# Optimization of Residual Wall Thickness Uniformity in Short-Fiber-Reinforced Composites Water-Assisted Injection Molding Using Response Surface Methodology and Artificial Neural Network-Genetic Algorithm

Authors: Haiying Zhou; Hesheng Liu; Tangqing Kuang; Qingsong Jiang; Zhixin Chen; Weipei Li
Journal: Advances in Polymer Technology
 (2020)

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## Abstract

This study aimed at improving the residual wall thickness uniformity (RWTU), which was closely related to the mechanical properties of plastic parts with a hollow cross-section, in short-fiber reinforced composites (SFRC) overflow water-assisted injection molding (OWAIM). The influences of five independent process parameters (melt temperature, mold temperature, delay time, water pressure, and water temperature) on RWTU were investigated through the methods such as central composite design, regression equation, and analyses of variance. Response surface methodology (RSM) and artificial neural network (ANN) optimized by genetic algorithm (GA) were employed to map the relationship between the process parameters and the standard deviation (SD) depicting the RWTU. Comparison assessments of three models (RSM, ANN, and ANN-GA) were carried out through some statistical indexes. It was concluded that the effect of melt temperature, delay time, and water temperature were significant to RWTU; the hybrid ANN-GA model had the best performance for predicting SD compared with RSM and ANN; the least SD obtained in optimization using ANN-GA as a fitness function was 0.0972.


---

## Body

## 1. Introduction

Overflow water-assisted injection molding (OWAIM) is a promising method for producing functional plastic parts with hollow sections and thin residual wall thickness (RWT) [1–3]. The process of OWAIM includes two steps. First, the functional part cavity is filled with the melted polymer. Second, after a short delay time, the high-pressure water is injected into the core to push the melt into the overflow cavity to form a functional part with a hollow cross-section. This technology has many advantages such as polymer saving, short cycle time, lower injection pressure, less warpage, better surface quality, enhanced flexibility in mold design, etc., [4].Great attention has been paid to the RWT which is an important indicator for assessing the quality of overflow water-assisted injection molded parts [5–9]. The experiments and simulations indicated that the distribution of the RWT was uneven in OWAIM. The plastic parts with thin, uneven RWT are difficult to meet the mechanical performance requirement in special application. Using short-fiber reinforced composites (SFRC) as raw materials can significantly improve the mechanical properties of a plastic part [10, 11]. But it makes the process of OWAIM more complicated which results in a more uneven RWT. The residual wall thickness uniformity (RWTU) of a plastic part is related to the overall mechanical properties. Thus, for the wide application in different fields, it is urgent to improve the RWTU of plastic parts in OWAIM.In the traditional plastic manufacturing industry, product quality improvement mainly depends on the workers’ experience and trial and error, which is costly, time-consuming, and greatly decrease the product competitiveness [12]. Fortunately, the development of information processing technology, using statistical methods, and artificial intelligence algorithm for modeling and optimizing quality objectives, significantly shorten the cycle time of product designing and reduce the product cost [13–15]. RWTU is influenced by the many factors such as material properties, mold structure, process parameter, etc. Generally, adjusting the process parameter setting for optimization is an approach adopted by industry plants. Thus, it is crucial to construct the relationships between the process parameters and RWTU.Response surface methodology (RSM), based on statistical theory, is a classic and effective approach and has been widely applied for modeling and optimization. RSM is very useful for developing, improving, and optimizing the responses that are affected by multiple independent variables [16, 17]. RSM can be applied to evaluate the correlation between the responses and the independent variables and define the influences of the independent variables individually or in combination. However, the nonlinearity of OWAIM processes may be difficult for RSM to achieve better model accuracy and generalization. Artificial neural network (ANN), as an effective method for mapping linear and nonlinear relationships between factors and targets, is widely used for modeling, prediction, classification, and pattern recognition [18, 19]. However, the performance of ANN trained by the gradient decent algorithm is greatly affected using the inappropriate initial weights and bias, which causes local minima [20]. Genetic algorithm (GA), inspired by the biological evolution theory, is a global optimization tool and can be used to search the optimal initial weights and bias for ANN. The combination of ANN and GA (ANN-GA) has been successfully used in optimization studies [21, 22].Up to our knowledge, limited worthwhile research has been implemented for the improvement of RWTU in SFRC OWAIM. In this study, the numerical experiments, arranged using a central composite design (CCD), have been carried out. RSM and ANN-GA were employed to map the relationship between the RWTU and the process parameters (melt temperature, mold temperature, delay time, water pressure, and water temperature). The significance of five process parameters was studied through the analyses of variance (ANOVA). The prediction performance of RSM, ANN, and ANN-GA models were compared using the linear regression equation and statistical indicators. Finally, the model with the best prediction performance was used as the fitness function of the GA to optimize the RWTU of the plastic part in SFRC OWAIM.


