Frontiers in Computing and Intelligent Systems 
ISSN: 2832-6024 | Vol. 2, No. 2, 2022 

 

75 

Quantitatively evaluate the cylindricity of Large size 
pipe fitting via laser displacement sensor and Digital 
twin technology 

Jie Ren1,2 *, Kuosheng Jiang1,2,3,4, a, Hui Guo5, b, Dongyang He1,2, c, Zhongwen Hu1,2, d, Ziyang Yin1,2, e 

1 State Key Laboratory of Mining Response and Disaster Prevention and Control in Deep Coal Mines, Huainan 232001, China 
2 School of Mechanical Engineering, Anhui University of Science and Technology, Huainan 232001, China 
3Shaanxi Steam Huainan Special Purpose Automobile Co., LTD., Huainan 232001, China 
4Key Laboratory of Conveyance Equipment, Ministry of Education, Nanchang 330013, China 
5Avic Aircraft Landing Gear Co. LTD, Changsha 410200, China 

* Corresponding author: Jie Ren (Email: 1447896707@qq.com), a jiangkuosheng333@stu.xjtu.edu.cn, b guohui1984126@163.com,  

c 576194225@qq.com, d 3143621962@qq.com, e 1632134392@qq.com 

 

Abstract: The rapid development of intelligent detection technology guarantees accuracy in the assembly process. Aiming to 

solve the quantitative inspection of the cylindricity of Large size pipe fitting, this paper presents an online method technology 

using a laser sensor and Digital twin technology. The detection system comprises visual positioning, servo drive, and laser 

displacement sensor information acquisition systems. After positioning by the machine vision camera system, the servo system 

and laser displacement sensor scan the large-size pipe fitting layer by layer and establish the information interaction between 

physical space and virtual space through digital twinning technology. The digital twin scatters information model was found to 

calculate the maximum tangent circle and minimum peripheral circle, fitting the curve area of the closed point cloud layer by 

layer. And the least square method was used to calculate the center of the layered circle. The radial deviation of pipe fitting was 

evaluated comprehensively. The system makes a linear fitting of the center of the most miniature square circle of each layer, 

compares its deflection Angle with the solid center line, and calculates the center line deviation of the hole. Finally, the precision 

of the proposed method was validated by varying experiments. The cylindricity measurement of pipe fittings with an inner 

diameter of 300mm and height of 270mm was carried out by a pair of C-shaped semicircles fixed by the radial assembly. The 

cylindricity of the pipe fitting is 0.2372mm. 

Keywords: Cylindricity; Laser displacement sensor; Digital twin technology; Large size pipe fitting; Machine vision system. 

 

1. Introduction 

With the high-speed development of sensor technology and 

digital twin technology, high-precision real-time detection in 

the online assembly process becomes possible. In this paper, 

the quantitative evaluation of the cylindricity error in 

processing large objects is carried out. Cylindricity can be 

considered as the superposition of three kinds of deviations: 

radial deviation, centerline deviation, and cross-section 

deviation. The existing traditional cylindricity error 

measurement is mainly based on the contact method, which 

includes a primarily two-point or Three-point method, a 

cylindricity meter, and a three-coordinate measuring 

instrument. The measurement accuracy of the two-point and 

three-point methods is greatly affected by manual operation; 

when the cylindricity instrument detects the roundness and 

cylindricity errors, a precision rotary table is required to drive 

the workpiece to rotate and detect, the three-coordinate 

measuring instrument is expensive. Moreover, the detection 

steps are complicated, and the measurement time is long, 

which is only suitable for measuring a small number of 

precision parts. The cylindricity of part elements, large or 

small dimensions, and complex shapes is even more 

challenging to achieve through traditional tactile 

measurement methods. Compared with the conventional 

contact measurement method, the sensor-based non-contact 

measurement method has the advantages of high 

measurement accuracy and high measurement efficiency. 

