Multi-objective optimization method for injection molding process parameters of thin-wall shell plastic part

Abstract

The invention discloses a thin-wall shell plastic part injection molding process parameter multi-objective optimization method, which is based on an RIME-RF-MOGWO framework, takes a simulation sample as a research object, selects a volume shrinkage rate and a buckling deformation amount as optimization objectives, and firstly adopts SMOTE to process a data imbalance problem; establishing a nonlinear mapping relation between the process parameters and the quality target by using RF; an RIME is introduced to optimize the hyper-parameter of the RF; multi-objective optimization of process parameters is realized in combination with MOGWO, and a Pareto frontier solution set is obtained through non-dominated sorting and a congestion degree control mechanism. A multi-round optimization and simulation verification result shows that the multi-objective optimization method for the injection molding process parameters of the thin-wall shell plastic part can effectively obtain an optimal process parameter combination, the volume shrinkage rate is reduced by 19.02%, the buckling deformation amount is reduced by 50.63%, and the molding quality of the thin-wall plastic part can be remarkably improved.

Description

TECHNICAL FIELD

[0001] The application relates to a multi-objective optimization method for injection molding process parameters of a thin-wall shell plastic part, in particular to a multi-objective optimization method for injection molding process parameters of a thin-wall shell plastic part based on RIME-RF-MOGWO, and belongs to the technical field of injection molding. BACKGROUND

[0002] With the rapid development of modern manufacturing, injection molding has become one of the core processes for the production of plastic products. Thin-wall plastic parts are widely used in the manufacturing of complex structural parts such as automotive interior parts and household appliances. Especially, thin-wall plastic parts are widely used in the automotive interior field due to their excellent specific strength and lightweight characteristics. However, thin-wall parts have very high requirements for dimensional accuracy and appearance quality, and at the same time, the molding efficiency and manufacturing cost need to be considered; common quality problems such as volume shrinkage and warping deformation can significantly weaken the product performance, prolong the manufacturing cycle and increase the cost. Therefore, under the premise of ensuring quality, realizing multi-objective process optimization has become the focus of research in the industry and academia.

[0003] Injection molding is a typical multi-physical field coupling process, and the melt flow, temperature field and cooling shrinkage jointly determine the final shrinkage and warping behavior. There is significant interaction between process parameters, making it difficult to effectively apply traditional single-objective or step-by-step trial-and-error methods. In contrast, data-driven multi-objective optimization can establish a process-quality proxy model under the condition of limited simulation or experimental samples, and efficiently search for the Pareto front while meeting the constraints.

[0004] For "process parameter-quality response" modeling, academia and industry have proposed various data-driven methods. GRNN was proposed by Donald F. Specht, based on the conditional probability density estimation of radial basis kernel, with fast training and good small sample interpolation ability, but sensitive to bandwidth selection and prone to "dimension disaster" in high-dimensional space; XGBoost was proposed by Tianqi Chen and Carlos Guestrin, which can describe high-order interactions and suppress overfitting through gradient boosting and regularization of additive trees, with high precision, but sensitive to learning rate and tree depth, and the cost of tuning and early stopping is high; SVR is based on the statistical learning theory of Vladimir N. Vapnik, using ε-insensitive loss and kernel techniques, which performs stably in small and medium samples and complex feature space, but needs to be modeled for multi-output tasks, and is also sensitive to kernel parameters and regularization coefficients; CNN was proposed by Yann LeCun et al., which is good at end-to-end convolutional feature learning and suitable for inputs with spatial or spatio-temporal structure, and has obvious advantages in "parameter + field map" multi-modal tasks, but its performance is limited and the computational cost is high in the case of only containing tabular process parameters; RF was proposed by Breiman based on bagging and random subspace, which can remain stable in high-dimensional nonlinear and strong interaction conditions, and is not sensitive to hyperparameters, and has been successfully applied in multi-objective modeling of complex manufacturing processes such as injection molding. However, actual injection data often shows non-uniform and sparse distribution in response space: some process regions (such as high shear-low mold temperature combination) have few samples, while common working conditions have dense samples, which leads to insufficient learning of the model in the sparse area and the boundary solution, thereby weakening the description of the Pareto front and the generalization ability. SUMMARY

[0005] To solve the above problems, the present application provides a thin-walled shell plastic injection molding process parameter multi-objective optimization method, which can effectively reduce the warpage and volume shrinkage of thin-walled shell plastic parts, and further improve the molding quality of thin-walled shell plastic parts.

