Injection molding process parameter coupling simulation multi-objective optimization method

Abstract

The application discloses a kind of injection molding process parameter coupling simulation multi-objective optimization method, first minimum warping deformation, minimum volume shrinkage, minimum locking force as quality optimization goal, constructs the integration framework of test design and fusion prediction model, obtains optimal prediction model after optimization;Then the MSI-MOCGO optimization framework is constructed to the multi-objective process parameter optimization of optimal prediction model output;Finally, based on optimal prediction model and MSI-MOCGO, the three targets of comprehensive optimization are carried out, and the pareto frontier is obtained and the optimal process parameter combination is selected.The process parameter combination optimized by the method of the application has a verification error of less than 5% in Moldflow simulation, and the warping deformation, volume shrinkage and locking force are reduced by 24%, 6.3% and 7.4% respectively, and the structure strength is verified in ANSYS, and the results show that the plastic part has good structural safety and stiffness.

Description

Technical Field

[0001] This invention relates to a multi-objective optimization method for coupled simulation of injection molding process parameters, specifically a multi-objective optimization method for injection molding process parameters based on SHAP-IRUN-MLP-XGBoost and MSI-MOCGO, belonging to the field of injection molding technology. Background Technology

[0002] In the field of injection molding technology in modern manufacturing, the optimization of process parameters is crucial for improving product quality, reducing scrap rates, and increasing production efficiency. Warpage, volume shrinkage, and clamping force are three key quality indicators in the injection molding process, which respectively affect the molding accuracy, dimensional stability, equipment operational stability, and energy consumption of the plastic parts. These three factors often exhibit nonlinear coupling and optimization conflicts, and how to achieve their synergistic minimization has become a research hotspot in the field of injection molding process optimization.

[0003] With the development of CAE simulation technology, platforms such as Moldflow and ANSYS are widely used for injection molding and structural performance prediction, effectively assisting in process design and defect analysis. However, a single simulation platform cannot cover the entire process analysis between molding and structural performance. Therefore, process-structure coupled simulation methods have gradually emerged and become a key path to improve the accuracy and engineering practicality of comprehensive performance evaluation of injection molded parts. For example, He Hong et al. constructed a collaborative simulation framework for quality defects and tire rolling performance, realizing the linked prediction from process parameters to structural response; Krizsma S et al. improved the fiber orientation-structure coupling accuracy between Moldflow and ANSYS through mesh mapping.

[0004] While simulation provides effective support for modeling and verification, obtaining evenly distributed data samples and establishing high-precision, highly generalizable predictive models in high-dimensional process parameter spaces remains challenging. On one hand, the computational cost of simulation limits the feasibility of large-scale sampling, and traditional sampling methods suffer from insufficient coverage in capturing boundaries and nonlinear interactions. On the other hand, the injection molding process is highly nonlinear, and single predictive models are prone to overfitting or undergeneralization when faced with small samples and high-dimensional inputs.

[0005] In terms of optimization methods, traditional single-objective optimization methods struggle to balance multiple performance indicators due to significant conflicts between warpage, volume shrinkage, and clamping force. In recent years, multi-objective optimization algorithms such as NSGA-Ⅲ, MOGWO, and MOSSA have been widely applied in injection molding process optimization, effectively obtaining the Pareto front. However, standard algorithms still suffer from low search efficiency and uneven solution distribution in high-dimensional complex search spaces. Currently, determining the optimal trade-off scheme to achieve the best overall objective remains a challenging problem in multi-objective optimization research of injection molding process parameters. Summary of the Invention

[0006] To address the aforementioned problems, this invention provides a multi-objective optimization method for coupled simulation of injection molding process parameters, which can effectively reduce warpage, volume shrinkage, and clamping force, thereby ensuring the molding accuracy, dimensional stability, and equipment operational stability of the plastic parts, as well as lower energy consumption.

[0007] To achieve the above objectives, this injection molding process parameter coupled simulation multi-objective optimization method specifically includes the following steps:

[0008] Step 1: Taking the minimum warpage deformation, minimum volume shrinkage rate, and minimum clamping force as the quality optimization objectives, the process parameters that affect these three objectives are selected as optimization design variables, and an integrated framework of experimental design and fusion prediction model is constructed. After optimization, the optimal prediction model is obtained.

[0009] Step 2: Construct the MSI-MOCGO optimization framework to optimize the multi-objective process parameters of the optimal prediction model output;

[0010] Step 3: Based on the optimal prediction model and MSI-MOCGO, perform comprehensive optimization of the three objectives to obtain the Pareto front and select the optimal combination of process parameters.

[0011] Furthermore, in Step 1, when constructing the integrated framework for experimental design and fusion prediction models,

[0012] The experimental design incorporates LHS local sampling on top of a CCD.

[0013] We constructed weighted fusion prediction models XGBoost-MLP, XGBoost-LSTM, RF-MLP, and RF-LSTM using RF, XGBoost, MLP, and LSTM. We then optimized the fusion weights and hyperparameters using the IRUN algorithm, which replaces the random population initialization method in RUN with a GPS initialization strategy. The optimal prediction models XGBoost-MLP and XGBoost-LSTM were obtained through optimization.

[0014] Furthermore, when introducing LHS local sampling on top of CCD, the calculation method for LHS test points is as follows:

[0015]

[0016] In the formula: This is the LHS test point for the left clearance; For the right gap LHS test point; ub i lb is the upper limit of the parameter. i The lower bound of the parameter; center i r is the center value of the parameter.i A random number between [0, 1];

[0017] The Minimin strategy was used to optimize the minimum spacing of sampling points, and LHS samples were selected as supplementary test points.