Typical non-contact measurement methods include laser 

triangulation, ultrasonic measurement, and machine vision 

measurement, widely used in the surface measurement of 

complex parts, shape tolerance measurement, and 

dimensional measurement of mechanical parts. Gangfeng 

Xiao proposed an online dimensional accuracy measurement 

method based on machine vision technology, which realized 

real-time measurement of straightness and roundness. The 

real-time image of the conical spinning workpiece is obtained 

through the image acquisition system, the camera is calibrated, 

and then a series of image processing techniques such as 

region of interest (ROI) extraction, image deblurring, 

denoising, and edge detection are used to extract the conical 

rotating workpiece the edge of. Finally, the straightness and 

roundness of the rotating workpiece are automatically 

calculated by a calculation program. Another device that uses 

a CCD camera to detect the inner wall of the pipeline was 

proposed by Moraleda and further developed by Choi. This 

system can use a pipeline robot crawling along a curved 

channel to carry a CCD camera and related lighting 

equipment. The CCD camera captures images of the inner 

wall in real time and uses manual or computer algorithms to 

process the captured images to identify defects on the inner 

wall. Its main technical difficulty and innovation lie in the 

design of the crawling robot rather than the inner wall 

detection part. Its disadvantage is that it can only identify and 

detect surface defects but cannot measure geometric 

quantities. Japan's TOKUJI OKADA and others use a pipeline 

robot carrying a closed-circuit television for pipeline 



 

76 

inspection. Through experimental tests, we know that the 

analysis of images in this solution is more detailed, and the 

judgment is flexible and convenient. Still, there are problems, 

such as difficulty in automatic pipeline detection and high 

detection error values. Zhang Maowei et al.  established a 

more comprehensive measurement model based on the two-

dimensional linear laser sensor measurement technology, 

including component eccentricity error e, sensor lateral offset 

error d, sensor forward tilts error θ(x), and lateral sensor tilts. 

The error θ(y), and the tilt error of the turntable are modeled 

and separated step by step. The particle swarm optimization 

algorithm is used to solve the model error parameters. And 

through the residual simulation, observe the influence of 

different levels of offset errors on the measurement results. 

Kühnel et al.  introduced an automated device for non-tactile 

high-precision measurement of roundness and cylindricity of 

ring gauges. The measurement system with dual 

interferometers and workpiece alignment combined with a 

high-precision turntable and automatic four-axis adjustment 

unit reduces classic problems in tactile and radial roundness 

measurements, such as errors in the alignment of the used 

turntable and workpiece influence, thereby improving 

accuracy and reducing measurement time. 

The concept of the digital twin is widely accepted as a new 

generation of digital manufacturing research concepts and 

plays a vital role in the era of Industry 4.0. As the premise of 

deep application of digital assembly manufacturing, it is 

essential to collect, model, and utilize historical data of the 

machining process and detection of parts to provide data 

support for the whole manufacturing scene. Qiangwei Bao 

proposed an assembly-oriented digital twin modeling method 

for details. The design information of the part is obtained from 

the three-dimensional model through the model-based 

definition method. But the processing characteristics are 

defined and identified in advance. Then, the assembly 

constraint relationship in the assembly units in which the parts 

participate can be obtained, based on which the deviation 

transfer analysis can be completed, and the critical assembly 

features can be screened as the carrier of processing and 

detection data. JiekangHaw proposed a digital twin-based 

additive manufacturing virtual part inspection concept. 

Minghui HU proposed the gas turbine digital twin model and 

its application in performance fault warning. It combined the 

machine model and the measured data to build a high-

precision performance model. The specific method is to adapt 

the initial point of the model to make the simulation 

performance match the actual performance. Then, the relative 

precision control strategy is proposed to improve the 

modeling efficiency. And the calculation amount of the model 

is appropriately reduced to avoid overstimulation and non-

convergence. Therefore, the digital twin model obtained will 

meet the need for higher accuracy and lower cost. Finally, 

according to the model results, the deviation degree is defined 

as the warning feature of the gas turbine performance fault. 

Jinfeng Liu proposed a multi-dimensional modeling method 

(DT) technique for machining processes. The design and 

execution stages of the machining process are used to support 

intelligent machining based on interpreting the modeling and 

application methods of machining process design, the 

inspection process, fault diagnosis, and quality prediction 

based on digital twin technology. The working mechanism of 

machining process modeling, simulation, prognosis, and 

control was expounded. 

