An injection molding quality optimization method for plastic alloy products

Abstract

The present invention discloses a method for optimizing the injection molding quality of plastic alloy products. Taking the warpage deformation amount and volume shrinkage rate of PC / ABS plastic alloy injection molded products as the quality optimization objectives, firstly, the experimental scheme results are obtained based on CAE simulation and orthogonal experimental design. Then, the water cycle algorithm (WCA) is used to continuously iterate to search for the optimal kernel extreme learning machine (KELM) kernel function parameter σ and regularization coefficient C, and a KELM prediction model optimized by the water cycle algorithm (WCA-KELM) is constructed. Then, the multi-objective seagull optimization algorithm (MOSOA) is used to find the Pareto optimal front. Finally, the grey relational evaluation method is used to obtain the optimal solution from the Pareto optimal front. The present invention can effectively reduce the warpage deformation amount and volume shrinkage rate of PC / ABS plastic alloy injection molded products, and can provide a theoretical basis and data support for obtaining the optimal combination of process parameters for PC / ABS plastic alloy injection molding.

Description

Technical Field

[0001] The present invention relates to a method for optimizing the molding quality of injection molded products, specifically a method for optimizing the injection molding quality of plastic alloy products based on WCA-KELM and MOSOA, belonging to the technical field of injection molding processing. Background Art

[0002] Plastic alloy is a new type of high-performance, functionalized and specialized material obtained by physical blending or chemical grafting methods. Plastic alloys can improve or enhance the properties of existing plastics and reduce costs, and have become one of the most active varieties in the plastics industry. Plastic alloys include general plastic alloys (such as PVC, PE, PP, etc.), engineering plastic alloys (such as PTFE, PA, PBT, etc.) and PC / ABS plastic alloys. PC / ABS plastic alloy is a thermoplastic plastic formed by mixing polycarbonate (PC) and acrylonitrile-butadiene-styrene (ABS). It combines the excellent properties of the two materials, the moldability of ABS material and the mechanical properties, impact strength, heat resistance and ultraviolet resistance (UV) of PC, and is widely used in automotive interior parts, office machines, communication equipment, household appliances and lighting equipment. In recent years, the output of PC / ABS plastic alloy has been increasing at a rate of about 10% per year, and currently the research on PC / ABS plastic alloying has become a hot spot in the research of polymer plastic alloys.

[0003] Injection molding is the main molding method for PC / ABS plastic alloy products. Different from other processes, injection molding is a complex non-linear dynamic process, involving the interaction of machine parameters, material properties and process variables. The injection process is affected by various factors: material properties, mold wear, temperature fluctuations, process parameters, etc. Warping and volume shrinkage are two common quality defects in the injection molding process of PC / ABS plastic alloy products.

[0004] The forming quality of injection-molded products depends to a great extent on process parameters. Traditional methods for optimizing process parameters require repeated mold trials, resulting in a waste of time costs. In recent years, researchers have begun to use mathematical surrogate models to establish the relationship between quality objectives and process parameters, and then obtain the optimal combination of process parameters through search-based optimization algorithms, thereby significantly shortening the research time and improving production efficiency. For example, Cao Y et al. used the Random Forest (RF) algorithm to establish a regression model, and used the genetic algorithm to search for the minimum value of the regression model established by RF to find the optimal process parameters for improving the quality of plastic parts and reducing energy consumption; Chu H et al. used the Kriging model to fit the relationship between the warpage of the gating system and structural parameters, and used the genetic algorithm to optimize the minimum warpage to obtain the optimal structural parameters; Hazwan MHM et al. used optimization methods such as the Response Surface Method (RSM), Genetic Algorithm (GA) and Glowworm Swarm Optimization (GSO) in their research to achieve the goal of minimizing the warpage of the front panel housing formed by acrylonitrile-butadiene-styrene (ABS).

[0005] In addition, due to the usually multiple defects, multi-objective optimization has always been the focus of many researchers. From the perspective of multiple objectives, all objectives are mutually restrictive, and improving one objective may come at the expense of other objectives. For the multi-objective problem in the field of injection molding process parameter optimization, it is usually to apply a variety of comprehensive evaluation methods to transform the multi-objective problem into a single-objective problem, and then select the optimal solution. For example, Li S et al. applied the multi-criteria fuzzy decision-making method based on fuzzy set theory; Li C et al. used the NSGA-II algorithm to solve the model to obtain the Pareto optimal front, and used the entropy weight TOPSIS method to evaluate the Pareto optimal front to obtain the optimal solution; Liu X et al. used MOFA to find the Pareto optimal front, and used the GRA-TOPSIS method to find the optimal solution from the Pareto optimal front. Currently, in the research on multi-objective optimization of injection process parameters, researchers often determine the final Pareto optimal solution based on engineering experience and repeated tests. Therefore, for the optimization of injection molding process parameters of PC / ABS plastic alloy parts, how to determine the optimal trade-off scheme to achieve the best comprehensive purpose is still a difficult problem in the industry. Summary of the Invention

[0006] In view of the above problems, the present invention provides a method for optimizing the injection quality of plastic alloy products, which can effectively reduce the warpage deformation and volume shrinkage rate of PC / ABS plastic alloy injection-molded products, and then obtain high-quality PC / ABS plastic alloy parts products, and can provide a theoretical basis and data support for obtaining the optimal combination of optimal process parameters for PC / ABS plastic alloy injection molding.