[0018] By calculating the Euclidean distance and setting a deduplication threshold, samples that are too close to each other are excluded.

[0019] Furthermore, when constructing a weighted fusion prediction model and optimizing the fusion weights and hyperparameters using the IRUN algorithm,

[0020] The final predicted value is obtained by combining the predicted values ​​of multiple base models through a weighted average. The calculation method is as follows:

[0021]

[0022] In the formula: The final predicted value is represented by k; k represents the number of models involved in the fusion. w represents the predicted output of the i-th model. i Its corresponding weight;

[0023] The original sample points generated by GPS are normalized, scaled, and mapped according to the following formula:

[0024]

[0025] In the formula: This represents the value of the i-th individual in the j-th hyperparameter dimension; Let p be the lower and upper bounds of the j-th hyperparameter, respectively; j Let be the prime number corresponding to the j-th dimension; N is the population size; D is the hyperparameter dimension;

[0026] Meanwhile, the candidate solution X in the IRUN optimization algorithm new Obtained through the following update method:

[0027] X new =(X c +r×SF×g×X c )+SF×SM+μ×(X m -X c )

[0028] In the formula: X new X is a candidate solution; c The current solution is represented by r; the random factor is represented by g; the individual influence factor is represented by μ; the local and global search factors are represented by SF; the adaptive factor controls the search step size is represented by SM; and the search direction is represented by X. m This is the current optimal solution.

[0029] Furthermore, in Step 2, when constructing the MSI-MOCGO optimization framework, GPS initialization improvement strategy, Cauchy local mutation improvement strategy, Lévy flight mutation improvement strategy, and adaptive PBI distance ranking strategy are introduced on the basis of standard MOCGO, as follows:

[0030] ① Improved GPS initialization strategy: The GPS initialization strategy replaces the traditional random population initialization strategy of MOCGO. The initial parameter combination generated by GPS is scaled as follows:

[0031]

[0032] In the formula: This represents the value of the i-th individual in the j-th process parameter dimension; Let p be the lower and upper limits of the j-th process parameter, respectively; j Let N be the prime number corresponding to the j-th dimension; N is the population size.

[0033] ②Cauchy Local Mutation Improvement Strategy: The Cauchy local mutation strategy is used to replace the random seed generation strategy of the traditional MOCGO algorithm. The implementation method is as follows:

[0034]

[0035] In the formula: x new Candidate solutions generated for local Cauchy mutations; x is a local optimum; C(0,1) is a random variable of the standard Cauchy distribution; γ is a jump amplitude factor that controls the jump amplitude, which is set to 0.5;

[0036] ③ Lévy flight mutation improvement strategy: Based on the four diverse seed generation strategies of the traditional MOCGO algorithm, a fifth seed generation strategy is added, which is a local perturbation strategy based on the Lévy flight distribution. The expression is as follows:

[0037]

[0038] In the formula: X new Candidate solutions generated for Lévy flight mutation; x is a local optimum; u is a solution with mean 0 and variance . is a normal distribution; v is a standard normal distribution with a mean of 0 and a variance of 1; ub is the upper limit of the process parameter; lb is the lower limit of the process parameter; β is the Lévy exponent, β∈(1,2], and is taken as 1.5; a is the scaling factor, and is taken as 0.5;

[0039] ④ Adaptive PBI Distance Ranking Strategy: Based on the traditional PBI method, an adaptive PBI distance ranking strategy is introduced, expressed as follows:

[0040] PBI i =d1+θ·d2

[0041] Where: PBI i d1 is the PBI distance value of the i-th solution; d2 is the projected distance; d3 is the vertical offset distance; θ is the penalty factor, used to adjust the penalty intensity for the solution deviating from the ideal direction;

[0042] Improvement strategy for penalty factor θ:

[0043] θ i =θ base ·(1+δ·||f i norm -f norm ||)

[0044] In the formula: θ i θ is the penalty factor value for the i-th solution; base The initial value for the penalty factor is 1.0; δ is the adjustment coefficient, set to 0.5; f i norm f is the average vector of the i-th solution; norm The average vector of the normalization objective.

[0045] Compared with existing technologies, this injection molding process parameter coupled simulation multi-objective optimization method addresses the problems of warpage, volume shrinkage, and clamping force defects in injection molding. It constructs an integrated framework of experimental design, fusion model prediction, and multi-objective optimization. By introducing LHS local sampling on top of CCD, it achieves uniform data spatial distribution. A weighted fusion prediction model is constructed using RF, XGBoost, MLP, and LSTM, and the IRUN algorithm is combined to optimize the fusion weights and hyperparameters, improving prediction performance. SHAP analysis further verifies the interpretability and physical consistency of the optimal models XGBoost-MLP and XGBoost-LSTM. In terms of optimization, the MSI-MOCGO algorithm is proposed, incorporating GPS initialization strategy, Cauchy perturbation, and Lévy flight variation. An adaptive PBI ranking mechanism is used to enhance search performance, along with MSEA... Compared with algorithms such as MOCGDE and NSGA-III, MSI-MOCGO outperforms in terms of solution quality and distribution. The optimal parameter combination obtained was verified in Moldflow simulation with an error of less than 5%. Warpage deformation, volume shrinkage rate, and clamping force were reduced by 24%, 6.3%, and 7.4%, respectively, verifying the effectiveness of the prediction and optimization strategy. Structural strength verification was completed in ANSYS. The results show that the maximum deformation and equivalent stress of the plastic part under assembly and use loads are far below the design limits and material yield strength. The strain distribution is uniform, and it has good structural safety and stiffness. Overall, the results show that the multi-objective optimization method of injection molding process parameters coupled simulation can balance accuracy and practicality. It can provide a feasible and reliable solution for optimizing injection molding process parameters to ensure the molding accuracy, dimensional stability, equipment operation stability, and low energy consumption of plastic parts. Attached Figure Description