## 2. Methods

### 2.1. Related Mathematical Model

During the simulation of OWAIM, the melt flow is regarded as nonisothermal, transient, and nonNewtonian. It is assumed that the melt is incompressible, laminar, and the inertia term is ignored. The basic governing equations for melt flow are as follows.(1)∂P∂t+∇·ρu=0,(2)∂∂tρu+∇·ρuu−τ=ρg,(3)ρCp∂T∂t+u·∇T=∇·k∇T+ηγ2,(4)τ=−pI+η∇u+∇uT,whereP is the pressure; T the temperature; t the time; u the speed; τ the stress tensor; ρ the density; η the viscosity; k the thermal conductivity; Cp the specific heat; and γ the shear strain.A constitutive equation with seven parameters is used to describe the relationship between melt viscosity and temperature and shear rate.(5)ηγ˙,T,P=η0T,P1+η0γ˙/τ∗1−n,(6)η0T,P=D1exp−A1T−TcA2+T−Tc,(7)Tc=D2+D3P,(8)A2=A∼2+D3P,whereη is the viscosity; η0 the zero shear viscosity; γ˙ the shear rate; τ∗ the material constant; n the power rate index; T the melt temperature; Tc the glass transition temperature; D1, D2, D3, A1, and A∼2 are the relative constants associated with the selected material.In the high-pressure water filling stage, the volume of fluid (VOF) model is used to track the interface of the melt and water.Fi is the volume fraction of the i-th phase, and 0 ≤ Fi ≤ 1. When a unit is completely occupied by the i-th phase, Fi takes a value of 1. When a unit does not have the i-th phase, Fi takes a value of zero.(9)∂Fi∂t+∇⋅uFi=0


### 2.2. Geometric Model in Simulation

As shown in Figure1, the geometric model used in the simulation was composed of a runner, an overflow cavity and a functional plastic part with a diameter 16 mm and two elbows. The model built by Pro/E was meshed using the commercial software of Moldex3D. The numbers of mesh nodes and mesh elements were 60175 and 195118, respectively. The short glass fiber reinforced PP (Fiberfil J-68/20/E with a short fiber mass fraction of 20% and an aspect ratio of 20) was selected as the raw material in the simulation and its properties were available in the data bank of Moldex3D.Figure 1
Geometric model for simulation.


### 2.3. Definition of Residual Wall Thickness Uniformity

The values of RWT were measured at ten different locations along the central axis of the functional part as shown in Figure2. Standard deviation (SD), which reflects the degree of dispersion among individuals in a group, was defined as an indicator for evaluating the RWTU. The formula of SD can be expressed as the following:(10)SD=1N∑i=1NRi−Ravg2,Figure 2
Locations for measuring residual wall thickness.whereRi is the value of RWT measured at the i-th point; Ravg is the average value of RWT; N is the total number of points.


### 2.4. Experimental Design

The process parameters such as melt temperature, mold temperature, delay time, water pressure, and water temperature were considered in this study. In general, those process parameters were easily controlled in the experiments and production for adjusting the important indicators of plastic parts. The process windows recommended for OWAIM were melt temperature [210°C, 230°C], mold temperature [42°C, 62°C], delay time [1 s, 5 s], water pressure [8 MPa, 12 MPa], and water temperature [20°C, 30°C]. In order to reduce the experiment times and comprehensively examine the influences of the process parameters on RWTU, the CCD based on RSM was applied to arrange the simulation experiments. The coded and actual values of five independent process parameters are shown in Table1. Fifty experiments composed of 42 factorial and axial points and 8 center points are demanded for the CCD with three levels and five factors. The center points with the same process parameters result in the same RWT in the simulations. Therefore, the total number of experiments is 43. The details of the arrangements are revealed in Table 2.Table 1
Factors and level of process parameters.
Process parameter
Level
Low
Mean
High
Melt temperature (X1)/[°C]
−1 (210)
0 (220)
1 (230)
Mold temperature (X2)/[°C]
−1 (42)
0 (52)
1 (62)
Delay time (X3)/[s]
−1 (1)
0 (3)
1 (5)
Water pressure (X4)/[MPa]
−1 (8)
0 (10)
1 (12)
Water temperature (X5)/[°C]
−1 (20)
0 (25)
1 (30)Table 2
Experimental matrix and corresponding results.
No.
X
1
X
2
X
3
X
4
X
5
SD
No.
X
1
X
2
X
3
X
4
X
5
SD
1
0
0
−1
0
0
0.177
23
−1
1
−1
−1
1
0.180
2
−1
−1
−1
1
1
0.185
24
0
0
0
0
0
0.150
3
1
−1
1
1
1
0.183
25
1
−1
1
−1
−1
0.125
4
0
0
0
−1
0
0.164
26
0
0
0
1
0
0.163
5
−1
−1
1
−1
1
0.163
27
1
1
−1
1
1
0.189
6
−1
−1
−1
1
−1
0.224
28
1
−1
1
−1
1
0.215
7
1
1
1
−1
1
0.239
29
−1
−1
1
1
1
0.16
8
1
−1
−1
1
1
0.230
30
−1
1
−1
1
1
0.207
9
1
−1
−1
−1
1
0.200
31
−1
1
−1
1
−1
0.187
10
0
0
0
0
−1
0.162
32
1
0
0
0
0
0.190
11
1
−1
−1
−1
−1
0.201
33
0
0
1
0
0
0.158
12
1
1
1
1
−1
0.154
34
−1
1
1
1
1
0.157
13
1
−1
−1
1
−1
0.214
35
1
1
−1
−1
1
0.231
14
−1
−1
1
−1
−1
0.163
36
1
1
1
1
1
0.187
15
−1
1
1
1
−1
0.112
37
−1
1
1
−1
1
0.138
16
0
0
0
0
1
0.157
38
1
−1
1
1
−1
0.154
17
−1
1
−1
−1
−1
0.150
39
−1
−1
−1
−1
1
0.173
18
0
−1
0
0
0
0.165
40
0
1
0
0
0
0.177
19
−1
−1
1
1
−1
0.148
41
−1
0
0
0
0
0.130
20
1
1
−1
−1
−1
0.169
42
1
1
1
−1
−1
0.135
21
−1
−1
−1
−1
−1
0.151
43
1
1
−1
1
−1
0.190
22
−1
1
1
−1
−1
0.167


