JLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024

Technical Communication

Machine Learning for Scanning Path Prediction in Laser Forming- Application of Structured Patterns and CNN Ping-Hsien Chou1,2, Keiji Yamada*1, Yean-Ren Hwang2, Eisuke Sentoku3, Ryutaro Tanaka1, and Katsuhiko Sekiya1
1

Graduate School of Advanced Science and Engineering, Hiroshima University, Japan
Department of Mechanical Engineering, National Central University, Taiwan (R.O.C)
3
Department of Mechanical Engineering, National Institute of Technology, Fukui College, Japan*
Corresponding author’s e-mail: keiji@hiroshima-u.ac.jp
2

For prototype design and small batch production, laser forming has more advantages for manufacturing metal sheet products than conventional processes. However, predicting and optimizing therequired conditions for the product's final shape is difficult, especially in multi-stage forming, where
many governing factors affect the shape intricately. In this study, the convolution neural network(CNN) is proposed to simulate the correlations between the scanning paths and the final deformationsof a metal sheet. The imaginary data, which used values to present the distribution of deformation
height of metal sheets, was used to examine the feasibility of applying CNN. On the other hand, thesimulated images of a structured pattern projected on the sheet surface were used to train and test the
CNN. The results demonstrate that CNN can use imaginary data in the training dataset to predict thescanning path determined by two points on the edge of the metal sheet with high accuracy. Although
the performance of the test dataset needed to be better to prove the general-purpose ability, this research validates the feasibility of applying CNN for scanning path prediction in laser forming.
DOI: 10.2961/jlmn.2024.02.3001
Keywords: laser forming, convolution neural network, scanning path prediction, structured pattern,machine learning
1. Introduction
Laser forming is a process using thermal stress to deforma metal sheet without expensive dies and models. Due to thehigh flexibility and faster process [1-4], custom-made production, prototyping, and reshaping of formed products are
fields where laser forming has the advantage.
With the extensive investigation of laser forming, many
researchers have studied the relationship between deformation and process conditions [5-8]. Difficulty in controlling the process is attributed to that many governing factors
change during the process. For example, repeatedly bending
metal plates using laser forming increases the anisotropy ofbending and accumulates the work hardening during consecutive stages. Furthermore, laser irradiation also causes thermal influences such as changes in metallographic structures,
hardness, and absorptivity of the laser beam.
Machine Learning (ML) is a computer algorithm that extracts valuable knowledge called features from teaching dataand effectively improves machining manufacturing [9-11].
A mathematical model builds in the ML algorithm based on
sample data, known as "training data," to make predictions
or decisions. And then, "test data" is used to prove that theaccuracy and robustness of the model are suitable for the application. In recent years, ML has been frequently used tosolve problems that only can be solved with a lot of experience or data.
In many ML methods, CNN can extract valuable featuresfrom images or matrices and be applied to classification or
regression work. Based on the convenience of using images
to predict and the powerful convolution ability to extract thefeatures, CNN has been applied to many types of research inmechanical engineering field. For example, Xuefeng et al.
used CNN to develop a detection system that automaticallyrecognizes tool wear types and obtains the flank wear width
in the face milling process. It can collect the wear images of
all the inserts of a face milling cutter during the machining
gap, and no downtime for measurement [12]. Guo et al. proposed a novel hierarchical learning rate adaptive deep convolution neural network based on an improved algorithm,
and applied it to diagnose the bearing faults and to identify
both size and severity of faults in a bearing [13]. The resultsof experiments with bearing data demonstrated the superiority of the proposed ADCNN model to other fault-diagnosis
methods, such as traditional deep CNN. Rifai et al. compared 5 kinds of loss functions for the convolutional neuralnetwork proposed to evaluate the surface roughness from theimage of machined surface [14]. The average error of surface roughness prediction using CNN was verified to bewithin 10% of the actual measured surface roughness. At thesame time, the computational time for estimation is within
the desired range.
Thus, ML methods excel at recognizing patterns and extracting meaningful information from the amount of teaching data. The authors also applied a back propagation neuralnetwork (BPNN) to identify the condition of grinding wheel
surface [15]. The grinding sound was recorded and used fortraining, and then appropriate dressing interval was estimated for Resinoid-bonded cubic boron nitride wheels. In
addition, the corner wear of drill bit was predicted by learned
model using BPNN, too [16]. Specially defined static anddynamic features were extracted from different frequency
bands in frequency spectra of forces. Besides, MLJLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024

