Injection molding process parameter multi-objective optimization method

Abstract

The invention discloses a multi-objective optimization method for injection molding process parameters. The method comprises the following steps: firstly, obtaining a simulation result data set based on Moldflow simulation analysis and CCF; then, an NGO-XGBoost is adopted to construct an injection molding quality optimization model; then explaining and analyzing the NGO-XGBoost model by using an SHAP method to obtain importance and positive and negative influences of each optimization design variable on a prediction quality optimization target, and performing multi-target optimization through MOMVO to obtain a Pareto leading edge; and finally, determining an optimal combination of process parameters through a CRITIC-TOPSIS evaluation method. According to the method, the buckling deformation and the volume shrinkage of the ABS plastic injection molding plastic part can be effectively reduced, so that a high-quality ABS plastic part product is obtained, and a theoretical basis and data support can be provided for obtaining an optimal technological parameter combination of ABS plastic injection molding.

Description

Technical Field

[0001] The invention relates to a multi-objective optimization method for injection molding process parameters, in particular to a multi-objective optimization method for injection molding process parameters based on SHAP-NGO-XGBoost and MOMVO, and belongs to the technical field of injection molding processing. Background Art

[0002] ABS plastic is a terpolymer of acrylonitrile, butadiene and styrene. ABS plastic has excellent high toughness, heat resistance and good processing performance. It is a "tough, hard and rigid" material with easy raw materials, good comprehensive performance, low price and wide application. It is widely used in manufacturing industries such as machinery, electrical, textile, automobile, aircraft, and shipbuilding, as well as chemical industry. Sensor housings are usually made of ABS plastic. For example, in automotive parts, ABS plastic sensor housings are used in anti-lock braking systems to improve braking effects and vehicle stability; in electronic products, ABS plastic sensor housings are used to protect sensor components to ensure their normal operation. However, ABS plastics will inevitably have injection defects such as warping and volume shrinkage during the injection molding process. Especially for thin-walled plastic parts, how to adjust and optimize process parameters such as temperature, time, and pressure to improve the quality of plastic parts, reduce defects, and achieve the accuracy of plastic part dimensions, appearance quality, and stability of physical properties is an important part of ABS plastic injection molding research.

[0003] At present, combining simulation analysis and mathematical model prediction is a common method for optimizing process parameters. Generally, the injection molding process of thin-walled plastic parts is first simulated and analyzed by Moldflow software to analyze the cooling effect and flow performance, and then a mathematical model is constructed based on the simulation data to construct the relationship between the quality target and the process parameters. Finally, the optimal combination of process parameters is obtained through a search-based optimization algorithm. For example, Cao Y et al. constructed an adaptive network fuzzy inference system (ANFIS) between warpage and process parameters, and used a genetic algorithm (GA) to obtain the optimal solution for process parameters; Sun Zheng et al. constructed a mathematical proxy model between warpage, volume shrinkage and process parameters based on the gradient enhanced Kriging (GEK) model, used a multi-objective differential evolution (MODE) algorithm to search for Pareto solutions, and determined the optimal solution for process parameters based on weighted coefficients; Liu X et al. constructed a mathematical proxy model between warpage, volume shrinkage and process parameters with the help of an extreme learning machine (ELM) model optimized by GA, and applied a multi-objective firefly algorithm and combined it with the GRA-TOPSIS multi-objective decision-making method to determine the final optimal solution for process parameters.

[0004] In the study of practical problems of injection molding, multiple interrelated objectives and constraints usually need to be considered and weighed. For example, when the cooling rate is reduced to minimize the warpage, the volume shrinkage will also increase due to the extension of the cooling time. Multi-objective optimization is a method for solving optimization problems involving multiple conflicting objectives. Its purpose is to find a reasonable trade-off between multiple objectives and generate a Pareto frontier of a set of multi-objective optimal values. At present, the research on multi-objective optimization usually transforms the multi-objective problem into a single-objective problem through the idea of ​​weighted combination. Commonly used methods include grey relational analysis (GRA), topology of successive ideal solutions (TOPSIS), entropy weight and fuzzy comprehensive evaluation (FCE). However, from the perspective of multiple objectives, all objectives are usually mutually constrained, 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. At present, in the study of 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] In view of the above problems, the present invention provides a multi-objective optimization method for injection molding process parameters, which can effectively reduce the warpage deformation and volume shrinkage of ABS plastic injection-molded parts, thereby obtaining high-quality ABS plastic products, and can provide a theoretical basis and data support for obtaining the optimal process parameter combination for ABS plastic injection molding.