### 2.5. Response Surface Methodology

The method of RSM based on the statistical technology was employed for the multiple regression analysis of experimental data obtained from the CCD. The relationship between the independent process parameters and the response SD is depicted using a second-order polynomial equation.(11)SD=β0+∑i=15βiXi+∑i=14∑j=i+15βijXiXj+∑i=15βiiXi2,whereXi and Xj are the independent process parameters; β0 is the intercept constant; βi is the linear coefficient; βij is the interaction coefficient and βii is the quadratic coefficient. The regression studies and ANOVA were implemented using the software of Design-Expert 8.0.


### 2.6. Artificial Neural Network

ANN inspired by biologic neural system is a computing model used to map linear or nonlinear factors and responses relationships. An ANN model comprises three parts: one input layer, one or more hidden layers, and one output layer. Each layer consists of a number of neurons. The numbers of neurons in the input layer and the output layer are determined by the numbers of factors and responses, respectively. In this study, an ANN model with one hidden layer was employed for modeling. The gradient descent algorithm was used for training model. The transfer functions of “Tansig” and “Purelin” were applied in the hidden layer and the output layer, respectively. By changing the number of neurons in the hidden layer from 5 to 15, the ANN topology of 5–11–1 was determined according to the minimum mean square error between the targets and the outputs. The ANN model is demonstrated in Figure 3.Figure 3
Topology of artificial neural network.


### 2.7. Genetic Algorithm

The genetic algorithm based on natural selection and survival of fitness is a global searching algorithm, and it is widely used in the fields of optimization, pattern recognition, robots, and prediction. Compared with other optimization methods, GA has many advantages including being not easy to be trapped into the local minima, requiring little prior information about the searched objectives, and easy identification of the optima in a complex search space.The major operations of GA are summarized as follows: (1) Selection: individuals are selected based on their fitness so that better individuals are given a higher chance of being chosen, (2) Crossover: exchange the information of the two parents to generate a new individual according to the crossover probability, (3) Mutation: randomly alter the information of each chromosome according to the mutation probability.


### 2.8. Hybrid Model of Artificial Neural Network and Genetic Algorithm

GA was utilized to optimize the initial weights and bias for improving the prediction performance of ANN. The flow chart of ANN-GA is illustrated in Figure4. The chromosome codes of GA consisted of the weights and bias of ANN. The mean square error between the experimental value and the prediction of ANN was used as the fitness function of GA. Then, genetic operations, such as selection, crossover, and mutation, were conducted to reproduce the new generation. As the new individuals replaced the parent individuals, the populations of GA were renewed. The abovementioned process repeated until the predefined generation number or the optimization criterion was satisfied.Figure 4
Flow chart of the hybrid model of ANN-GA.Before training model, all the process parameter vectors and the observations in the simulations were normalized into the range [−1, 1] using the “mapmaxmin” function. All the calculations and optimizations were conducted under the environment of Matlab R2015b.


### 2.9. Statistical Analysis

To evaluate the performance of the different model for predicting SD, two statistic indicators including root mean square error (RMSE) and correlative coefficient (R) were calculated. These statistical parameters are defined as the following:(12)RMSE=∑i=1Nyi−xi2N,(13)R=∑i=1Nxi−xavgyi−yavg∑i=1Nxi−2∑i=1Nyi−yavg2,wherexi is the experimental value; yi is the corresponding prediction; xavg is the average of the experimental values; yavg is the average of the predictions; N is the total number of simulations.


## 2.1. Related Mathematical Model

During the simulation of OWAIM, the melt flow is regarded as nonisothermal, transient, and nonNewtonian. It is assumed that the melt is incompressible, laminar, and the inertia term is ignored. The basic governing equations for melt flow are as follows.(1)∂P∂t+∇·ρu=0,(2)∂∂tρu+∇·ρuu−τ=ρg,(3)ρCp∂T∂t+u·∇T=∇·k∇T+ηγ2,(4)τ=−pI+η∇u+∇uT,whereP is the pressure; T the temperature; t the time; u the speed; τ the stress tensor; ρ the density; η the viscosity; k the thermal conductivity; Cp the specific heat; and γ the shear strain.A constitutive equation with seven parameters is used to describe the relationship between melt viscosity and temperature and shear rate.(5)ηγ˙,T,P=η0T,P1+η0γ˙/τ∗1−n,(6)η0T,P=D1exp−A1T−TcA2+T−Tc,(7)Tc=D2+D3P,(8)A2=A∼2+D3P,whereη is the viscosity; η0 the zero shear viscosity; γ˙ the shear rate; τ∗ the material constant; n the power rate index; T the melt temperature; Tc the glass transition temperature; D1, D2, D3, A1, and A∼2 are the relative constants associated with the selected material.In the high-pressure water filling stage, the volume of fluid (VOF) model is used to track the interface of the melt and water.Fi is the volume fraction of the i-th phase, and 0 ≤ Fi ≤ 1. When a unit is completely occupied by the i-th phase, Fi takes a value of 1. When a unit does not have the i-th phase, Fi takes a value of zero.(9)∂Fi∂t+∇⋅uFi=0