algorithms can effectively model complex nonlinear relationships between input and output variables, allowing for
more accurate predictions and efficient strategies. Therefore,
the authors also applied the neural network for forward prediction, where the metal sheet deformation was predictedfrom the process parameters in laser forming [16]. The forward prediction acts as a laser forming simulator giving theforesight of effects by process parameters and preventing
possible problems.
This paper reported the results when the CNN method
is applied to predicting laser scanning passes in multi-stage
laser forming processing. The input and output data were
the deformation change of a metal sheet after the processing and the sequential laser scanning pass during theprocessing, respectively. The pass has a significant impact
on the processing results.
ML encompasses supervised, unsupervised, and semisupervised learning, distinguishing whether the data has corresponding labels. The deformation data of this research is
obtained through laser scanning paths or simulations. However, this study used deformation data for backward prediction for the scanning path. Therefore, each deformation datais labeled with its corresponding path. Consequently, this research opts for supervised learning.
2. Method
This research used the metal sheet's shape as teachingdata to predict the laser scanning path. However, the plate
shape measuring to collect the deformational distribution
takes too much time, generally. Therefore, in the present paper, 'Imaginary data' deductively expected distributions ofdeformation within metal sheets were used for each given
irradiating conditions of laser [17]. Specifically, the imaginary data was deduced by the superposition of plate bending

2.1 Collecting data on laser forming
For simplification in the feasibility study, forming
stages are limited to 4, and the laser conditions are shown in
Table 1. Scanning paths are randomly chosen to acquire
general predictability for various shapes caused bysuperposing consecutive bending along those paths. In
addition, the laser beam is scanned 4 times (= 2 reciprocating
on a path) at a single stage of forming to obtain adequately
large deformation.
As shown in Fig. 1 (a), two endpoints were randomly
chosen from discrete 16 candidate points to consider as eachstraight scanning path. Those candidates were arranged witheven spacing of 20 mm on each edge, and two endpoints had
not to be chosen on the same edge to avoid making the pathoverlaid the edge. In addition, lines interfering with the
fixing bolt were also excluded. For example, solid lines <16> and <3-14> are the correct paths, while broken line <210> is not chosen because of the interference with the fixing
bolt, as shown in Fig. 1 (b).

Table 1 Process conditions.
Laser forming parameter
Number of stages
Number of scans per stages
Bending angle per stage [°]Workpiece
Material
Size [mm]Diode laser
Average power [W]
Scan speed [mm/min]
Spot diameter d [mm]444(a) Simulated multiple scanning paths

JIS SS400
100 × 100 × 1.5
220.9±1.5800
1.7consecutively generated in forming stages with the particular values of average laser power, scanning speed, and spot
diameter shown in Table 1. Thus, this simulation assumes
that the bending angle 𝜃𝜃 = 4° is determined without influences of the gradual change in plate rigidity by previous
stages. Using simulated data is expected to give enough plate
shape diversity to acquire high versatility in path prediction.
The feasibility of applying CNN was examined through thetraining with imaginary data and the verification of predicted
paths for target shapes.

(b) Experimental apparatus on NC table
Fig. 1 Experimental procedure in laser forming tests.

JLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024

In the laser forming experiment, a laser distance meter
was used to sample the surface of the workpiece and then get
the height of each sampling point after each forming stage
by simple calculation. Therefore, the simulation also built
enough imaginary height distribution data, like Fig. 4 (a), totrain the machine learning model [17]. Additionally, CNNs
excel at extracting features from images. This study aims tointroduce a novel optical data collection method by directly
capturing images of the workpiece or projecting particularpatterns onto the workpiece surface and inputting them to
the CNN for feature extraction to predict the laser scanning
path. This research tried to validate the feasibility of path
prediction using imaginary images with particular patterns
at first. The imaginary images with particular patterns will
be introduced in Chapter 2.3.

(a) Designed patterns(b) Examples of projected
patternFig. 2 Four different structured patterns used.

Regularly repeated geometric patterns enable the detection of distortion of a surface on which the patterns are projected. In three-dimensional measurement, using fringe projection techniques for generating surface information is oneof the most active research areas in optical metrology [1820]. Most of these methods use sinusoidal fringe patterns,
and phase analysis is conducted to obtain the surface information of the target, including the human face, apple, andany 3-D diffuse objects. However, this research proposed an
idea that applied the binary fringe pattern in different directions, as shown in Fig. 2(a), and used the projected patternsof the metal surface through CNN to predict irradiation conditions. In contrast to the reference paper, this study employed binary fringe patterns instead of sinusoidal ones, andthe phase analysis was not considered to obtain surface deformation. This research tried to apply CNN to extract thefeatures of bending lines on the workpiece surface and predict the scanning path. In order to ensure omnidirectionality
in scanning path prediction, designed patterns had varying

