Injection molding process parameter coupling simulation multi-objective optimization method

Abstract

The invention discloses an injection molding process parameter coupling simulation multi-objective optimization method, which comprises the following steps: firstly, by taking minimum buckling deformation, minimum volume shrinkage and minimum mold locking force as quality optimization objectives, constructing an integrated framework of test design and a fusion prediction model, and obtaining an optimal prediction model after optimization; then, an MSI-MOCGO optimization framework is constructed to carry out multi-target process parameter optimization on the output of the optimal prediction model; and finally, based on the optimal prediction model and the MSI-MOCGO, three-target comprehensive optimization is carried out, a Pareto leading edge is obtained, and an optimal process parameter combination is selected. The verification error of the technological parameter combination optimized through the method in Moldflow simulation is smaller than 5%, the buckling deformation amount, the volume shrinkage rate and the mold clamping force are reduced by 24%, 6.3% and 7.4% respectively, meanwhile, structural strength verification is carried out in ANSYS, and the result shows that the plastic part has good structural safety and rigidity.

Description

TECHNICAL FIELD

[0001] The application relates to a multi-objective optimization method for coupling simulation of injection molding process parameters, in particular to a multi-objective optimization method for injection molding process parameters based on SHAP-IRUN-MLP-XGBoost and MSI-MOCGO, and belongs to the technical field of injection molding processing. BACKGROUND

[0002] In the field of injection molding processing technology in modern manufacturing, the optimization of process parameters is crucial for improving product quality, reducing waste rate and improving production efficiency. Warpage, volume shrinkage and clamping force as three key quality indicators in the injection molding process, respectively affect the molding precision, dimensional stability and equipment operation stability of the plastic parts, and energy consumption. The three often have nonlinear coupling and optimization conflicts. How to achieve their collaborative 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 in injection molding and structural performance prediction, which can effectively assist process scheme design and defect analysis. However, a single simulation platform cannot cover the whole process analysis between the molding process and the structural performance. Therefore, process-structure coupling simulation methods have gradually emerged and have become a key path to improve the accuracy and engineering practicability of comprehensive performance evaluation of injection molded parts. For example, He Hong et al. constructed a collaborative simulation framework of quality defects and tire rolling performance, realizing the linkage prediction from process parameters to structural response; Krizsma S et al. improved the fiber orientation-structure coupling accuracy between Moldflow and ANSYS through grid mapping.

[0004] Although simulation methods provide effective support for modeling and verification, it is still challenging to obtain evenly distributed data samples and establish high-precision, strong generalization ability prediction models in high-dimensional process parameter space. On the one hand, the cost of simulation calculation limits the feasibility of large-scale sampling, and traditional sampling methods have the problem of insufficient coverage in capturing boundaries and nonlinear interactions. On the other hand, the injection molding process has high nonlinearity, and single prediction model is prone to overfitting or insufficient generalization when facing small samples and high-dimensional inputs.

[0005] In terms of optimization methods, due to the significant conflict between warpage, volume shrinkage and clamping force, traditional single-objective optimization methods cannot consider multiple performance indicators. In recent years, multi-objective optimization algorithms such as NSGA-III, MOGWO, MOSSA, etc. have been widely used in injection molding process optimization, which can effectively obtain the Pareto front. However, standard algorithms still have problems such as low search efficiency and uneven solution distribution in high-dimensional complex search space. At present, in the research of multi-objective optimization of injection molding process parameters, how to determine the optimal trade-off scheme to achieve the best comprehensive purpose is still a difficult problem in the industry. SUMMARY

[0006] In order to solve the above problems, the present application provides an injection molding process parameter coupling simulation multi-objective optimization method, which can effectively reduce warpage, volume shrinkage and clamping force, thereby ensuring the molding precision, dimensional stability and equipment operation stability of the plastic parts and lower energy consumption.

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

[0008] Step 1, taking the minimum warpage, the minimum volume shrinkage and the minimum clamping force as the quality optimization objectives, selecting the process parameters affecting the three objectives as the optimization design variables, constructing an integrated framework of experimental design and fusion prediction model, and obtaining the optimal prediction model after optimization;

[0009] Step 2, constructing an MSI-MOCGO optimization framework to perform multi-objective process parameter optimization on the optimal prediction model output;

[0010] Step 3, based on the optimal prediction model and MSI-MOCGO, performing comprehensive optimization of the three objectives, obtaining the Pareto frontier and selecting the optimal process parameter combination.

