Deep Learning-based Area Estimation for
Unmanned Aircraft Systems using 3D Map
Masatoshi Hamnanaka
Center for Advanced Intelligence Project
RIKEN
Tokyo, Japanmasatoshi.hamanaka@riken.jp

Abstract—A method for estimating the flight area of
unmanned aircraft systems (UAS) based on deep learning is
described. The position of a UAS can be detected by using the
global positioning system (GPS). However, GPS sometimes has
difficulty capturing signals from satellites that are shielded by
mountains and/or buildings. Moreover, GPS signals are very
weak and subject to a variety of disturbances. Such problems
increase the chance of a crash when flying a GPS-controlled
UAS. As a solution, we propose a flight area estimation method
using a 3D map created on the basis of deep learning. Our
method could estimate the flight area with 92.2% accuracy in asimulation and 98.4% accuracy in a field experiment.
Keywords— deep learning; 3D topographic map; lidar

I. INTRODUCTION
We propose a method for estimating the flying area of
unmanned aircraft systems (UAS) by using a 3D map
created by deep learning. Position detection is extremely
important for controlling the UAS and for preventing
collisions. At present, most drones use the global positioning
system (GPS) for position detection. However, GPSsometimes cannot indicate a proper position when signals
from the satellites are shielded by buildings and/or
mountains. Furthermore, GPS signals are very weak andhence are easily affected by a variety of interference [1, 2].
To enable better control of a UAS with GPS, we propose
a deep learning [3, 4]-based area estimation method using a
3D map to which the UAS can refer when GPS signals
cannot be received. Although deep learning has been used
for estimating the positions of persons and objects fromcamera images, until now no such method has been proposed
for estimating the position of a UAS [5, 6]. In order todevelop a position estimating method using a 3D
topographic map based on deep learning, we have toconsider the following six points.

Therefore, in this research, we equipped the UAS
with a compact, lightweight two-dimensional LiDAR
that was originally developed for automated drivingof automobiles and used it to acquire a twodimensional surface cross section (Fig. 1). We
describe the acquisition of the 2D shape vector of theground surface in Section II.A.
• Machine learning:
Simple pattern matching between a 3D map and the2D surface vector obtained by the UAS would take anenormous amount of calculations, making it difficult
to do in real time.
Therefore, we divided up the flight area and labeledeach divided area in order to apply the machinelearning for position estimation and reduce thenumber of calculations. We describe the area divisionin Section II.B.
• Deep learning:
A machine learning technique such as those using
support vector machines (SVMs) [7] does not work
well for learning the relationship between the 2D
surface vector and the label of the flight area because
the amount of data obtained from the 3D map isenormous. SVMs would require exponentially
increasing resources for constructing a model on suchlarge datasets, which is infeasible.

LiDAR• 2D LiDAR:
The flight area of a UAS can be estimated by using
pattern matching of the 3D topographical map andthe ground surface shape acquired by the UAS. In
this case, it is easier to perform pattern matching
between 3D shapes acquired using three-dimensional
LiDAR. However, 3D LiDAR is heavy and difficult
to mount on small UASs.

Fig. 1. Acquisition of 2D surface vector by 2D LiDAR.