orientations. To avoid situations where the fringe patterns do
not deviate when parallel with the scanning path, potentiallyaffecting the CNN from extracting helpful features in that
region. Figure. 2(b) shows the patterns projected onto themetal plates bent during laser forming tests. However, capturing many of these images presents challenges due to two
disturbance influences. Firstly, the clarity of the fringe patterns on the workpiece's surface is susceptible to variations
in lighting conditions, including both the projector's lightsource and ambient lighting. Maintaining consistent illumination is crucial to ensure the quality of captured images.
Secondly, the relative positions of the workpiece and thecamera cannot be perfectly fixed between each machining
operation and image capture step. This variability complicates following data processing steps, requiring careful calibration and registration procedures to reduce these positional variations.
Nevertheless, the present study aims to demonstrate theefficacy of proposed path prediction method using CNN.
Therefore, the authors considered that inputting those captured photos directly to the CNN should be continuously investigated in our future study, rather than included prematurely in the present study. Instead, imaginary data of the
projected patterns was simulated on the assumption that influences of any disturbance were removed.
2.2 Convolution neural network and datasets
In order to predict laser scanning paths from the sheet
shape, machine learning was conducted using a CNN shownin Fig. 3. Structure of the CNN contains two parts: convolutional layers for extraction of features from the input, andfully connected layers for extraction of features in shapes ofcalculating the prediction by imitating the nonlinear function.
Training and testing of the CNN are conducted withteaching datasets consisting of the matrix data for input andthe labels for output. 1000 datasets were prepared in thisstudy, 80% were used for training CNN, and the rest were
for testing. These data were obtained by deductive reasoning
so that they could be obtained in a shorter time than the experiment and exclude disturbance influences.
Tables 2 to 7 list all the convolution neural network
structures. These listed networks have not been fully optimized, and the author believes there is still room for adjustment in each network. Each training for the CNN involves<4–6>< 1 – 16 >< 12 – 14 >< 12 – 13 >

1st
→
2nd
→
3rd
→
4th
(a) Gray images presenting height distribution

Fig. 3 Structure of convolution neural network used.

1st
→
2nd
→
3rd
→
4th
(b) Vertical fringes converted from upper gray images
Fig. 4Transition on plate shape during four stages.

JLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024

loading data and training the network for 1-4 forming stages,
which consumes a substantial amount of time. While not optimal, the results obtained in this experiment are generated
through training with the respective network architectures.
The training parameters not explicitly listed are all default
ones of TensorFlow. All training used the Adam optimizer inthis study.

2.3 Input data for CNN
As mentioned in Section 2.1, the imaginary data contains:
1. Height distribution data is used to simulate the data collected by the laser distance meter.

Table 2 CNN structure of Height distribution input, input data scheme A, and binary encoding method.
First stage

Second stage

Third stage

Fourth stage

Input

400 × 400 × 1

←

←

←

Conv2D+ ReLu(5×5)
396 × 396 × 8(3×3)
398 × 398 × 8←←

MaxPool

198 ×198 × 8

199 ×199 × 8

←

←

Con2D
+ ReLu(3×3)
197 × 197 × 8(3×3)
197 × 197 × 16←

MaxPool

98 × 98 × 8

98 × 98 × 16

←

Con2D
+ ReLu(3×3)
96 × 96 × 8(3×3)
96 × 96 × 32←

MaxPool

48 × 48 × 848 × 48 × 32

←

Con2D
+ ReLu(3×3)
46 × 46 × 8(3×3)
46 × 46 × 32

←

33856
1280
320
32

67712

←
←

Flatten
Dense + ReLu
Dense + ReLu
Sigmoid

313632
32
16

←
←
48

640
64

Table 3 CNN structure of Height distribution input, input data scheme A, and Cartesian encoding.
First stage

Second stage

Third stage

Fourth stage

Input

400 × 400 × 1

←

←

←

Con2D
+ ReLu(3×3)
398 × 398 × 4(5×5)
396 × 396 × 8(5×5)
396 × 396 × 4(5×5)
396 × 396 × 8

MaxPool

199 ×199 × 4

198 ×198 × 8

198 ×198 × 4

198 ×198 × 8

Con2D+ ReLu(3×3)
197 × 197 × 8(5×5)
194 × 194 × 8

←

(5×5)
194 × 194 × 16

MaxPool

98 ×98 × 8

97 × 97 × 8←

97 × 97 × 16

Con2D
+ ReLu(5×5)
93 × 93 × 8(5×5)
93 × 93 × 16

(5×5)
93 × 93 × 64

MaxPool

46 × 46 × 8

46 × 46 × 16

46 × 46 × 64

Con2D
+ ReLuFlatten
Dense + ReLu
Dense + ReLu
Dropout
Sigmoid

42 × 42 × 64
36864
128
64

16928
2000
2000

4

8

33856

112896

320
50%
12

16

←

←
←
←

JLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024

Table 4 CNN structure of Height distribution input, input data scheme B, and binary encoding.
First stage

Second stage

Third stage

Fourth stage

Input

400 × 400 × 1

400 × 400 × 2

400 × 400 × 3

400 × 400 × 4

Con2D+ ReLu(5×5)
396 × 396 × 8

←

(5×5)
396 × 396 × 4←

MaxPool

198 ×198 × 8←

198 ×198 × 4

←
←
←
←

Con2D
+ ReLu(5×5)
194 × 194 × 8←

MaxPool

97 × 97 × 8

←

Con2D
+ ReLu(5×5)
93 × 93 × 8(5×5)
93 × 93 × 16

MaxPool
Flatten
Dense + ReLu
DropoutDense + ReLu
Dropout
Sigmoid

46 × 46 × 8
16928
2000

46 × 46 × 16
33856

313632
32

←

320
16

32

48

←
←
←

50%

←

50%
64

Table 5 CNN structure of Height distribution input, input data scheme B, and Cartesian encoding.
First stage