[0011] Further, in Step 1, when constructing the integrated framework of experimental design and fusion prediction model,

[0012] The experimental design adopts LHS local sampling introduced on the basis of CCD;

[0013] RF, XGBoost, MLP and LSTM are used to construct weighted fusion prediction models XGBoost-MLP, XGBoost-LSTM, RF-MLP and RF-LSTM, and the IRUN algorithm is used to optimize the fusion weight and hyperparameters by replacing the random population initialization method in RUN with the GPS initialization strategy, and the optimal prediction models XGBoost-MLP and XGBoost-LSTM are obtained.

[0014] Further, when LHS local sampling is introduced on the basis of CCD, the calculation method of LHS test points is as follows:

[0015]

[0016] In the formula: LHS test points on the left gap; LHS test points on the right gap; ub i Upper limit of the parameter; lb i Lower limit of the parameter; center i Parameter center value; ri is a random number between 0 and 1;

[0017] The minimum distance of the sampling points is optimized by using the Maximin strategy, and the LHS samples are screened as the supplementary test points.

[0018] By calculating the Euclidean distance and setting a de-duplication threshold, samples with too close distances are excluded.

[0019] Further, a weighted fusion prediction model is constructed, and the fusion weight and hyperparameters are optimized by combining the IRUN algorithm,

[0020] The final prediction value is obtained by weighted average combination of the prediction values of multiple base models The calculation method is as follows:

[0021]

[0022] In the formula: is the final prediction value; k is the number of models participating in fusion; represents the prediction output of the i-th model, w i is the corresponding weight;

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

[0024]

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

[0026] At the same time, the candidate solution X new is obtained by the following update method:

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

[0028] In the formula: X new is the candidate solution; X c is the current solution; r is a random factor; g is an individual influence factor; μ is a local and global search factor; SF is an adaptive factor controlling the search step; SM is a search direction; X m is the current optimal solution.

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

[0030] ① GPS initialization improvement strategy: the GPS initialization strategy is used to replace the random population initialization strategy of the traditional MOCGO, and the initial parameter combination generated by GPS is scaled as follows:

[0031]

[0032] In the formula: represents the value of the ith individual in the jth process parameter dimension; are the lower limit and the upper limit of the jth process parameter, respectively. j p is a prime number corresponding to the jth dimension; and N is the population size.

[0033] ② Cauchy local variation improvement strategy: the Cauchy local variation strategy is used to replace the random seed generation strategy of the traditional MOCGO algorithm, and the implementation is as follows:

[0034]

[0035] In the formula: x new is the candidate solution generated by Cauchy local variation; x is the local optimal solution; C(0, 1) is a random variable of standard Cauchy distribution; and γ is a jump amplitude factor for controlling the jump amplitude, and is taken as 0.5.

[0036] ③ Lévy flight variation improvement strategy: on the basis of the four diversification seed generation strategies of the traditional MOCGO algorithm, a local disturbance strategy based on Lévy flight distribution is added as the fifth seed generation strategy, and the expression is as follows:

[0037]

[0038] In the formula: X new is the candidate solution generated by Lévy flight variation; x is the local optimal solution; u is a normal distribution with a mean of 0 and a variance of ; 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 index, β ∈ (1, 2], and is taken as 1.5; and a is the scaling factor, and is taken as 0.5.

[0039] ④ Adaptive PBI distance sorting strategy: the adaptive PBI distance sorting strategy is introduced on the basis of the traditional PBI method, and the expression is as follows:

[0040] PBI i = d1 + θ · d2

[0041] where: PBI i is the PBI distance value of the i-th solution; d1 is the projection distance; d2 is the perpendicular offset distance; θ is the penalty factor to adjust the punishment intensity of the solution deviating from the ideal direction;

[0042] The improvement strategy of the penalty factor θ:

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

[0044] where: θ i is the penalty factor value of the i-th solution; θ base is the initial value of the penalty factor, taking 1.0; δ is the adjustment coefficient, taking 0.5; f i norm is the average vector of the i-th solution; f norm is the average vector of the normalized target.