[0006] To achieve the above purpose, the multi-objective optimization method of injection molding process parameters specifically includes the following steps:

[0007] 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 design the CCF test with the value range of each process parameter as the experimental design space, and perform injection molding simulation based on Moldflow to obtain the quality optimization target test results;

[0008] Step 2: Based on the simulation test results, the XGBoost model is optimized using the NGO optimization algorithm to construct the NGO-XGBoost injection molding quality prediction model;

[0009] Step 3: Analyze the NGO-XGBoost model through the SHAP interpretation method to obtain the importance and positive and negative impact of each optimization design variable on the prediction quality optimization target, and obtain the Pareto frontier of the quality optimization target through multi-objective optimization through MOMVO;

[0010] Step 4: Determine the optimal combination of process parameters in the Pareto frontier of the obtained quality optimization target through the CRITIC-TOPSIS evaluation method.

[0011] Furthermore, in Step 2, the objective function obj of the XGBoost model is defined as follows:

[0012]

[0013] Where: is the loss function, where y i represents the actual value of sample i, represents the predicted value of sample i; Ω(f k ) is a regularization term, which represents the model complexity of the k-th decision tree, where f K represents the Kth decision tree;

[0014] The objective function regularization term of the XGBoost model is defined as follows:

[0015]

[0016] Where: γ is the difficulty coefficient of node segmentation; T is the depth of the current subtree; λ is the regularization parameter that controls the weight; ω is the weight of the leaf node.

[0017] Furthermore, in Step 2, when the NGO optimization algorithm is used to optimize the XGBoost model, the learning rate, the maximum depth of the tree, and the minimum weight of the leaf node are used as hyperparameters to be optimized. The initialization value of the number of hyperparameter combinations and the maximum number of iterations of the NGO optimization algorithm are set. The XGBoost model is trained by using a hyperparameter combination with a number as the initialization value of the number of hyperparameter combinations in each iteration process. Finally, the fitness value of the corresponding hyperparameter combination is calculated according to the model performance index. The lower the fitness value, the better the hyperparameter combination.

[0018] Furthermore, in Step 3, the NGO-XGBoost model is analyzed by the SHAP interpretation method, as follows:

[0019] ①Use TreeExplainer as the SHAP interpreter;

[0020] ② Calculate the SHAP value of each feature by providing a sample of the dataset of the NGO-XGBoost model;

[0021] ③ Use the visualization function of the SHAP interpretability tool to explain the prediction logic of the model and generate a SHAP summary graph.

[0022] Furthermore, in Step 3, the Pareto frontier of the quality optimization objective is obtained through multi-objective optimization through MOMVO, as follows:

[0023] ① Set MOMVO parameters, clarify the objective function, and initialize related variables and archives;

[0024] ② Calculate the wormhole existence probability WEP, travel distance rate TDR and fitness value in the main loop;

[0025] ③ Sort the solutions according to the fitness value, select the non-dominated solutions, update the solution set and save it in the archive.

[0026] ④ Check whether the file size of the current solution set exceeds the specified size. If the file size exceeds the preset range, perform a trimming operation to remove the excess solution;

[0027] ⑤Use the roulette method to select a solution from the archive and update its position;

[0028] ⑥ Check the termination condition. If the maximum number of iterations has not been reached, continue the loop until the end to obtain the Pareto frontier.

[0029] Furthermore, in Step 4, when determining the optimal combination of process parameters in the Pareto frontier of the obtained quality optimization target through the CRITIC-TOPSIS evaluation method, firstly, the CRITIC method is used to assign weights to each evaluation indicator, and the weights of the warpage deformation and volume shrinkage are calculated according to the correlation coefficient and standard deviation between each target; then, following the steps of the TOPSIS method, the degree of proximity of each evaluation object to the idealized target is calculated according to the obtained weights to obtain a comprehensive evaluation score.