[0007] To achieve the above object, the injection molding quality optimization method for the plastic alloy product specifically includes the following steps:

[0008] Step1, taking the warpage deformation amount and the volume shrinkage rate as the optimization objectives, selecting the injection molding process parameters and their value ranges as the optimization design variables, conducting experimental design according to the value ranges of each process parameter, and performing injection molding simulation to obtain the simulation test results;

[0009] Step2, improving KELM based on the simulation test results:

[0010] ELM consists of three layers: N input layers, L hidden layers, and M output layers. For N different samples (x i ,y i )∈R N ×R M , i = 1, 2, …, N. If the output is denoted as T, the output of ELM is expressed as:

[0011]

[0012] β = H + T

[0013] H + = H T (HH T ) -1

[0014] In the formula: H and h(x) are the output matrices of the hidden layer; H T is the transpose matrix of H; H + is the generalized inverse matrix of H; K is the number of hidden layer neurons; g(·) is the activation function; β is the connection weight between the hidden layer neurons and the output layer neurons; ω is the weight vector between the input layer neurons and the hidden layer neurons; b is the bias of the hidden layer neurons;

[0015] Introduce a kernel function to measure the similarity between samples, and define the kernel matrix of KELM according to the Mercer condition, which is expressed as follows:

[0016]

[0017] In the formula: K(x i ,x j ) is the kernel function, which is set as the RBF kernel, and the kernel function is expressed as follows:

[0018] K(x i ,x j ) = exp{-||x i - x j || / 2σ 2}

[0019] where: σ is the kernel function parameter;

[0020] The expression of the output function of the KELM model is:

[0021]

[0022] where: H and h(x) are the output matrices of the hidden layer; H T is the transpose matrix of H; I is the identity matrix; C is the regularization coefficient; T represents the expected output;

[0023] Use WCA to continuously iterate to search for the optimal KELM kernel function parameter σ and KELM regularization coefficient C, and construct the WCA-KELM prediction model;

[0024] Step3, use MOSOA to iteratively optimize on the WCA-KELM prediction model to obtain the Pareto optimal front;

[0025] Step4, use grey relational evaluation to obtain the optimal solution from the Pareto optimal front.

[0026] Furthermore, in Step3, the selection of MOSOA iterative optimization is based on fitness, retaining individuals with high fitness and eliminating individuals with low fitness.

[0027] Furthermore, in Step4, the specific process of grey relational evaluation is as follows:

[0028] ① Judge the type of the original data. Suppose there are n evaluation objects and m evaluation indicators. X ij represents the original value of the jth indicator in the ith evaluation scheme, then the original matrix is denoted as Z ij , both the warping deformation amount and the volume shrinkage rate belong to the extremely small type of indicators. The original matrix is normalized to obtain the normalized matrix, so that both the warping deformation amount and the volume shrinkage rate are converted into the extremely large type of indicators;

[0029] ② Preprocess the normalized matrix. The formula is as follows:

[0030]

[0031] where: k is the sequence length; i is the number of rows of the matrix;

[0032] ③ Take the maximum value of each row of the preprocessed matrix to form a fictitious mother sequence:

[0033] The reference sequence is denoted as: X'0(k) = {x0(1), x0(2), …, x0(k)}

[0034] The comparison sequence is denoted as: X' i (k) = {xi (1), x i (2), …, x i (k)}

[0035] ④ Calculate the minimum difference a and the maximum difference b between the two poles. The formula is as follows:

[0036]

[0037] In the formula: a is the minimum difference between the two poles; b is the maximum difference between the two poles;

[0038] ⑤ Calculate the correlation coefficients between each index in the subsequence and the mother sequence. The formula is as follows:

[0039]

[0040] In the formula: ρ is the resolution coefficient, which takes values between (0, 1);

[0041] ⑥ Calculate the grey correlation degrees between each index and the mother sequence. The formula is as follows:

[0042]

[0043] In the formula: n is the number of evaluation objects;

[0044] ⑦ Calculate the weights of each index. The formula is as follows:

[0045] w n = y n (x0, x1) / (y1(x0, x1)+y2(x0, x2)+…+y n (x0, x n ))

[0046] In the formula: w n is the weight;

[0047] ⑧ Calculate the score of the k-th evaluation object. The formula is as follows:

[0048]

[0049] In the formula: S k is the score of the k-th evaluation object; Z ki is the matrix obtained after the preprocessing in step ② above; m is the number of evaluation indexes, and in this embodiment, m = 2.