[0045] Compared with the prior art, the injection molding process parameter coupling simulation multi-objective optimization method aims at the warping deformation, volume shrinkage and clamping force defect problems in injection molding, builds an integrated framework of test design, fusion model prediction and multi-objective optimization, realizes the uniform distribution of data space by introducing LHS local sampling based on CCD, adopts RF, XGBoost, MLP and LSTM to build a weighted fusion prediction model, and combines the IRUN algorithm to optimize the fusion weight and super parameter, thereby improving the prediction performance, and the SHAP analysis further verifies the explainability and physical consistency of the optimal models XGBoost-MLP and XGBoost-LSTM; in the optimization aspect, the MSI-MOCGO algorithm is proposed, the GPS initial strategy, Cauchy disturbance and Lévy flight variation are introduced, and the adaptive PBI sorting mechanism is used to strengthen the search performance, compared with the MSEA, MOCGDE and NSGA-III algorithms, the MSI-MOCGO is better in the solution quality and distribution, the verification error of the obtained optimal parameter combination in the Moldflow simulation is less than 5%, the warping deformation, volume shrinkage and clamping force are reduced by 24%, 6.3% and 7.4% respectively, and the effectiveness of the prediction and optimization strategies is verified; the structural strength verification is completed in ANSYS, and the results show that the maximum deformation and equivalent stress of the plastic part under the assembly and use load are far lower than the design limit and the material yield strength, the strain distribution is uniform, and the plastic part has good structural safety and rigidity; the overall results show that the injection molding process parameter coupling simulation multi-objective optimization method can balance the accuracy and practicality, and can provide a feasible and reliable injection molding process parameter optimization solution for ensuring the molding accuracy, dimensional stability and equipment operation stability of the plastic part and lower energy consumption. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 is a three-dimensional model diagram of the ABS plastic injection molding sensor shell plastic part of the embodiment of the application, wherein (a) is a front view of the sensor shell plastic part, and (b) is a back view of the sensor shell plastic part;

[0047] Figure 2 is an initial parameter simulation result diagram of the embodiment of the application, wherein (a) is a warping deformation simulation result diagram, (b) is a volume shrinkage simulation result diagram, and (c) is a clamping force simulation result diagram;

[0048] Figure 3 is a CCD+LHS hybrid data set distribution diagram of the embodiment of the application;

[0049] Figure 4 is a model evaluation index comparison diagram of the embodiment of the application, wherein (a) is a warping deformation evaluation index comparison diagram, (b) is a volume shrinkage rate evaluation index comparison diagram, and (c) is a clamping force evaluation index comparison diagram;

[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] To balance the structural strength, assembly accuracy and heat dissipation performance, the filling, packing, cooling and warpage analysis were carried out in sequence by Moldflow to preliminarily evaluate the molding quality.

[0058] The finite element mesh was divided by high-quality triangular elements to avoid numerical instability caused by slender elements. The mesh matching rate was 92% (flow analysis) and 93% (warpage analysis), which met the simulation accuracy requirements. The point gate was used for the gating system, and the cooling system was designed to cover the key hot zone. The cooling stage accounted for about 2 / 3 of the molding cycle, which was 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] Warpage deformation: As shown in Figure 2 (a), the maximum warpage deformation of the plastic part was 0.7645mm, which exceeded the design requirement of 0.6mm. The stress concentration caused by temperature gradient and uneven shrinkage led to the final molding accuracy.

[0061] Volume shrinkage: As shown in Figure 2 (b), the maximum volume shrinkage rate of the plastic part was 7.124%, which was slightly higher than the upper limit of the design tolerance of 7%. This was due to the uneven cooling rate and the difference in solidification shrinkage between the inner and outer layers of the material, which led to the overall size shrinkage deviation and affected the product assembly accuracy.

[0062] Clamping force: As shown in Figure 2 (c), the maximum clamping force of the plastic part was 163.454t, which did not reach the equipment load limit, but the higher clamping force corresponded to higher energy consumption, which might exacerbate mold fatigue and maintenance pressure.

