F. LIN et al.: OPTIMIZATION OF INJECTION MOLDING QUALITY BASED ON BP NEURAL NETWORK AND PSO
491–497
OPTIMIZATION OF INJECTION MOLDING QUALITY BASED ON
BP NEURAL NETWORK AND PSO
OPTIMIZACIJA KVALITETE INJEKCIJSKEGA BRIZGANJA NA
OSNOVI NEVRONSKIH MRE@ IN ALGORITMA OPTIMIZACIJE
Z ROJEM DELCEV
Feng Lin
1
, Jingying Duan
2
, Qiuxia Lu
2
, Xibing Li
3,4,
*
1
Fuzhou Polytechnic, College of Mechanical and Electronic Engineering, Fuzhou, China
2
Shandong Labor Vocational and Technology College, Jinan, China
3
Fujian Agriculture and Forestry University, College of Mechanical and Electronic Engineering, Fuzhou, China
4
Fujian Key Laboratory of Agricultural Information Sensing Technology, Fuzhou, China
Prejem rokopisa – received: 2022-06-08; sprejem za objavo – accepted for publication: 2022-07-25
doi:10.17222/mit.2022.516
An electronic product shell is prone to uneven shrinkage, warpage and sink marks, resulting in a large number of unqualified
products and increased costs. Therefore, volumetric shrinkage, warpage deformation and sink mark index are selected as optimi-
zation goals. Based on the orthogonal test and entropy weight method, a multi-objective optimization was transformed into a
comprehensive evaluation optimization. A BP neural network combined with a particle swarm optimization algorithm was used
to obtain the optimal combination of process parameters, simulated by Moldflow to reduce volumetric shrinkage to 3.46 %,
warpage deformation to 2.538 mm, and the sink mark index to 1.87 % so as to improve the injection molding quality of the plas-
tic parts and meet the requirements of qualified parts. The combination of the BP neural network and particle swarm optimiza-
tion algorithm can prevent the defects such as large shrinkage, warpage and sink marks.
Keywords: orthogonal test, entropy weight, neural network, particle swarm optimization
Plasti~na ohi{ja elektronskih izdelkov so med postopkom injekcijskega brizganja nagnjena k neenakomernemu kr~enju,
ukrivljanju in izgubljanja napisov ali oznak oz. potencialnemu kr~enju zaradi vro~e sredice (SMI; angl.: sink mark index), kar
privede do nastanka nekakovostnih izdelkov in pove~anja stro{kov. Zaradi tega so se avtorji ~lanka posvetili optimizaciji
volumskih skr~kov, deformacij zaradi krivljenja in kr~enju zaradi vro~e sredice. Na osnovi ortogonalnih testov in metode
analize entropije (angl.: entropy weight method) so ve~ objektno optimizacijo transformirali v obse`no optimizacijsko
ovrednotenje. Z uporabo kombinacije metod povratno napredovanih (BP; angl.: back propagation) nevronskih mre` in algoritma
optimizacije z rojem delcev (PSO; angl.: particle swarm optimization) so dobili optimalno kombinacijo procesnih parametrov,
ki so jih simulirali s programskim orodjem Moldflow in tako zmanj{ali volumski skr~ek na 3,46 %, deformacijo zaradi
ukrivljanja na 2,538 mm in kr~enje zaradi vro~e sredice na 1,87 %. S tem so izbolj{ali kakovost procesa injekcijskega brizganja
plasti~nih izdelkov in dosegli zahtevano kakovost le-teh. Pokazali so, da uporaba kombinacije metod povratno napredovanih
nevronskih mre` in algoritma optimizacije z rojem delcev lahko pomaga pri re{evanju napak kot so razne deformacije in
krivljenja, ki nastajajo med postopkom injekcijskega brizganja plasti~nih ohi{ij za elektronske sestavne dele.
Klju~ne besede: ortogonalni test, analiza entropije, nevronske mre`e, optimizacija z rojem delcev
1 INTRODUCTION
1.1 General
With the advent of the intelligent era, electronic prod-
ucts began to be applied extensively. The speed of the re-
newal of plastic housings for electronic products is ac-
celerating, placing higher demand on the quality of
plastic parts. The quality of injection plastic parts is
jointly determined by the injection process parameters
and mold structure. By optimizing the injection process
parameters, quality defects of plastic parts such as
warpage deformation can be avoided.