[0050] Furthermore, in step ⑤, the value of ρ is 0.5.

[0051] Furthermore, in Step1, the experimental design adopts an orthogonal experiment.

[0052] Compared with the prior art, the injection molding quality optimization method for the plastic alloy product aims at the warpage deformation amount and volume shrinkage rate of the PC / ABS plastic alloy injection molding product. First, the experimental scheme results are obtained based on CAE simulation and orthogonal experimental design. Then, the water cycle algorithm (WCA) is used to continuously iterate to search for the optimal kernel extreme learning machine (KELM) kernel function parameter σ and KELM regularization coefficient C, and a prediction model of the kernel extreme learning machine optimized by the water cycle algorithm (WCA-KELM) is constructed. Then, the multi-objective seagull optimization algorithm (MOSOA) is used to find the Pareto optimal front. Finally, the grey relational evaluation method is used to obtain the optimal solution from the Pareto optimal front, which can effectively reduce the warpage deformation amount and volume shrinkage rate of the PC / ABS plastic alloy injection molding product, and then obtain high-quality PC / ABS plastic alloy plastic parts. The simulation verification shows that the prediction error of the warpage deformation amount and volume shrinkage rate by the WCA-KELM prediction model is controlled within 5%, and the prediction accuracy of the model is good. Moreover, the warpage deformation amount and volume shrinkage rate of the PC / ABS plastic alloy plastic parts after optimization are significantly lower than the simulation results before optimization, which can provide a theoretical basis and data support for obtaining the optimal combination of process parameters for PC / ABS plastic alloy injection molding. Description of the Drawings

[0053] Figure 1 is the three-dimensional solid diagram of the plastic part of the vacuum pump rear shell;

[0054] Figure 2 is the injection molding simulation diagram of the plastic part of the vacuum pump rear shell, where (a) is the gate matching analysis diagram and (b) is the gating system and cooling system diagram;

[0055] Figure 3 is the model structure diagram of KELM;

[0056] Figure 4 is the prediction comparison diagram between the WCA-KELM model and the KELM model, where (a) is the prediction comparison diagram of the warpage deformation amount and (b) is the prediction comparison diagram of the volume shrinkage rate;

[0057] Figure 5 is the optimal Pareto front diagram obtained by MOSOA;

[0058] Figure 6 is the grey relational evaluation scoring diagram;

[0059] Figure 7 is the optimization flow chart of the present invention;

[0060] Figure 8It is a graph of the injection molding simulation analysis results. Among them, (a) is the mold flow graph of the warpage deformation amount before optimization, (b) is the mold flow graph of the warpage deformation amount after optimization, (c) is the mold flow graph of the volume shrinkage rate before optimization, and (d) is the mold flow graph of the volume shrinkage rate after optimization. Specific implementation manner

[0061] The injection molding quality optimization method for this plastic alloy product takes the warpage deformation amount and volume shrinkage rate of PC / ABS plastic alloy injection molded products as the quality optimization objectives. First, obtain the test plan results based on CAE simulation and orthogonal experimental design; then construct an injection molding quality optimization model of kernel extreme learning machine optimized by water cycle algorithm (WCA-KELM); then use multi-objective seagull optimization algorithm (MOSOA) to find the Pareto optimal front; finally, use the grey relational evaluation method to find the optimal solution from the Pareto optimal front. The optimization flow chart of the present invention is as Figure 7 shown.

[0062] The following takes the vacuum pump rear shell plastic part injection molded from PC / ABS plastic alloy as an example to specifically illustrate the present invention.

[0063] The geometric model of the vacuum pump rear shell plastic part is as Figure 1 shown. The outer dimensions of this plastic part are 96mm×151mm×54.5mm, with a uniform thickness distribution, an average wall thickness of about 2.16mm, including structural features such as ribs, bosses, and knob holes. The material used is PC / ABS from LG Company, with the grade of HP5008. Table 1 is the recommended process parameter table for PC / ABS. To ensure the mutual assembly and fit between the front and rear covers of the plastic part, the plastic part is required to have a smooth surface and no flash. Therefore, according to the molding requirements in production, the warpage deformation amount of the plastic part should be less than 1.1mm, and the volume shrinkage rate should be less than 10%.