## 2.2. Geometric Model in Simulation

As shown in Figure1, the geometric model used in the simulation was composed of a runner, an overflow cavity and a functional plastic part with a diameter 16 mm and two elbows. The model built by Pro/E was meshed using the commercial software of Moldex3D. The numbers of mesh nodes and mesh elements were 60175 and 195118, respectively. The short glass fiber reinforced PP (Fiberfil J-68/20/E with a short fiber mass fraction of 20% and an aspect ratio of 20) was selected as the raw material in the simulation and its properties were available in the data bank of Moldex3D.Figure 1
Geometric model for simulation.


## 2.3. Definition of Residual Wall Thickness Uniformity

The values of RWT were measured at ten different locations along the central axis of the functional part as shown in Figure2. Standard deviation (SD), which reflects the degree of dispersion among individuals in a group, was defined as an indicator for evaluating the RWTU. The formula of SD can be expressed as the following:(10)SD=1N∑i=1NRi−Ravg2,Figure 2
Locations for measuring residual wall thickness.whereRi is the value of RWT measured at the i-th point; Ravg is the average value of RWT; N is the total number of points.


## 2.4. Experimental Design

The process parameters such as melt temperature, mold temperature, delay time, water pressure, and water temperature were considered in this study. In general, those process parameters were easily controlled in the experiments and production for adjusting the important indicators of plastic parts. The process windows recommended for OWAIM were melt temperature [210°C, 230°C], mold temperature [42°C, 62°C], delay time [1 s, 5 s], water pressure [8 MPa, 12 MPa], and water temperature [20°C, 30°C]. In order to reduce the experiment times and comprehensively examine the influences of the process parameters on RWTU, the CCD based on RSM was applied to arrange the simulation experiments. The coded and actual values of five independent process parameters are shown in Table1. Fifty experiments composed of 42 factorial and axial points and 8 center points are demanded for the CCD with three levels and five factors. The center points with the same process parameters result in the same RWT in the simulations. Therefore, the total number of experiments is 43. The details of the arrangements are revealed in Table 2.Table 1
Factors and level of process parameters.
Process parameter
Level
Low
Mean
High
Melt temperature (X1)/[°C]
−1 (210)
0 (220)
1 (230)
Mold temperature (X2)/[°C]
−1 (42)
0 (52)
1 (62)
Delay time (X3)/[s]
−1 (1)
0 (3)
1 (5)
Water pressure (X4)/[MPa]
−1 (8)
0 (10)
1 (12)
Water temperature (X5)/[°C]
−1 (20)
0 (25)
1 (30)Table 2
Experimental matrix and corresponding results.
No.
X
1
X
2
X
3
X
4
X
5
SD
No.
X
1
X
2
X
3
X
4
X
5
SD
1
0
0
−1
0
0
0.177
23
−1
1
−1
−1
1
0.180
2
−1
−1
−1
1
1
0.185
24
0
0
0
0
0
0.150
3
1
−1
1
1
1
0.183
25
1
−1
1
−1
−1
0.125
4
0
0
0
−1
0
0.164
26
0
0
0
1
0
0.163
5
−1
−1
1
−1
1
0.163
27
1
1
−1
1
1
0.189
6
−1
−1
−1
1
−1
0.224
28
1
−1
1
−1
1
0.215
7
1
1
1
−1
1
0.239
29
−1
−1
1
1
1
0.16
8
1
−1
−1
1
1
0.230
30
−1
1
−1
1
1
0.207
9
1
−1
−1
−1
1
0.200
31
−1
1
−1
1
−1
0.187
10
0
0
0
0
−1
0.162
32
1
0
0
0
0
0.190
11
1
−1
−1
−1
−1
0.201
33
0
0
1
0
0
0.158
12
1
1
1
1
−1
0.154
34
−1
1
1
1
1
0.157
13
1
−1
−1
1
−1
0.214
35
1
1
−1
−1
1
0.231
14
−1
−1
1
−1
−1
0.163
36
1
1
1
1
1
0.187
15
−1
1
1
1
−1
0.112
37
−1
1
1
−1
1
0.138
16
0
0
0
0
1
0.157
38
1
−1
1
1
−1
0.154
17
−1
1
−1
−1
−1
0.150
39
−1
−1
−1
−1
1
0.173
18
0
−1
0
0
0
0.165
40
0
1
0
0
0
0.177
19
−1
−1
1
1
−1
0.148
41
−1
0
0
0
0
0.130
20
1
1
−1
−1
−1
0.169
42
1
1
1
−1
−1
0.135
21
−1
−1
−1
−1
−1
0.151
43
1
1
−1
1
−1
0.190
22
−1
1
1
−1
−1
0.167


## 2.5. Response Surface Methodology

The method of RSM based on the statistical technology was employed for the multiple regression analysis of experimental data obtained from the CCD. The relationship between the independent process parameters and the response SD is depicted using a second-order polynomial equation.(11)SD=β0+∑i=15βiXi+∑i=14∑j=i+15βijXiXj+∑i=15βiiXi2,whereXi and Xj are the independent process parameters; β0 is the intercept constant; βi is the linear coefficient; βij is the interaction coefficient and βii is the quadratic coefficient. The regression studies and ANOVA were implemented using the software of Design-Expert 8.0.