Second stage

Third stage

Fourth stage

Input

400 × 400 × 1

400 × 400 × 2

400 × 400 × 3

Con2D+ ReLu(3×3)
398 × 398 × 4(5×5)
396 × 396 × 8←

400 × 400 × 4

MaxPool

199 ×199 × 4

198 ×198 × 8

198 ×198 × 4

Con2D+ ReLu(3×3)
197 × 197 × 8(5×5)
194 × 194 × 8←←

MaxPool

98 ×98 × 8

97 × 97 × 8

←
←

←

Con2D
+ ReLuMaxPool
Flatten
Dense + ReLu
DropoutDense + ReLu
Sigmoid(5×5)
93 × 93 × 8
36864
320

46 × 46 × 8
16928
2000

64
4

2000
8

2. Fringe image data is used to simulate data of specific patterns projected onto the workpiece surface.
Figure 4(a) gives height distributions visualized bygrayscale images converted from the vertical deformation.
The grayscale image enables easy observation of the change
in sheet shape through forming stages. Figure 4(b) shows
another type of input data for CNN: imaginary photo images
simulated as if the pattern is projected with an incident angle(5×5)
396 × 396 × 4

←

(5×5)
93 × 93 × 16←←←

46 × 46 × 16
33856

50%

←
←

12

16

of 45°. Each image corresponds to the height distribution in
Fig. 4(a).
Because the bending angle in laser forming is small,multi-stage forming is required to obtain complex shapes or
to draw deeply. Target shapes at each stage are provided byprocess-design work, and the difference between two consecutive shapes is that the deformation ought to be gained ateach stage. This study also tried different sizes of input dataand investigated the influences of that. Table 8 shows two

JLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024

Table 6 CNN structure of fringe image input, input data scheme B, and binary encoding.
First stage

Second stage

Third stage

Fourth stage

Input

400 × 400 × 1

400 × 400 × 2

400 × 400 × 4

Con2D+ ReLu(5×5)
396 × 396 × 8←

400 × 400 × 3

MaxPool

198 ×198 × 8

←

(5×5)
396 × 396 × 4←

198 ×198 × 4

←
←
←
←

Con2D
+ ReLu(5×5)
194 × 194 × 8←

MaxPool

97 × 97 × 8

←

Con2D
+ ReLu(5×5)
93 × 93 × 8(5×5)
93 × 93 × 16

MaxPool
Flatten
Dense + ReLu
DropoutDense + ReLu
Dropout
Sigmoid

46 × 46 × 8
16928
2000

46 × 46 × 16
33856

313632
128

2000
16

32

←
←
←
←
←
←

←

50%
320
50%
48

64

Table 7 CNN structure of fringe image input, input data scheme B, and Cartesian encoding.
First stage

Second stage

Third stage

Fourth stage

Input

400 × 400 × 1

400 × 400 × 2

400 × 400 × 4

Con2D+ ReLu(5×5)
396 × 396 × 4←

400 × 400 × 3(5×5)
396 × 396 × 8(5×5)
396 × 396 × 4

MaxPool

198 ×198 × 4

198 ×198 × 8

198 ×198 × 4

Con2D+ ReLu(5×5)
194 × 194 × 8←←

MaxPool

97 × 97 × 8

←

←

Con2D
+ ReLu(5×5)
93 × 93 × 16

←
←

(5×5)
93 × 93 × 8(5×5)
93 × 93 × 16

MaxPool
Flatten
Dense + ReLu
DropoutDense + ReLu
Dropout
Sigmoid

46 × 46 × 16
33856
640

←
←
←

46 × 46 × 16
33856

64

←

46 × 46 × 8
16928
2000
50%

4

8

schemes to prepare the data. In Scheme A, only the present
target shape, meaning the formed workpiece shape, wasgiven in the data for any number of stages. For example, forthe path prediction during 3-stage forming, paths in all
stages were predicted from the shape just after the third stage,
as shown on the left side of Table 9. As indicated in Table 8,
the dimension of input data arrays was the same regardlessof the number of stages. So, the CNN is expected to use lessmodel memory footprint in training progress.