[0006] To achieve the above purpose, the thin-walled shell plastic injection molding process parameter multi-objective optimization method specifically includes the following steps:

[0007] Step 1: Taking simulation samples as the research object, selecting volume shrinkage and warpage as the optimization objectives; introducing SMOTE in the sample construction stage, generating synthetic samples based on neighborhood interpolation and adding noise in the response sparse area;

[0008] Step 2, using RF to establish the nonlinear mapping relationship between process parameters and quality objectives;

[0009] Step 3, using RIME to automatically tune the key hyperparameters of RF;

[0010] Step4, the tuned RF is coupled with MOGWO to obtain the Pareto front solution set through the non-dominated sorting and crowding control mechanism.

[0011] Further, in Step1, orthogonal experimental design method is used to design the experiment, and Moldflow is used for simulation.

[0012] Further, in Step2, the data flow of using RF to establish the nonlinear mapping relationship between process parameters and quality targets is as follows: after removing outliers and cleaning, feature selection is performed based on RF replacement importance; then, Z-score standardization is performed on the features and labels, and the data is divided into training / validation / test sets, and regression type data augmentation is performed on the training / validation / test three groups of data.

[0013] Further, in Step3, when RIME is used to automatically tune the key hyperparameters of RF, the median of multiple resampling errors is used as the performance indicator, and a mild complexity penalty term is introduced. After optimization, the optimal hyperparameters obtained are used to retrain the volume shrinkage proxy model RF_shrink model and the warping deformation proxy model RF_warp model on the merged “training+validation” dataset, and the performance is evaluated on the independent test set.

[0014] Further, the specific process of Step4 is as follows:

[0015] ① Initialization: generate a population in the feasible domain , and each individual represents a set of process parameters; the proxy model is provided by the two trained single-input RFs;

[0016] ② Iterative search: generate candidate solutions according to the surround-approximation update formula of GWO each generation; evaluate with the minimum RF prediction output as the target; identify the front using fast non-dominated sorting, calculate the crowding degree, and maintain the diversity of the solution set by truncating the archive;

[0017] ③ Parameter setting: set the population size and the maximum number of iterations;

[0018] ④ Output: return the external archive as the approximate Pareto front when the iteration is completed.

[0019] Further, a “optimization-simulation-retraining” closed loop is constructed to improve the accuracy of the proxy model and the quality of the front, which is as follows:

[0020] ① Select several representative solutions from the approximate Pareto front, call Moldflow to obtain their high-fidelity responses, and compare them with the initial RF predictions to evaluate the reliability of the first round of optimization;

[0021] ②The newly obtained simulation samples are incorporated into the original data set to form an enhanced training set, and on this basis, the RF agent is retrained and fed back to the MOGWO to carry out the next round of multi-objective optimization;

[0022] ③After multiple rounds of closed-loop, the frontiers gradually approach the real Pareto frontier.

[0023] Compared with the prior art, the thin-walled shell plastic part injection molding process parameter multi-objective optimization method based on the RIME-RF-MOGWO framework takes simulation samples as the research object, selects the volume shrinkage and warpage deformation as the optimization objectives, first uses the synthetic minority over-sampling technique (SMOTE) to process the data imbalance problem to enhance the representativeness of the minority class samples; then uses the random forest regression model (RF) to establish the nonlinear mapping relationship between the process parameters and the quality objectives; in order to improve the prediction accuracy of the model, the RIME algorithm is introduced to optimize the hyperparameters of the random forest, thereby strengthening the search ability of the model; further combining the multi-objective grey wolf optimization algorithm (MOGWO) to realize the multi-objective optimization of the process parameters, and obtaining the Pareto frontier solution set through the non-dominated sorting and congestion control mechanism. The results of multiple optimization and simulation verification show that the thin-walled shell plastic part injection molding process parameter multi-objective optimization method can effectively obtain the optimal process parameter combination, reduce the volume shrinkage by 19.02% and the warpage deformation by 50.63%, and can significantly improve the forming quality of the thin-walled plastic part. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 is a flowchart of the present application;

[0025] Figure 2 is a model diagram of the thin-walled shell plastic part of the injection molding of the embodiment of the present application, wherein (a) is a three-dimensional model of the plastic part, and (b) is a finite element model of the plastic part;

[0026] Figure 3 is a feature importance diagram of the tree model of the embodiment of the present application;

[0027] Figure 4 is a sample quantity comparison diagram of the embodiment of the present application;

[0028] Figure 5 is a feature distribution comparison box plot diagram before and after SMOTE data enhancement of the embodiment of the present application;

[0029] Figure 6 is a data distribution comparison diagram before and after SMOTE data enhancement of the embodiment of the present application;

[0030] Figure 7 is a RIME iteration curve diagram of the embodiment of the present application;

[0031] Figure 8is a primary Pareto frontier chart of an embodiment of the present application;

[0032] Figure 9 is an iterative Pareto frontier chart of an embodiment of the present application. DETAILED DESCRIPTION