[0046] Figure 1 This is a three-dimensional model of the ABS plastic injection molded sensor housing part according to an embodiment of the present invention, wherein (a) is a front view of the sensor housing part and (b) is a back view of the sensor housing part;

[0047] Figure 2 These are simulation results of the initial parameters in an embodiment of the present invention, wherein (a) is a simulation result of warpage deformation, (b) is a simulation result of volume shrinkage, and (c) is a simulation result of clamping force.

[0048] Figure 3 This is a diagram illustrating the distribution of the CCD+LHS hybrid dataset according to an embodiment of the present invention;

[0049] Figure 4 These are comparative charts of evaluation indicators for the model in an embodiment of the present invention, wherein (a) is a comparative chart of evaluation indicators for warpage deformation, (b) is a comparative chart of evaluation indicators for volume shrinkage rate, and (c) is a comparative chart of evaluation indicators for clamping force.

[0050] Figure 5 These are SHAP summary diagrams of embodiments of the present invention, wherein (a) is a SHAP summary diagram of warpage deformation, (b) is a SHAP summary diagram of volume shrinkage rate, and (c) is a SHAP summary diagram of clamping force;

[0051] Figure 6 These are illustrations of the MSI-MOCGO algorithm results in an embodiment of the present invention, wherein (a) is a performance comparison illustration of the MSI-MOCGO algorithm and (b) is a Pareto front illustration of the MSI-MOCGO algorithm;

[0052] Figure 7 These are simulation verification results of embodiments of the present invention, wherein (a) is a simulation verification result of warpage deformation, (b) is a simulation verification result of volume shrinkage rate, and (c) is a simulation verification result of clamping force. Detailed Implementation

[0053] This injection molding process parameter coupled simulation multi-objective optimization method is a process-structure integrated optimization method that integrates prediction models and improved multi-objective optimization algorithms. The multi-strategy improved multi-objective chaotic game optimization (MSI-MOCGO) algorithm is used to optimize the fusion prediction model established by warpage deformation, volume shrinkage rate and clamping force, obtain the Pareto front, and verify the process-structure coupling based on the Moldflow and ANSYS platforms. Finally, the optimal configuration of process parameters and the comprehensive improvement of structural performance are achieved.

[0054] The present invention will be specifically described below using an injection-molded ABS sensor housing as an example.

[0055] Construct a three-dimensional geometric model of the sensor housing plastic part, such as 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. 3 The 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.

[0056] 1. Moldflow simulation analysis

[0057] Aiming to balance structural strength, assembly accuracy, and heat dissipation performance, Moldflow was used to sequentially perform filling, holding pressure, cooling, and warpage analysis to preliminarily assess the molding quality.

[0058] The finite element mesh uses high-quality triangular elements to avoid numerical instability caused by slender elements. The mesh matching rate is 92% (flow analysis) and 93% (warpage analysis), meeting the simulation accuracy requirements. The gating system uses a point gate arrangement, and the cooling system is designed to cover critical hot zones. The cooling stage accounts for approximately 2 / 3 of the molding cycle and is crucial for controlling warpage and shrinkage.

[0059] Based on the initial process parameters recommended by Moldflow (melt temperature 210℃, mold temperature 45℃, filling pressure 80MPa, molding cycle 30s), the following simulation results were obtained:

[0060] Warping deformation: such as Figure 2 As shown in (a), the maximum warpage of the plastic part is 0.7645 mm, which exceeds the design requirement of 0.6 mm. This is mainly due to stress concentration caused by temperature gradient and uneven shrinkage, which affects the final molding accuracy.

[0061] Volume shrinkage: such as Figure 2 As shown in (b), the maximum volume shrinkage rate of the plastic part is 7.124%, slightly higher than the design tolerance limit of 7%. This is due to uneven cooling rate and differences in solidification shrinkage between the inner and outer layers of the material, resulting in overall dimensional shrinkage deviation and affecting the product assembly accuracy.

[0062] Clamping force: such as Figure 2 As shown in (c), the maximum clamping force of the plastic part is 163.454t. Although it does not reach the equipment load limit, the higher clamping force corresponds to greater energy consumption and may exacerbate mold fatigue and maintenance pressure.

[0063] It is evident that the current process parameters have not yet met the standards in terms of warpage control and dimensional accuracy, and the clamping force is too high. Further multi-objective optimization is needed to achieve a synergistic improvement in process performance.

[0064] 2. Data Sampling

[0065] This embodiment selects seven injection molding process parameters as input variables, including melt temperature (T). m / ℃), mold temperature (T) e / ℃), injection pressure (P) i / MPa), holding pressure (P) k / MPa), injection time (t) i / s), holding time (t) k / s), Cooling time (t) cA total of seven process parameters were used as experimental variables, with warpage (W / mm), volume shrinkage (V / %), and clamping force (C / t) as molding quality targets. The range of process parameters was mainly based on the ABS (PA-757) material technical manual, supplemented by international injection molding process standards. The specific ranges are as follows: T m (180, 230), T e (50, 70), P i (70, 90), P k (50, 70), t i (3, 5), t k (15, 30), t c (15, 30). Considering the interaction effects between variables and the requirement for sample uniformity, the sampling strategy combines central composite design (CCD) and Latin hypercube sampling (LHS) to improve the model's generalization ability and optimization accuracy.