1
By replacing re-
peated test molds with reasonable orthogonal experimen-
tal design and Moldflow numerical simulation technol-
ogy, Y. Nie et al. obtained optimized injection process
parameters based on a range analysis and variance analy-
sis instead.
2–4
G. Xu et al. studied the impact of injection
process parameters on the multi-objective quality of
plastic parts using orthogonal experimental design, sig-
nal-to-noise ratio calculation and gray correlation analy-
sis, and then obtained the optimal combination of pro-
cess parameters.
5–7
H. G. Zhang et al. transformed a
multi-objective optimization problem into a single-objec-
tive optimization problem based on the entropy weight
method and obtained the optimal process parameter
combination through a comprehensive evaluation.
8,9
In the present work, an electronic product backshell
was selected as the object of study. Based on the numeri-
cal simulation technology (Moldflow) and orthogonal
test, the entropy weight method was introduced to get the
test data. Then, a back propagation (BP) neural network
model was established using Python to find a better com-
bination of the process parameters through global opti-
mization of the particle swarm optimization algorithm.
Materiali in tehnologije / Materials and technology 56 (2022) 5, 491–497 491
UDK 620.172.23 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 56(5)491(2022)
*Corresponding author's e-mail:
lxbwjj@163.com (Xibing Li)

1.2 3D model and mesh division of the back cover of
an electronic product
The 3D model of the backshell of this electronic
product is shown in Figure 1. The maximum size of the
backshell is (376 × 308 × 45) mm, with the average wall
thickness of 2.25 mm. The material is an acrylonitrile-
butadiene-styrene copolymer, named ABS. It has a good
overall performance with the recommended range of pa-
rameters: mold temperature (40–70 °C), melt tempera-
ture (190–220 °C), holding pressure (65–95 MPa), pres-
sure holding time (6–12 s), injection pressure
(70–130 MPa) and injection time (0.9–1.3 s).
The backshell of the electronic product has four con-
vex platform holes and many reinforcement plates, and
there are square holes on the sides. The product structure
is complex and prone to quality defects such as deforma-
tion and uneven shrinkage after molding. Meanwhile, the
structure of the plastic part has many features such as
chamfers and edges, which are favorable to injection
molding, but unfavorable to the mesh division of a nu-
merical simulation. The CADdoctor2018 software was
used to simplify the structure of the 3D model of the
product, and then the file was imported into
Moldflow2019 for a mesh division. The plastic part is
thin-walled, with a uniform wall thickness. Using a dou-
ble-layer grid, the average aspect ratio of the grid is 2.12,
the match percentage is 91.2 % and the reciprocal per-
centage is 91.3 %, meeting the requirements of the dou-
ble-layer-grid numerical-simulation analysis.
The sequence analysis of the fill pressure warp was
selected. At the recommended mold temperature of
50 °C, melt temperature of 205 °C and other default pa-
rameters, the volumetric shrinkage obtained by the
Moldflow simulation was 5.57 %, the warpage deforma-
tion was 2.563 mm and the sink mark index was 3.57 %.
However, a qualified injection product needs to have a
volumetric shrinkage of less than 4.5 %, a maximum
warpage deformation of less than 3 mm and as small as
possible, and no sink marks if possible. When an injec-
tion mold structure has been determined, the injection
process parameters should be optimized to reduce the
volumetric shrinkage, warpage deformation and sink
mark index in order to improve the yield.
2 EXPERIMENTAL PART
2.1 Orthogonal experimental design
According to the orthogonal experimental design, the
volumetric shrinkage, warpage deformation and sink
mark index were selected as experimental targets. Ac-
cording to the molding characteristics of the ABS mate-
rial, the mold temperature, melt temperature, holding
pressure, pressure-holding time, injection pressure and
injection time were selected as the experimental factors.
Four levels were selected for each factor, as shown in Ta-
ble 1.
10,11
An L32 (4
6
) orthogonal array test table was
adopted, and the orthogonal test design and simulation
results are shown in Table 2.