## 2.6. Artificial Neural Network

ANN inspired by biologic neural system is a computing model used to map linear or nonlinear factors and responses relationships. An ANN model comprises three parts: one input layer, one or more hidden layers, and one output layer. Each layer consists of a number of neurons. The numbers of neurons in the input layer and the output layer are determined by the numbers of factors and responses, respectively. In this study, an ANN model with one hidden layer was employed for modeling. The gradient descent algorithm was used for training model. The transfer functions of “Tansig” and “Purelin” were applied in the hidden layer and the output layer, respectively. By changing the number of neurons in the hidden layer from 5 to 15, the ANN topology of 5–11–1 was determined according to the minimum mean square error between the targets and the outputs. The ANN model is demonstrated in Figure 3.Figure 3
Topology of artificial neural network.


## 2.7. Genetic Algorithm

The genetic algorithm based on natural selection and survival of fitness is a global searching algorithm, and it is widely used in the fields of optimization, pattern recognition, robots, and prediction. Compared with other optimization methods, GA has many advantages including being not easy to be trapped into the local minima, requiring little prior information about the searched objectives, and easy identification of the optima in a complex search space.The major operations of GA are summarized as follows: (1) Selection: individuals are selected based on their fitness so that better individuals are given a higher chance of being chosen, (2) Crossover: exchange the information of the two parents to generate a new individual according to the crossover probability, (3) Mutation: randomly alter the information of each chromosome according to the mutation probability.


## 2.8. Hybrid Model of Artificial Neural Network and Genetic Algorithm

GA was utilized to optimize the initial weights and bias for improving the prediction performance of ANN. The flow chart of ANN-GA is illustrated in Figure4. The chromosome codes of GA consisted of the weights and bias of ANN. The mean square error between the experimental value and the prediction of ANN was used as the fitness function of GA. Then, genetic operations, such as selection, crossover, and mutation, were conducted to reproduce the new generation. As the new individuals replaced the parent individuals, the populations of GA were renewed. The abovementioned process repeated until the predefined generation number or the optimization criterion was satisfied.Figure 4
Flow chart of the hybrid model of ANN-GA.Before training model, all the process parameter vectors and the observations in the simulations were normalized into the range [−1, 1] using the “mapmaxmin” function. All the calculations and optimizations were conducted under the environment of Matlab R2015b.


## 2.9. Statistical Analysis

To evaluate the performance of the different model for predicting SD, two statistic indicators including root mean square error (RMSE) and correlative coefficient (R) were calculated. These statistical parameters are defined as the following:(12)RMSE=∑i=1Nyi−xi2N,(13)R=∑i=1Nxi−xavgyi−yavg∑i=1Nxi−2∑i=1Nyi−yavg2,wherexi is the experimental value; yi is the corresponding prediction; xavg is the average of the experimental values; yavg is the average of the predictions; N is the total number of simulations.


## 3. Results and Discussion

### 3.1. Simulation Results

The process of OWAIM includes a melt filling stage and a high-pressure filling stage. As shown in Figure5(a), the mold cavity of the functional plastic part is filled with the high-temperature melt. During the short delay time, the outer layer of the melt is affected by the mold cavity, resulting in a decrease of temperature. Therefore, a thin melt layer with high viscosity is formed due to the heat conduction. Figure 5(b) demonstrates the result of high-pressure water penetration. After the delay time, water is injected into the mold cavity and penetrates along the core with the least flow resistance. The melt is pushed forward to form a plastic part with a hollow cross-section.Figure 5
Simulation result and (a) melt filling stage, (b) water filling stage.
(a)
(b)