Therefore, we used deep learning instead. In deeplearning, learning data can be divided into groups
called mini batches. By using mini batches, deeplearning can handle a lot more data than SVMs can.
We describe our multi-layer perceptron (MLP) [4],which is a type of deep learning, in Section III.
• Acquisition rate of learning data:
Deep learning makes it possible to learn therelationship between the 2D surface vector and its
label, but there is still a problem in that a long time isrequired when a large amount of data is involved.
Since the surface shape will change along with thegrowth of plants and the construction of buildings,
learning needs to be continued in batches in order tosustain the operation of the area estimation system.
Therefore, the shorter the learning time, the fewer
computing resources are needed.
In deep learning, when the learning data becomeslarger than the memory on the GPGPU, the learning
speed suddenly becomes slow. When the learning
data is smaller than the GPGPU memory, the numberof data items and the learning time are almost
proportional.
Therefore, if we reduce the learning data by random
sampling, the learning time can be shortened;however, if we reduce the amount of learning data,
the accuracy will decrease. Section IV.A describes
the acquisition rate of the data used for learning andthe performance evaluation of discriminating theareas.
• Area margin:
It is difficult to identify a label near the boundary ofan area because ground surface shapes are similar yet
the labels are different. We therefore create a marginnear the boundary and exclude learning data in themargin. Sections IV.B and IV.C show how theperformance of discriminating the areas changes
depending on the margin width.
• Simulation and field experiments:
Although a UAS can fly above 50 meters,commercially available LiDAR for automobiles has
weak output signals and can only measure up to about
50 meters. We performed experiments under thislimitation.
First, in simulations, we verified the basic
performance of discriminating the areas by using a
3D map acquired by a satellite. We also evaluated theacquisition rate and area margin in these simulations,as the data for field experiments was too small.
Second, in a field experiment, we flew a UAS at analtitude lower than 50 meters and evaluated its
performance of discriminating the areas. In theseexperiments, we evaluated in a limited area where it
is possible to estimate correctly even in situations
where there are missing data, such as when there is a
puddle or the distance from the surface is too far.

The simulation results showed that after learning using
an MLP consisting of 11 layers each with 3,000 units, thearea on the 3D map could be estimated from the 2D surface
vector with an accuracy of 92.2%. The field experimentshowed that an MLP consisting of three layers with 1,500
units in the first hidden layer and a gradually decreasing
number of units in the subsequent hidden layers (to 23 units
in the deepest hidden layer) could estimate the area on a 3D
map from the 2D surface vector acquired by the UAS withan accuracy of 98.4%.
Section II of this paper explains the data used forlearning, and Section III describes the method for estimating
the flying area by deep learning. Sections IV and V explain
how we evaluated the method. We conclude in Section VI
with a brief summary and mention of future work.
II. LEARNING AND EVALUATION DATA
Estimating the flight area of a UAS by using deeplearning consists of two steps. First, the 2D surface vector isacquired by the 2D LiDAR mounted on the UAS. Next, thearea is estimated from the 2D surface vector by using a
network learned in advance. In this section, we describe theconstruction of the learning and evaluation data.
A. Acquisition of 2D ground surface shape
A 2D LiDAR (LD-MRS, SICK AG) is mounted on the
UAS to acquire the ground cross-sectional shape. The
altitude of the ground surface can be measured to an
accuracy of about 20 centimeters if a LiDAR with an angularresolution of 0.125 degrees is mounted facing verticallydownward and the UAS flies 100 meters above the ground[8]. In a simulation, we used 100 measurement points, one
every 20 centimeters on the left and right of the flight path,and recorded the differences in height between the 100
points as a 100-dimensional 2D surface vector.
The number of measurement points varied between thesimulation and field experiment, since the simulation
covered a vast area while the field experiment used our own
airspace, the area of which was limited. The distance
between the measurement points also varied between thesimulation and field experiment, as the resolutions of the 3D
maps were different. Specifically, in the field experiments,
we used 50 measurement points, one for every one meter,
and the UAS acquired a 50-dimensional 2D surface vector.
B. Dividing up the flight area
We divided the flight area into a lattice and assigned
different labels to its elements. The initial position of the
UAS was randomly determined, and a set of the groundshape vectors calculated from the 3D map and the labels of
the area were used as learning data.
Near the boundary of the flight area, it is difficult todistinguish the labels because labels may be different despite
similar terrain information. Therefore, the performance was
improved by providing a certain margin around the area.
We compared two types of area division in thesimulations: 2D and 3D (Fig. 2). The height of the UAS was
fixed at 100 meters in the simulation using 2D divisions. Inthe field experiment, the area was not divided up in theheight direction.
C. 3D map from satellite
We used Advanced Land Observation Satellite (ALOS)
Phased Array type L-band Synthetic Aperture Radar(PALSAR) data for making the 3D map [9] in thesimulations. Although high-resolution 3D maps (resolution:~10 cm) are available for a fee, we were not certain one
would be necessary, so we used the free ALOS PALSARdata.
The ALOS PALSAR has a resolution of 30 meters. We
reduced the scale to 1/150 in order use it as a 3D map with
20-cm resolution, which is the resolution that was used for
acquiring the 2D surface vector in the simulation. The area
was a cube with a side of 30 meters, and five areas wereoverlaid in(a) 2D divisions