[0066] 2.1 Global Data Sampling Based on CCD

[0067] The CCD experimental design employed a full factorial design, setting the axis distance coefficient α = 0.6 to ensure that the axis points were within the actual operating range of the parameters, avoiding infeasible combinations of process parameters, and covering parameter boundary characteristics. Ultimately, the CCD experimental design comprised 152 sets of test points, structured as follows:

[0068] ① 128 sets of cube points (each parameter takes the upper or lower limit value);

[0069] ② 10 sets of center points (all parameters are taken at the center level);

[0070] ③ 14 sets of axis points (one parameter takes the value of α, and the other parameters take the center value).

[0071] 2.2 Local Data Optimization Sampling Based on LHS

[0072] LHS (Layered Hierarchical Sampling) ensures that the value of each variable uniformly covers its defined range through random stratified sampling, improving the representativeness of the parameter space. This embodiment uses 38 LHS gap samples based on high, medium, and low levels of CCD experimental data, with 19 samples taken from the left gap (low to medium level) and 19 from the right gap (medium to high level) to optimize the uniform coverage of the parameter space. The calculation method for LHS experimental points is as follows:

[0073]

[0074]

[0075] In the formula: This is the LHS test point for the left clearance; For the right gap LHS test point; ub i lb is the upper limit of the parameter. i The lower bound of the parameter; center i r is the center value of the parameter. i The number is a random number between [0, 1], ensuring a random uniform distribution of the sample.

[0076] To improve the dispersion of the sample distribution, the Maximin strategy was used to optimize the minimum spacing of the sampling points, and 38 LHS samples were finally selected as supplementary test points.

[0077] To avoid overlap between new samples and original CCD data, Euclidean distance is calculated, and a deduplication threshold is set to exclude samples that are too close together, ensuring the independence and representativeness of the sampled data. The Euclidean distance calculation formula is d = min(||X||). LHS -X CCD ||2), the deduplication threshold ε=1×10 -2 With T m (180, 230), P i (70, 90), t i Taking (3, 5) as an example, the distribution of the CCD+LHS hybrid dataset is as follows: Figure 3 As shown.

[0078] 3. Construction and optimization of quality prediction models

[0079] To construct a prediction model with higher accuracy and stronger generalization ability, this embodiment adopts a fusion model optimization strategy based on the improved Runge-Kutta (IRUN) optimization algorithm. The fusion model consists of four basic models: RF, XGBoost, MLP, and LSTM. Before formally entering the hyperparameter search and weight adjustment, it is necessary to analyze the prediction performance of each individual model on different objectives to provide a reference for subsequent optimization.

[0080] 3.1 Single-model performance analysis

[0081] The regression performance of the four basic models on three representative target variables (warpage (W / mm), volume shrinkage (V / %), and clamping force (C / t)) was compared using the coefficient of determination (R²). 2 R is used as an evaluation indicator. 2 The results are shown in Table 1 below:

[0082] Table 1 Single Model R 2 Indicator Comparison

[0083]

[0084] As shown in Table 1, LSTM performs best in predicting warpage and clamping force, while XGBoost performs best in predicting volume shrinkage and has stable overall performance. Therefore, when constructing the initial fusion model, each sub-model is assigned a corresponding weight based on its predictive performance, which serves as the initial value for weight optimization.

[0085] 3.2 Model Weight Initialization

[0086] The fusion model combines the predictions from multiple base models using a weighted average to obtain the final prediction. The calculation method is as follows:

[0087]

[0088] In the formula: The final predicted value is represented by k; k represents the number of models involved in the fusion. w represents the predicted output of the i-th model. i Set its corresponding weight.

[0089] Taking the combined RF-MLP model as an example, in warpage prediction, the R-values ​​of the two models... 2 If the values ​​are 0.94 and 0.95 respectively, then the initial weight allocation is as follows:

[0090]

[0091] 3.3 Definition and Combination of Hyperparameter Space

[0092] Besides the fusion weights, each sub-model in the fusion model contains multiple hyperparameters to be optimized. Therefore, to improve the overall performance of the fusion model, this invention employs the RUN optimization algorithm to jointly and globally optimize the model weight coefficients and the hyperparameters of each sub-model.

[0093] To further improve the performance of the RUN algorithm, this invention adopts the Hua Luogeng Best Point Set (GPS) initialization strategy to replace the random population initialization method in RUN, resulting in the IRUN optimized algorithm. Considering that the hyperparameters in the fusion model all have well-defined upper and lower bounds, the original sample points generated by GPS can be normalized, scaled, and mapped according to the following formula to ensure that their distribution is within the effective range of each parameter:

[0094]

[0095] In the formula: This represents the value of the i-th individual in the j-th hyperparameter dimension; Let p be the lower and upper bounds of the j-th hyperparameter, respectively; j Let be the prime number corresponding to the j-th dimension; N be the population size; and D be the hyperparameter dimension.