[0030] Compared with the existing technology, the multi-objective optimization method of injection molding process parameters is firstly based on Moldflow simulation analysis and central composite surface design (CCF) to obtain the simulation result data set; then the Northern Goshawk Optimized Extreme Gradient Boosting (NGO-XGBoost) based on data set fitting is used to construct the injection molding quality optimization model, and the NGO algorithm is used to explore the hyperparameter space, which can achieve the goals of improving model prediction accuracy, balancing model complexity, and preventing overfitting, and then determine the most effective configuration of the XGBoost model; then the SHAP (SHapley Additive exPlanations) method is used to interpret and analyze the NGO-XGBoost model, and the importance and positive and negative effects of each optimized design variable on the prediction quality optimization goal are obtained, and the Pareto frontier is obtained by multi-objective optimization through the multi-objective multiverse optimization algorithm (MOMVO); finally, the optimal combination of process parameters is determined by the CRITIC-TOPSIS evaluation method. Simulation verification shows that the prediction error of the NGO-XGBoost model for warpage and volume shrinkage is controlled within 5%, the model prediction accuracy is good, and the optimized warpage and volume shrinkage are significantly lower than the simulation results before optimization, which can provide a theoretical basis and data support for obtaining the optimal process parameter combination for ABS plastic injection molding. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a three-dimensional model diagram of a sensor housing plastic part made of ABS plastic injection molding, wherein (a) is a front view of the sensor housing plastic part, and (b) is a back view of the sensor housing plastic part;

[0032] Figure 2 1 is a mold flow simulation analysis model diagram, wherein (a) is a front view of the mold flow simulation analysis model, and (b) is a back view of the mold flow simulation analysis model;

[0033] Figure 3 The warpage and volume shrinkage views simulated based on the process parameter combination recommended by Moldflow software before optimization, where (a) is the simulation view of the warpage and (b) is the simulation view of the volume shrinkage;

[0034] Figure 4 It is the iterative convergence diagram of NGO;

[0035] Figure 5 SHAP summary diagrams, wherein (a) is a SHAP summary diagram of warpage, and (b) is a SHAP summary diagram of volume shrinkage;

[0036] Figure 6 It is a multi-objective optimization flowchart based on the MOMVO algorithm;

[0037] Figure 7 This is the Pareto frontier diagram obtained after multi-objective optimization based on the MOMVO algorithm;

[0038] Figure 8 : It is the simulation view of the optimal combination of warpage deformation and volume shrinkage after optimization, where (a) is the simulation view of warpage deformation and (b) is the simulation view of volume shrinkage; DETAILED DESCRIPTION

[0039] This multi-objective optimization method for injection molding process parameters takes the warpage deformation and volume shrinkage of ABS plastic products as quality optimization targets. Firstly, a simulation result data set is obtained based on Moldflow simulation analysis and central composite surface design (CCF). Then, an injection molding quality optimization model is constructed by using Northern Goshawk Optimized Extreme Gradient Boosting (NGO-XGBoost) based on data set fitting. Then, the SHAP (SHapley Additive exPlanations) method is used to interpret and analyze the NGO-XGBoost model, and the Pareto frontier is obtained by multi-objective optimization through the multi-objective multiverse optimization algorithm (MOMVO). Finally, the optimal combination of process parameters is determined by the CRITIC-TOPSIS evaluation method.

[0040] The present invention is specifically described below by taking a sensor housing plastic part made of ABS plastic injection molding as an example.

[0041] The geometric model of the sensor housing plastic part made of ABS plastic injection molding is as follows: Figure 1 (a) Figure 1 As shown in (b), the characteristics of the sensor housing require that it meet the requirements of sufficient heat dissipation and lightweight design. The overall dimensions of the plastic part are 216mm×154mm×50mm and the volume is 239292mm 3 The average wall thickness is 2.16mm. The plastic parts are internally and at the edges of the parts with reinforced ribs to disperse the external load and reduce local stress concentration. At the same time, the surface quality of the matching hole column and the matching hole is strictly required to ensure the matching accuracy and stability with other parts. The plastic parts require that the warpage deformation and volume shrinkage should not be greater than 0.584mm and 7% respectively.