[0064] Table 1 Recommended process parameter table for PC / ABS

[0065]

[0066] In the Moldflow simulation software, a double-sided surface is selected to divide and repair the mesh of the vacuum pump rear shell, resulting in a total of 23,094 mesh elements, with a matching rate of over 90%, meeting the requirement of the minimum matching rate. The finite element analysis model is as Figure 2 shown. Using the Moldflow gate location analysis function, determine the best gate location, and the analysis result is as Figure 2(As shown in (a), since the plastic part has a large size and the large flat surface is rectangular, a single center gate cannot ensure balanced filling, and there will be over-packing in the width direction, resulting in large warpage deformation. Therefore, two point gates are evenly arranged to achieve balanced filling in both the length and width directions. Since the optimal gate on the left side of the analysis is located at the junction of the large flat plate and the side wall and is not suitable for setting the gate, referring to the optimal gate position on the right side, two point gates are set up, and the gating system and cooling system are established and the connectivity is tested, as shown in Figure 2 (b). Generally, it is necessary to first complete the optimization of cooling, filling, and holding pressure analysis, and then perform warpage analysis on the plastic part. Therefore, the analysis sequence is selected as "filling + cooling + holding pressure + warpage", and the recommended process parameters are used for analysis. The initial value of the maximum warpage deformation is 1.611 mm, and the initial value of the maximum volume shrinkage rate is 10.46%, which has exceeded the requirements of the vacuum pump rear shell plastic part (warpage deformation of 1.1 mm and volume shrinkage rate of 10%), and will directly affect the assembly with the front shell. Therefore, further optimization is required.

[0067] Step1. Determine the quality optimization objectives, select the injection process parameters and their value ranges, use the value ranges of each process parameter as the experimental design space, design an orthogonal experiment according to the value ranges of each process parameter, and perform injection simulation based on Moldflow to obtain the experimental results of the quality optimization objectives.

[0068] Take the warpage deformation (y1; mm) and volume shrinkage rate (y2; %) as the optimization objectives, select 7 process parameters that affect these two objectives as the optimization design variables. These 7 process parameters include melt temperature (A; °C), mold temperature (B; °C), holding pressure (C; MPa), holding time (D; s), injection pressure (E; MPa), injection time (F; s), and cooling time (G; s). All design variables are selected with 5 experimental levels. The upper and lower limits of the design variables are selected according to past production experience. Using the orthogonal experimental design method, establish an injection molding optimization process experimental plan with 7 factors and 5 levels. The orthogonal experimental factor levels are shown in Table 2, and the orthogonal experimental results are shown in Table 3.

[0069] Table 2 Orthogonal experimental factor levels

[0070]

[0071] Table 3 Experimental results

[0072]

[0073]

[0074] Step2. Build a WCA-KELM prediction model based on the simulation test results.

[0075] Extreme Learning Machine (ELM) is a single-hidden layer feedforward neural network with randomly initialized weight matrix and bias vector. Different from traditional neural networks, it does not need to update network parameters, does not need to adjust the weights of the input layer and the biases of the hidden layer, and does not need to train the network by setting a large number of parameters like traditional neural networks. Moreover, ELM has a faster convergence speed and higher learning efficiency. ELM consists of three layers: N input layers, L hidden layers, and M output layers. For N different samples (x i , y i ) ∈ R N ×R M , (i = 1, 2, …, N), if the output is denoted as T, then the output of ELM can be expressed as:

[0076]

[0077] β = H + T (3)

[0078] H + = H T (HH T ) -1 (4)

[0079] In the formula: H and h(x) are the output matrices of the hidden layer; H T is the transpose matrix of H; H + is the generalized inverse matrix of H; K is the number of hidden layer neurons; g(·) is the activation function; β is the connection weight between the hidden layer neurons and the output layer neurons; ω is the weight vector between the input layer neurons and the hidden layer neurons; b is the bias of the hidden layer neurons.

[0080] Huang et al. introduced the kernel function into ELM and proposed the Kernel ELM (KELM) algorithm based on the kernel method, which provides a unified learning framework for regression, binary classification, and multi-classification problems. By using kernel mapping to replace the random mapping in ELM, KELM has better generalization and robustness.

[0081] When the specific form of the feature mapping h(x) in the hidden layer is unknown, it is necessary to introduce a kernel function to measure the similarity between samples. The kernel matrix of KELM can be defined according to the Mercer condition as follows:

[0082]

[0083] The kernel function has an important impact on the performance of the KELM model. Therefore, selecting the correct kernel function is the first step in solving a specific problem. Wang et al. introduced seven kernel functions of KELM, such as Gaussian kernel function, linear kernel function, polynomial kernel function, Fourier kernel function, and so on. In fact, the Gaussian kernel function is one of the most commonly used kernel equations, also known as the radial basis function (RBF), which can be written as:

[0084] K(x i ,x j )=exp{-||x i -x j || / 2σ 2} (6)

[0085] Where: σ is the kernel function parameter.

[0086] Then the expression of the KELM model output function is:

[0087]

[0088] Where: H and h(x) are the output matrices of the hidden layer; H T is the transpose matrix of H; I is the identity matrix; C is the regularization coefficient, and its setting will affect the performance of KELM; T represents the expected output.

[0089] The model structure of KELM is as Figure 3 shown, K(,) represents the introduced kernel function. Since introducing the kernel function parameter σ and the regularization coefficient C will affect the performance of the KELM algorithm, σ determines the range of action of the kernel function, and C will affect the stability of the model structure. Therefore, selecting appropriate parameters is crucial for the KELM model. To make it have optimal performance, it is necessary to optimize the two parameters.