In this paper, the laser displacement sensor is used to scan 

the inner wall of the pipeline layer by layer, establish the 

three-dimensional point cloud data, calculate the maximum 

tangent circle and minimum peripheral circle, fit the curve 

area of the closed point cloud layer by layer, and calculate the 

center of the layered process by using the least square method, 

and establish the digital model layer by layer. The information 

interaction between physical space and virtual space was 

established by digital twinning technology. The diameters of 

the maximum tangent circle and minimum peripheral circle 

were calculated, and the distribution of diameters was 

calculated. The radial deviation of holes was evaluated 

comprehensively. The center of the smallest square circle of 

each layer is fitted with a straight line, and the deflection 

Angle between the bar and the actual center line is calculated 

to calculate the deviation of the middle line of the pipeline. In 

this paper, the laser displacement sensor is used to scan the 

inner wall of the pipeline layer by layer, establish the three-

dimensional point cloud data, calculate the maximum tangent 

circle and minimum peripheral circle, fit the curve area of the 

closed point cloud layer by layer and calculate the center of 

the layered circle by using the least square method, and 

establish the digital model layer by layer. The information 

interaction between physical space and virtual space was 

established by digital twinning technology. The diameters of 

the maximum tangent circle and minimum peripheral circle 

were calculated, and the distribution of diameters was 

calculated. The radial deviation of holes was evaluated 

comprehensively. The center of the smallest square circle of 

each layer is fitted with a straight line, and the deflection 

Angle between the bar and the actual center line is calculated 

to calculate the deviation of the middle line of the pipeline. 

2. Real-time evaluation method of 
cylindricity error 

2.1. Evaluation of midline error 

The roundness and cylindricity error evaluation methods 

include the least region method, the least square method, the 

least external cylindrical method, and the maximum internal-

circle column method. In the measuring system, because the 

least square method is a local optimization algorithm, the 

calculation is convenient, the program is simple, and the 

calculation result is accurate. Hence, the author uses the least 

square method to calculate the scent of the oss-section. 

Suppose a total of N sections are measured, and M points are 

uniformly measured for each team. The cartesian coordinates 

of each end of the actual contour (𝑥𝑖 , 𝑦𝑖), poar coordinates 

are (𝑟𝑖 , 𝜃𝑖) , i11,2... M, the lmostdiminutivesquare circle 

center coordinate is 𝑂(𝑎, 𝑏), then: 

{
 
 

 
 𝑎 =

2

𝑀
∑𝑥𝑖 =

2

𝑀
∑𝑟𝑖 cos 𝜃𝑖

𝑀

𝑖=1

𝑀

𝑖=1

𝑏 =
2

𝑀
∑𝑦𝑖 =

2

𝑀
∑𝑟𝑖 sin 𝜃𝑖

𝑀

𝑖=1

𝑀

𝑖=1

 

Find the least squares center O of each section in turn, then 

the center O of space 𝑂(𝑎𝑙 , 𝑏𝑙 , 𝑧𝑙), 𝑙 11,2... N, carry out the 

least square space linear fitting for the center of the space 

𝑂(𝑎𝑙 , 𝑏𝑙 , 𝑧𝑙). 
𝑥 − 𝑥0
𝑚

=
𝑦 − 𝑦0
𝑛

=
𝑧 − 𝑧0
𝑝

 

By equivalent transformation of this equation, we can 

obtain: 



 

77 

x =
𝑚

𝑝
(𝑧 − 𝑧0) + 𝑥0 = 𝑘1𝑧 + 𝑏1 

y =
𝑛

𝑝
(𝑧 − 𝑧0) + 𝑦0 = 𝑘2𝑧 + 𝑏2 

Among them, the 𝑘1 =
𝑚

𝑝
, 𝑏1 = 𝑥0 −

𝑚

𝑝
𝑧0, 𝑘2 =

𝑛

𝑝
, 𝑏2 =

𝑦0 −
𝑛

𝑝
𝑧0, (𝑚, 𝑛, 𝑝)for the linear equations in the direction of 

the vector;(𝑥0, 𝑦0, 𝑧0) is a point on the line? 

According to the space line fitted by the least square 

method, the center line error of the workpiece is calculated. 

2.2. Minimum region circle fitting 

The distance between each point and the center of the circle 

is calculated according to the section least squares center of 

the process. The small circle radius 𝑅𝑚𝑖𝑛 of the cylindrical 

surface in the minimum region is the closest distance from the 

center of all the measuring points, and the large circle radius 

𝑅𝑚𝑖𝑛 of the cylindrical surface in the minimum region is the 

farthest distance from all the measuring points to the center of 

the circle. So, the cylindricity error ∅ = 𝑅𝑚𝑎𝑥 − 𝑅𝑚𝑖𝑛. 