Table 1: Table of the orthogonal-test factor levels
Level
Factor
A/°C B/°C C/MPa D/s E/MPa F/s
1 40 190 95 6 70 0.9
2 50 200 85 8 90 1.1
3 60 210 75 10 110 1.3
4 70 220 65 12 130 1.5
A – mold temperature (°C), B – melt temperature (°C), C – holding
pressure (MPa), D – pressure-holding time (s), E – injection pressure
(MPa), F – injection time (s), numbers 1–4 indicate the level of each
test factor
Table 2: Orthogonal experimental design and simulation results
Test
No.
A/°C B/°C
C/
MPa
D/s
E/
MPa
F/s Y
1
/%
Y2
/
mm
Y
3
/%
1 40 190 95 6 70 0.9 4.742 2.606 2.716
2 40 200 85 8 90 1.1 6.985 2.473 2.748
3 40 210 75 10 110 1.3 8.3 2.821 3.333
4 40 220 65 12 130 1.5 8.751 2.878 3.794
5 50 190 95 8 90 1.3 6.807 2.457 2.468
6 50 200 85 6 70 1.5 6.93 2.54 3.484
7 50 210 75 12 130 0.9 5.311 2.703 3.017
8 50 220 65 10 110 1.1 8.646 2.789 3.628
9 60 190 85 10 130 0.9 4.965 2.669 2.549
10 60 200 95 12 110 1.1 4.45 2.371 2.607
11 60 210 65 6 90 1.3 6.038 2.922 4.166
12 60 220 75 8 70 1.5 7.545 2.425 4.309
13 70 190 85 12 110 1.3 5.625 2.575 2.514
14 70 200 95 10 130 1.5 7.649 2.292 3.222
15 70 210 65 8 70 0.9 7.621 5.520 4.427
16 70 220 75 6 90 1.1 8.744 2.469 4.72
17 40 190 65 6 130 1.1 6.423 3.119 3.666
18 40 200 75 8 110 0.9 7.818 2.852 3.019
19 40 210 85 10 90 1.5 7.867 2.536 2.774
20 40 220 95 12 70 1.3 5.643 2.537 2.866
21 50 190 65 8 110 1.5 6.062 3.201 3.872
22 50 200 75 6 130 1.3 7.702 2.851 3.427
23 50 210 85 12 70 1.1 5.148 2.532 2.781
24 50 220 95 10 90 0.9 5.364 2.301 3.577
F. LIN et al.: OPTIMIZATION OF INJECTION MOLDING QUALITY BASED ON BP NEURAL NETWORK AND PSO
492 Materiali in tehnologije / Materials and technology 56 (2022) 5, 491–497
Figure 1: 3D model of the back cover of the electronic product

25 60 190 75 10 70 1.1 5.717 3.985 3.936
26 60 200 65 12 90 0.9 7.129 5.46 5.172
27 60 210 95 6 110 1.5 8.326 2.353 4.013
28 60 220 85 8 130 1.3 9.055 2.407 4.249
29 70 190 75 12 90 1.5 6.311 6.583 4.079
30 70 200 65 10 70 1.3 6.643 4.694 4.605
31 70 210 95 8 130 1.1 8.365 2.216 3.977
32 70 220 85 6 110 0.9 8.486 2.270 4.667
In Table 2,Y
1
,Y
2
and Y
3
represent the volumetric
shrinkage (%), warpage deformation (mm) and sink
mark index (%).
2.2 Analysis of the single-objective optimization result
Through the orthogonal test, the experiment result
that minimizes the single target in 32 sets could be
found, but the combination of injection process parame-
ters could not be optimized. The range analysis allows us
to find the optimal combination of process parameters
and the ranking of the degree of influence of the process
parameters on the target.
12,13
A statistical analysis was
conducted on the test results from Table 2 to obtain the
mean value of each level of volumetric shrinkage and the
range analysis was used for the factors, as shown in Ta-
ble 3.
As shown in Table 3, for the volumetric shrinkage,
the optimal process parameter combination is
A2-B1-C1-D4-E1-F1, i.e., the mold temperature is
50 °C, the melt temperature is 190 °C, the holding pres-
sure is 95 MPa, the pressure-holding time is 12 s, the in-
jection pressure is 70 MPa and the injection time is 0.9 s.