### 3.2. Multiple Regression and Analysis of Variance

Based on the CCD, the results of the experiments are listed in Table2. A second-order polynomial equation depicting the relationship between five independent process parameters and SD was determined.(14)SD=0.15+0.012X1−0.0025X2−0.015X3+0.0024X4+0.011X5+0.0013X1X2+0.0005X1X3−0.0034X1X4−0.0084X1X5+0.0017X2X3−0.0042X2X4+0.0042X2X5−0.0082X3X4+0.0055X3X5−0.0051X4X5+0.0003X12+0.011X22+0.0078X32+0.0038X42−0.0002X52.The adequacy and fitness of the quadratic model were further studied by ANOVA (Table3). P-value < 0.05 is a criterion for judgment about the significance of each term, and shows significant variables at 95% confidence level. The regression model (F=4.61 and p=0.0001) was statistically significant, which indicates that there was a good fit between the experimental data and predicted data obtained by RSM. As listed in Table 3, the linear coefficients of melt temperature, delay time, and water temperature were noted to be significant with the F‐ and p‐value of (F=15.2, p=0.0005), (F=22.5, p<0.0001) and (F=13.55, p=0.0009), respectively; the interaction between melt temperature and water temperature seemed to be predominant with F‐ and p‐value of (F=7.02,  p=0.0129), which was followed by the interaction between delay time and water pressure (F=6.51, p=0.0162); all quadratic coefficients were insignificant.Table 3
ANOVA for Response Surface Quadratic Model.
Source
Sum of Squares
df
Mean Square
F Value
p-value Prob > F
Model
0.03
20
1.51E−03
4.61
0.0001
Significant
X
1
4.97E−03
1
4.97E−03
15.2
0.0005
Significant
X
2
2.13E−04
1
2.13E−04
0.65
0.4266
X
3
7.35E−03
1
7.35E−03
22.5
<0.0001
Significant
X
4
1.88E−04
1
1.88E−04
0.58
0.454
X
5
4.43E−03
1
4.43E−03
13.55
0.0009
Significant
X
1
X
2
5.25E−05
1
5.25E−05
0.16
0.6914
X
1
X
3
9.03E−06
1
9.03E−06
0.028
0.8691
X
1
X
4
3.71E−04
1
3.71E−04
1.14
0.2952
X
1
X
5
2.30E−03
1
2.30E−03
7.02
0.0129
Significant
X
2
X
3
8.78E−05
1
8.78E−05
0.27
0.6082
X
2
X
4
5.53E−04
1
5.53E−04
1.69
0.2036
X
2
X
5
5.70E−04
1
5.70E−04
1.74
0.1971
X
3
X
4
2.13E−03
1
2.13E−03
6.51
0.0162
Significant
X
3
X
5
9.57E−04
1
9.57E−04
2.93
0.0977
X
4
X
5
8.30E−04
1
8.30E−04
2.54
0.1218
X
1
2
2.18E−07
1
2.18E−07
6.66E−04
0.9796
X
2
2
3.16E−04
1
3.16E−04
0.97
0.3338
X
3
2
1.50E−04
1
1.50E−04
0.46
0.503
X
4
2
3.57E−05
1
3.57E−05
0.11
0.7435
X
5
2
1.02E−07
1
1.02E−07
3.13E−04
0.986
Residual
9.48E−03
29
3.27E−04
Lack of fit
9.48E−03
22
4.31E−04
Pure error
0
7
0
Cor total
0.04
49


### 3.3. Initial Weights and Bias of ANN-GA

The optimization of the initial weights and bias of ANN was implemented using GA. 37 of the 43 data sets were used to train the ANN-GA, and the rest were used to test this model. The mean square error between the predicted values and experimental values was used as a fitness function. As shown in Figure6, during the training process, the fitness value firstly decreased sharply and then ran steadily after the 150th generation. The minimum fitness value was 4.3E−4 after the preset generations, which meant that the predictions were in good agreement with the targets. The initial weights and bias (Table 4) were fixed and assigned to ANN-GA model.Figure 6
Evolution of fitness value for optimizing ANN-GA model.Table 4
Optimal weights and bias for ANN-GA model.
Hidden layer
Output layer
Weights
Bias
Weights
Bias
−0.045
0.411
−0.219
0.327
−0.389
−0.209
0.307
−0.243
0.426
0.463
0.239
−0.256
−0.302
−0.058
−0.240
0.358
0.336
−0.062
0.349
−0.042
−0.381
0.065
0.419
−0.104
0.147
0.428
−0.221
−0.220
−0.480
−0.007
0.348
−0.322
−0.248
0.489
0.188
−0.187
0.229
0.316
0.388
0.454
0.258
0.113
−0.141
0.439
−0.174
−0.413
−0.289
0.171
−0.002
−0.411
0.414
0.471
−0.374
0.078
0.055
0.286
0.075
−0.166
0.453
0.077
0.004
0.491
−0.454
0.002
0.471
0.452
0.362
−0.397
−0.316
−0.403
0.285
−0.074
−0.175
−0.020
0.394
0.271
0.035
−0.088


### 3.4. Comparison of the Prediction Ability of RSM, ANN and ANN-GA

Figures7(a)–7(c) showed the comparative plots of the experimental values to predicted values obtained by three models (RSM, ANN, and ANN-GA). The linear coefficient of the fitting line for RSM, ANN, and ANN-GA models were 0.8147, 0.9839, and 1.001, respectively. The data points of RSM were scattered on both sides of the fitting line, while the data points of ANN and ANN-GA were very close to the fitting line. Moreover, the effectiveness of RSM, ANN, and ANN-GA models was statistically evaluated in terms of RMSE and R values between the experimental values and predicted values. Table 5 gives the statistical parameters of RMSE and R for RSM, ANN, and ANN-GA models, respectively. In general, the closeness of the RMSE value to zero and the R value to unity represents more accuracy of response predicted by three models. Through the analysis abovementioned, it was concluded that the three models (RAM, ANN, and ANN-GA) could well map the relationship between the independent process parameters and SD, and therefore can provide predictions with acceptable accuracy for unseen data sets; the best performance of prediction was ANN-GA followed by ANN and RSM, which indicates that the ANN-GA model has the strongest ability to be generalized. Hence, the ANN-GA model was selected as the final prediction model in the optimization process.Figure 7
Predicted values versus the actual values, (a) RSM, (b) ANN, (c) ANN-GA.
(a)
(b)
(c)Table 5
Statistical parameters of RSM, ANN and ANN-GA model.
Model
RMSE
R
RSM
0.0142
0.8731
ANN
0.0114
0.9397
ANN-GA
0.0010
0.9994