Minimum area 

cylinder

Actual cylindrical 

surface

Y
X

Z

maxR

minR

 
Fig.1 Diagram of Cylindricity Error 

2.3. Simulation of cylindricity error 

The digital twinning three-dimensional point cloud map 

was constructed by establishing simulation data points. The 

feasibility of using a laser displacement sensor and digital 

twinning technology in the cylindricity detection of large-size 

pipe fitting was simulated and analyzed. As shown in fig. 2, it 

can be seen that in three-dimensional space, the three-

dimensional point cloud image can directly know the 

diameter distribution inside the pipe fitting and the center of 

the section fitted by calculation and observe the midline error 

of the pipe fitting. Using the three-dimensional point cloud 

data, the minimum regional circle formed by each pipe fitting 

team can be calculated, and the cylindricity error of the 

cylinder can be calculated by comparing the maximum 

tangent circle and the minimum peripheral circle of all the 

measured sections. 

X
Y

Z

 
Fig.2 Simulation Point Cloud Image 

3. System development 

3.1. Measurement system requirements 

As shown in Figure 3, the tested object is composed of two 

C-type semi-circular parts connected by four pairs of bolts 

and nuts in the axial direction instead of the traditional radial 

fastening method. Due to this particular connection mode, 

extremely high assembly accuracy is required during 

assembly, and the bolts on both sides need to adjust the torque 

to achieve high-precision assembly. Moreover, the resolution 

of cylindricity detection should reach more than 0.05mm, and 

the high-precision real-time detection and error display of 

cylindricity cannot be realized using traditional detection 

methods. Because the unique structure of the test object 

cannot be stuck on the high-precision rotary shaft, cannot be 

aligned by clamping, and cannot rotate or move in a straight 

line, the detection mechanism must carry out active alignment 

and feed movement. 

Nut
Bolt

Hanging Ear

Type C Unit

After 

assembly

 
Fig.3 Explosion Diagram of Large Size Pipe Fitting 

3.2. Set up the system 

As shown in Figure 4, the vision detection system 

comprises a three-axis motion system and a sensor scanning 

system. The motion system uses three servo motors to control 

the ball screw to drive the sensor scanning system to move in 

the direction of XYZ in space. At the same time, the servo 

system records feedback on the position of the scanning 

system and constructs the digital twin space coordinate 

system through the motion system. The scanning system 

includes a CCD camera, servo motor, and laser displacement 

sensor. First of all, the CCD camera takes the vertical photos 



 

78 

of the workpiece, combines the image processing technology, 

locates the center of the workpiece, realizes the active 

alignment, determines the diameter of the workpiece, assists 

the laser displacement sensor in adjusting the rotation radius, 

and recognizes the optimal range of data acquisition. After 

judging the center of the workpiece through the image 

information collected by the vision system, the motion system 

controls the sensor scanning system to move to the designated 

position and sets the scanning layer distance according to the 

measurement accuracy. The miniature servo motor drives the 

laser displacement sensor to scan the workpiece layer by layer. 

The detection system establishes the connection between the 

spatial coordinate information, the rotation Angle information 

of the servo motor, and the information of the laser 

displacement sensor. The digital twin virtual space of 

cylindricity detection was constructed, and the 3D model of 

the workpiece and the cylindricity detection results were 

displayed synchronically. 

Z-axis Drives the 

Motor

Sensor rotating 

motor

Laser displacement 

sensor

Large Size 

Pipe Fitting

Type C Part 

Connection

CCD Camera

Travel Switch

Travel Switch

Travel Switch

X-axis Drives 

the Motor

Y-axis Drives 

the Motor

 
Fig.4 Test Platform Diagram 

Parts

Sensor rotating motor

CCD Camera

Z-axis Drives the 

Motor

X-axis Drives 

the Motor

Y-axis Drives the 

Motor

Precision base

 
Fig.5 Physical inspection system diagram 

3.3. Build a digital twin model 

To realize the online detection and sorting process of 

cylindricity of large-size pipe fittings based on digital 

twinning. It is necessary to establish the connection between 

virtual space and physical space. According to the five-

dimensional model theory of the digital twin, the virtual entity 

of the digital twin needs to be described and portrayed from 

four aspects: geometry, physics, behavior, and rules. 