[0042] The three-dimensional model of the plastic part is imported into the Moldflow software for meshing. The mesh is divided into triangular units. Since the flow pressure, temperature and velocity may change drastically during the flow analysis, which may lead to analysis failure, long and thin units 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 incorrectly oriented unit is 0, and the aspect ratio is less than 6.00. The divided mesh meets the requirements of the three-dimensional model and can ensure the accuracy of the model analysis results. It should also be noted that the mesh matching rate of the surface mesh model must reach more than 85% before the flow + pressure holding analysis can be performed. For the warpage deformation analysis, the matching rate must reach more than 90%.

[0043] After the grid is divided, create Figure 2 (a) Figure 2 (b) shows the mold flow simulation analysis model including the pouring system and the cooling system. The red pipe is the pouring system, which consists of the gate and the main channel, and can smoothly fill the mold cavity with the plastic melt to obtain a plastic product with a clear outline and excellent internal quality. The blue pipe is the cooling system, which consists of a straight water channel and a circular water channel. During the molding cycle of the plastic part, the cooling time of the mold accounts for more than 2 / 3 of the entire cycle, so the cooling effect has a great influence on the molding efficiency and the quality of the plastic part.

[0044] The analysis sequence of Moldflow simulation is set as: cooling-filling-holding-warping. The ABS material grade is PA-757, and the process parameter combination recommended by the software is: melt temperature 210℃, mold temperature 45℃, holding pressure 80MPa, and molding cycle time 30s. After the analysis is completed, Figure 3 (a) Figure 3 As shown in (b), the quality target warpage deformation and volume shrinkage are 0.7645 mm and 7.124% respectively, both of which do not meet the requirements of plastic products.

[0045] Step 1. Determine the quality optimization target, select the injection molding process parameters and their value ranges, use the value ranges of each process parameter as the experimental design space, design the CCF test according to the value ranges of each process parameter, and perform injection molding simulation based on Moldflow to obtain the quality optimization target test results.

[0046] Taking the warpage (W / mm) and volume shrinkage (V / %) as the quality optimization targets, according to the process parameters recommended by Moldflow software and the influencing factors of the mold flow analysis process, the process parameters are subdivided into melt temperature (A / ℃), mold temperature (B / ℃), injection pressure (C / MPa), holding pressure (D / MPa), injection time (E / s), holding time (F / s) and cooling time (G / s). The seven process parameters are used as input variables of CCF design, and the warpage (W / mm) and volume shrinkage (V / %) are used as output variables.

[0047] The process parameters refer to the commonly used range of injection molding, the upper limit of the parameters is: (230, 70, 90, 70, 5, 30, 30), and the lower limit of the parameters is: (180, 50, 70, 50, 3, 15, 15). The experimental level arrangement shall not exceed the cubic boundary, so the a value is 0.6, making the parameter level (-1, -a, 0, a, 1), ensuring that the experimental design fully considers the high and low levels of the process parameters and can be accurate within the design range.

[0048] As shown in Table 1, the CCF test design division part uses Minitab software, and the entire test arrangement consists of the following three experimental points:

[0049] ①Cube point, the coordinates of each point are 1 or -1, this is the part of the composition factor experiment.

[0050] ② Center point: the three-dimensional coordinates of each point are 0.

[0051] ③Axial point: except for one coordinate which is ±0.6, all other coordinates are 0.

[0052] Table 1 Experimental scheme and simulation results

[0053]

[0054]

[0055] Step 2. Based on the simulation test results, the northern goshawk optimized extreme gradient boosting (NGO-XGBoost) based on data set fitting is used to construct an injection molding quality prediction model.

[0056] The XGBoost model is a supervised learning algorithm that implements the integration of multiple CART trees through Gradient Tree Boosting. In the CART tree generation algorithm, the regression tree selects the one with the smallest sum of squared errors as the optimal split point for splitting. After a tree is generated, it is pruned to improve generalization ability. The tree generated in the kth round will learn the "residual" between the true value and the predicted value of the k-1th round model, so that the model prediction results gradually approach the true value.