Moldflow was used for the numerical simulation; the op-
timized volumetric shrinkage was 4.02 % and the sink
mark index was 2.14 %, but the warpage deformation
was 2.573 mm, which was not optimized.
Consequently, the following conclusions could be
drawn. For the warpage deformation, the optimal combi-
nation of process parameters is A2-B4-C1-D1-E4-F2.
The optimized warpage deformation was 2.154 mm, but
the volumetric shrinkage was 8.49 %, and the sink mark
index was 4.36 %. The volumetric shrinkage and sink
mark index were not optimized. For the sink mark index,
the best combination of process parameters is
A1-B1-C1-D4-E3-F3. The optimized sink mark index
was 2.43 %, but the volumetric shrinkage was 7.07 %
and the warpage deformation was 2.597 mm. The volu-
metric shrinkage and warpage deformation were not
optimized. The injection molding process parameters of
the backshell of this electronic product have different de-
grees of influence on the volumetric shrinkage, warpage
deformation and sink mark index, so the optimization of
multiple objectives could not be achieved simulta-
neously.
2.3 Comprehensive assessment
Considering that volumetric shrinkage, sink mark in-
dex and warpage deformation have different effects on a
comprehensive evaluation of products, the entropy
weight method was introduced to determine the weight
of each index and convert the multi-objective optimiza-
tion problem into a single-objective comprehensive eval-
uation problem.
14–16
In order to eliminate the effect of
different dimensions, it is necessary to normalize all the
indicators. As smaller values of all the indicators are
better, negative indicators are adopted for the normaliza-
tion, and the formula is shown below:
Y
YY
YY
ij
ji j
jj
*
max( )
max( ) min( )
=
−
−
(1)
In Equation (1), j = 1–3, I = 1–32, Y
ij
*
represents the
i-th sample of the j-th indicator, MAX(Y
j
) is the maxi-
mum value of the j-th indicator and MIN(Y
j
) is the mini-
mum value of the j-th indicator. After the normalization,
a data normalization table was obtained as shown in Ta-
ble 4. Then the entropy value was calculated based on
the normalized evaluation index, and the entropy value e
j
of the j-th evaluation index is shown in Equation (2).
e
n
Z
Z
Z
Z
j
ij
ij
i
n
i
n
ij
ij
i
n
=−
=
=
=
∑
∑
∑
1
1
1
1
ln (2)
In Equation (2), n = 32, and when
Z
ij
=0, ln
Z
Z
ij
ij
i
n
=
∑
=
1
0
Finally, the corresponding weight coefficient was cal-
culated in accordance with the entropy value. The weight
coefficient of the j-th evaluation index is shown in Equa-
F. LIN et al.: OPTIMIZATION OF INJECTION MOLDING QUALITY BASED ON BP NEURAL NETWORK AND PSO
Materiali in tehnologije / Materials and technology 56 (2022) 5, 491–497 493
Table 3: Range analysis table for the volumetric shrinkage from the orthogonal test
Level
A – mold temper-
ature (°C)
B – melt tempera-
ture (°C)
C – holding pres-
sure (MPa)
D – pressure
holding time (s)
E – injection
pressure (MPa)
F – injection time
(s)
1 7.0661 5.8315 6.4183 7.1739 6.2486 6.4295
2 6.4963 6.9133 6.8826 7.5323 6.9057 6.8098
3 6.6531 7.1220 7.1810 6.8939 7.2141 6.9766
4 7.4305 7.7793 7.1641 6.0460 7.2776 7.4301
Range 0.9342 1.9478 0.7627 1.4863 1.0290 1.0006
Influence degree 516234
Best combination 50 190 95 12 70 0.9

tion (3), and the weight coefficients of volumetric
shrinkage, warping deformation and sink mark index
were 0.533, 0.159 and 0.308, respectively. In accordance
with Equation (4), weighted comprehensive evaluation
scores were calculated as shown in Table 4.
W
e
e
j
j
j
j
=
−
−
=
∑
1
1
1
3
(3)
ZY WY WY W
iii i
=++× ()
11 22 33
100 (4)
Table 4: Normalized data standardization table and comprehensive
evaluation scores
Test
No.