[0090] The Water cycle algorithm (WCA) is a global optimization algorithm proposed by Hadi Eskandar et al. inspired by the process of water in nature flowing from streams, rivers, and lakes to the ocean during the water cycle, where water evaporates from the ocean to form rain, and the rain regenerates streams and rivers, and the streams and rivers ultimately flow into the ocean. Currently, WCA has been applied in fields such as engineering optimization. The specific process of WCA is as follows:

[0091] ①Precipitation initialization.

[0092] In an N var -dimensional optimization problem, a raindrop is a set of vectors of size 1×N var , which can be expressed as follows:

[0093] Raindrop=[x1,x2,…,x N (17)

[0094] Assume the number of rainfall layers is N pop , generate the initial rainfall layer of N pop ×N var matrix X:

[0095] X = LB + rand × (UB - LB) (18)

[0096] Where: UB and LB are the upper and lower boundaries of the variable respectively; rand is a random number uniformly distributed between 0 and 1.

[0097] Its expanded expression is:

[0098]

[0099] ② Fitness function.

[0100] The fitness function of the raindrop individual is expressed by the following formula:

[0101]

[0102] Where: N pop is the raindrop (initial population); N vars is the dimension of the variable to be optimized.

[0103] ③ Determine the number of oceans and rivers.

[0104] Select N sr from the best individual (minimum value) as the ocean and river. The raindrop with the minimum value is considered the ocean. The single ocean is calculated by the following formula:

[0105] N sr = NumberofRivers + 1 (21)

[0106] The rest of the raindrop (forming the raindrop flow to the river or directly to the sea) is calculated by the following formula:

[0107] N Raindrops = N pop - N sr (22)

[0108] Use the following formula to determine the intensity of the raindrop flowing to the river and the ocean:

[0109]

[0110] Where: NS n is the number of streams flowing to a specific river or ocean.

[0111] ④ Confluence.

[0112] During the water cycle, rainfall forms streams. Some of the streams flow into rivers, and the other part flows directly into the sea. Here, it is assumed that all rivers and streams will eventually flow into the sea. If the fitness value given by a stream is better than that of the river it is connected to, the positions of the river and the stream are swapped. This kind of exchange can also occur between a river and the sea. The new positions of the stream and the river can be expressed as:

[0113]

[0114] where: rand is a random number uniformly distributed between 0 and 1; respectively represent the positions of the stream, the river, and the sea in the i-th iteration.

[0115] ⑤ Evaporation.

[0116] Evaporation can prevent the algorithm from premature convergence. During the water cycle, water continuously evaporates from the water surface (or the ground, plant surfaces, etc.), turns into water vapor, rises into the atmosphere to form clouds, then condenses, and returns to the earth's surface in the form of rainfall, and finally returns to the sea.

[0117] In the WCA algorithm indicates the end of the evaporation and rainfall processes. A larger d max value reduces the search intensity near the sea; while a smaller d max value increases the search intensity near the sea. Therefore, d max controls the search intensity near the sea area. The adaptive decrease of the d max value can be expressed as:

[0118]

[0119] where: d max is a very small value close to 0; T is the maximum number of iterations.

[0120] Therefore, if the distance between the river and the sea is less than d max , it indicates that the river has reached or flowed into the sea.

[0121] ⑥ Precipitation.

[0122] After meeting the evaporation conditions, the precipitation process is entered to form new precipitation. The precipitation is expressed as follows:

[0123]

[0124] where: UB and LB are the upper and lower boundaries of the variable respectively; rand is a random number uniformly distributed between 0 and 1.

[0125] To ensure the convergence speed and good optimization performance of the algorithm, when the newly formed stream is near the sea and flows directly into the sea, the precipitation is expressed as follows:

[0126]

[0127] In the formula: μ represents the coefficient of the search area range near the ocean; randn is a random number of normal distribution.

[0128] The smaller μ is, the closer the search range is to the ocean (optimal solution). Generally, μ is taken as 0.1. After forming new precipitation, it re-enters the new cycle process.

[0129] When constructing the WCA-KELM prediction model, first use WCA to search for the optimal kernel function parameters and the hyperparameters of KELM. Through an iterative process, WCA updates the position and velocity of each individual according to the fitness value of each individual to find the optimal solution. In each iteration, the position and velocity of the individual are updated according to the magnitude of the fitness value until the stopping condition is reached. In this embodiment, the initial population N pop = 20, the total number of rivers plus the sea is N sr = 4, the optimization accuracy d max = 1e-16, the maximum number of iterations max_it is 50. During the optimization process, WCA-KELM further improves the regression prediction performance of KELM by searching for the optimal kernel function parameters and the hyperparameters of KELM. By optimizing the kernel function parameters, the non-linear characteristics of the input data can be better captured; by optimizing the hyperparameters of KELM, the complexity and generalization ability of the model can be adjusted.