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

[0064] 2、Data sampling

[0065] In this example, 7 injection molding process parameters were selected as input variables, including melt temperature (T m / ℃), mold temperature (T e / ℃), injection pressure (P i / MPa), packing pressure (P k / MPa), injection time (t i / s), packing time (t k / s), and cooling time (t c7 process parameters as experimental variables, with warpage deformation (W / mm), volume shrinkage (V / %) and clamping force (C / t) as the molding quality objectives. The process parameter ranges are mainly based on the ABS (PA-757) material technical manual, supplemented by international injection molding process standards. The specific intervals 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 effect between variables and the uniformity of samples, the sampling strategy comprehensively uses central composite design (CCD) and Latin hypercube sampling (LHS) to improve the model generalization ability and optimization accuracy.

[0066] 2.1 Global data sampling based on CCD

[0067] The CCD experimental design uses full factorial design, and sets the axial distance coefficient α = 0.6 to ensure that the axis points are within the actual operating range of the parameters, avoid the appearance of unfeasible process parameter combinations, and cover the parameter boundary characteristics. Finally, the CCD experimental design contains 152 test points, which are composed as follows:

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

[0069] ② 10 center points (all parameters take the center level);

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

[0071] 2.2 Local data optimization sampling based on LHS

[0072] LHS ensures that the values of each variable are uniformly covered in its defined interval through random stratified sampling, improving the representativeness of the parameter space. In this embodiment, 38 LHS gap samples are based on the high, medium and low levels of the CCD test data, of which 19 are taken from the left gap (low level-medium level) and 19 are taken from the right gap (medium level-high level) to optimize the uniform coverage of the parameter space. The calculation method of LHS test points is as follows:

[0073]

[0074]

[0075] In the formula: is the left gap LHS test point; 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] From Table 1, it can be seen that LSTM performs best in the prediction of warpage and clamp force, while XGBoost is the most stable in the prediction of volume shrinkage. Therefore, when constructing the initial fusion model, each sub-model is assigned a corresponding weight according to its prediction performance, which serves as the initial value of weight optimization.

[0085] 3.2 Model weight initialization

[0086] The fusion model combines the prediction values of multiple base models through weighted averaging to obtain the final prediction value The calculation method is as follows:

[0087]

[0088] In the formula: is the final prediction value; k is the number of models participating in fusion; represents the prediction output of the i-th model, w i is the corresponding weight.

[0089] Taking the combined model RF-MLP as an example, in the prediction of warpage, the R 2 of the two models are 0.94 and 0.95, respectively, so the initial weight distribution is:

[0090]

[0091] 3.3 Hyperparameter space definition and combination

[0092] In addition to the fusion weight, each sub-model in the fusion model contains multiple hyperparameters to be optimized. Therefore, to improve the overall performance of the fusion model, the present application adopts the RUN optimization algorithm to jointly perform global optimization on the model weight coefficients and the hyperparameters of each sub-model.

[0093] To further improve the performance of the RUN algorithm, the present application adopts the Guo-Ping Shao's good point set (GPS) initialization strategy to replace the random population initialization method in RUN, obtaining the IRUN optimization algorithm. Considering that the hyperparameters in the fusion model all have clear upper and lower limits, the original sample points generated by GPS can be normalized and scaled according to the following formula to ensure that they are distributed within the effective value range of each parameter:

[0094]

[0095] In the formula: represents the value of the i-th individual in the j-th hyperparameter dimension; are the lower limit and the upper limit of the j-th hyperparameter, respectively; p j is the corresponding prime number of the j-th dimension; N is the population size; D is 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] Firstly, melt temperature has significant influence on all targets, SHAP value distribution shows that its high value (red) corresponds to significant negative contribution (-0.6~ -1) in warpage target, indicating that high temperature helps to improve fluidity and inhibit warpage; while in volume shrinkage and clamp force, it shows positive contribution (+0.5~ +1), revealing that high temperature is beneficial to filling but increases shrinkage and mold load, which exists typical target conflict.

[0114] Secondly, the influence of holding pressure on warpage, volume shrinkage and clamp force, its SHAP distribution shows that high value produces negative influence on warpage and volume shrinkage (-0.2~ -0.5), but strong positive contribution on clamp force (+0.3~ +1), indicating that increasing holding pressure can inhibit shrinkage stress, but also increase mold load.