### 3.5. Optimization Result of ANN-GA and Validation

The optimization of RWTU was carried out with the principle “the smaller, the better”. The expression based of ANN-GA for calculating SD was used as the fitness function of GA. The evolution of this optimization process was recorded in Figure8. The lines representing fitness value run steadily after the 40th generation. The optimized process parameters of melt temperature = 219°C, mold temperature = 59.8°C, water injection delay time = 5 s, water pressure = 10.2 MPa and water temperature = 20°C were considered. With the optimized process parameters, the SD predicted by ANN‐GA model was 0.0972, which was smaller than any observation in simulation.Figure 8
Evolution of fitness value in 100 generations.Using the optimal process parameters, a simulation experiment and real experiments were carried out to verify the optimization results. As shown in Figure9, the value of SD obtained by the simulation experiment was 0.09, which was slightly smaller than the predicted value of ANN-GA and smaller than any observation in the simulation experiments (Table 2). The results of the real experiments showed that the RWTU obtained by the optimal process parameters was improved.Figure 9
Simulation results with optimal process parameters.


## 3.1. Simulation Results

The process of OWAIM includes a melt filling stage and a high-pressure filling stage. As shown in Figure5(a), the mold cavity of the functional plastic part is filled with the high-temperature melt. During the short delay time, the outer layer of the melt is affected by the mold cavity, resulting in a decrease of temperature. Therefore, a thin melt layer with high viscosity is formed due to the heat conduction. Figure 5(b) demonstrates the result of high-pressure water penetration. After the delay time, water is injected into the mold cavity and penetrates along the core with the least flow resistance. The melt is pushed forward to form a plastic part with a hollow cross-section.Figure 5
Simulation result and (a) melt filling stage, (b) water filling stage.
(a)
(b)


## 3.2. Multiple Regression and Analysis of Variance

Based on the CCD, the results of the experiments are listed in Table2. A second-order polynomial equation depicting the relationship between five independent process parameters and SD was determined.(14)SD=0.15+0.012X1−0.0025X2−0.015X3+0.0024X4+0.011X5+0.0013X1X2+0.0005X1X3−0.0034X1X4−0.0084X1X5+0.0017X2X3−0.0042X2X4+0.0042X2X5−0.0082X3X4+0.0055X3X5−0.0051X4X5+0.0003X12+0.011X22+0.0078X32+0.0038X42−0.0002X52.The adequacy and fitness of the quadratic model were further studied by ANOVA (Table3). P-value < 0.05 is a criterion for judgment about the significance of each term, and shows significant variables at 95% confidence level. The regression model (F=4.61 and p=0.0001) was statistically significant, which indicates that there was a good fit between the experimental data and predicted data obtained by RSM. As listed in Table 3, the linear coefficients of melt temperature, delay time, and water temperature were noted to be significant with the F‐ and p‐value of (F=15.2, p=0.0005), (F=22.5, p<0.0001) and (F=13.55, p=0.0009), respectively; the interaction between melt temperature and water temperature seemed to be predominant with F‐ and p‐value of (F=7.02,  p=0.0129), which was followed by the interaction between delay time and water pressure (F=6.51, p=0.0162); all quadratic coefficients were insignificant.Table 3
ANOVA for Response Surface Quadratic Model.
Source
Sum of Squares
df
Mean Square
F Value
p-value Prob > F
Model
0.03
20
1.51E−03
4.61
0.0001
Significant
X
1
4.97E−03
1
4.97E−03
15.2
0.0005
Significant
X
2
2.13E−04
1
2.13E−04
0.65
0.4266
X
3
7.35E−03
1
7.35E−03
22.5
<0.0001
Significant
X
4
1.88E−04
1
1.88E−04
0.58
0.454
X
5
4.43E−03
1
4.43E−03
13.55
0.0009
Significant
X
1
X
2
5.25E−05
1
5.25E−05
0.16
0.6914
X
1
X
3
9.03E−06
1
9.03E−06
0.028
0.8691
X
1
X
4
3.71E−04
1
3.71E−04
1.14
0.2952
X
1
X
5
2.30E−03
1
2.30E−03
7.02
0.0129
Significant
X
2
X
3
8.78E−05
1
8.78E−05
0.27
0.6082
X
2
X
4
5.53E−04
1
5.53E−04
1.69
0.2036
X
2
X
5
5.70E−04
1
5.70E−04
1.74
0.1971
X
3
X
4
2.13E−03
1
2.13E−03
6.51
0.0162
Significant
X
3
X
5
9.57E−04
1
9.57E−04
2.93
0.0977
X
4
X
5
8.30E−04
1
8.30E−04
2.54
0.1218
X
1
2
2.18E−07
1
2.18E−07
6.66E−04
0.9796
X
2
2
3.16E−04
1
3.16E−04
0.97
0.3338
X
3
2
1.50E−04
1
1.50E−04
0.46
0.503
X
4
2
3.57E−05
1
3.57E−05
0.11
0.7435
X
5
2
1.02E−07
1
1.02E−07
3.13E−04
0.986
Residual
9.48E−03
29
3.27E−04
Lack of fit
9.48E−03
22
4.31E−04
Pure error
0
7
0
Cor total
0.04
49