[0057] The objective function obj of the XGBoost model is defined as follows:

[0058]

[0059] Where: is the loss function, where y i represents the actual value of sample i, represents the predicted value of sample i; Ω(f k ) is a regularization term, which represents the model complexity of the k-th decision tree, where f K Represents the Kth decision tree.

[0060] Unlike the AdaBoost model, which only has a loss function as its objective function, the XGBoost model’s objective function consists of two terms: a loss function and a regularization term. The loss function is used to evaluate the error or loss between the model’s predicted value and the true value, while the regularization term is used to control the complexity of the model, tending to select a simpler model to avoid overfitting.

[0061] The regularization term is defined as follows:

[0062]

[0063] Where: γ is the difficulty coefficient of node segmentation; T is the depth of the current subtree; λ is the regularization parameter that controls the weight; ω is the weight of the leaf node.

[0064] In the above formula, the first term γT controls the complexity of the tree through the number of leaf nodes and their coefficients. The larger the value, the larger the objective function, thus suppressing the complexity of the model. is the L2 regularization term, which is used to control the weight score of the leaf node (i.e., the weight of the leaf node is controlled by the regularization parameter), so that the model is not easily affected by data noise.

[0065] NGO is a swarm-based metaheuristic algorithm that mimics the behavior of the northern goshawk during hunting, with two main actions in the hunting process: prey identification and attack, and pursuit and escape. These two actions also correspond to the exploration and exploitation stages respectively.

[0066] ① Prey recognition and attack

[0067] The northern goshawk searches for potential prey while circling in the air, and once it finds a target, it adjusts its position to attack. In the optimization algorithm, the solution is regarded as potential prey, and the goal of the algorithm is to find the optimal solution, that is, the most nutritious prey. Therefore, in the search phase, the global exploration ability of the algorithm is enhanced by randomly selecting prey in the search space to determine the best area.

[0068] ② Chase and escape actions

[0069] After the northern goshawk attacks its prey, the prey tries to escape. Therefore, in a series of chases and escapes, the northern goshawk continues to chase its prey. Due to the high-speed maneuverability of the northern goshawk, they can chase their prey in almost any situation and eventually capture it. This behavior simulation enhances the algorithm's ability to search locally in the search space.

[0070] In order to determine the most effective configuration of the XGBoost model, the NGO algorithm is used to explore the hyperparameter space, so as to achieve the goals of improving model prediction accuracy, balancing model complexity, and preventing overfitting. As shown in Table 2, the learning rate, the maximum depth of the tree, and the minimum weight of the leaf node are the hyperparameters that need to be optimized. The value ranges of the three hyperparameters are between (0, 100), (1, 8), and (1, 3), respectively. Therefore, the population size (number of hyperparameter combinations) of the NGO optimization algorithm is set to 50 for initialization, and the maximum number of iterations is 100. The XGBoost model is trained for 50 hyperparameter combinations for each iteration. Finally, according to the model performance indicators (RMSE, MAE, MAPE), the fitness value of the corresponding hyperparameter combination is calculated. The lower the fitness value, the better the hyperparameter combination. Figure 4 As shown, it is clear that after 40 iterations, the fitness value of the model reached the lowest point of 0.0872, which indicates that the hyperparameter combination has reached the optimal configuration at this time.

[0071] Table 2 Hyperparameter combinations

[0072]

[0073] The R of the four models of NGO-XGBoost, XGBoost, AdaBoost-SVM, and AdaBoost-ELM 2 , RMSE, MAE, MAPE comparison, R 2 It reflects the linear relationship between the predicted value and the simulated value. The closer to 1, the better. RMSE, MAE, and MAPE reflect the first-order and second-order relative errors between the predicted value and the simulated value. The smaller the error value, the better the model fitting effect. As shown in Table 3, in the prediction model of warpage deformation, the R 2The ranking is: NGO-XGBoost > XGBoost > AdaBoost-SVM > AdaBoost-ELM, and the ranking of the RMSE, MAE, and MAPE of the models is: NGO-XGBoost < XGBoost < AdaBoost-SVM < AdaBoost-ELM. As shown in Table 4, in the prediction model of volume shrinkage, the R 2 The ranking is: NGO-XGBoost > XGBoost > AdaBoost-SVM > AdaBoost-ELM, and the ranking of the RMSE, MAE, and MAPE of the models is: NGO-XGBoost < XGBoost < AdaBoost-SVM < AdaBoost-ELM. In summary, the NGO-XGBoost model has the best prediction ability in the prediction of warpage deformation and volume shrinkage.