←

12

←

←

320
50%
16

On the other hand, in Scheme B, the input data included
all target shapes, which are consecutively obtained at eachstage. For example, target shapes at the first, second, andthird stages were used to predict scanning paths during 3stage forming, as shown on the right side of Table 9. As indicated in Table 8, the dimension of input data arrays increased proportionally to the number of stages. High prediction accuracy and adaptability for complex shapes are expected because the shape change of each stage is included in

JLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024

the input data. Due to space constraints, complete explanatory diagrams for all stages 1-4 are not provided here. Therefore, only schematic representations for stages 2 and 3 arepresented.
2.4 Output data for CNN
The output data for CNN was a vector (an array of variables) to which the laser scanning path positions were encoded. For encoding these paths, two methods were employed, and their prediction performance was compared.
Firstly, as the ‘binary encoding method,’ a 16-digit binary
number was made by putting a flag on two digits corresponding to two endpoints of the scanning path. For example,
to present path <1-6>, the values in index 1 and 6 of the array
were 1, and the others were set as 0 (Fig. 5(a)). Therefore,
the encoded data represents a distribution of certainty in theclassification problem. The sigmoid function was used as theactivation function from fully connected layer to output
layer, and a BCE (binary cross entropy) was employed as theloss function. The following equation gives the BCE for thebinary encoding, which calculates the difference, 𝐿𝐿𝐵𝐵𝐵𝐵𝐵𝐵 , b
tween a correct path and a predicted path.
𝑁𝑁d1
𝐿𝐿𝐵𝐵𝐵𝐵𝐵𝐵 =� 𝑙𝑙𝐵𝐵𝐵𝐵𝐵𝐵
𝑁𝑁d𝑁𝑁d 𝑁𝑁o1 −1� �{𝑦𝑦𝑖𝑖 ln(𝑦𝑦�𝑖𝑖 ) + (1 − 𝑦𝑦𝑖𝑖 ) ln (1 − 𝑦𝑦�𝑖𝑖 )} ,=𝑁𝑁d 𝑁𝑁o(1)𝑖𝑖

Table 8 Input data given for CNN.
Scheme A: Target shape at present stage is used as input for CNN
Number of stages n
1
2

3

4

3rd shape
400×400×1

4th shape
400×400×1

3

4

1st - 3rd shape
400×400×3

1st - 4th shape
400×400×4

Input data

Dimension of data

1st shape
400×400×1

2nd shape
400×400×1

Scheme B: Target shapes before present stage are used as input for CNN
Number of stages n
1
2

Input data

Dimension of data

SchemeForming stage

1st shape
400×400×1

1st - 2nd shape
400×400×2

Table 9 Different training conditions in 2nd and 3rd forming stage.
A
B
SecondThird
Second

Third

Input

OutputTwo scanning paths

Three scanning paths

Two scanning paths

Three scanning paths

JLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024

where the size of the output label is No=16n (n: the numberof stages), Nd is the number of datasets, 𝑦𝑦𝑖𝑖 is the correct pathin the teaching data, and 𝑦𝑦�𝑖𝑖 is the path predicted by CNN.
Secondly, as ‘Cartesian encoding method’, the output wasvalues of Cartesian coordinates x and y for each of the two
endpoints of the path. In addition, normalization was
employed for the coordinates values to avoid loss diverges
in training progress. For example, to present path <1-6>, thenormalized value in output (0.2, 1.0, 1.0, 0.6) was converted
from the actual coordinates (-30, 50, 50, 10), as shown in Fig.
5(b). Therefore, the encoded coordinates are similar to thedependent variable in the regression problem. The Sigmoid
function was used as the activation function from fully connected layer to output layer, and a GD (geometric distance)
defined in equation (2) was employed as the loss function.
The loss function was a mean geometric distance between acorrect and predicted path, 𝐿𝐿𝐺𝐺𝐺𝐺 . In this study, it was definedas the mean value of length from the endpoint of the correct
path to the endpoint of a corresponding predicted path.
𝑁𝑁d1
𝐿𝐿𝐺𝐺𝐺𝐺 =� 𝑙𝑙𝐺𝐺𝐺𝐺
𝑁𝑁d
𝑁𝑁d

𝑛𝑛

1
�����������=� �( S�����������
pred Scor + Gpred Gcor ) ,
𝑁𝑁d

(2)

where n is the number of stages, and S and G represent theendpoint of a path as shown in Fig. 6, and subscripts ‘cor’and ‘pred’ represent correct and predicted path, respectively.

3. Results and Discussions
This research applied different methods to examine thefeasibility of CNN, including two encoding methods and different sizes of input data. As shown in Table 10, the height
distribution of metal sheet and imaginary fringe image were
two kinds of input types of CNN. The label of the output of
CNN was given by two encoding methods: binary encoding
and Cartesian encoding. CNN was employed as a machinelearning tool for analyzing different sizes of input data as
shown in Table 8. These results are introduced in the following sections.
3.1 Prediction results by means of height distribution
Figure 7 shows the transition of loss function as training
by scheme A for the path prediction in multi-stage (n up to4). The input data was height distributions with a size of(400×400×1), and the scanning paths were encoded with thebinary encoding method. The loss function for binary encoding, the binary cross entropy LBCE decreased and converged
to a small value for the training datasets. It should be notedthat the training was completed for a very short period compared to the previous study [17]. The same dataset was used
to train CNN and a fully connected network with the binary
encoding method. Figure 9 shows the training loss trend of
the first forming stage. It can be observed that the number of
epochs and training time required for CNN is significantly
lower than that of fully connected network. Nevertheless, thebinary cross entropy LBCE converged only in single stage
forming for the test datasets, while it diverged in multi-stage
forming.
For considering the influences of input data preparation
procedure, Fig. 8 shows the transition of binary cross entropy LBCE as training by scheme B where the size of input
data was (400×400×n). There was no significant difference
for training datasets when comparing Figs 7(a) and 8(a). In
contrast, comparing Figs 7(b) and 8(b), the binary cross entropy LBCE was obviously improved by scheme B, while it
was still large values for larger forming stages. This suggeststhat scheme B acquired higher versatility than scheme A.
The detailed loss trends of each stage are shown in Figs 18
to 21 on the final page.