[0033] The multi-objective optimization method of the thin-walled shell plastic injection molding process parameters aims to build a RIME-RF-MOGWO integrated optimization framework for thin-walled injection molding. Through the collaborative design of "synthetic minority oversampling - high robustness agent - multi-objective intelligent optimization", the systematic improvement of molding quality and efficiency is realized. Specifically: in the sample construction stage, the synthetic minority oversampling technique (SMOTE) is introduced, and synthetic samples are generated based on neighborhood interpolation and noise application in the response sparse area to enhance the coverage and robustness of the agent model in the difficult learning area; At the same time, the frost and ice optimization algorithm (RIME) is used to automatically optimize the key hyperparameters of RF, improving the prediction accuracy and model stability; On this basis, the optimized RF and multi-objective grey wolf optimization algorithm (MOGWO) are coupled to form a closed-loop structure of "agent - optimization - retraining", so as to more evenly approach the contracted and warped Pareto frontier, and realize the collaborative optimization of multiple quality objectives.

[0034] The flowchart of the multi-objective optimization method of the thin-walled shell plastic injection molding process parameters is shown in Figure 1 The present application will be specifically described below taking a certain injection-molded thin-walled shell plastic part as an example.

[0035] 1 Finite element modeling and experimental design

[0036] 1.1 Establishment of plastic part finite element model

[0037] A three-dimensional geometric model of a thin-walled plastic part is constructed in UG as shown in Figure 2 (a). The model takes a rectangular base as the main body, with multiple bending edges, support structures and hole features arranged. The wall thickness is 0.9-1.8mm, and the ratio of the minimum material thickness to the square root of the maximum projected area is 0.00589, which is much smaller than 0.045, so it is a thin-walled component. At the same time, the bottom of the plastic part is a large flat surface with a thickness of 1mm. Calculation shows that the ratio of the material thickness to the square root of the projected area in this area is 0.00654, which is much smaller than 0.045, so the large flat thin-walled injection molding part in this area is prone to warping deformation and volume shrinkage. This study focuses on this feature.

[0038] Geometric modeling adhered to product design specifications and manufacturability constraints, focusing on optimizing areas sensitive to melt flow and cooling paths, such as support roots, opening edges, and insert transition fillets, to mitigate the induced warpage caused by sharp corners and abrupt thickness changes. The model was then imported into Moldflow, where a shell element model was created using dual-domain triangular elements. Figure 2 As shown in (b) of the diagram. This mesh type is suitable for complex curved surfaces of thin-walled parts, accurately characterizing shear-dominated melt flow and surface heat transfer characteristics while maintaining computational efficiency. Local mesh refinement was implemented around the insert, in the thin-walled convergence zone, and in the support transition zone, with quality control achieved through indicators such as element connectivity, aspect ratio, and matching rate. The final finite element mesh contains 31,302 elements, with a maximum aspect ratio of 6.76, an average aspect ratio of 1.76, and a geometric matching rate of 94.2%, meeting the accuracy requirements for subsequent process simulations. For materials, PC+ABS alloy produced by KATE Corporation was selected. This material combines excellent impact resistance, thermal stability, and comprehensive mechanical properties, making it suitable for the forming and service requirements of thin-walled structures in the automotive and home appliance industries.

[0039] 1.2 Selection of process parameters and quality objectives

[0040] To evaluate the quality of thin-walled shell injection molding, seven key process parameters were selected as shown in Table 1: injection pressure ( ), injection time ( Holding pressure () ), holding time ( ), melt temperature ( ), mold temperature ( ) and cooldown time ( ), with volume shrinkage rate ( ) and warping deformation ( This is a quality response index used to characterize the dimensional stability and shape deviation of a part. In production, a volume shrinkage rate of 12%–13% and a warpage of less than 0.3 mm are required.

[0041] Table 1. Process Parameter Level Combination Table

[0042]

[0043] 1.3 Orthogonal Experimental Design

[0044] To systematically evaluate the impact of multiple process parameters on molding quality, an orthogonal experimental design method was used to organize numerical experiments. This method can efficiently plan multi-factor, multi-level experimental combinations, significantly reducing the number of experiments and computational costs while ensuring information coverage. First, L49 ( An orthogonal array is used to combine seven factors ( ~ The feasible region was discretized into five levels, resulting in 49 experimental schemes. Based on this, and considering the principles of model uncertainty and spatial homogeneity, AI-aided design was used to expand the schemes to 95, enhancing the coverage of the boundary and parameter interaction regions. All schemes underwent Moldflow simulation calculations under consistent material cards, mesh generation, and boundary conditions to obtain the volume shrinkage rate (…). ) and warping deformation ( This provides reliable data support for subsequent proxy modeling and multi-objective optimization. Some experimental schemes are shown in Table 2. None of the data sets in the table simultaneously satisfy both a volume shrinkage rate of 12%–13% and a warpage deformation of less than 0.3 mm. Therefore, further optimization of process parameters is needed to ensure that the quality of the plastic parts meets production requirements.