[0096] This initialization mechanism effectively enhances the global exploration capability of the IRUN optimization algorithm, especially on small sample datasets, reducing the risk of getting trapped in local optima. Simultaneously, the candidate solutions X in the IRUN optimization algorithm... new Obtained through the following update method:

[0097] X new =(X c +r×SF×g×X c )+SF×SM+μ×(X m -X c )

[0098] In the formula: X new X is a candidate solution; c The current solution is represented by r, the random factor, g, the individual influence factor, and μ, the local and global search factors used to control the balance between random factors, individual influence, and local and global search. SF is an adaptive factor controlling the search step size, which varies with the number of iterations. SM is the search direction, calculated using the Runge-Kutta method. X m This is the current optimal solution.

[0099] Table 2 below shows examples of the key hyperparameters and search ranges for each model:

[0100] Table 2 Hyperparameter Combinations

[0101]

[0102] Taking the fusion model RF-MLP as an example, its hyperparameters to be optimized include the following:

[0103] ① Two hyperparameters of RF (such as n_estimators, max_depth);

[0104] ② The three hyperparameters of MLP (such as num_layers, layer_sizes, lambda);

[0105] ③ Weighting parameters (e.g., w) RF Another one consists of 1-w RF (Result)

[0106] 3.4 Construction and Analysis of Prediction Model

[0107] In this embodiment, four weighted ensemble-based fusion prediction models (XGBoost-MLP, XGBoost-LSTM, RF-MLP, and RF-LSTM) were constructed, and the IRUN optimization algorithm was used to globally optimize their hyperparameters to improve the overall performance of the models in multi-objective prediction tasks.

[0108] like Figure 4(a) Figure 4 As shown in (b), the XGBoost-MLP model exhibits the best predictive performance on the two key quality indicators: warpage deformation and volume shrinkage rate. Its error indices are as follows: warpage deformation (MAE = 0.0107, RMSE = 0.013, R... 2 =0.99), volume shrinkage (MAE=0.031, RMSE=0.039, R 2 =0.98), demonstrating extremely high accuracy and stability, significantly outperforming other comparative models. For example... Figure 4 As shown in (c), the XGBoost-LSTM model exhibits the best performance in the clamping force prediction task, with prediction error metrics of MAE = 5.98, RMSE = 8.25, and R0 = 0.05. 2 =0.97. Besides the optimal model mentioned above, other fusion structures (such as RF-MLP, RF-LSTM, etc.) can achieve varying degrees of performance improvement based on the original single model.

[0109] To ensure fairness and consistency in the optimization process, all models were uniformly set to 100 iterations for the IRUN algorithm and a population size of 50. As shown in Table 3, the hyperparameter combinations of each fusion model in the optimal state are as follows: XGBoost-MLP (warping deformation): [100, 8, 1, 2, 24, 0.004, 0.50]; XGBoost-MLP (volume shrinkage): [72, 7, 2, 2, 7, 0.017, 0.44]; XGBoost-LSTM (mode-locking force): [33, 4, 2, 1, 32, 2, 0.012, 0.41]. The parameters represent, in order: the number of decision trees, maximum depth, and minimum leaf node for XGBoost; the number of network layers, number of neurons, and regularization coefficient for MLP; and the number of stacked layers, number of units per layer, dropout rate, learning rate, and model weights used for weighted fusion for LSTM.

[0110] Table 3 Optimal configuration of model hyperparameters

[0111]

[0112] To reveal the nonlinear impact of key process parameters on product quality indicators, an interpretive analysis of the prediction model was conducted based on the SHAP method. For example... Figure 5 As shown, the importance and mechanism of action of different parameters vary significantly in different objectives.

[0113] First, melt temperature has a significant impact on all targets. The SHAP value distribution shows that its high value (red) corresponds to a significant negative contribution (-0.6 to -1) in the warpage target, indicating that high temperature helps improve flowability and suppress warpage; while it shows a positive contribution (+0.5 to +1) in volume shrinkage and clamping force, revealing that although high temperature is beneficial for filling, it will increase shrinkage and mold load, indicating a typical target conflict.

[0114] The effect of holding pressure on warpage, shrinkage and clamping force: Secondly, its SHAP distribution shows that high values ​​have a negative effect on both warpage and shrinkage (-0.2 to -0.5), but a strong positive contribution to clamping force (+0.3 to +1), indicating that increasing the holding pressure can suppress shrinkage stress, but will also increase the mold load.

[0115] Injection pressure has the most significant impact on clamping force. SHAP value analysis shows that high values ​​have a continuous positive effect on clamping force (+0.2 to +0.4), while having an overall negative effect on warpage and shrinkage, highlighting its dual effect between filling and mold load-bearing.

[0116] Injection time has a certain impact on volume shrinkage and clamping force, producing a negative SHAP value. If it is too low, it will increase volume shrinkage and clamping force, which manifests as insufficient filling due to short injection time, but it will have a certain increasing effect on warpage.

[0117] In comparison, mold temperature, holding time, and cooling time all showed lower importance among the three objectives. The SHAP value distribution was flat and the range of variation was small, indicating that its direct impact on the output under the experimental conditions was weak, and it was more of a synergistic compensation effect with the dominant parameters.

[0118] 4. MOCGO Multi-Objective Optimization Based on Multi-Strategy Enhancement

[0119] To further minimize warpage, volume shrinkage, and clamping force, this invention constructs the MSI-MOCGO optimization framework to optimize multi-objective process parameters of the prediction model output. Given the significant nonlinear coupling and conflicting characteristics of the three quality objectives, three improved strategies (GPS initialization, Cauchy local mutation, and Lévy flight mutation) and a sorting strategy (adaptive PBI distance) are introduced on top of the standard MOCGO to enhance optimization performance.