Area 1Margin of area 1

Area 3

Area 2Margin of area 2each direction to generate 125 areas (Fig. 2(b)). The
simulation used a satellite 3D map of 35°00'00'' to 35°12'29''
of north latitude and east longitude of 135°40'00'' to135°52'29''. The height of the UAS ranged from 100 meters
to 250 meters above the ground.
D. 3D map from UAS
The 3D map used in the field experiment was created byflying the UAS equipped with LiDAR. The UAS flew overan area 200 meters square (36.6217 to 36.619900 northlatitude and east longitude 139.1090 to 139.111240), which
had a difference in ground altitude of 100 meters. Because
the GPS equipped on the UAS (Matrice 600 from DJI) [10]has an error of 1 meter, we conducted ten flights at aconstant altitude and calculated the average altitude obtainedwith a resolution of 1 meter (Fig. 3).
E. Acquistion rate of learning data
The flight area in the simulation had a resolution of 20
centimeters for each axis. If we acquired data from all areas
where five cubes with 30-m sides are stacked vertically andhorizontally, even if the flight direction of the UAS were
fixed, the number of data would exceed 400 million. It isdifficult to calculate on such large data in the limited
memory we had available. Moreover, if we divided up thedata, the learning time would be unrealistically long.
Therefore, we randomly sampled from all data of each area
at an acquisition rate with which the calculation would becompleted in a realistic amount of time.

Area 4

F. Evaluation data
Margin of area 3

Margin of area 4(b) 3D divisions

The evaluation data for the simulation experiment was
randomly extracted from the 3D map. We avoided using thesame data in the learning and evaluation in the simulation.
The evaluation data for the field experiment were acquiredby flying a UAS equipped with LiDAR.

[m]

[m]

200

Margin200 [m]Fig. 2. 2D and 3D division and area margin.

Fig. 3. 3D map from UAS.

III. FLIGHT AREA ESTIMATION BASED ON DEEPLEARNING
Pattern matching between the 3D map and the groundsurface vector acquired by 2D LiDAR normally requires avery large number of matchings, which makes it difficult toperform in real time. We estimated the flight area from theshape of the ground surface in real time by using MLP [4].
Deep learning methods include convolution neuralnetworks [11], MLPs, deep belief networks [12], etc. The
advantage of MLP is that it can be used for any purpose. We
chose to use MLP here because it is difficult to find meaning
in the ground surface vector data itself.
The MLP for estimating the flight area is shown in Fig. 4.
The input for the simulation experiment was 100 units
corresponding to the 100-dimensional ground surface vector.
We used 50 input units corresponding to the 50-dimensional
ground surface vector in the field experiment, as the LiDAR
signal was too weak to detect the ground shape if the heightof the UAS was more than 50 meters. Each dimension of thesurface vector was normalized to zero mean and varianceone. The output units of the MLP were area labels. The MLP
had n hidden layers; i.e., we varied n and the number of units
in the experiments. The input layer, intermediate layers, andoutput layer were all fully connected.
Supervised learning with back propagation was used todetermine all of the parameters of the network, including thebias of the units and the weights of the connections between
the units.
Hidden Hidden
layer n-1 layer n

Outputlayer
Area 1
Area 2
Area 3
Area 4……………...

……………...

……………...

（100/50 dim.）……………...

……………...

Groundsurface
vectorHiddenlayer 1

……..

Input
layer

……..
Fig. 4. MLP for estimating the area labels.

IV. SIMULATION EXPERIMENTThe simulation examined the effect of area division in
two dimensions and in three dimensions.
A. Performance evaluation varying acquisition rate in thecase of 2D division
We compared the performance of discriminating the fourareas shown in Fig. 2(a) for learning data acquisition rates of
40%, 20%, and 10%. The total number of data was 2.25
million (30 meters (length of one side) / 0.2 (resolution of 20cm)) ^ 2 (two directions in the vertical and horizontal
directions) × 4 (the number of areas). Thus, 40% of the dataamounted to 0.9 million (2.25 million × 0.4). The evaluation

data comprised 10% of the total data, and it did not include
any of the learning data. Although we could have extracted
more than 40% of the data, it could not be stored in thememory on the GPGPU (NVIDIA Quadro M600) that we
used.
Table I lists the accuracies for the data acquisition rates,
which were obtained by subtracting the error rates from 1.
The highest accuracy was for the 40% rate, then 20%, andthen 10%. These results show that, as the number of data
used for learning increases, the accuracy increases, and as
the number decreases, the accuracy decreases. Because of
the high accuracy, we could use an MLP consisting of sevenhidden layers with 60 units each and 3,000 learning epochs.
TABLE I.