[0045] Table 2 Partial Orthogonal Experiment Data Table

[0046]

[0047] 2. Establishment of a multi-objective optimization model

[0048] 2.1 Feature Selection for Tree Models

[0049] Feature selection is a crucial step in machine learning preprocessing, aiming to sift out a subset of features with high representativeness and predictive power from raw data. Unlike feature extraction, feature selection effectively reduces data dimensionality and model complexity by removing redundant information and irrelevant features, thereby improving the model's generalization ability. After outlier removal and data cleaning, this invention employs a tree model for feature selection to identify key process parameters affecting the quality of thin-walled plastic parts.

[0050] Tree models can naturally handle nonlinear relationships and interactions between features, effectively reducing redundancy and improving training efficiency and prediction accuracy. The importance of features in tree models is as follows: Figure 3 As shown, Figure 3 This indicates that injection time, holding pressure time, and melt temperature have a significant impact on the warpage and volume shrinkage of thin-walled plastic parts, and are key process parameters for optimizing the molding process; meanwhile, holding pressure and cooling time are of positive importance. Based on the above analysis, this invention selects injection time (… ), holding pressure ( ), holding time ( ), melt temperature ( ) and cooldown time ( Five factors were used as characteristic variables.

[0051] 2.2 SMOTE Synthesis of Minority Class Oversampling Data Enhancement

[0052] 2.2.1 Overview of SMOTE

[0053] To solve the problem of uneven distribution of test data, the application introduces a synthetic minority over-sampling technique (SMOTE). The basic principle is to take the minority class sample as the center in the feature space, and generate new synthetic samples between its neighborhood samples by linear interpolation method, so as to improve the distribution density of data in the sparse area. The core computing idea is as follows:

[0054] ① For each minority class sample in the feature space , a neighbor sample is randomly selected from its nearest neighbor samples, and a new synthetic sample is generated by the following formula:

[0055]

[0056] In the formula: [0, 1] is a randomly generated proportion coefficient, which is used to control the strength of interpolation.

[0057] ② In the regression or multi-objective optimization scene, in order to maintain the physical reasonableness and continuity of the synthetic data, the response variable (target output) also needs to be interpolated:

[0058]

[0059] In the formula: is a controllable noise term, which is used to enhance the authenticity of the synthetic data and prevent model overfitting.

[0060] The synthetic samples generated by this strategy are in the same local manifold as the original samples, which not only maintains the geometric continuity of data distribution, but also expands the representativeness of sample space.

[0061] 2.2.2 SMOTE data enhancement

[0062] In order to alleviate the modeling deviation caused by uneven distribution of test data, the application applies SMOTE technology to the injection molding process parameter data set, realizes sample balancing and data structure optimization. The sample quantity comparison chart is as shown in Figure 4 , and the Figure 4It can be seen that the original data is obviously unbalanced in the number of samples in the three groups: group 1 and group 3 are both 32, while group 2 is only 18, which belongs to the sparse area. In order to alleviate this imbalance problem, this paper uses SMOTE to generate synthetic samples by linear interpolation between the same group of neighborhood samples, and introduces a strategy of allocation according to the degree of scarcity in the aspect of "how many samples to generate": first, take the reciprocal of the proportion of the number of samples in the group to the total number of samples as the weight, and normalize it. The smaller the number of samples, the lower the proportion, the greater the weight; correspondingly, more synthetic samples will be allocated during sample enhancement, while the group with more samples will be allocated relatively less. Since the original sample of group 2 is the least, its weight is 4.5556, so the sample enhancement amplitude is the largest; the original samples of group 1 and group 3 are relatively more, the weight is 2.5625, and the sample enhancement amplitude is relatively small. Finally, the number of samples in the three groups is increased to 67, 56, and 67 respectively, the number of samples in group 2 is significantly supplemented, and the overall distribution is more balanced, thereby reducing the bias of model training to the majority sample area and improving the learning ability of the model to the sparse area, providing a more stable data foundation for subsequent agent modeling.