[0120] 4.1 Initialization of the optimal point set

[0121] To improve the distribution quality of the initial population in the MOCGO algorithm, this embodiment uses the Hua Luogeng GPS method instead of the traditional random initialization strategy of MOCGO. Considering that the seven key process parameters in the injection molding process have specific upper limits (ub) and lower limits (lb), the initial parameter combination generated by GPS needs to be scaled as follows:

[0122]

[0123] In the formula: This represents the value of the i-th individual in the j-th process parameter dimension; Let p be the lower and upper limits of the j-th process parameter, respectively; j Let be the prime number corresponding to the j-th dimension; N is the population size.

[0124] 4.2 Replace the fourth update strategy (Cauchy local mutation)

[0125] The traditional MOCGO algorithm employs four diverse seed generation strategies (global exploration seed, bootstrapping seed, historical seed, and random seed) to achieve a dynamic balance between global search and local exploration. However, in actual optimization, the uniform perturbation of the random seed among the four generation strategies may lead to insufficient exploration of local regions.

[0126] Therefore, this invention introduces a Cauchy local mutation strategy to replace the fourth seed update method. Its core idea is: based on the current optimal solution (Leader), a perturbation term following a Cauchy distribution is introduced, with the perturbation amplitude gradually decreasing according to the iteration process, achieving adaptive fine perturbation of the solution. The implementation method is as follows:

[0127]

[0128] In the formula: x new γ is a candidate solution generated for local mutation of Cauchy; x is a local optimum; C(0,1) is a random variable of standard Cauchy distribution; γ is a jump amplitude factor that controls the jump amplitude, which is 0.5.

[0129] 4.3 Added a fifth type of local perturbation seed (Lévy flight variant)

[0130] To further enhance the population's ability to jump within local areas, a fifth type of seed generation mechanism is added: a local perturbation strategy based on Lévy flight distribution. new The final solution vector needs boundary processing to ensure it lies within the allowed search space [lb, ub]. This strategy generates a perturbation using a Lévy distribution that mixes long and short steps to break through local optima (x). leader The expression is as follows:

[0131]

[0132] In the formula: X new Candidate solutions generated for Lévy flight mutation; x is a local optimum; u is a solution with mean 0 and variance . denoted as , and v as a standard normal distribution with mean 0 and variance 1; ub as the upper limit of the process parameter; lb as the lower limit of the process parameter; β as the Lévy index, β∈(1,2], taken as 1.5; a as the scaling factor, taken as 0.5.

[0133] 4.4 Adaptive PBI Distance Strategy

[0134] To further improve the accuracy and diversity of multi-objective optimization algorithms in Pareto front ranking, this invention introduces an adaptive PBI distance ranking strategy for refined evaluation and selection of Pareto fronts generated by MOCGO, based on the traditional boundary cross-aggregation (PBI) method. The PBI method maps the solution to two distances on a preset direction vector: projected distance d1 and vertical offset distance d2, and then calculates the "deviation" of the solution from the ideal direction. Its core idea is as follows:

[0135] PBI i =d1+θ·d2

[0136] Where: PBI i d1 is the PBI distance value of the i-th solution; d2 is the projected distance; d3 is the vertical offset distance; θ is the penalty factor, used to adjust the penalty intensity for the solution deviating from the ideal direction.

[0137] However, in practical applications, a fixed θ parameter often fails to simultaneously ensure the convergence of the solution set in dense regions and its distribution in sparse regions. Therefore, this invention proposes the following improvement strategy:

[0138] θ i =θ base ·(1+δ·||f i norm -f norm ||)

[0139] In the formula: θ i θ is the penalty factor value for the i-th solution; base The initial value for the penalty factor is 1.0; δ is the adjustment coefficient, set to 0.5; f i norm f is the average vector of the i-th solution; norm The average vector of the normalization objective.

[0140] This strategy can impose a stronger penalty when the solution deviates further from the mean, thereby improving the selectivity of the sorting.

[0141] 4.5 Pareto Front and Selection of Optimal Process Parameters

[0142] To achieve a comprehensive improvement in the quality of the injection molding process, based on the constructed regression prediction model (XGBoost-MLP, XGBoost-LSTM) and MS-IMOCGO, a three-objective comprehensive optimization is performed to obtain the Pareto front and select the optimal combination of process parameters.

[0143] To evaluate the performance of the MSI-MOCGO algorithm, this invention uses three mainstream multi-objective optimization metrics—Inverse Generational Distance (IGD), Hypervolume (HV), and Spacing—for comparison with MSEA, MOCGO, MOCGDE, and NSGAⅢ. Figure 6 As shown in (a), the MSI-MOCGO algorithm significantly outperforms the comparison algorithms in both IGD (3.452) and Spacing (0.690), indicating that it performs better in terms of solution set distribution uniformity and proximity to the optimal frontier. Although its HV (238.50) is slightly lower than MSEA and MOCGDE, its overall optimization quality is the most balanced.

[0144] Pareto front distribution as follows Figure 6 As shown in (b), the model achieves a good compromise between the three objectives—warpage deformation, volume shrinkage rate, and clamping force. For example, the seventh solution (0.973mm, 6.058%, 111.648t) ensures minimum clamping force while controlling warpage and shrinkage well, making it suitable for scenarios sensitive to energy consumption and equipment requirements; while the fourth solution (0.533mm, 6.497%, 159.875t) excels in reducing warpage, making it suitable for products with extremely high molding accuracy requirements. Furthermore, by analyzing the single-objective extreme points, we can obtain: W min 0.3859mm (Group 85), V min It was 5.2474% (Group 38), C min The value is 109.5951t (Group 76), which can provide a reference for different optimization tendencies.