[0130] In this embodiment, 40 groups are randomly selected according to the ratio of 8:2 as the training set of the WCA-KELM model, and the remaining 10 groups are used as the test set. After continuous debugging and multiple trainings, the model with the smallest training error is saved. Through the global search and the ability to adaptively adjust parameters of WCA, the optimal kernel function parameter σ for the warpage deformation amount is 10, and the optimal regularization coefficient C is 100; the optimal kernel function parameter σ for the volume shrinkage rate is 2.7734, and the optimal regularization coefficient C is 20.2643. Use the trained WCA-KELM model to predict the test set, and the prediction results are as Figure 4 shown. This figure also includes the prediction results of the unoptimized KELM on the same test set for comparison. As Figure 4 (a), Figure 4 (b) shows that it can be seen that compared with the unoptimized KELM, the predicted values of the WCA-KELM model are closer to the true values. For the WCA-KELM models of warpage deformation and volume shrinkage, the prediction errors are both less than 5%, indicating that the established WCA-KELM model has good prediction accuracy.

[0131] Kernel extreme learning machine regression prediction optimized based on the water cycle algorithm is a method that combines WCA and KELM to improve the performance and accuracy of regression prediction. Through the global search and the ability to adaptively adjust parameters of WCA, the hyperparameters of KELM can be optimized to further improve the regression prediction performance of KELM.

[0132] Step 3: Use the multi-objective seagull optimization algorithm (MOSOA) to find the Pareto optimal front.

[0133] The seagull optimization algorithm (SOA) was proposed by Gaurav Dhiman and Vijay Kumar in 2019. The main inspiration of this algorithm comes from the migration and predation behaviors of seagulls in nature. Seagulls migrate between different regions with the change of seasons to search for food. The predation process of seagulls consists of a migration stage and a predation stage: in the migration stage, seagulls maintain the flight independence of individuals according to certain rules to avoid collisions with each other; in the predation stage, seagulls launch attacks on prey in a spiral flight pattern. The specific process of SOA is as follows:

[0134] ① Migration (global search)

[0135] During the migration process, the algorithm simulates how a seagull flock moves from one position to another. In this stage, to avoid collisions between seagulls and their neighbors (other seagulls), the algorithm uses an additional variable A to calculate the new position of the seagull, which can be expressed as follows:

[0136] C s (t) = A * P s (t) (29)

[0137] A = f c -(t * (f c / Max iteration )) (30)

[0138] In the formula: C s (t) represents the new position that does not conflict with the positions of other seagulls; P s (t) is the current position of the seagull; t represents the current iteration; A is an additional variable representing the movement behavior of the seagull in the given search space; f c represents the frequency that can control the additional variable A, and the value of f c decreases linearly from 2 to 0.

[0139] After avoiding overlapping positions with other seagulls, the seagull will move in the direction of the best position, which can be expressed as follows:

[0140] M s (t) = B * (P bs(t)-P s (t)) (31)

[0141] B = 2 * A 2 *r d (32)

[0142] Where: M s (t) represents the direction where the optimal position is located; B is a random number responsible for balancing global and local searches; r d is a random number within the range of [0, 1]; P bs (t) represents the current optimal position of the seagull.

[0143] After the seagull moves to a position where it does not collide with its neighbors (other seagulls), it moves in the direction of the optimal position and reaches a new position, which can be expressed as follows:

[0144] D s (t) = |C s (t) + M s (t)| (33)

[0145] Where: D s (t) is the new position of the seagull.

[0146] ② Attack (local search)

[0147] During migration, seagulls can continuously change their attack angles and speeds. When attacking prey, they perform a spiral motion in the air, and the motion behavior is described as follows:

[0148] x = r * cos(θ)

[0149] y = r * sin(θ) (34)

[0150] z = r * θ

[0151] r = u * e θv (35)

[0152] Where: r is the radius of each spiral; θ is a random angle value within the range of [0, 2π]; u and v are constants related to the spiral shape; e is the base of the natural logarithm.

[0153] Then, the attack position of the seagull is expressed as follows:

[0154] P s (t) = D s (t) * x * y * z + P bs (t) (36)

[0155] Where: P s (t) is the attack position of the seagull.

[0156] The Multi-Objective Seagull Optimization Algorithm (MOSOA) realizes the simultaneous optimization of multiple objective functions by introducing a constrained non-dominated sorting mechanism and an external archive mechanism into the SOA. The selection is based on fitness, and individuals with high fitness are retained, while those with low fitness are eliminated, thus iteratively saving the optimal solutions.