## 3.3. Initial Weights and Bias of ANN-GA

The optimization of the initial weights and bias of ANN was implemented using GA. 37 of the 43 data sets were used to train the ANN-GA, and the rest were used to test this model. The mean square error between the predicted values and experimental values was used as a fitness function. As shown in Figure6, during the training process, the fitness value firstly decreased sharply and then ran steadily after the 150th generation. The minimum fitness value was 4.3E−4 after the preset generations, which meant that the predictions were in good agreement with the targets. The initial weights and bias (Table 4) were fixed and assigned to ANN-GA model.Figure 6
Evolution of fitness value for optimizing ANN-GA model.Table 4
Optimal weights and bias for ANN-GA model.
Hidden layer
Output layer
Weights
Bias
Weights
Bias
−0.045
0.411
−0.219
0.327
−0.389
−0.209
0.307
−0.243
0.426
0.463
0.239
−0.256
−0.302
−0.058
−0.240
0.358
0.336
−0.062
0.349
−0.042
−0.381
0.065
0.419
−0.104
0.147
0.428
−0.221
−0.220
−0.480
−0.007
0.348
−0.322
−0.248
0.489
0.188
−0.187
0.229
0.316
0.388
0.454
0.258
0.113
−0.141
0.439
−0.174
−0.413
−0.289
0.171
−0.002
−0.411
0.414
0.471
−0.374
0.078
0.055
0.286
0.075
−0.166
0.453
0.077
0.004
0.491
−0.454
0.002
0.471
0.452
0.362
−0.397
−0.316
−0.403
0.285
−0.074
−0.175
−0.020
0.394
0.271
0.035
−0.088


## 3.4. Comparison of the Prediction Ability of RSM, ANN and ANN-GA

Figures7(a)–7(c) showed the comparative plots of the experimental values to predicted values obtained by three models (RSM, ANN, and ANN-GA). The linear coefficient of the fitting line for RSM, ANN, and ANN-GA models were 0.8147, 0.9839, and 1.001, respectively. The data points of RSM were scattered on both sides of the fitting line, while the data points of ANN and ANN-GA were very close to the fitting line. Moreover, the effectiveness of RSM, ANN, and ANN-GA models was statistically evaluated in terms of RMSE and R values between the experimental values and predicted values. Table 5 gives the statistical parameters of RMSE and R for RSM, ANN, and ANN-GA models, respectively. In general, the closeness of the RMSE value to zero and the R value to unity represents more accuracy of response predicted by three models. Through the analysis abovementioned, it was concluded that the three models (RAM, ANN, and ANN-GA) could well map the relationship between the independent process parameters and SD, and therefore can provide predictions with acceptable accuracy for unseen data sets; the best performance of prediction was ANN-GA followed by ANN and RSM, which indicates that the ANN-GA model has the strongest ability to be generalized. Hence, the ANN-GA model was selected as the final prediction model in the optimization process.Figure 7
Predicted values versus the actual values, (a) RSM, (b) ANN, (c) ANN-GA.
(a)
(b)
(c)Table 5
Statistical parameters of RSM, ANN and ANN-GA model.
Model
RMSE
R
RSM
0.0142
0.8731
ANN
0.0114
0.9397
ANN-GA
0.0010
0.9994


## 3.5. Optimization Result of ANN-GA and Validation

The optimization of RWTU was carried out with the principle “the smaller, the better”. The expression based of ANN-GA for calculating SD was used as the fitness function of GA. The evolution of this optimization process was recorded in Figure8. The lines representing fitness value run steadily after the 40th generation. The optimized process parameters of melt temperature = 219°C, mold temperature = 59.8°C, water injection delay time = 5 s, water pressure = 10.2 MPa and water temperature = 20°C were considered. With the optimized process parameters, the SD predicted by ANN‐GA model was 0.0972, which was smaller than any observation in simulation.Figure 8
Evolution of fitness value in 100 generations.Using the optimal process parameters, a simulation experiment and real experiments were carried out to verify the optimization results. As shown in Figure9, the value of SD obtained by the simulation experiment was 0.09, which was slightly smaller than the predicted value of ANN-GA and smaller than any observation in the simulation experiments (Table 2). The results of the real experiments showed that the RWTU obtained by the optimal process parameters was improved.Figure 9
Simulation results with optimal process parameters.


## 4. Conclusions

The simulations of SFRC OWAIM were carried out, and the SD was used to characterize the RWTU of plastic parts with hollow cross-sections. RSM-CCD with five independent variables (melt temperature, mold temperature, delay time, water pressure, and water temperature) at three levels and ANN-GA with one hidden layer were employed to construct models for predicting SD. The influences of five process parameters on RWTU were studied using ANOVA, indicating melt temperature, delay time, and water temperature were predominant. The prediction abilities of three models (RSM, ANN, and ANN-GA) were compared through some statistical criteria and the results demonstrated that the ANN-GA model had the best performance followed by ANN and RSM. The optimization of RWTU was implemented using ANN-GA as a fitness function and got the minimum SD 0.097 which was smaller than any other experimental result. It is noteworthy that our interesting findings will be provided new solutions for the subsequent optimization of warpage and shrinkage of plastic parts in SFRC OWAIM.



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*Source: 6154694-2020-02-26.xml*