[0063] The SMOTE data enhancement result is shown in Figure 5 、 Figure 6 . Figure 5 For the comparison of box plots of each feature before and after sample enhancement, it can be seen that the upper whisker and lower whisker positions of each feature remain basically the same before and after sample enhancement, indicating that the sample enhancement process does not introduce obvious abnormal new values that exceed the original range, and the synthetic samples are mainly distributed within the value interval of the original data; at the same time, the box body after sample enhancement is more "full", reflecting that the data distribution is further enriched after the number of samples increases. Specifically, the median line of feature (pressure holding time) shifts to the negative value direction compared to the original data, indicating that more samples are supplemented in the negative value interval of this feature; the median line of feature (cooling time) shifts to the positive value direction, indicating that sample enhancement has enhanced sample coverage in the positive value area of this feature, thereby filling the originally relatively sparse value segment. Figure 6 For the comparison of data distribution before and after sample enhancement, the coordinate range of data points before and after expansion has changed significantly, the distribution of original data is relatively dispersed, and the data points after expansion are concentrated in a smaller range, especially in the negative value interval (in the upper middle area), 108 groups of data are expanded, which shows that the new samples generated by sample enhancement effectively improve the data distribution, especially fill the originally sparse area, so that the density of the expanded samples in these areas increases. In summary Figure 5 and Figure 6It can be seen that SMOTE, while maintaining the overall value range stability, specifically supplements the sparse intervals, making the data distribution more complete and enhancing the coverage of boundary regions. Further experiments show that the prediction error of the model in sparse regions after data augmentation ( / The importance of features decreased significantly, and the ranking of feature importance became more stable.

[0064] 2.3 Random Forest (RF)

[0065] Random forests are integrated using the bagging method. Each of the following regression trees is trained on a bootstrap sampling subset and searches for the optimal split only within a randomly selected subset of features at each split point. For the input... The prediction is expressed as follows:

[0066]

[0067] In the formula: Random forest is a type of input The predicted output; It is the first The prediction function of a regression tree; It is the index of the tree.

[0068] Regression tree in node sample set The split is performed by minimizing the variance-type impurity, i.e.

[0069]

[0070] In the formula: and By features With threshold The resulting left and right subsets; and These are the means of the left and right subsets, respectively.

[0071] RF uses the outside of the bag ( The unbiased generalization estimate of the sample is expressed as follows:

[0072]

[0073] In the formula: It is the first The true label of each sample It is the first Outside the bag of each sample ( Predicted value, Mean squared error is the average of the squared differences between the predicted and actual values, and it is an indicator that measures the difference between the predicted and actual values.

[0074] and has variance reduction property where is the correlation coefficient between trees, is the variance of a single tree.

[0075] The data flow is as follows: after removing outliers and cleaning, feature selection is performed based on RF permutation importance; then Z-score standardization is performed on the features and labels, and the data is divided into training / validation / test sets in the ratio of 7:2:1; to enhance the sample density in the long-tail area, only regression-type data augmentation is performed on the training and validation sets, and the test set remains unchanged to ensure fair evaluation.

[0076] 2.4 Frosting and Icing Optimization Algorithm

[0077] The frosting and icing optimization algorithm is inspired by the mechanism of rime growth. It covers the global area with small-step random exploration like "soft rime", and makes fine development with dimension puncture exchange like "hard rime", and improves convergence efficiency with "positive greed" acceptance criteria.

[0078] Let the iteration index be (the number of iterations), and the adhesion coefficient control the transition from global to local. Let the th individual be , where is the dimension, and the current global optimum is , and the target is to minimize .

[0079] ① Soft Rime Update (Global Exploration)

[0080] Stepwise perturbation is performed with a probability , which is represented as follows:

[0081]

[0082] In the formula: is the candidate position of the th individual in the th iteration, is a random vector used to randomly scale each dimension that "moves towards the optimal solution", ; is a random perturbation vector used to increase exploration and help escape local optima, ; ⊙ is the Hadamard product; , is the step size, .

[0083] To satisfy the variable boundary, projection is used.

[0084] In the formula: For feasible regions The projection operator maps candidate solutions that may go out of bounds back into the feasible region.

[0085] ② Hard rime puncture (localized treatment)

[0086] Information exchange at the dimensional level accelerates the convergence to the optimal solution. The normalized fitness is defined as follows:

[0087]

[0088] In the formula: It is the first During the nth iteration, the 1st Normalized fitness corresponding to each individual position; Individual The original fitness value; and They are the first In the next iteration, all individuals in the population The maximum and minimum values; It is an introduced minimal positive offset, the purpose of which is to ensure that the denominator is never zero in the calculation, thereby preventing the undefined case where the denominator is zero.

[0089] From the dimensional subset Sampling one by one ,like Then a piercing swap will be performed (using the better option as the anchor point):

[0090]

[0091] In the formula: It is in the The iteration, the... The individual in the first Update values ​​in each dimension It is the first In the nth iteration, the globally optimal individual in the population is at the nth iteration. Component values ​​in each dimension.

[0092] along with This mechanism is triggered more frequently and is used for later, more detailed development.

[0093] ③ Positive greed (improved acceptance)

[0094] For candidates Using a greedy acceptance approach, it can be represented as follows:

[0095]

[0096] In the formula: It is the first the candidate position obtained by the individual in the i-th iteration; the candidate position obtained by the individual in the i-th iteration; is a target function, indicates that the candidate solution is not worse than the current solution.