PERFORMANCE EVALUATION: EXTRACTION RATE IN 2D
DIVISIONSExtraction rate

40%

20%

10%

Accuracy [%]

97.8

86.4

85.0

B. Comparison with and without margin in 2D division
We compared the discrimination performances with andwithout the margin for the data acquisition rate of 40%.
Three margin widths were compared: 0% (no margin), 1%(30 cm), and 5% (150 cm), where one side of the area was 30
meters. The evaluation data and numbers of hidden layers,
units, and epochs were the same as the previous simulation.
Table II shows that the 0% margin had the highest
accuracy and the 5% margin had the lowest accuracy. This
result means that discrimination performance is highregardless of the margin being small or large as long as there
is sufficient learning data.
TABLE II.

PERFORMANCES EVALUATION: WIDTH OF MARGIN

Extraction rate

0%

1%

5%

Accuracy [%]

97.8

96.7

92.0

C. Comparison with and without margin in 3D division
We compared the accuracies with and without the marginwhen discriminating a cubic area consisting of 125 cubic
areas 30 meters on each side (Fig. 2(b)).
Here, we tested only a 10% acquisition rate with andwithout a 5% margin on the side of the 30 meter cubes, as
the learning time would have been too long and the memory
capacity of the GPGPU would have been exceeded if thehigher rate were used. The evaluation data was 1/4 of thelearning data for the cases with and without the margin.
We evaluated the effect of changing the number of units
and layers, i.e., 1,000, 2,000, and 3,000 units and 1 to 15
layers, and varying the epoch number. The network with thehighest performance had 11 hidden layers with 3,000 units
each. Table III shows the results using this network wherecase (a) included the margin in both the learning and theevaluation data, case (b) included the margin in the learningdata but not the evaluation data, case (c) included the margin
in the evaluation data but not the learning data, and case (d)did not include the margins in the learning or the evaluation
data, all for up to 3,000 epochs of learning. Figure 5 shows
the learning curves. The learning time for 3,000 epochs was
about half a day.

• Even if the surface shape just below the UAV is
acquired with a LiDER, the surface shape of the rightend and the left end might not be acquired because
the LiDAR signal is too weak. Therefore, we
carefully examined the structure of MLP in order toincrease the interpolation capability.

There were many errors in detection due to the margin incases (a) and (b), while case (d) showed the best accuracy.
These results demonstrate that it is better not to include amargin in the learning data when the UAS already knows its
position by GPS.

• The surface vector obtained by UAS includes errors
because of the effect of UAV and wind. Therefore,
we used zinbal (Dji Ronin-MX) for mounting the
LiDAR on the UAV and flew the UAV at constant
speed (Fig. 6).

The performance was very low in case (c), which did notinclude the margin in the learning data but included one in
the evaluation data. This result means that when the UAS
position is obtained only by this method, it is better to use a
network learned with data including a margin.
TABLE III.

PERFORMANCE WITH AND WITHOUT MARGIN(a)

Learning data
Evaluation data
Accuracy [%]

(b)

(c)

(d)
Without

With

With

Without

marginmarginmarginmarginWith

Without

With

Without

marginmarginmarginmargin

84.7

86.3

72.2

92.2

Fig. 6. Matrice 600 equipped with LD-MRS.

[Accuracy]
100

80

(d)
(b)
(a)

70

(c)

90

60
50

0

500

1000

1500

2000

2500

3000

[Epochs]Fig. 5. Learning curves with and without margin.