Y
1
*
Y
2
*
Y
3
*
Comprehensive
evaluation
scores Z
i
Sorting
1 0.9366 0.9107 0.9083 92.3672 2
2 0.4495 0.9411 0.8964 66.6724 10
3 0.1640 0.8615 0.6801 43.5561 21
4 0.0660 0.8484 0.5096 32.8714 27
5 0.4882 0.9448 1.0000 71.9898 9
6 0.4615 0.9258 0.6243 58.6221 15
7 0.8130 0.8885 0.7970 82.0123 6
8 0.0888 0.8688 0.5710 36.3091 26
9 0.8882 0.8963 0.9700 91.4844 3
10 1.0000 0.9645 0.9486 97.8385 1
11 0.6552 0.8383 0.3720 59.6700 14
12 0.3279 0.9521 0.3192 42.5071 22
13 0.7448 0.9178 0.9830 84.6340 5
14 0.3053 0.9826 0.7212 54.2593 17
15 0.3114 0.2434 0.2755 28.9399 28
16 0.0675 0.9421 0.1672 23.8344 32
17 0.5716 0.7932 0.5570 60.2494 13
18 0.2686 0.8544 0.7962 52.5898 18
19 0.2580 0.9267 0.8868 55.9924 16
20 0.7409 0.9265 0.8528 80.5305 7
21 0.6499 0.7744 0.4808 61.7421 12
22 0.2938 0.8546 0.6453 49.2510 19
23 0.8484 0.9276 0.8842 87.2204 4
24 0.8015 0.9805 0.5899 76.4550 8
25 0.7249 0.5949 0.4571 62.1066 11
26 0.4182 0.2572 0.0000 26.2813 30
27 0.1583 0.9686 0.4286 37.1756 25
28 0.0000 0.9563 0.3413 25.8819 31
29 0.5959 0.0000 0.4042 44.1120 20
30 0.5238 0.4326 0.2097 41.1816 23
31 0.1498 1.0000 0.4419 37.6414 24
32 0.1236 0.9876 0.1868 28.1405 29
3 PROCESS PARAMETER OPTIMIZATION AND
VALIDATION
3.1 Comprehensive evaluation and analysis
According to the ranking of comprehensive evalua-
tion scores from Table 4, test No. 10 had the highest
comprehensive evaluation score. In order to further ana-
lyze the significant impacts of process parameters on the
comprehensive evaluation indexes and determine the op-
timal process parameters, the range analysis was used to
analyze the comprehensive evaluation scores from Ta-
ble 4. The order of the influence of each process parame-
ter on the comprehensive evaluation index was B > C >
A>D>F>E.Theoptimal process parameter combina-
tion was A2-B1-C1-D4-E1-F1, which was the same as
the optimal process parameter combination of the mini-
mum volumetric shrinkage. Compared with the test re-
sult for No. 10, the volumetric shrinkage was reduced by
about 9.6 %, the sink mark index was reduced by about
18 %, while the warpage deformation increased. How-
ever, due to the small weight proportion, the warpage de-
formation had little influence on the comprehensive eval-
uation. Therefore, according to the comprehensive
evaluation, the overall quality of the plastic part was im-
proved.
3.2 BP-PSO process parameter optimization
To find a better combination of injection process pa-
rameters, a BP neural network was used to fit the in-
put-output relationship model, and the optimal value of
the model was obtained with the particle swarm optimi-
zation algorithm.
3.2.1 Establishing an input-output relationship
prediction model based on the BP neural network
The BP neural network is a classical error feed-
forward neural network, widely used in scientific re-
search fields due to its multi-dimensional nonlinear map-
ping capability.
17–19
In terms of the structure, this work
adopted a four-layer BP neural network model. The input
layer had 6 nodes, the second hidden layer had 11 nodes,
the third hidden layer had 11 nodes, and there were 3
nodes in the output layer of the model. The 6 process pa-
rameters and the comprehensive evaluation were taken as
the input and output of the BP neural network. 90 % of
the 32 sets of orthogonal test data was randomly selected
as the training data, and the rest was used as the test data
set. Before training the neural network, the input and
output data were normalized with Equation (5). The
Keras library of Python was used to build the BP neu-
ral-network framework. The tb.keras.regularizers.l2
method was used for the hidden layer to avoid over-fit-
ting, and then it was activated with the Relu function.
