection molding quality prediction model. Step 4: Analyze the MIC-GAN-KOA-IVYA-XGBoost injection molding quality prediction model using the SHAP interpretation method. By generating a feature importance map, clarify the degree of influence of each process parameter on the prediction results and provide the optimized process parameter search range. Step 5: Use MOCGO and MIC-GAN-KOA-IVYA-XGBoost prediction models to perform multi-objective optimization on the optimized process parameter range and obtain the Pareto front of the quality optimization objective. Step 6: Calculate the comprehensive score of each solution in the Pareto front of the obtained quality optimization objective using 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 using MIC, the specific steps are as follows: ① Generate a scatter plot of variables and divide it into grids: This involves processing parameters... and quality objectives The values ​​are represented in two-dimensional space using a scatter plot, and the data is divided into grids. ② Calculate the mutual information for each grid: Given a grid division, when calculating mutual information, the probability distribution of variables is replaced by the frequency of scattered points distributed in the grid, and the process parameters are measured through mutual information. and quality objectives Dependencies between them; ③ Obtain the maximum value of mutual information: Calculate the mutual information values ​​under all grid divisions and select the maximum value among them; ④ Calculate MIC: This involves considering multiple parameters representing different process parameters. The number of rows and the values ​​representing different quality objectives Given a certain number of columns, the maximum mutual information value is calculated using the following formula: In the formula: For mutual information; It is a normalization adjustment of the grid division; ⑤ Screening of important process parameters: After calculating the MIC values ​​of all process parameters for the quality target, compare the MIC values ​​with the preset thresholds. Select process parameters with MIC values ​​greater than or equal to the thresholds, which are considered to have 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 using GAN, the specific steps are as follows: ① Initialize the generator and discriminator networks: Configure the generator and discriminator The initial parameters; ② Set training parameters: Configure the generator Input random noise Dimensions, batch size, total number of training epochs, learning rate, optimizer, momentum parameter; ③ Define the overall optimization objective: The expression for the overall optimization objective is as follows: In the formula: Discriminator For real data The probability of it being determined to be true; Represents generator According to random noise Generated fake samples; ④ Training cycle: By using random noise Input generator Generate initial synthetic data and input it into the discriminator along with real data. Classification, discriminator By calculating the loss function and optimizing its own parameters, the generator can enhance its ability to distinguish between real and generated data. According to the discriminator The feedback optimizes its own parameters, making the generated data gradually approach the real data, until the discriminator... It cannot effectively distinguish between real data and generated data, and ultimately outputs synthetic data. ⑤ When the discriminator When the generated data cannot be distinguished, 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 dimensionality of the data for visualization analysis.

4. The multi-objective optimization method for injection molding process parameters based on a high-precision prediction model according to claim 3, characterized in that, In Step 3, the KOA-IVYA hybrid optimization algorithm is used as follows: ①KOA Global Search: The KOA individual location update formula is as follows: In the formula: yes The position updated after the next iteration; yes The position after the next iteration; It's a sign that the search direction has changed; It is a celestial body The speed required to reach the new location; It is the gravitational function between the current position and the position of the optimal solution; These are numbers randomly generated based on a normal distribution. This is the current position of the optimal solution; ②Partial development of IVYA: The IVYA individual location update formula is as follows: In the formula: It is a gain vector used to increase randomness; ③ Dynamic population adjustment: The formula for changing the population size through the number of iterations is as follows: In the formula: The size of the KOA population; The population size of IVYA; This represents the initial total number of individuals; This represents the current iteration number; This represents 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 location, based on the optimal solution and the mean population, based on the mean population and the optimal solution, and completely randomized generation. Based on the current global optimal solution, generate new candidate solutions: Generate new solutions around the position of the average solution: Generate new solutions around the location of the optimal solution: In the formula: It is a randomly generated scaling factor, where The numbers are 1, 2, and 3. It is a randomly generated integer, 1 or 2, which controls the relative influence between the leader and the mean group. The numbers are 1, 2, 3, 4, 5, 6. This is the current optimal solution; It is the average position of the population; Introducing random variations at the solution location, the formula is: In the formula: It is a uniformly distributed random number generator, generating values ​​within upper and lower bounds. and between; The fitness of the generated potential solutions is evaluated using the objective function, and their dominance is compared with other solutions. Non-dominated solutions are retained, and the Pareto front is formed after the iteration is completed.

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 Using AHP (Analytical Hierarchy Process) to construct pairwise comparison matrices between indicators based on expert judgment, the subjective weight ratio W of each indicator is given. AHP ; ② Calculate the objective weight ratio W using data distribution information through EW. EW Quantify the importance of each indicator; ③ By integrating subjective and objective weights through GM, the advantages of both are combined to generate the final weight ratio WGM; ④ Based on the final weights, each solution in the solution set is scored, and the solutions on the Pareto front are sorted to select the combination of process parameters with the best overall performance.

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