[0115] Injection pressure has the most significant influence on clamp force, SHAP value analysis shows that its high value has a sustained positive influence on clamp force (+0.2~ +0.4), while on warpage and volume shrinkage, it shows negative effect as a whole, emphasizing its dual effect between filling and mold load.

[0116] Injection time has certain influence on volume shrinkage and clamp force, producing negative SHAP value, too low will increase volume shrinkage and clamp force, which shows that short injection time leads to insufficient filling, but has certain increasing influence on warpage deformation.

[0117] Relatively speaking, mold temperature, holding time and cooling time show lower importance in three targets, SHAP value distribution is gentle, with small change range, indicating that its direct influence on output is weak under the test conditions, more showing the synergistic compensation effect with dominant parameters.

[0118] 4. Multi-strategy enhanced MOCGO multi-objective optimization

[0119] To further realize the collaborative minimization of warpage deformation, volume shrinkage and clamp force, the MSI-MOCGO optimization framework is constructed to optimize the multi-objective process parameters of the prediction model output. In view of the significant nonlinear coupling and mutual conflict characteristics of the three quality targets, three improved strategies (GPS initialization, Cauchy local variation, Lévy flight variation) and ordering strategies (adaptive PBI distance) are introduced to improve the optimization performance on the basis of standard MOCGO.

[0120] 4.1 Initialization of good point set

[0121] To improve the distribution quality of the initial population of the MOCGO algorithm, the present embodiment adopts the Hua Luo Geng GPS method to replace 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: represents the value of the ith individual in the jth process parameter dimension; respectively, the lower limit and the upper limit of the jth process parameter; p j is the corresponding prime number of the jth dimension; N is the population size.

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

[0125] The traditional MOCGO algorithm adopts four diversification seed generation strategies (global exploration seed, guided seed, historical seed and random seed) to achieve the dynamic balance of global search and local development. However, in the actual optimization process, the uniform disturbance of the random seed in the four generation strategies may lead to insufficient exploration of the local region.

[0126] Therefore, the present application introduces a Cauchy local mutation strategy to replace the fourth seed update method. The core idea is: on the basis of the current optimal solution (Leader), a disturbance term obeying Cauchy distribution is introduced, and the disturbance amplitude is gradually reduced according to the iteration process, realizing adaptive fine disturbance of the solution, and the implementation is as follows:

[0127]

[0128] In the formula: x new is the candidate solution generated by Cauchy local mutation; x is the local optimal solution; C(0,1) is a random variable of standard Cauchy distribution; γ is a jump amplitude factor controlling the jump amplitude, taking 0.5.

[0129] 4.3 Add the fifth type of local disturbance seed (Lévy flight mutation)

[0130] In order to further enhance the jumping ability of the population in the local region, a fifth type of seed generation mechanism is added, that is, a local disturbance strategy based on Lévy flight distribution. X new The final solution vector needs to be processed to ensure that it is within the allowed search space [lb, ub], and this strategy generates a long-short step mixed disturbance through Lévy distribution to break through the local optimal solution (x leader ), and the expression is as follows:

[0131]

[0132] In the formula, X new is a candidate solution generated by Lévy flight variation; x is a local optimal solution; u is a normal distribution with a mean of 0 and a variance of ; v is a standard normal distribution with a mean of 0 and a variance of 1; ub is an upper limit of a process parameter; lb is a lower limit of a process parameter; β is a Lévy index, β ∈ (1, 2], and is 1.5; a is a scaling factor, and is 0.5.

[0133] 4.4 Adaptive PBI distance strategy

[0134] To further improve the expression accuracy and difference of multi-objective optimization algorithm in the sorting of Pareto front, the application introduces an adaptive PBI distance sorting strategy for fine evaluation and optimization of the Pareto front generated by MOCGO on the basis of the traditional boundary intersection aggregation (PBI) method. The PBI method maps the solution to two distances on the preset direction vector: the projection distance d1 and the vertical offset distance d2, and then calculates the “deviation degree” of the solution to the ideal direction. The core idea is:

[0135] PBI i = d1 + θ · d2

[0136] In the formula, PBI i is the PBI distance value of the i th solution; d1 is the projection distance; d2 is the vertical offset distance; θ is a penalty factor, which is used to adjust the deviation penalty intensity of the solution outside the ideal direction.