The loss function was MSE.
x
XX
XX
ij j
jj
*
min( )
max( ) min( )
=
−
−
(5)
After 2000 iterations, the evaluation indexes were as
follows: mae = 0.0457, mse = 0.004, val_mae = 0.0587
and val_mse = 0.0055. After the training of the BP neu-
ral network, the predicted values of the comprehensive
evaluation scores were obtained, and the predicted values
were compared with the real values as shown in Fig-
ure 2. It can be seen from this figure that the real values
and predicted values of the comprehensive evaluation re-
F. LIN et al.: OPTIMIZATION OF INJECTION MOLDING QUALITY BASED ON BP NEURAL NETWORK AND PSO
494 Materiali in tehnologije / Materials and technology 56 (2022) 5, 491–497

mained largely consistent, although there were errors.
The BP neural network model obtained reflects the rela-
tionship between the input and output very well.
The remaining data set was used for the test. The real
values of the comprehensive evaluation scores (36.3091,
92.3672, 82.0123) for the test set were basically consis-
tent with the predicted values (37.8348, 88.2714,
74.5526). This proved that the established BP neural net-
work model was feasible.
3.2.2 Optimization of process parameters based on
PSO
The PSO algorithm, i.e., the particle swarm optimiza-
tion algorithm, is an intelligent optimization algorithm
that simulates the foraging behavior of a flock of birds
and optimizes the flock with the information exchange
among the individuals of the flock.
20,21
The negative
value of comprehensive evaluation score Z of the neural
network prediction was taken as the objective of the min-
imum optimization, and the optimal process parameters
were globally searched for by the PSO algorithm for the
prediction model.
The particle swarm optimization algorithm was con-
structed based on the sko.PSO toolkit of Python. The di-
mension of the search space dim was 6, population size
POP was 20, the maximum number of iterations
(max_iter) was 100, the inertia weight was 0.8, the learn-
ing factors C1 = C2 were 0.5, and the constraints were:
A (40–70 °C); B (190–220 °C); C (60–95 MPa); D (6–12
F. LIN et al.: OPTIMIZATION OF INJECTION MOLDING QUALITY BASED ON BP NEURAL NETWORK AND PSO
Materiali in tehnologije / Materials and technology 56 (2022) 5, 491–497 495
Figure 2: Comparison between the real values and predicted values of
the training set
Figure 3: Optimal fitness value curve Figure 6: Optimized sink mark index
Figure 5: Optimized warpage deformation
Figure 4: Optimized volumetric shrinkage

s); E (70–130 MPa); and F (0.9–1.3 s). The variation in
the optimal fitness value was obtained as shown in Fig-
ure 3. After 10 iterations, the optimal fitness value of the
PSO algorithm reached the minimum, and the optimized
combination of process parameters obtained with the op-
eration included a mold temperature of 40 °C, melt tem-
perature of 190 °C, holding pressure of 95 MPa, pres-
sure-holding time of 12 s, injection pressure of 70 MPa
and injection time of 0.9 s. The optimized volumetric
shrinkage was 3.9 %, the warpage deformation was
2.606 mm and the sink mark index was 2.2 % according
to the numerical simulation based on Moldflow. The vol-
umetric shrinkage was slightly reduced, the warpage de-
formation and the sink mark index were slightly in-
creased, and the quality of the plastic part was not
significantly improved.
The constraints were further adjusted as A (30–80 °C);
B (180–230 °C); C (55–105 MPa), D (4–14 s);
E (60–140 MPa); and F (0.7–1.5 s). The optimized pro-
cess parameter combination was obtained again with the
particle swarm algorithm; the mold temperature was
30 °C, the melt temperature was 180 °C, the holding
pressure was 105 MPa, the pressure-holding time was
14 s, the injection pressure was 108.4 MPa, and the in-
jection time was 0.7 s. Using Moldflow, the optimized
volumetric shrinkage was reduced to 3.46 %, as shown
in Figure 4. The warpage deformation decreased to
2.538 mm, as shown in Figure 5. The sink mark index
dropped to 1.87 %, as shown in Figure 6. The three indi-
cators were further reduced and the quality of the plastic
parts was fully optimized.