Therefore, based on the analysis of the detection elements, the 

digital twin model is established with a space motion module, 

camera, laser displacement sensor, and pipe fitting as the 

primary physical objects. 

Module of motion Sensor

Scanning Machine

Physical Space

Parts

Virtual Motion Module Virtual Sensor

Virtual Scanning Machine

Virtual Space

Virtual Parts

 
Fig.6 Digital Twin System 

4. Experimental analysis- 

4.1. Principle of experiment 

Select proper measuring equipment according to the 

principle of the detection scheme, and finally, build the 

detection platform as shown in Figure 4-2. Choose the 

Japanese Panasonic HL-G103-A-C5 diffusion-reflective laser 

displacement sensor. The sensor has a measuring accuracy of 

up to 0.5μm, a measuring range of 4mm (28mm to 32mm), 

and a sampling period of 200μs. The Z-axis servo motor 

drives the acquisition part to move up and down. The servo 

motor of the scanning system rotates and collects different 

sections of the cavity parts to obtain multiple measurement 

results, which are used for the last fitting of cylindricity. The 

effective stroke of the Z-axis feed is 300mm, the linearity is 

0.01mm, and the accuracy is ±0.01mm. The servo motor of 

the scanning system rotates and drives the laser displacement 

sensor to turn 360° to measure a section inside the cavity. The 

sensor obtains multiple measuring points, and the rotation 

angles correspond to the measured data points one by one. 

According to the size of the sensor, the radius range of the 

measuring tube and shell of the measuring system is 

calculated to be 140 mm~260 mm. In the detection system, 

the motion of the sensor scanning system in XYZ space and 

the drive of the laser displacement sensor rotation is realized 

by the upper computer control PLC, and the measured 

distance value of the laser displacement sensor is received 

through the RS-422 interface.  

4.1.1. Scanning system center correction 

Firstly, the CCD camera is used for preliminary positioning 

of the workpiece, and then the scanning system is used for 

rotation center correction. The scanning system scans the 

inner wall of the workpiece once, calculates the maximum 

scanning distance value 𝑙𝑚𝑎𝑥 and the measurement value 𝑙1 

of the distance at the angle corresponding to the rotation of 

180°. Set the radius of the workpiece to be detected as 𝑅0, 

the rotation radius of the laser displacement sensor 𝑟0, and the 

rotation angle at the maximum distance as 𝜃1, the Angle of 

𝑙1 here is 𝜃1 +
𝜋

2
 ,then: 

2𝑟0 + 𝑙𝑚𝑎𝑥 + 𝑙1 = 2𝑅0 

The rotation center of the relative laser displacement sensor 

is the origin of the coordinates, and the coordinates of the 

above two measuring points can be calculated as follows: 

𝐴(𝑥𝑚𝑎𝑥, 𝑦𝑚𝑎𝑥) {
𝑥𝑚𝑎𝑥 = (𝑟0 + 𝑙𝑚𝑎𝑥) ∗ cos 𝜃1
𝑦𝑚𝑎𝑥 = (𝑟0 + 𝑙𝑚𝑎𝑥) ∗ sin 𝜃1

 



 

79 

𝐵(𝑥1, 𝑦1) {
𝑥1 = (𝑟0 + 𝑙1) ∗ cos (𝜃1 +

𝜋

2
)

𝑦1 = (𝑟0 + 𝑙1) ∗ sin (𝜃1 +
𝜋

2
)

 

The rotation center of the laser displacement sensor moves 

|
𝑙𝑚𝑎𝑥−𝑙1

2
|  along the direction of 𝐵𝐴⃗⃗⃗⃗  ⃗ , and this point is the 

rotation center of the scanning system after correction. 

lm ax

l1

R 0
1

0r

Laser 

Displacement 

Sensor

Large Size Pipe 

Fitting

( )maxmax,A yx

( )11,B yx

 
Fig.7 Scan Center Deviation 

4.1.2. Data Collection 
After camera positioning and center calibration, the Z-axis 

servo motor, scanning system rotation servo motor, and laser 

displacement sensor move together through the upper 

computer. The cavity height is 240mm, the cross-section 

spacing is 10mm, and 20 cross-sections are scanned. The 

rotating servo motor speed of the scanning system is set to 

3r/min, and the sampling frequency of the laser displacement 

sensor is set to 5kHz.The scanning system rotates around to 

obtain 100,000 measurement points for each section. Record 

the Angle of each moment from the starting measurement 

position. 