[0074] Table 3 Comparison of warpage deformation prediction models

[0075]

[0076] Table 4 Comparison of volume shrinkage prediction models

[0077]

[0078] Step 3: Use the SHAP (SHapley Additive exPlanations) method to analyze and explain the NGO-XGBoost model, and perform multi-objective optimization through the multi-objective multi-universe optimization algorithm (MOMVO) to obtain the Pareto front of the quality optimization objective.

[0079] SHAP is a method for explaining the predictions of machine learning models. Based on the concept of Shapley values in cooperative game theory, it quantifies the contribution of parameters to the model predictions. Perform SHAP explanations on the NGO-XGBoost model to obtain the contribution of each process parameter to the prediction quality objective, that is, the SHAP value. Moreover, if the SHAP value is positive, the quality objective increases; if the SHAP value is negative, the quality objective decreases. Use red to represent the low level of the parameter and blue to represent the high level of the parameter. For the warpage deformation amount and volume shrinkage rate, the smaller the two, the better the quality of the plastic part.

[0080] Analyze the NGO-XGBoost model through the SHAP explanation method as follows:

[0081] ①Build SHAP interpreter: In order to explain the decision-making process of the NGO-XGBoost model, use SHAP's tree model interpreter (TreeExplainer), which is designed for tree structure models and is the core tool in SHAP for explaining tree models (such as XGBoost and LightGBM). TreeExplainer can quickly and efficiently calculate the SHAP value of each feature by analyzing the split nodes of the tree model.

[0082] ② Calculate SHAP value: After the SHAP interpreter is built, the SHAP value of each feature can be calculated by providing a data set sample of the NGO-XGBoost model. The SHAP value reflects the positive or negative contribution of the process parameters to the model prediction results and is the core indicator for quantifying the influence of process parameters.

[0083] ③ Visual analysis: In order to intuitively display the distribution of SHAP values ​​and the contribution of each process parameter to the model, the visualization function of the SHAP interpretability tool is used to explain the prediction logic of the model and generate a SHAP summary diagram.

[0084] Generate a SHAP summary graph like Figure 5 As shown, Figure 5 As shown in (a), in the NGO-XGBoost warpage prediction model, the importance ranking is: melt temperature (A) > holding pressure (D) > injection pressure (C) > injection time (E) > cooling time (G) > holding time (F) > mold temperature (B). The significant factor melt temperature is explained. Low melt temperature will increase warpage, and high melt temperature will reduce warpage. Figure 5 As shown in (b), in the prediction model of volume shrinkage rate of NGO-XGBoost, the importance is ranked as follows: melt temperature (A) > injection time (E) > holding pressure (D) > cooling time (G) > holding time (F) > mold temperature (B) > injection pressure (C). Similarly, the significant factor melt temperature is explained. Low melt temperature will reduce volume shrinkage, and high melt temperature will increase volume shrinkage. According to SHAP analysis, high melt temperature will reduce warpage deformation and increase volume shrinkage. Therefore, the prediction model must be combined with multi-objective optimization methods to find the best process parameter combination.

[0085] MOMVO is a multi-objective MVO algorithm inspired by the multiverse theory, in which white holes, black holes and wormholes are the three core elements. In the MOMVO algorithm, white holes represent the generation points of new solutions, which are potential optimal solutions in the search space; black holes are used to eliminate bad solutions, which are suboptimal solutions or invalid solutions in multi-objective optimization problems; wormholes are regarded as a mechanism for jumping or exchanging solutions, allowing solutions to move and exchange quickly in the search space to speed up the optimization process or avoid local optimal solution traps.