4 CONCLUSION
1) Based on an orthogonal test and single-objective
range analysis, the combination of process parameters
that allows a single-objective optimization is determined,
but the multi-objective optimization cannot be achieved
at the same time.
2) The entropy weight was used to transform a
multi-objective problem into a single-objective problem,
obtaining the following results: the optimal process pa-
rameter combination was A2-B1-C1-D4-E1-F1, i.e., the
volumetric shrinkage was 4.02 %, the warpage deforma-
tion was 2.573 mm, and the sink mark index was 2.14 %.
The overall quality of the plastic part was further im-
proved.
3) After the BP neural network fitting and PSO, fur-
ther optimal process parameters were found, i.e., a mold
temperature of 30 °C, a melt temperature of 180 °C, a
holding pressure of 105 MPa, a pressure-holding time of
14 s, an injection pressure of 108.4 MPa, and an injec-
tion time of 0.7 s. The optimized volumetric shrinkage
was reduced to 3.46 %, the warpage deformation was re-
duced to 2.538 mm, the sink mark index was reduced to
1.87 %, and the injection quality of the plastic part was
optimized comprehensively.
Acknowledgment
This work was sponsored by the Natural Science
Foundation Program of the Fujian Province
(2022J01609), Special Foundation for Science and Tech-
nology Innovation of the Fujian Agriculture and Forestry
University (No.CXZX2020132B) and 2021 Fujian Prov-
ince Young and Middle-Aged Teachers’ Education and
Research Project (No.JAT210819).
5 REFERENCES
1
R. Khavekar, H. Vasudevan, B. Modi, A comparative analysis of
Taguchi methodology and Shainin system DoE in the optimization of
injection molding process parameters, IOP Conf. Ser.: Mater. Sci.
Eng., 225 (2017) 1, doi:10.1088/1757-899X/225/1/012183
2
Y. Nie, H. M. Zhang, J. T. Niu, Optimization of the Injection
Molding Process Parameters Based on Moldflow and Orthogonal Ex-
periment, Key Engineering Materials, 561 (2013), 239–243,
doi:10.4028/www.scientific.net/KEM.561.239
3
X. F. Li, H. B. Liu, Optimization of Injection Molding Process Pa-
rameters Based on Taguchi Design of Experiment, Applied Me-
chanics and Materials, 233 (2012) 11, 335–338, doi:10.4028/
www.scientific.net/AMM.233.335
4
F. Wang, Z. L. Chen, Research on Process Optimization of Thin-Wall
Plastics Injection Based on Moldflow and Orthogonal Experiment,
Advanced Materials Research, 399–401 (2012), 1646–1649,
doi:10.4028/www.scientific.net/AMR.399-401.1646
5
G. Xu, Z. T. Yang, Multiobjective optimization of process parameters
for plastic injection molding via soft computing and grey correlation
analysis, The International Journal of Advanced Manufacturing
Technology, 78 (2015) 1–4, 525–536, doi:10.1007/s00170-014-
6643-4
6
A. Sadeghi, A. Babakhani, S. M. Zebarjad, H. Mostajabodaveh, Use
of grey relational analysis for multi-objective optimisation of NiTiCu
shape memory alloy produced by powder metallurgy process, Journal
of Intelligent Material Systems and Structures, 25 (2014) 16,
2093–2101, doi:10.1177/1045389X13517312
7
S. Q. Sun, S. K. Zhang, M. X. Huang, Optimization of injection
molding process parameters based on signal-to-noise ratio and gray
relational grade, Journal of Plasticity Engineering, 23 (2016)1 ,
141–145, doi:10.3969/j.issn.1007-2012.2016.01.026
8
H. G. Zhang, Z. Y. Zhang, F. P. Wan, Y. Y. Liu, Q. X. Hu, Multi-ob-
jective optimization for DPVC process based on entropy-weight and
RSM, Computer Integrated Manufacturing Systems, 20 (2014)8 ,
1887–1895, doi:10.13196/j.cims.2014.08.zhangzhuangya.1887.9.