[0157] In this embodiment, the final selection of the injection molding process parameters should ensure that the performance and quality of the vacuum pump rear shell plastic part meet the usage requirements. Therefore, the optimization variables need to satisfy multiple condition constraints. Select the melt temperature (x1), mold temperature (x2), holding pressure (x3), holding time (x4), injection pressure (x5), injection time (x6), and cooling time (x7) as variables, and take the warpage deformation amount f1(x) and volume shrinkage rate f2(x) as the optimization objectives. Then, the multi-objective optimization model of the injection molding process parameters in this embodiment can be expressed as:

[0158]

[0159] In this embodiment, the population size of MOSOA is set to 200, the maximum number of iterations is 100, the dimension of the optimization parameter is 7, the number of grids in each dimension is set to 30, and other parameters remain at their default values. The optimal Pareto front obtained by MOSOA is as Figure 5 shown.

[0160] Step4. Use the grey relational evaluation method to obtain the optimal solution from the Pareto optimal front.

[0161] The grey relational analysis method makes up for the deficiencies of the mathematical statistics method, is not restricted by the sample size and whether the samples are regular, and has a wider applicability. The specific process of grey relational evaluation is as follows:

[0162] ① Judge the type of original data. Assume there are n evaluation objects and m evaluation indicators. X ij represents the original value of the j-th indicator in the i-th evaluation scheme. Then the original matrix is denoted as Z ij . Both the warpage deformation amount and the volume shrinkage rate belong to the extremely small type of indicators. The original matrix is normalized to obtain a normalized matrix, so that both the warpage deformation amount and the volume shrinkage rate are converted into extremely large type of indicators.

[0163] ② Preprocess the normalized matrix. The formula is as follows:

[0164]

[0165] In the formula: k is the sequence length. In this embodiment, there are fifty groups of data, so the value of k is 200; i is the number of rows of the matrix. In this embodiment, there are seven factors, so i = 1, 2,..., 7.

[0166] Preprocessing can remove the dimension and narrow the variable range, which is convenient for comparing the influence of different independent variables on the dependent variable.

[0167] ③ Take the maximum value of each row of the preprocessed matrix to form a fictional mother sequence:

[0168] The reference sequence is denoted as: X'0(k) = {x0(1), x0(2), …, x0(k)} (9)

[0169] The comparison sequence is denoted as: X' i (k) = {x i (1), x i (2), …, x i (k)} (10)

[0170] ④ Calculate the minimum difference a and the maximum difference b between the two poles. The formula is as follows:

[0171]

[0172] In the formula: a is the minimum difference between the two poles; b is the maximum difference between the two poles.

[0173] ⑤ Calculate the correlation coefficient between each index in the subsequence and the mother sequence. The formula is as follows:

[0174]

[0175] In the formula: ρ is the resolution coefficient, which takes values between (0, 1), and generally takes the value of 0.5.

[0176] ⑥ Calculate the grey correlation degree between each index and the mother sequence. The formula is as follows:

[0177]

[0178] In the formula: n is the number of evaluation objects. In this embodiment, n = 200.

[0179] ⑦ Calculate the weight of each index. The formula is as follows:

[0180] w n = y n (x0,x1) / (y1(x0,x1)+y2(x0,x2)+…+y n (x0,x n )) (15)

[0181] In the formula: w n is the weight.

[0182] ⑧ Calculate the score of the kth evaluation object. The formula is as follows:

[0183]

[0184] Where: S k is the score of the k-th evaluation object; Z ki is the matrix obtained after the preprocessing in step ② above; m is the number of evaluation indicators, and in this embodiment, m = 2.

[0185] According to the above steps, in this embodiment, the weight of the warpage deformation amount is calculated to be 0.5004, and the weight of the volume shrinkage rate is 0.4996.

[0186] Run in the Matlab environment to obtain the scoring results of the multi-objective comprehensive evaluation method. The evaluation coefficient reflects the pros and cons of each scheme. The higher the score, the better the scheme, and the lower the score, the worse the scheme. The grey relational evaluation scores of 100 groups of data are as Figure 6 shown, and the highest score and the lowest score are marked. It can be seen from the figure that the score of the 24th group is the highest, which is 0.104. The corresponding best set of process parameter combinations is: melt temperature 230.6826 °C, mold temperature 50.0056 °C, holding pressure 74.7280 MPa, holding time 19.4587 s, injection pressure 115.3913 MPa, injection time 3.8371 s, cooling time 29.9317 s. The predicted warpage deformation amount is 0.9795 mm, and the volume shrinkage rate is 8.2186%.

[0187] Substitute the best process parameters into the Moldflow software for injection molding simulation verification. The mold flow analysis results are as Figure 8 shown. As Figure 8 (a), Figure 8 (b) shown, it can be seen that the maximum warpage deformation amount before optimization is 1.611 mm, and the maximum warpage deformation amount after optimization is 0.9388 mm. The warpage is effectively reduced by 41.73%. As Figure 8 (c), Figure 8 (d) shown, it can be seen that the maximum volume shrinkage rate before optimization is 10.46%, and the maximum volume shrinkage rate after optimization is 8.538%. The volume shrinkage rate is effectively reduced by 18.37%. In addition, comparing with the values predicted above in Table 3, the verification errors are all within 5%, indicating that the model prediction accuracy is also good.