[0145] To verify the effectiveness of the proposed adaptive PBI multi-objective optimization strategy under quality constraints, this embodiment sets warpage not exceeding 0.6 mm and volume shrinkage rate not exceeding 7% as screening criteria. The optimization results are filtered and analyzed, ultimately yielding nine feasible solutions, as shown in Table 4. The results show that the warpage deformation of all solutions is controlled between 0.4700 and 0.5642 mm, and the volume shrinkage rate is between 6.3982% and 6.8762%, both better than the preset thresholds, verifying the effectiveness of the adaptive PBI strategy in guiding the search direction. Among them, the solution with the lowest score (PBI score 2.21) achieves excellent levels in both warpage (0.5642 mm) and volume shrinkage (6.6913%), while significantly reducing the clamping force (153.6680 t), realizing a good balance between quality and energy consumption, demonstrating strong engineering practicality and comprehensive advantages.

[0146] Table 4 Pareto Frontier Score Solution

[0147]

[0148] 5. Moldflow-ANSYS Coupled Simulation Verification

[0149] To verify the engineering feasibility of the optimal combination of process parameters, a full-process coupled simulation analysis of the molding quality and structural performance of the plastic parts in the example was conducted using Moldflow and ANSYS. First, the quality target was verified through injection molding simulation in Moldflow; then, the simulation results were imported into ANSYS to conduct structural strength analysis, in order to comprehensively evaluate the practical application value of the optimized scheme.

[0150] 5.1 Moldflow Injection Molding Analysis

[0151] Among all solutions satisfying the constraints, the optimal combination of process parameters with the lowest score is: melt temperature 215.12℃, mold temperature 58.63℃, injection pressure 81.14MPa, holding pressure 59.70MPa, injection time 4.90s, holding time 25.77s, and cooling time 26.20s. Inputting this parameter combination into Moldflow for simulation analysis yielded the following molding quality indicators: warpage 0.5775mm, volume shrinkage 6.675%, and clamping force 151.233t. Figure 7 As shown.

[0152] Compared with the molding results under the initial combination of process parameters, the three key quality indicators were reduced by 24.0% (warpage), 6.3% (volume shrinkage), and 7.4% (clamping force), respectively, which fully verified the effectiveness of the optimization scheme in improving the quality of the parts.

[0153] In addition, to verify the reliability of the prediction model at the optimal solution, the predicted values ​​(0.5642mm, 6.691%, 153.668t) were compared with the simulated values. The three errors were 2.3%, 0.2%, and 1.6%, respectively, all within 5%, which verified the accuracy and reliability of the prediction model at the optimal solution.

[0154] 5.2 ANSYS Structural Strength Analysis

[0155] To evaluate the structural performance of molded plastic parts in practical applications, the results of the plastic parts under the optimal combination of process parameters obtained based on Moldflow (including residual stress, deformation, temperature field, etc.) were imported into ANSYS as the initial state to perform structural strength analysis under two typical working conditions.

[0156] Assembly load condition: A vertical clamping force of 60N is applied to each of the four screw holes, with a total assembly load of 240N. Simulation results show that the maximum total deformation is 0.3947mm, far below the allowable tolerance of 0.6mm, indicating good assembly accuracy. The maximum equivalent stress (von Mises) is 4.4548MPa, only 9.9% of the yield strength of ABS material (45–60MPa), corresponding to a safety factor of approximately 10.1, indicating sufficient structural strength. The maximum equivalent elastic strain is 0.0017603, within the material's elastic range, with no plastic deformation, uniform stress distribution, and no obvious concentration areas.

[0157] Operational pressing condition: A 40N vertical concentrated load was applied to the center of the top of the plastic part, and a fixed constraint was set at the bottom to simulate the actual installation state. Simulation results show that the maximum total deformation is 0.01416mm, which is significantly smaller than the deformation under assembly conditions, indicating that the structure has good compressive stiffness and deformation control capability. The maximum von Mises stress is 38.68MPa, which is close to the lower yield limit of the material but still within the safe range, with a safety factor of approximately 1.2, indicating that the structure has a certain load-bearing margin. The maximum equivalent stress is 0.0003424, which is still within the elastic limit of the material, and no plastic deformation has occurred. The stress concentration area is obvious but does not lead to the risk of local failure.

[0158] By verifying the structural strength in ANSYS, the plastic part structure of the embodiment did not exhibit excessive deformation or material yielding under assembly load and service load. Its maximum deformation and equivalent stress were far below the design limit and material yield strength. The strain distribution was uniform, and it had good structural safety and stiffness. This verified the structural safety and applicability of the plastic part in actual molding and use scenarios under the optimal combination of process parameters.

[0159] This multi-objective optimization method for coupled simulation of injection molding process parameters addresses the problems of warpage, volume shrinkage, and clamping force defects in injection molding. It constructs an integrated framework of experimental design, fusion model prediction, and multi-objective optimization. By introducing LHS local sampling on top of CCD, it achieves uniform data spatial distribution. Weighted fusion prediction models are built using RF, XGBoost, MLP, and LSTM, and the IRUN algorithm is combined to optimize the fusion weights and hyperparameters, improving prediction performance. SHAP analysis further verifies the interpretability and physical consistency of the optimal models XGBoost-MLP and XGBoost-LSTM. In terms of optimization, MSI-MOCGO is proposed, incorporating GPS initialization strategy, Cauchy perturbation, and Lévy flight variation, and employing an adaptive PBI sorting mechanism to enhance search performance. Compared with algorithms such as MSEA, MOCGDE, and NSGA-III, MSI-MOCGO outperforms in terms of solution quality and distribution. The obtained optimal parameter combination was verified in Moldflow simulation with an error of less than 5%. Warpage deformation, volume shrinkage and clamping force were reduced by 24%, 6.3% and 7.4% respectively, verifying the effectiveness of the prediction and optimization strategy.