20140811
9
X. Y. Lu, L. X. Fan, Y. Y. Ding, Multi-Objective Optimization of
FDM Molding Process Parameters Combined With Entropy Weight
TOPSIS, Mechanical Science and Technology, 4 (2017) 11,
1715–1721, doi:10.13433/j.cnki.1003-8728.2017.1113
10
T. Peng, H. Jun, W. D. Shi, Optimization of a Centrifugal Pump Used
as a Turbine Impeller by Means of an Orthogonal Test Approach,
FDMP: Fluid Dynamics & Materials Processing, 15 (2019)2 ,
139–151, doi:10.32604/fdmp.2019.05216
11
H. Oktem, T. Erzurumlu, I. Uzman, Application of Taguchi optimiza-
tion technique in determining plastic injection molding process pa-
rameters for a thin-shell part, Materials & Design, 28 (2007)4 ,
1271–1278, doi:1016/j.matdes.2005.12.013
12
M. Cong, S. Zhang, D. Sun, K. Zhou, Optimization of Preparation of
Foamed Concrete Based on Orthogonal Experiment and Range Anal-
ysis, Frontiers in Materials, 8 (2021), 488, doi:10.3389/fmats.
2021.778173
13
K. Q. Zhong, Y. Xiao, X. Lu, J. Deng, Orthogonal Experimental De-
sign and Range Analysis of TPCT Extraction of Coal Fire Heat,
F. LIN et al.: OPTIMIZATION OF INJECTION MOLDING QUALITY BASED ON BP NEURAL NETWORK AND PSO
496 Materiali in tehnologije / Materials and technology 56 (2022) 5, 491–497

China Safety Science Journal, 31 (2021) 09, 135–141,
doi:10.16265/j.cnki.issn1003-3033.2021.09.019
14
Z. H. Zou, Y. Yi, J. N. Sun, Entropy method for determination of
weight of evaluating indicators in fuzzy synthetic evaluation for wa-
ter quality assessment, Journal of Environmental Sciences, 18 (2006)
5, 1020–1023, doi:10.3321/j.issn:1001-0742.2006.05.032
15
C. Qiao, Y. Wang, C. H. Li, B. Q. Yan, Application of Extension
Theory Based on Improved Entropy Weight Method to Rock Slope
Analysis in Cold Regions, Geotechnical and Geological Engineering,
39 (2021) 6, 4315–4327, doi:10.1007/s10706-021-01760-9
16
Y. L. Cao, X. Y. Fan, Y. H. Guo, S. Li, H. Y. Huang, Multi-objective
optimization of injection-molded plastic parts using entropy weight,
random forest, and genetic algorithm methods, Journal of Polymer
Engineering, 40 (2020) 4, 360–371, doi:10.1515/polyeng-2019-0326
17
Y. Kinouchi, G. Ohara, H. Nagashino, T. Soga, F. Shichijo, K.
Matsumoto, Dipole source localization of MEG by BP neural net-
works, Brain Topography, 8 (1996) 3, 317–321, doi:10.1007/
BF01184791
18
Z. Y. Song, S. M. Liu, X. X. Wang, Z. X. Hu, Optimization and pre-
diction of volume shrinkage and warpage of injection-molded
thin-walled parts based on neural network, The International Journal
of Advanced Manufacturing Technology, 109 (2020) 3, 755–769,
doi:10.1007/s00170-020-05558-6
19
M. L. Cong, S. S. Zhang, D. D. Sun, K. P. Zhou, Optimization of In-
jection Molding Process of Bearing Stand Based on BP Network
Method, Transactions of Nanjing University of Aeronautics and As-
tronautic, 31 (2014) 2, 180–185, doi:10.3969/j.issn.1005-1120.2014.
02.014
20
K. H. Fuh, S. B. Wang, Force modeling and forecasting in creep feed
grinding using improved BP neural network, International Journal of
Machine Tools and Manufacture, 37 (1997) 8, 1167–1178,
doi:10.1016/S0890-6955(96)00012-0
21
D. Kramar, D. Cica, Predictive model and optimization of processing
parameters for plastic injection moulding, Materiali in tehnologije /
Materials and Technology, 51 (2017) 4, 597–602, doi:10.17222/
mit.2016.129
F. LIN et al.: OPTIMIZATION OF INJECTION MOLDING QUALITY BASED ON BP NEURAL NETWORK AND PSO
Materiali in tehnologije / Materials and technology 56 (2022) 5, 491–497 497