[0097] and update the candidate solution in time according to the target function value and the candidate position. The "forward greediness" guarantees the monotonicity of the optimal trajectory, improves the convergence efficiency and suppresses premature convergence.

[0098] ④Computational complexity and convergence characteristics

[0099] If the population size , the dimension , the maximum iteration , and the cost of one fitness evaluation are , then the update and puncture of each generation are , and the overall complexity is represented as , wherein is determined by the time consumption of the proxy model evaluation or simulation.

[0100] Under the adaptive scheduling of , the algorithm presents an asymptotic convergence of "fast first and stable later": random disturbance is used to promote global search in the early stage, and puncture + greediness is used to develop strong local areas in the later stage.

[0101] The RIME iteration curve is shown in Figure 7 , RIME realizes large-step global exploration through "soft fog" in the early stage, and the fitness decreases rapidly; then under the action of "hard fog" dimension puncture and forward greediness acceptance, it enters the fine development stage, and the curve tends to be stable (≈0.108) at about the 40th generation, showing that the search has stabilized in the near-optimal region and there is no overfitting.

[0102] 2.5 Random forest model training and feature importance evaluation

[0103] In order to construct a stable and reliable process-quality proxy model, the present application takes seven process parameters shown in Table 2 as input features, and takes volume shrinkage and warping deformation as output targets, and trains two independent random forest regression models respectively.

[0104] In order to avoid the subjectivity and uncertainty brought by manual parameter tuning, the key hyperparameters of random forest (including the number of trees , the maximum depth and the minimum sample size of leaf nodes) are automatically optimized by the RIME algorithm. RIME performs wide global exploration in the early stage through the "soft time" mechanism, and carries out fine local search in the later stage, so as to balance the search breadth and convergence accuracy. The optimization objective function is set as the out-of-bag error (OOB Error) or the validation set RMSE.

[0105] To improve the robustness of the model, the median of multiple resampling errors is used as the performance indicator, and a mild complexity penalty term is introduced to prevent overfitting and increase the computational burden due to excessive depth or complexity of the model structure. After optimization, the RF_shrink model and the RF_warp model are retrained on the combined "training + validation" dataset using the optimal hyperparameters obtained, and the performance is evaluated on the independent test set.

[0106] Taking the warping deformation surrogate model RF_warp as an example, the optimal hyperparameter combination obtained by RIME search is: the number of trees , the minimum number of leaf nodes = 1. Under this configuration, the error indicators of the model on each dataset are shown in Table 3.

[0107] Table 3 Error indicators of the model on each dataset

[0108]

[0109] The results show that the random forest model optimized by RIME exhibits highly consistent fitting and generalization performance on the training set, validation set, and test set. The R 2 MSE of the validation set and the test set remains stable at around 0.94, and the increase in root mean square error (RMSE) and mean absolute error (MAE) is within a controllable range. This performance can prove that the RIME-RF framework has strong robustness to noise and imbalance in data. The volume shrinkage surrogate model (RF_shrink) adopts the same training and evaluation process, and exhibits similar error levels and consistency. Finally, these two trained surrogate models have been encapsulated as reusable prediction interfaces. These interfaces will be directly called by subsequent multi-objective optimization algorithms, laying a reliable foundation for searching for optimal process parameters.

[0110] 3 Multi-objective optimization

[0111] 3.1 Multi-objective grey wolf optimization algorithm

[0112] The multi-objective grey wolf optimization algorithm is based on the social hierarchy of grey wolves and cooperative hunting, and approaches the Pareto front through the iterative mechanism of "global exploration - local development", and maintains the coverage and uniformity of the solution set by combining non-dominated sorting and crowding distance. ① Enclosure and approximation behavior (core update of single-objective GWO)

[0113] Let the position of a wolf in the

[0114] th generation be , the reference individual be , and its update be represented as follows:

[0115] ​

[0116]

[0117] where is the Hadamard product, and linearly decreases; is the convergence factor vector, which controls the step size and direction of the individual updating around the head wolf position, and its magnitude determines the exploration or exploitation tendency, tendency exploration, tendency exploitation; is the perturbation factor vector, which is used to introduce random perturbation in the distance calculation to enhance search diversity; is a random vector (independent in each dimension); is the control parameter, which linearly decreases with the iteration number, and is used to gradually transit from global exploration to local exploitation; is the current iteration number; is the maximum iteration number.

[0118] The standard GWO is guided by three head wolves together, which is expressed as follows:

[0119]

[0120] where is the distance vector between the current gray wolf and the three head wolves, is the updated position vector of the gray wolf in the th iteration.