[0137] However, in actual application, the fixed θ parameter is often difficult to balance the convergence of the solution set in the dense area and the distribution in the sparse area. Therefore, the application designs the following improvement strategy:

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

[0139] In the formula, θ i is the penalty factor value of the i th solution; θ base is the initial value of the penalty factor, and is 1.0; δ is an adjustment coefficient, and is 0.5; f i norm is the average vector of the i th solution; f norm is the average vector of the normalized target.

[0140] The strategy can apply strong punishment when the solution deviates from the mean value, so as to improve the selectivity of the sorting.

[0141] 4.5 Pareto front and optimal process parameter selection

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

[0143] To evaluate the performance of MSI-MOCGO algorithm, three mainstream multi-objective optimization indicators: inverse generational distance (IGD), hyper volume (HV) and spacing index are adopted for comparison with MSEA, MOCGO, MOCGDE and NSGA III. As shown in Figure 6 (a), MSI-MOCGO algorithm is significantly better than the comparison algorithms in IGD (3.452) and spacing (0.690) two indicators, indicating that it performs better in solution set distribution uniformity and close to the optimal front; although its HV (238.50) is slightly lower than MSEA and MOCGDE, but the overall optimization quality is the most balanced.

[0144] The Pareto front distribution is shown in Figure 6 (b), the model obtains a good compromise solution among the three objectives: warping deformation, volume shrinkage and clamping force. For example, the 7th solution (0.973 mm, 6.058%, 111.648 t) ensures the minimum clamping force while controlling warping and shrinkage well, which is suitable for scenarios sensitive to energy consumption and equipment requirements; while the 4th solution (0.533 mm, 6.497%, 159.875 t) performs outstanding in reducing warping, which is suitable for products with extremely high molding precision requirements. Further, by analyzing the single-objective extreme points, it can be obtained that W min is 0.3859 mm (85th group), V min is 5.2474% (38th group), and C min is 109.5951 t (76th group), which can provide a reference basis for different optimization tendencies.

[0145] To verify the effectiveness of the proposed adaptive PBI multi-objective optimization strategy under the quality constraints, this embodiment sets the warping of no more than 0.6 mm and the volume shrinkage of no more than 7% as the screening criteria, filters and analyzes the optimization results, and finally obtains 9 groups of feasible solutions as shown in Table 4. The results show that the warping deformation of all solutions is controlled in the range of 0.4700-0.5642 mm, and the volume shrinkage is in the range of 6.3982%-6.8762%, which are better than the preset threshold, 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) has a relatively optimal level of warping (0.5642 mm) and volume shrinkage (6.6913%), while significantly reducing the clamping force (153.6680 t), achieving a good balance between quality and energy consumption, and reflecting strong engineering practicability and comprehensive advantages.

[0146] Table 4 Pareto front score solution

[0147]

[0148] 5. Moldflow-ANSYS coupling simulation verification

[0149] To verify the engineering feasibility of the optimal process parameter combination, Moldflow and ANSYS are combined to perform full-process coupling simulation analysis on the molding quality and structural performance of the plastic part of the embodiment. First, the quality target is verified by injection molding simulation in Moldflow; then the simulation results are imported into ANSYS for structural strength analysis to comprehensively evaluate the practical application value of the optimization scheme.

[0150] 5.1 Moldflow injection molding analysis

[0151] Among all the solutions that meet the constraint conditions, the optimal process parameter combination with the lowest score is: melt temperature 215.12°C, mold temperature 58.63°C, injection pressure 81.14 MPa, holding pressure 59.70 MPa, injection time 4.90 s, holding time 25.77 s, and cooling time 26.20 s. The parameter combination is input into Moldflow for simulation analysis to obtain the following molding quality index results: warping deformation 0.5775 mm, volume shrinkage 6.675%, and clamping force 151.233 t, as shown in Figure 7 .

[0152] Compared with the molding results under the initial process parameter combination, the three key quality indicators are reduced by 24.0% (warping deformation), 6.3% (volume shrinkage), and 7.4% (clamping force), respectively, fully verifying the effectiveness of the optimization scheme in improving the quality of the product.