𝜃𝑖 =
2𝜋

𝑀
∗ 𝑖 

Where: 𝜃𝑖 is the Angle of the first measuring point relative 

to the initial measuring point, and M is the number of points 

obtained by the section. 

4.1.3. Data processing 

The upper computer collects the scanning information of 

the laser displacement sensor and associates the length 

information with the Angle information to calculate the 

coordinates of each point. 

The coordinate of the NTH measurement point 𝑖  in the 

NTH row (𝑥𝑁𝑖 , 𝑦𝑁𝑖 , 𝑧𝑁) is 

{

𝑥𝑁𝑖 = (𝑟0 + 𝑙𝑖) ∗ cos 𝜃𝑖
𝑦𝑁𝑖 = (𝑟0 + 𝑙𝑖) ∗ sin 𝜃𝑖
𝑧𝑁 = 240 − 10𝑁

 

Where, 𝑙𝑖  is the distance between the sensor and the 

measuring point 𝑖 , and 𝜃𝑖  is the angle value of each 

measuring point relative to the initial measuring point; xNiis 

the horizontal coordinate of the measuring point 𝑖  on the 

NTH layer, 𝑦𝑁𝑖 is the ordinate of the measuring point on the 

NTH layer; i = 1, 2, 3,···, n;  N = 1, 2, 3,···, n; 

4.2. Analysis- Real-time evaluation curve of 

cylindricity 

The interior of the pipe fitting was scanned layer by layer 

to establish the data model. A total of 20 sections were 

observed in this experimental model. The scanned data were 

processed, and the results are shown in Figure 8. The 

coordinates in the X and Y directions of the center of the 

smallest square circle of each section were different, and the 

roundness error of the team fluctuated all the time. After the 

scanning of all areas is completed, the tangent circle's 

maximum radius and the outer circle's minimum radius in all 

sections are selected to construct the curve of the tangent 

circle's maximum radius and the outer circle's minimum 

radius, as shown in FIG. 9. The minimum cylindrical surface 

was constructed by calculating the maximum radius curve of 

the minimum outer circle and the minimum radius curve of 

the maximum tangent circle. The cylindricity error was 

calculated as 1149.9129-149.675710.2372.  

X
Y

Z

 
Fig. 8 Digital twin scatter plot 

2 4 6 8 10
149.65

149.7

149.75

149.8

149.85

149.9

149.95

150

12 14 16 18 20

Maximum Diameter of 

External Circle

Minimum Diameter of 

Tangent Circle

Minimum  Radius 

 Curve of Section

Maximum Radius 

 Curve of Section

149.9129

149.6757

Number of 

scanning layers

Radius of 

workpiece

 
Fig. 9 Cylindricity evaluation curve 

5. Conclusion 

This paper introduces a technology that quantitatively uses 

a laser sensor and digital twin technology to detect the 

cylindricity of large-sized pipe fittings online. By building a 

virtual and real interaction system, building a detection 

platform to carry out online real-time detection of pipe fittings, 

and using digital twin virtual models to intuitively reflect the 

significant cylindrical error of the object, as well as adjust the 

direction, improve the assembly efficiency and accuracy of 

axial fixed large-size pipe fittings, and increase the product 

qualification rate. And according to the size and range of the 

laser displacement sensor, the system can measure large pipe 

fittings with an inner diameter of 70-800mm and a depth of 

30-350mm; of course, the system can replace different laser 

displacement sensors according to actual needs.  



 

80 

Acknowledgments 

This work was carried out within the projects supported by 

the National Key Research and Development Program of 

China (2020YFB1314203 and 2020YFB1314103), the Open 

Project of State Key Laboratory of Mining Response and 

Disaster Prevention and Control in Deep Coal Mines 

(SKLMRDPC21KF03), the Open Project of Key Laboratory 

of Conveyance and Equipment (KLCE2021-05), the Science 

and Technology Research Project of Jiangxi Provincial 

Department of Education (GJJ210639), the supply and 

Demand Linking Employment Education Project of the 

Ministry of Education (20220100621), the Graduate 

Innovation Fund Project of Anhui University of Science and 

Technology (2021CX2050). 

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