[0086] According to the constructed NGO-XGBoost model, the MOMVO algorithm is used to perform global optimization. Figure 6As shown, first, the initial parameters of MOMVO are set, including the size of the population, the number of universes (i.e., solutions), the probability of white holes / black holes, the number of iterations, etc. The maximum number of iterations is set to 150, the initial number of universes is 100, the maximum archive storage value is 100, the objective function is clarified, and the relevant variables and archives are initialized. Then, in the main loop, the wormhole existence probability WEP, the travel distance rate TDR and the universe expansion rate (i.e., fitness value) are calculated. The wormhole existence probability (WEP) and the travel distance rate (TDR) are the two core coefficients of MOMVO, which affect the iteration and optimization process, so that the MOMVO algorithm can perform more accurate development and local search around the optimal universe. WEP represents the probability of the existence of a white hole. As the iteration proceeds, the WEP value will gradually increase, which means that the influence of white holes in the later stage is greater. TDR is used to control the wormhole crossing distance between black holes and white holes. Calculating the universe expansion rate (i.e., fitness value) refers to calculating the fitness value or objective function value of each solution, with the purpose of evaluating the quality of the solution. Then, the optimal solution is updated with the help of the elitist strategy, that is, the universe (i.e., solution) is sorted according to the universe expansion rate (i.e., fitness value), and the non-dominated solution is selected (if no other solution is better than this solution in all objectives, then this solution is a non-dominated solution), and the solution set is updated and saved in the archive. During the update and archive process, it is necessary to deal with the possible full archive situation and check whether the archive size of the current solution set exceeds the limited size. If the archive size exceeds the predetermined range, pruning and removing the excess solutions are performed to keep the archive size reasonable, and the update is performed through ranking and pruning; then the roulette method is used to select A universe (i.e., solution) is selected from the archive and its position is updated. The roulette mechanism is used to select different universes (i.e., solutions) to determine the universe that can be retained and optimized. Then, through the white hole and black hole mechanisms, the passage of matter from one universe to another is simulated to generate new solutions. Finally, the termination condition is checked, and the algorithm starts from the initial number of iterations. After one iteration is completed, the number of iterations is increased by 1, and the above steps are repeated until the preset maximum number of iterations is reached. If the current number of iterations is less than the maximum number of iterations, the algorithm continues to execute, otherwise it ends and outputs the Pareto frontier.

[0087] The final Pareto frontier is as follows Figure 7 shown.

[0088] Step 4: Determine the optimal combination of process parameters through the CRITIC-TOPSIS evaluation method.

[0089] Aiming at the product requirements that the warpage deformation and volume shrinkage of the ABS plastic parts should not be greater than 0.584mm and 7% respectively, 13 groups of Pareto solutions that meet the requirements are screened out, and the optimal combination of process parameters is determined by the CRITIC-TOPSIS evaluation method. In the evaluation process, the CRITIC-TOPSIS method gives full play to the advantages of the CRITIC method and the TOPSIS method. First, the CRITIC method is used to assign weights to each evaluation index, and the weights of the warpage deformation and volume shrinkage are calculated to be [0.566, 0.434] according to the correlation coefficient and standard deviation between each target; then, following the steps of the TOPSIS method, the degree of proximity between each evaluation object and the idealized target is calculated according to the obtained weights, so as to obtain a comprehensive evaluation score. As shown in Table 5, the fifth group has the highest score, and the optimal warpage deformation and volume shrinkage fraction are 0.528 mm and 6.504% respectively. The corresponding process parameter combination is: melt temperature (A) = 207.783 ° C, mold temperature (B) = 59.739 ° C, injection pressure (C) = 82.767 MPa, holding pressure (D) = 69.559 MPa, injection time (E) = 4.358 MPa, holding time (F) = 29.352 s, cooling time (G) = 22.804 s.

[0090] Table 5 CRITIC-TOPSIS comprehensive evaluation results

[0091]

[0092] The highest scoring parameter combination obtained by CRITIC-TOPSIS evaluation is used for Moldflow simulation analysis, such as Figure 8 As shown in the figure, the warpage deformation and volume shrinkage are 0.506mm and 6.675% respectively, and the predicted values ​​of the model are 0.528mm and 6.504% respectively. The deviation values ​​of the two are 4.3% and 2.6% respectively, and the error is controlled within 5%, indicating that the model prediction accuracy is good. Compared with the initial process parameter combination, the warpage deformation and volume shrinkage are reduced by 30.9% and 8.7% respectively, achieving a simultaneous reduction in warpage deformation and volume shrinkage, indicating that the optimization effect is good.