[0153] In addition, to verify the reliability of the prediction model at the optimal solution, the predicted values (0.5642 mm, 6.691%, 153.668 t) were compared with the simulation values for errors, and the three errors were 2.3%, 0.2%, and 1.6%, respectively, all controlled within 5%, verifying 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 the molded plastic part in actual application, the results of the plastic part under the optimal process parameter combination 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 working condition: 60N vertical compression force was applied at each of the four screw hole positions, with a total assembly load of 240N. The simulation results showed that the maximum total deformation was 0.3947mm, which was far below the allowable tolerance value of 0.6mm, and the assembly precision was good. The maximum equivalent stress (von Mises) was 4.4548MPa, which was only 9.9% of the yield strength (45-60MPa) of ABS material, corresponding to a safety factor of about 10.1, indicating that the structural strength was sufficient. The maximum equivalent elastic strain was 0.0017603, which was within the material elastic range, and no plastic deformation occurred, the stress distribution was uniform, and there was no obvious concentration area.

[0157] Operation pressing working condition: a 40N vertical concentrated load was applied at the center of the top of the plastic part, and a fixed constraint was set at the bottom to simulate the actual installation state. The simulation results showed that the maximum total deformation was 0.01416mm, which was significantly smaller than the deformation under the assembly working condition, indicating that the structure had good compression stiffness and deformation control ability. The maximum von Mises stress was 38.68MPa, which was close to the lower limit of the material yield but still within the safety range, with a safety factor of about 1.2, and the structure had certain bearing margin. The maximum equivalent strain was 0.0003424, which was still within the material elastic limit, and no plastic deformation occurred, and the stress concentration area was obvious but did not cause local failure risk.

[0158] Through the completion of structural strength verification in ANSYS, the structure of the plastic part in the embodiment did not have excessive deformation or material yield under the action of assembly load and use load, and the maximum deformation and equivalent stress were far below the design limit and material yield strength, the strain distribution was uniform, and the structure had good structural safety and stiffness, verifying the structural safety and applicability of the plastic part under the optimal process parameter combination in actual molding and use scenarios.

[0159] This injection molding process parameter coupling simulation multi-objective optimization method aims at the warping deformation, volume shrinkage and clamping force defects in injection molding. An integrated framework of experimental design, model prediction and multi-objective optimization is constructed. LHS local sampling is introduced on the basis of CCD to realize the uniform distribution of data space. RF, XGBoost, MLP and LSTM are used to construct a weighted fusion prediction model, and the IRUN algorithm is used to optimize the fusion weight and hyperparameters to improve the prediction performance. SHAP analysis further verifies the explainability and physical consistency of the optimal models XGBoost-MLP and XGBoost-LSTM. In terms of optimization, MSI-MOCGO is proposed, which introduces GPS initial strategy, Cauchy disturbance and Lévy flight mutation, and uses adaptive PBI sorting mechanism to enhance search performance. Compared with MSEA, MOCGDE and NSGA-III, MSI-MOCGO performs better in solution quality and distribution. The optimal parameter combination obtained has a verification error of less than 5% in Moldflow simulation, and the warping deformation, volume shrinkage and clamping force are reduced by 24%, 6.3% and 7.4% respectively, which verifies the effectiveness of the prediction and optimization strategies.

Claims

1. A method of multi-objective optimization of injection molding process parameter coupling simulation, characterized in that, Specifically comprising the following steps: Step 1, with the minimum warping deformation, the minimum volume shrinkage and the minimum clamping force as the quality optimization objectives, selecting the process parameters affecting the three objectives as the optimization design variables, constructing an integrated framework of experimental design and fusion prediction model, and obtaining the optimal prediction model after optimization; Step 2, constructing an MSI-MOCGO optimization framework to optimize the multi-objective process parameters output by the optimal prediction model; Step 3, based on the optimal prediction model and MSI-MOCGO, performing comprehensive optimization of the three objectives, obtaining the Pareto frontier and selecting the optimal process parameter combination.

2. The multi-objective optimization method of injection molding process parameters coupling simulation according to claim 1, characterized in that, In Step 1, when constructing the integrated framework of experimental design and fusion prediction model, LHS local sampling is introduced based on CCD; RF, XGBoost, MLP and LSTM are used to construct weighted fusion prediction models XGBoost-MLP, XGBoost-LSTM, RF-MLP and RF-LSTM, and IRUN algorithm is used to optimize the fusion weights and hyperparameters, and the optimal prediction models XGBoost-MLP and XGBoost-LSTM are obtained.