Claims

1. A multi-objective optimization method for coupled simulation of injection molding process parameters, characterized in that, Specifically, the following steps are included: Step 1: Taking the minimum warpage deformation, minimum volume shrinkage rate, and minimum clamping force as the quality optimization objectives, the process parameters that affect these three objectives are selected as optimization design variables, and an integrated framework of experimental design and fusion prediction model is constructed. After optimization, the optimal prediction model is obtained. When constructing an integrated framework for experimental design and fusion prediction model, the experimental design adopts LHS local sampling based on CCD; the weighted fusion prediction models XGBoost-MLP, XGBoost-LSTM, RF-MLP, and RF-LSTM are constructed using RF, XGBoost, MLP, and LSTM, and the fusion weights and hyperparameters are optimized by combining the IRUN algorithm, which uses GPS initialization strategy to replace the random population initialization method in RUN, and the optimal prediction models XGBoost-MLP and XGBoost-LSTM are obtained through optimization. When constructing a weighted fusion prediction model and optimizing the fusion weights and hyperparameters using the IRUN algorithm, the final prediction value is obtained by combining the prediction values ​​of multiple base models through a weighted average. The calculation method is as follows: In the formula: This is the final predicted value; The number of models participating in the fusion; Indicates the first The predicted output of each model. Its corresponding weight; The original sample points generated by GPS are normalized, scaled, and mapped according to the following formula: In the formula: Indicates the first The individual in the first The values ​​of each hyperparameter dimension; , The first The lower and upper bounds of each hyperparameter; For the first The prime number corresponding to the dimension; N is the population size; D is the hyperparameter dimension; Meanwhile, candidate solutions in the IRUN optimization algorithm Obtained through the following update method: In the formula: Candidate solution; This is the current solution; For random factors; Individual influencing factors; For local and global search factors; An adaptive factor to control the search step size; Indicating the search direction; This is the current optimal solution; Step 2: Construct the MSI-MOCGO optimization framework to optimize the multi-objective process parameters of the optimal prediction model output; Step 3: Based on the optimal prediction model and MSI-MOCGO, perform comprehensive optimization of the three objectives to obtain the Pareto front and select the optimal combination of process parameters.

2. The injection molding process parameter coupled simulation multi-objective optimization method according to claim 1, characterized in that, When introducing LHS local sampling on top of CCD, the calculation method for LHS test points is as follows: In the formula: This is the LHS test point for the left clearance; This is the LHS test point for the right gap; This is the upper limit of the parameter; This is the lower limit of the parameter; The center value of the parameter; A random number between [0, 1]; The Minimin strategy was used to optimize the minimum spacing of sampling points, and LHS samples were selected as supplementary test points. By calculating the Euclidean distance and setting a deduplication threshold, samples that are too close to each other are excluded.

3. The injection molding process parameter coupled simulation multi-objective optimization method according to claim 1, characterized in that, In Step 2, when constructing the MSI-MOCGO optimization framework, the following strategies are introduced on the basis of the standard MOCGO: GPS initialization improvement strategy, Cauchy local mutation improvement strategy, Lévy flight mutation improvement strategy, and adaptive PBI distance ranking strategy, as detailed below: ① Improved GPS initialization strategy: The GPS initialization strategy replaces the traditional random population initialization strategy of MOCGO. The initial parameter combination generated by GPS is scaled as follows: In the formula: Indicates the first The individual in the first The values ​​of each process parameter dimension; , The first The lower and upper limits of each process parameter; For the first The prime number corresponding to dimension; N is the population size; ②Cauchy Local Mutation Improvement Strategy: The Cauchy local mutation strategy is used to replace the random seed generation strategy of the traditional MOCGO algorithm. The implementation method is as follows: In the formula: Candidate solutions generated for Cauchy local mutation; This is a locally optimal solution; For random variables with a standard Cauchy distribution; The jump amplitude factor, used to control the jump amplitude, is set to 0.5; ③ Lévy flight mutation improvement strategy: Based on the four diverse seed generation strategies of the traditional MOCGO algorithm, a fifth seed generation strategy is added, which is a local perturbation strategy based on the Lévy flight distribution. The expression is as follows: In the formula: Candidate solutions generated for Lévy flight mutation; x is a local optimum; With a mean of 0 and a variance of The normal distribution; It follows a standard normal distribution with a mean of 0 and a variance of 1. This represents the upper limit of the process parameters; This represents the lower limit of the process parameters; The Lévy index, ∈(1,2], take 1.5; The scaling factor is set to 0.

5. ④ Adaptive PBI Distance Ranking Strategy: Based on the traditional PBI method, an adaptive PBI distance ranking strategy is introduced, expressed as follows: In the formula: For the first The PBI distance values ​​of each solution; Projection distance; This is the vertical offset distance; This is a penalty factor used to adjust the intensity of the penalty for solutions deviating from the ideal direction; Punishment factor Improvement strategies: In the formula: For the first The penalty factor value for each solution; The initial value for the penalty factor is 1.0; The adjustment coefficient is set to 0.

5. For the first The average vector of the solutions; The average vector of the normalization objective.

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