(a)Binary encoding(b) Cartesian encoding
Fig. 5 Two encoding methods of scanning path.

(a) For training datasets(b) For test datasets

Fig. 7 Trends of binary cross entropy LBCE
in training process by scheme A.

Fig. 6 End points of laser scanning paths chosen and predicted.

Table 10 Different conditions of network training.
Input
Network
OutputHeightBinaryConvolution
distribution
encoding
neuronal netImaginary
Cartesianwork
fringe image
encoding

JLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024(a) For training datasets(b) For test datasets

Fig. 8 Trends of binary cross entropy LBCE
in training process by scheme B.

Fig. 9 Trends of binary cross entropy LBCEof two different neural networks.

The performance of prediction using the completely
trained CNN is presented in Fig. 10. Figure 10(a) contains
the bar charts illustrating distributions of the endpoints ofcorrect laser scanning paths against the ones of paths
predicted by the trained CNN shown in Fig. 7. On the other
hand, charts in Fig. 10(b) were obtained using the CNN
trained as shown in Fig. 8. In all bar charts, two axes on thebottom represent the candidate points chosen as endpoints ofthe correct and predicted paths. Each tile on the bottom
corresponds to a combination of the correct and predicted
endpoints. At the same time, the height of the bar graphindicates the frequency of the corresponding endpoint.
Therefore, if the prediction coincides with the correct data,tall bars stand on a diagonal of the square bottom. On the
1

2

3

4

(a) Scheme A

Number ofstages ncontrary, difficulty in the path prediction is presented as
dispersion of the frequency distribution. Because 80% of thewhole datasets were used for training, the number of candidate points was 800×2×n, where two endpoints in each scanning path, and n is the number of stages. Therefore, the upper limit of the scale vertical axis increases with the numberof stages, but the frequency distribution can be compared
between those charts.
As shown in all charts of Figs. 10(a) and 10(b), the prediction exhibited high accuracy, but scheme B seems slightly
better than scheme A. Based on this finding, it is believedthat scheme B, which contains the target shape of each stage,
helps to predict the sequence of scanning paths and is moreaccurate. For a detailed comparison, Fig. 10 also includes a

Correct predicted=100 %

87.32 %

83.54 %

83.23 %

Correct predicted=100 %

100 %

100 %

100 %

whole predicted(b) Scheme B

Correct prediction rate

Correct prediction rate

whole predicted

Fig. 10 Frequency distribution of predicted endpoints against ones for training datasets (in binary encoding, epoch for training<=100).

JLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024

correct prediction rate (=correctly predicted paths / whole
predicted paths). As can be seen, it is obvious that scheme B
achieved higher prediction accuracy.
Test datasets are used to evaluate and assess the model's
performance and versatility. Figure 11 shows theperformance of prediction obtained by test datasets. The
number of candidate points is 200×2×n, where the test
datasets number is 200 and n is the number of stages.
Scheme A had a high dispersion of prediction for the multiforming stages in Fig. 11(a), but scheme B maintained its
impressive performance in Fig. 11(b). According to theseresults, effective and reliable path prediction was achievablein the initial two forming stages, as the input data containedtarget shapes at each stage. However, it is noteworthy that in
the third and fourth forming stages, as illustrated in Fig.
Number ofstages n234=100 %

51.38 %

30.08 %

25.31 %

=100 %

96.25 %

75.25 %

46.69 %(a) Scheme A

111(b), overfitting issues were observed, indicating the needfor resolution. This result suggests that further optimization
and addressing overfitting challenges are essential for
extending the effectiveness of path prediction across all
forming stages.
Figures 12(a) and 12(b) show the transition of loss function for results using the input data prepared by schemes A
and B, respectively. The laser scanning paths were encodedby the Cartesian method. Geometrical distance has a length
dimension, and the value can be easily compared with otherquantities. In both Fig. 12(a) and 12(b), it is confirmed thatthe loss functions converged for tens of epochs in the training process. In the transition of LGD for test datasets, though
the divergence was not observed, the distance values werestill large, especially in higher stages. This result means theCorrect prediction rate

Correct predicted
whole predicted(b) Scheme B

3

Correct prediction rate

Correct predicted
whole predicted

Fig. 11 Frequency distribution of predicted endpoints against ones in test datasets (in binary encoding, epoch for training <= 100).
Training datasets

Test datasets

Training datasets

Test datasets(b) Scheme B(a) Scheme A
Fig. 12 Trend of mean geometrical distance LGD in training process with paths encoded by Cartesian.

JLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024

Number ofstages n(a) Scheme A(b) Scheme B

Mean LGD = 3.9 mm, Variance in lGD = 43 mm2

Mean LGD = 3.9 mm, Variance in lGD = 43 mm2

Mean LGD = 27.3 mm, Variance in lGD = 829 mm2

Mean LGD = 10.6 mm, Variance in lGD = 38 mm2

Mean LGD = 37.0 mm, Variance in lGD = 815 mm2

Mean LGD = 18.9 mm, Variance in lGD = 319 mm2

Mean LGD = 54.9 mm, Variance in lGD = 357 mm2

Mean LGD = 28.8 mm, Variance in lGD = 116 mm2

1

2

3

4

Fig. 13 Individual geometrical distance lGD for each training dataset (in Cartesian encoding).

Table 11 Mean geometrical distance LGD in different training conditions for height distribution.
Training datasets(unit: mm)

Test datasets

Encoding
for paths

Input
data size

Stage
n=1

Stage
n=2

Stage
n=3

Stage
n=4

Stage
n=1

Stage
n=2

Stage
n=3

Binaryencoding

Scheme A

0.0

17.4

22.0

25.6

0.0

135.0

273.9

394.5

Scheme B

0.0

0.0

0.0

0.0

0.0

14.0

138.3

221.8

Scheme A

3.9

27.3

37.0

54.9

2.8

66.6

262.8

374.4

Scheme B

3.9

10.6

18.9

28.8

2.8

16.0

55.4

142.6

Cartesianencoding

CNN model has an overfitting problem in the test dataset.
Thus, a highly effective ML procedure would be required forhigh prediction accuracy, including regularization and dropout methods.
Figures 13(a) and 13(b) give the loss of prediction by the
CNN trained using Cartesian encoded data. Blue dots represent the individual geometrical distance lGD calculated foreach dataset, and red lines represent the averaged distancefor all datasets. A small distance means that the error between the correct and predicted path was small. In Fig. 13(a),the prediction results using input data prepared by thescheme A shows that the prediction error was accumulated,

Stage
n=4

and the averaged distance became larger as the number oflaser forming stages n increased. The same trend is found in
Fig. 13(b), but scheme B resulted in lower prediction errors.
The variance of the individual geometrical distance lGD also
exhibited same trend; it increased with the number of laser
forming stage n, and scheme B resulted in smaller prediction
errors.
Figure 14 shows the predicted results obtained for test
datasets. The number of test datasets is 200. The mean geometrical distance LGD was larger than the training's result inboth schemes, which presents the overfitting problem, similar to the loss trend shown in Fig. 12. Compared to the result

JLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024

Numberof stages n(a) Scheme A(b) Scheme B

Mean LGD = 2.8 mm, Variance in lGD = 31 mm2

Mean LGD = 2.8 mm, Variance in lGD = 31 mm2

Mean LGD = 66.6 mm, Variance in lGD = 2276 mm2

Mean LGD = 16.0 mm, Variance in lGD = 55 mm2

Mean LGD = 262.8 mm, Variance in lGD = 10400 mm2

Mean LGD = 55.4 mm, Variance in lGD = 1680 mm2

Mean LGD = 374.4 mm, Variance in lGD = 11900 mm2

Mean LGD = 142.6 mm, Variance in lGD = 2350 mm2

1

2

3

4

Fig. 14 Individual geometrical distance lGD for each test dataset (in Cartesian encoding).

Training datasets

Test datasets

Training datasets

Test datasets(b) mean geometrical distance LGD for Cartesian encoding(a) binary cross entropy LBCE for binary encoding
Fig. 15 Trend of loss functions in training using fringe images (Scheme B).

of Scheme A, Scheme B still demonstrates impressive prediction performance using Cartesian encoding in test datasets. Figures 13 and 14 show that scheme B could suppress
the mean geometrical distance LGD lower than scheme A in
all multi-forming stages, and it also means scheme B exhibits sustained proficiency in the Cartesian encoding method.
In order to compare the prediction performance in different training conditions, the result of binary encoding wasshown by the geometrical distance and compared with Cartesian encoding in Table 11. Performance was substantially
excellent in single stage forming by any encoding method
and by any schemes for input data preparation. Scheme B
resulted in better prediction accuracy than scheme A, but theerror was still large. Thus, further optimization was expected.

JLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024

3.2 Prediction results by means of fringe images

Except for the height distribution, the imaginary fringe
image was also used as the input of CNN to simulate theTable 12 Mean geometrical distance LGD in different training conditions for fringe image.
Training datasets
Stage
n=2

Stage
n=3

Stage
n=4

Stage
n=1

Stage
n=2

Stage
n=3

Stage
n=4

Scheme B

0.0

0.0

0.4

0.0

0.0

4. 4

72.4

166.9

Scheme B

5.3

10.9

15.3

19.0

5.2

16.9

43.4

74.1

3

99.69%

4

99.56%

99.3%

whole predicted=100 %

Correct
prediction rate

Correct predicted(b) Test dataset=100 %

Correct
prediction rate

99.69%(a) Training dataset

99.56%

2

Stage
n=1

whole predicted

1

Input
data size

Correct predicted

Numberof stages n

Test datasets

99.3%

Encoding
for paths
Binaryencoding
Cartesianencoding(unit: mm)

Fig. 16 Frequency distribution of predicted endpoints against ones for Scheme B (in binary encoding, epoch for training<=100).

JLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024

Number ofstages n

photo of the experiment. After observing the result of the 3.1
section, it is finding applying Scheme B to CNN has a better
prediction performance than Scheme A. Therefore, in thissection, only Scheme B and two encoding methods wereused in training for the scanning path prediction by means of
the fringe images.
Figures 15(a) and 15(b) show the transition of the loss
function for results using the input data prepared by scheme
B, where scanning paths in datasets were encoded by different methods. It is confirmed that both methods completed
the training in a short time. And, comparing these resultswith Figs 7, 8 and 12, it should be noted that the overfitting
was suppressed by the fringe image slightly smaller than theheight distribution. The detailed loss trends of each stage areshown in Figs 22 and 23 at the final page.
Figure 16 contains the bar charts displaying distributionsof the endpoints of correct laser scanning paths against those(a) Training dataset

predicted paths by the CNN trained using the binary encoded
paths. Comparing Fig. 16 with Fig. 11, it is found that thefringe image archived higher prediction accuracy than theheight distribution as input data to train CNN. The correct
prediction rate was almost 100% for the training datasets in
Fig. 16(a), but the rate decreased for the test datasets as thenumber of forming stage increased in Fig. 16(b).
The training and testing results of using the Cartesian encoding method in training CNN are shown in Figs.17(a) and(b). Comparison with Figs. 13(b) and 14(b) described thatthe mean geometric distance LGD and the variance in individual geometric distance lGD were improved by using fringe
images. Thus, scheme B exhibited sustained proficiency inapplying the imaginary fringe images to train CNN.
The mean geometrical distance LGD using fringe images
are also summarized in Table 12. With increase in the number of stages, the training performance using the binary(b) Test dataset

1

Mean LGD = 5.3 mm, Variance in lGD = 4 mm2

Mean LGD = 5.2 mm, Variance in lGD = 3 mm2

2

Mean LGD = 10.9 mm, Variance in lGD = 23 mm2

Mean LGD = 16.9 mm, Variance in lGD = 96 mm2

Mean LGD = 15.3 mm, Variance in lGD = 27 mm2

Mean LGD = 43.4 mm, Variance in lGD = 420 mm2

Mean LGD = 19.0 mm, Variance in lGD = 40 mm2

Mean LGD = 74.1 mm, Variance in lGD = 881 mm2

3

4

Fig. 17 Individual geometrical distance lGD for each dataset with fringe images (in Cartesian encoding, Scheme B).

JLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024

encoding exceeded that by Cartesian encoding. However,the prediction performance of Cartesian encoding was more
excellent than the other ones in test datasets. Compared toTable 11, both errors of the two encoding methods werelower than the result using height distribution as input data.
The result proved the efficacy of applying the imaginary
fringe images to train CNN and gave the confidence to use
projected photos in training CNN.
4. Conclusions
In this study, laser scanning paths were predicted fromshapes of metal sheets using the CNN, which was trained byimaginary datasets containing height distribution or imaginary fringe images. The influences of encoding methods ofscanning paths and the input data size were investigated, andthen the feasibility of using projected images for path prediction was examined. Obtained results are concluded as follows:
1) The results demonstrated the feasibility of applying
CNN to predict the scanning paths from height distribution and fringe images in multi-stage laser forming.
2) Scheme B, which contains each forming stage's target
shape, helps CNN accurately predict the laser scanning
path in each stage.
3) The binary encoding method has more limitations than
Cartesian encoding in presenting the scanning path
endpoints. Therefore, CNN used binary encoding predicted better than the used Cartesian ones.
4) CNN took less training time and epochs number than afully connected neural network with two hidden layers
in previous study, because fully connected neural networks can be considered a rudimentary network structure in deep learning.
5) It is worth noting that using imaginary fringe images asteaching data enables more precise prediction than using height distribution data in no matter encoding
methods. From this result, the actual pattern projectedpicture will be used to build the CNN prediction system,
which can identify the real picture, in future research.

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(Received: June 15, 2023, Accepted: May 2, 2024)