Claims

1. A multi-objective optimization method for injection molding process parameters, 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 design the CCF test with the value range of each process parameter as the experimental design space, and perform injection molding simulation based on Moldflow to obtain the quality optimization target test results; Step 2: Based on the simulation test results, the XGBoost model is optimized using the NGO optimization algorithm to construct the NGO-XGBoost injection molding quality prediction model; Step 3: Analyze the NGO-XGBoost model through the SHAP interpretation method to obtain the importance and positive and negative impact of each optimization design variable on the prediction quality optimization target, and obtain the Pareto frontier of the quality optimization target through multi-objective optimization through MOMVO; Step 4: Determine the optimal combination of process parameters in the Pareto frontier of the obtained quality optimization target through the CRITIC-TOPSIS evaluation method.

2. The multi-objective optimization method for injection molding process parameters according to claim 1, characterized in that: In Step 2, the objective function obj of the XGBoost model is defined as follows: Where: is the loss function, where y i represents the actual value of sample i, represents the predicted value of sample i; Ω(f k ) is a regularization term, which represents the model complexity of the k-th decision tree, where f K represents the Kth decision tree; The objective function regularization term of the XGBoost model is defined as follows: Where: γ is the difficulty coefficient of node segmentation; T is the depth of the current subtree; λ is the regularization parameter that controls the weight; ω is the weight of the leaf node.

3. The multi-objective optimization method for injection molding process parameters according to claim 2, characterized in that: When the NGO optimization algorithm is used to optimize the XGBoost model in Step 2, the learning rate, the maximum depth of the tree, and the minimum weight of the leaf node are used as the hyperparameters that need to be optimized. The initialization value of the number of hyperparameter combinations and the maximum number of iterations of the NGO optimization algorithm are set. The XGBoost model is trained through the hyperparameter combination with the number of initialization values ​​of the hyperparameter combination in each iteration process. Finally, the fitness value of the corresponding hyperparameter combination is calculated according to the model performance index. The lower the fitness value, the better the hyperparameter combination.

4. The multi-objective optimization method for injection molding process parameters according to claim 3, characterized in that: In Step 3, the NGO-XGBoost model is analyzed using the SHAP interpretation method, as follows: ①Use TreeExplainer as the SHAP interpreter; ② Calculate the SHAP value of each feature by providing a sample of the dataset of the NGO-XGBoost model; ③ Use the visualization function of the SHAP interpretability tool to explain the prediction logic of the model and generate a SHAP summary graph.

5. The multi-objective optimization method for injection molding process parameters according to claim 4, characterized in that: In Step 3, MOMVO is used to perform multi-objective optimization to obtain the Pareto frontier of the quality optimization objective, as follows: ① Set MOMVO parameters, clarify the objective function, and initialize related variables and archives; ② Calculate the wormhole existence probability WEP, travel distance rate TDR and fitness value in the main loop; ③ Sort the solutions according to the fitness value, select the non-dominated solutions, update the solution set and save it in the archive. ④ Check whether the file size of the current solution set exceeds the specified size. If the file size exceeds the preset range, perform a trimming operation to remove the excess solution; ⑤Use the roulette method to select a solution from the archive and update its position; ⑥ Check the termination condition. If the maximum number of iterations has not been reached, continue the loop until the end to obtain the Pareto frontier.

6. The multi-objective optimization method for injection molding process parameters according to claim 1, characterized in that: In Step 4, when determining the optimal combination of process parameters in the Pareto frontier of the obtained quality optimization target through the CRITIC-TOPSIS evaluation method, firstly, the CRITIC method is used to assign weights to each evaluation indicator, and the weights of warpage deformation and volume shrinkage are calculated according to the correlation coefficient and standard deviation between each target; then, following the steps of the TOPSIS method, the degree of proximity of each evaluation object to the idealized target is calculated according to the obtained weights to obtain a comprehensive evaluation score.

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