[0121] The feasible region boundary is handled by projection: .

[0122] ② Multi-objective fitness: non-dominated sorting and crowding degree maintenance

[0123] Let the objective vector maintain the external Pareto archive and perform fast non-dominated sorting and crowding calculation on the population , which is as follows:

[0124] Dominance relationship: dominates if and only if and

[0125] Crowding distance: the crowding distance of individuals in the same front is expressed as follows:

[0126]

[0127] where​ It is the first The crowding distance of an individual within its non-dominated layer is such that a larger value indicates a sparser surrounding solution and a higher preservation value. It is the number of objective functions, that is, the dimension of the objective in multi-objective optimization; It is the first One objective function.

[0128] The individual congestion at the endpoint is denoted as After merging the current group with the archives, truncate them to the capacity limit based on priority of the frontier and crowding level, from largest to smallest. To balance convergence and distribution, From the front edge of the first floor The location is obtained by weighted sampling based on congestion, and then updated according to the above formula.

[0129] 3.2 Multi-objective optimization based on MOGWO

[0130] To simultaneously reduce volume shrinkage and warpage, let the decision vector be... The bi-objective minimization problem is represented as follows:

[0131]

[0132]

[0133] In the formula: and These are volume shrinkage rate and warpage deformation, respectively. The corresponding parameter levels are derived from orthogonal and expanded sample designs, serving as the basic data for surrogate modeling and optimization. It is a feasible region; These are the lower and upper bounds of the decision variable.

[0134] To efficiently characterize the strongly nonlinear mapping from "process parameters to quality indicators," random forest regression is used as a surrogate model for the objective function, coupled with MOGWO to solve for the Pareto front. RF exhibits good robustness and interpretability, making it suitable for high-dimensional parameter interaction scenarios; MOGWO achieves a balance between convergence and distribution through a three-leader mechanism and "non-dominated sorting + crowding distance + file management."

[0135] The implementation process is as follows:

[0136] ① Initialization: in the feasible region An internally generated population is formed, with each individual representing a set of process parameters; the surrogate model is provided by the aforementioned trained bi-objective RF.

[0137] ii. Iterative search: candidate solutions are generated in each generation by the GWO's encircling-preying update formula; RF prediction is used as objective evaluation; fast non-dominated sorting is used to identify the front, calculate the crowding distance and maintain the diversity of solution set by truncation archive.

[0138] iii. Parameter setting: population size , maximum number of iterations .

[0139] iv. Output: return the external archive as the approximate Pareto front at the end of iteration.

[0140] The first optimized front is shown in Figure 8 .

[0141] Unlike traditional single-objective or weighted sum, the above framework directly maintains the diversity and uniformity of the front in the objective space, avoiding the risk of local aggregation of the solution set, and providing representative parameter combinations for subsequent simulation verification and retraining.

[0142] 3.3 Precision improvement and prediction

[0143] To further improve the precision of the surrogate model and the quality of the front, the present invention constructs a "optimization-simulation-retraining" closed loop, as follows:

[0144] i. Select several representative solutions from the archive front, see Table 4, call Moldflow to obtain their high-fidelity responses, and compare them with the initial RF prediction to evaluate the reliability of the first round of optimization. Figure 8 Table 4 Comparison of the first generation Pareto front and simulation values

[0145]

[0146] ii. Since the simulation results in Table 4 do not meet the production requirements, the obtained simulation samples are incorporated into the original data set to form an enhanced training set; on this basis, the RF surrogate is retrained and fed back to the MOGWO for the next round of multi-objective optimization.

[0147] iii. After several cycles, the front gradually approaches the true Pareto front, with improvements in: higher prediction consistency, more complete extreme value coverage, and more continuous and smooth front morphology; the iteration results are shown in

[0148] Figure 9

[0149] Simulate the Pareto front shown in Figure 9 , the results are shown in Table 5. According to the key quality requirements of volume shrinkage and warping deformation in production, select the region that meets both small values from the Pareto front (already in Figure 9 ​​The middle circle is out), and finally determine the corresponding optimal process parameter combination of the area. After comparison, the 107th simulation result meets the production requirements and the simulation value and the prediction value error is small, which is the optimal process parameter: injection pressure 80 MPa, injection time 5.35 s, holding pressure 67.01 MPa, holding time 20.13 s, melt temperature 231.37℃, mold temperature 70℃, cooling time 35 s. Corresponding volume shrinkage rate 12.51%, warpage deformation amount 0.2962 mm, which is reduced by 19.02% and 50.63% respectively compared with before optimization. (Among them, the injection pressure ( ) and the mold temperature ( ) are removed after dimension reduction, and the optimal parameters 80 MPa and 70℃ before dimension reduction are selected during simulation.