3. The multi-objective optimization method of injection molding process parameter coupling simulation according to claim 2, characterized in that, When LHS local sampling is introduced based on CCD, the calculation method of LHS test points is as follows: wherein: LHS test point for left gap; LHS test point for right gap; ub i upper limit for parameter; lb i is the parameter lower limit; center i is the parameter center value; r i is a random number between [0, 1] The Minimax strategy is used to optimize the minimum distance of the sampling points, and the LHS samples are selected as supplementary test points; By calculating the Euclidean distance and setting a threshold for removing close samples.

4. The multi-objective optimization method of injection molding process parameter coupling simulation according to claim 2, characterized in that, When constructing weighted fusion prediction models and optimizing fusion weights and hyperparameters with IRUN algorithm, The final prediction value is obtained by weighted average combination of the prediction values of the plurality of base models It is calculated as follows: In the formula: is the final prediction value; k is the number of models participating in fusion; represents the prediction output of the i-th model, w i is the corresponding weight thereof; The original sample points generated by GPS are normalized and mapped according to the following formula: wherein: represents the value of the ith individual at the jth hyperparameter dimension; are the lower and upper bounds of the jth hyperparameter, respectively; p j is the prime number corresponding to the jth dimension; N is the population size; D is the hyperparameter dimension; At the same time, the candidate solution X in the IRUN optimization algorithm new is obtained by updating as follows: X new = (X c + r x SF x g x X c ) + SF x SM + μ x (X m - X c ) where X new is the candidate solution; X c is the current solution; r is a random factor; g is an individual influence factor; μ is a local and global search factor; SF is an adaptive factor that controls the step size of the search; SM is the search direction; X m is the current best solution.

5. The multi-objective optimization method of injection molding process parameter coupling simulation according to claim 1, characterized in that, In Step 2, when constructing the MSI-MOCGO optimization framework, the GPS initialization improvement strategy, Cauchy local mutation improvement strategy, Lévy flight mutation improvement strategy and adaptive PBI distance sorting strategy are introduced based on the standard MOCGO, as follows: ① GPS initialization improvement strategy: GPS initialization strategy is used to replace the random population initialization strategy of traditional MOCGO, and the initial parameter combination generated by GPS is scaled as follows: In the formula: represents the value of the ith individual in the jth process parameter dimension; respectively, the lower limit and the upper limit of the jth process parameter; p j is the prime number corresponding to the jth dimension; N is the population size; ② Cauchy local mutation improvement strategy: Cauchy local mutation strategy is used to replace the random seed generation strategy of traditional MOCGO algorithm, and the implementation is as follows: where: x new Cauchy local variation generated candidate solution; x is the local optimal solution; C(0,1) is a random variable of the standard Cauchy distribution; gamma is a jump amplitude factor controlling the jump amplitude, taking 0.5; ③ Lévy flight mutation improvement strategy: Based on the four diversification seed generation strategies of traditional MOCGO algorithm, a new local disturbance strategy based on Lévy flight distribution is added as the fifth seed generation strategy, and the expression is as follows: where: X new candidate solution generated by Lévy flight variation; x is a local optimum solution; u is a normal distribution with mean 0 and variance v is a standard normal distribution with mean 0 and variance 1; ub is an upper limit of process parameters; lb is the lower limit of the process parameter; β is the Lévy index, β ∈ (1, 2], and is taken as 1.5; a is the scaling factor, taken as 0.5; ④ Adaptive PBI distance sorting strategy: The adaptive PBI distance sorting strategy is introduced based on the traditional PBI method, and the expression is as follows: PBI i = d1 + θ · d2 PBI = d1 + d2 cos θ i PBI distance value for the ith solution; d1 is the projection distance; d2 is the perpendicular offset distance; θ is a penalty factor to adjust the strength of the penalty for deviation from the ideal direction; The improvement strategy of the penalty factor θ is: θ i = θ base ·(1 + δ · ||f i norm -f norm ||) where θ i is the penalty factor value for the i-th solution; θ base is the initial value of the penalty factor, taken as 1.0; δ is the adjustment coefficient, taken as 0.5; f i norm is the average vector of the i-th solution; f norm is the average vector of the normalized target.

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