[0188] Table 3 Error comparison between predicted values and simulated values

[0189]

[0190] The injection molding quality optimization method for this plastic alloy product can effectively reduce the warpage deformation amount and volume shrinkage rate of PC / ABS plastic alloy injection molded products, thereby obtaining high-quality PC / ABS plastic alloy plastic parts products, and can provide a theoretical basis and data support for obtaining the optimal combination of process parameters for PC / ABS plastic alloy injection molding.

Claims

1. A method for optimizing the injection molding quality of plastic alloy products, characterized in that, Specifically, it includes the following steps: Step 1: Taking the warpage deformation amount and volume shrinkage rate as the optimization objectives, selecting the injection molding process parameters and their value ranges as the optimization design variables, conducting experimental design according to the value ranges of each process parameter, and performing injection molding simulation to obtain the simulation test results; Step 2: Improving KELM based on the simulation test results: ELM consists of three layers: N input layers, L hidden layers, and M output layers. For N different samples (x i , y i ) ∈ R N ×R M , where i = 1, 2, …, N. If the output is denoted as T, the output of ELM is expressed as: β = H + T H + = H T (HH T ) -1 Where: H and h(x) are the output matrices of the hidden layer; H T is the transpose matrix of H; H + is the generalized inverse matrix of H; K is the number of neurons in the hidden layer; g(·) is the activation function; β is the connection weight between the neurons in the hidden layer and the neurons in the output layer; ω is the weight vector between the neurons in the input layer and the neurons in the hidden layer; b is the bias of the neurons in the hidden layer; Introducing a kernel function to measure the similarity between samples, and defining the kernel matrix of KELM according to the Mercer condition, which is expressed as follows: where: K(x i , x j ) is the kernel function. If it is set as the RBF kernel, the kernel function is expressed as follows: K(x i ,x j )=exp{-||x i -x j || / 2σ 2} In the formula: σ is the kernel function parameter; The expression of the KELM model output function is: Where: H and h(x) are the output matrices of the hidden layer; H T is the transpose matrix of H; I is the identity matrix; C is the regularization coefficient; T represents the expected output; Using WCA to continuously iterate to search for the optimal KELM kernel function parameter σ and KELM regularization coefficient C, and constructing a WCA-KELM prediction model; Step 3: Using MOSOA to iteratively optimize on the WCA-KELM prediction model to obtain the Pareto optimal front; Step 4: Using grey relational evaluation to obtain the optimal solution from the Pareto optimal front.

2. The injection molding quality optimization method for plastic alloy products according to claim 1, wherein In Step 3, the selection of MOSOA iterative optimization is based on fitness, retaining individuals with high fitness and eliminating individuals with low fitness.

3. The injection molding quality optimization method for plastic alloy products according to claim 1, wherein In Step 4, the specific process of grey relational evaluation is as follows: ①Judge the original data type. Suppose there are n evaluation objects and m evaluation indicators, and X ij represents the original value of the j-th indicator in the i-th evaluation plan. Then the original matrix is denoted as Z ij , both the warpage deformation amount and the volume shrinkage rate belong to the extremely small type of indicators. The original matrix is normalized to obtain a normalized matrix, so that both the warpage deformation amount and the volume shrinkage rate are converted into extremely large type of indicators; ② Preprocessing the matrix after positive normalization, and the formula is as follows: In the formula: k is the sequence length; i is the number of rows of the matrix; ③ Taking the maximum value of each row of the preprocessed matrix to form a fictitious mother sequence: The reference sequence is denoted as: X'0(k) = {x0(1), x0(2), …, x0(k)} The comparison sequence is denoted as: X' i (k) = {x i (1), x i (2), …, x i (k)} ④ Calculating the minimum difference a between the two poles and the maximum difference b between the two poles, and the formula is as follows: In the formula: a is the minimum difference between the two poles; b is the maximum difference between the two poles; ⑤ Calculating the correlation coefficient between each index in the subsequence and the mother sequence, and the formula is as follows: In the formula: ρ is the resolution coefficient, which takes values between (0, 1); ⑥ Calculating the grey relational degree between each index and the mother sequence, and the formula is as follows: In the formula: n is the number of evaluation objects; ⑦ Calculating the weight of each index, and the formula is as follows: w n = y n (x0,x1) / (y1(x0,x1)+y2(x0,x2)+…+y n (x0,x n )) where: w n is the weight; ⑧ Calculating the score of the kth evaluation object, and the formula is as follows: Where: S k is the score of the k-th evaluation object; Z ki is the matrix obtained after the preprocessing in step ②; m is the number of evaluation indicators, and m = 2.

4. The method for optimizing the injection molding quality of the plastic alloy product according to claim 3, wherein In Step ⑤, the value of ρ is 0.

5.

5. The method for optimizing the injection molding quality of the plastic alloy product according to claim 1, characterized in that, In Step 1, the experimental design adopts orthogonal experiment.

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