[0150] Table 5 Iterative Pareto front and simulation value comparison table

[0151]

[0152] The above results show that: while ensuring the search efficiency, the optimization strategy can significantly improve the generalization ability of the model and the quality of the solution set, and can give feasible and stable process guidance for actual production.

[0153] The present application proposes and verifies a closed-loop process optimization framework of "synthetic minority over-sampling - high-robust proxy modeling - multi-objective intelligent optimization" for the two quality bottlenecks of "volume shrinkage - warpage deformation" in thin-walled shell plastic injection molding. Based on the simulation samples obtained by orthogonal experiment, the data is expanded by synthetic minority over-sampling, the process-quality proxy model is established by random forest regression, and the hyperparameter optimization is completed by RIME algorithm; then combined with the MOGWO multi-objective intelligent optimization algorithm, the volume shrinkage rate and warpage deformation are cooperatively balanced under the production constraints, and the real Pareto front is gradually approached in the closed loop of "optimization-simulation-retraining". The results show that the volume shrinkage rate is reduced from 15.45% to 12.51%, and the warpage deformation amount is reduced from 0.6000 mm to 0.2962 mm, which is reduced by 19.02% and 50.63% respectively. Among them, the shrinkage rate of 12.51% falls within the range of 12% to 13% required by the factory, and the warpage of 0.2962 mm is less than 0.3 mm, both of which meet the production quality control threshold, which can significantly improve the molding quality and consistency, and can provide an engineering path for rapid optimization and batch production of thin-walled plastic injection molding process.

Claims

1. A multi-objective optimization method for injection molding process parameters of thin-walled shell plastic parts, characterized in that, Specifically, the following steps are included: Step 1: Taking the simulated sample as the research object, the volume shrinkage rate and warpage deformation are selected as optimization targets; SMOTE is introduced in the sample construction stage, and synthetic samples are generated by neighborhood interpolation and noise is applied in the sparse response region. Step 2: Use RF to establish a nonlinear mapping relationship between process parameters and quality objectives; Step 3: Use RIME to automatically tune the key hyperparameters of RF; Step 4: Couple the optimized RF with MOGWO and obtain the Pareto front solution set through non-dominated sorting and crowding control mechanisms.

2. The multi-objective optimization method for injection molding process parameters of thin-walled shell plastic parts according to claim 1, characterized in that, In Step 1, the orthogonal experimental design method is used to design the experiment, and Moldflow is used for simulation.

3. The multi-objective optimization method for injection molding process parameters of thin-walled shell plastic parts according to claim 1, characterized in that, In Step 2, the data flow for establishing a nonlinear mapping relationship between process parameters and quality objectives using RF is as follows: After outlier removal and cleaning, feature selection is performed based on the importance of RF permutation; then, Z-score standardization is applied to the features and labels, and the data is divided into training / validation / test sets, with regression data augmentation performed on all three sets of data.

4. The multi-objective optimization method for injection molding process parameters of thin-walled shell plastic parts according to claim 1, characterized in that, In Step 3, when using RIME to automatically tune the key hyperparameters of RF, the median of multiple resampling errors is used as the performance metric, and a mild complexity penalty term is introduced. After optimization, the volume shrinkage surrogate model RF_shrink and the warp surrogate model RF_warp are retrained on the merged "training + validation" dataset using the obtained optimal hyperparameters, and the performance is evaluated on the independent test set.

5. The multi-objective optimization method for injection molding process parameters of thin-walled shell plastic parts according to claim 4, characterized in that, The specific steps for Step 4 are as follows: ① Initialization: in the feasible region An internally generated population is used, with each individual representing a set of process parameters; the surrogate model is provided by two pre-trained single-input RFs. ② Iterative search: Each generation generates candidate solutions by surrounding GWO and approximating them. The evaluation objective is to minimize the RF prediction output; fast non-dominated sorting is used to identify the frontier, crowding degree is calculated and file truncation is used to maintain solution set diversity; ③ Parameter settings: Set the population size and maximum number of iterations; ④ Output: The iteration ends and returns the external file as the approximate Pareto front.

6. The multi-objective optimization method for injection molding process parameters of thin-walled shell plastic parts according to claim 5, characterized in that, A closed loop of "optimization-simulation-retraining" is constructed to improve the accuracy and cutting-edge quality of the surrogate model, as detailed below: ① Select several representative solutions from the approximate Pareto front, call Moldflow to obtain their high-fidelity responses, and compare them with the initial RF predictions to evaluate the reliability of the first round of optimization; ②Incorporate the newly obtained simulation samples into the original dataset to form an enhanced training set; on this basis, retrain the RF agent and feed it back into MOGWO to carry out the next round of multi-objective optimization; ③ After multiple closed loops, the frontier gradually approaches the real Pareto frontier.

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