V. FIELD EXPERIMENT
We evaluated the discrimination performance for the 3D
map shown in Fig. 3. The UAS was a Matrice 600
manufactured by DJI and equipped with LD-MRS LiDAR
made by SICK AG (Fig. 6).
It is harder to estimate the position in the field
experiment compared to the simulation, for three reasons.
• In the field experiment, the experiment area is limited
and so the learning data are fewer than in thesimulation. Therefore, we did not divide up the map
in the vertical direction, since the LiDAR could only
measure up to 50 meters.

A. Learning and evaluation data
We fixed the direction of the UAS to north and thealtitude to 35 meters above the average altitude in the area
because of the limited memory of the GPGPU; that is, wewould need fewer learning data compared to if we changed
the direction and altitude. The area was 200 meters square(Fig. 3). The LiDAR on the UAS scanned a width of 50
meters. The area in which the surface vectors could beacquired was 200 meters north to south and 150 meters east
to west. We made 30,000 (= 200 × 150) surface vectors intotal for learning, as the resolution of the 3D map was 1
meter (Fig. 7).
We constructed the evaluation data by flying the UAS
five times for 20 minutes at 35 meters (the average altitude)
over the area. The UAS detected the surface vector every
two seconds and collected a total of 3,000 (5 times × 20
minutes × 60 seconds / 2 seconds) surface vectors with arealabels. The flight route was programmed in advance and it
ran through multiple GPS points randomly selected in thearea.
In order to evaluate under open conditions, we did not
use the 3,000 surface vectors in the learning data that were
nearest the GPS point of each surface vector in theevaluation data. We thus used 27,000 surface vectors for thelearning data and 3,000 surface vectors for the evaluationdata.

Table VI shows the results of 30,000 epochs for the eight
networks whose accuracy is higher than 0.94 in Table V, andFig. 8 shows the learning curves of those networks. The
network with three hidden layers with a decrease rate of 0.6
had an accuracy of 0.9762 after 20,509 epochs, and the one
with seven hidden layers with a decrease rate of 0.5 had an
accuracy of 0.9759 after 29,677 epochs.

150 m

200 m

TABLE IV.

50 m

LEARNING UP TO 2,000 EPOCHS
Decrease rate of number of units

50 m
Number

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1

0.51

0.50

0.50

0.49

0.49

0.46

0.49

0.50

2

0.67

0.71

0.75

0.76

0.74

0.74

0.73

0.66

3

0.61

0.67

0.66

0.69

0.70

0.70

0.64

0.63

4

0.57

0.62

0.61

0.61

0.59

0.66

0.30

0.05

5

0.55

0.60

0.62

0.58

0.61

0.05

0.05

0.06

6

0.36

0.60

0.61

0.66

0.58

0.05

0.05

0.05

7

0.19

0.49

0.63

0.66

0.05

0.05

0.05

0.05

8

0.14

0.23

0.05

0.05

0.05

0.05

0.05

0.06

of layers

200 m

50 m

200 m

50 m

Fig. 7. Flight area in the field experiment.

B. Effect of varying the number of hidden layers andnumber of units
The performance of MLPs depends on the number ofhidden layers and the number of units. By randomlychanging the number of hidden layers and the number ofunits, we found that the performance was high with a deeply
layered network in which the number of units gradually
decreased the deeper the layer.
Therefore, we tried to determine the appropriate numberof hidden layers and units in a network in which the numberof units in the hidden layers gradually decreases at a constantrate. We changed the number of hidden layers from 1 to 7 inincrements of 1 and changed the decrease rate of the units
from 0.3 to 1.0 in increments of 0.1. The maximum numberof units was 3,000. For example, when the number of hidden
layers is 3 and the decrease rate is 0.5, the network consistsof a first hidden layer with 1,500 (3000 × 0.5) units, a second
hidden layer with 750 (1,500 × 0.5) units, and a third hidden
layer with 375 (750 × 0.5) units.
Since it takes a long time for deep networks to learn, we
attempted to save time by gradually narrowing the searcharea. Table IV shows the accuracy as a result of learning up
to 2,000 epochs for each network. Gray colored cells indicatethat the accuracy is lower than 0.5. The accuracies were low
in the following three cases.
• When the number of layers and the number of units
are high.
• When there is only one hidden layer.
• When the number of units near the output layer isvery low.
Table V shows the results of learning for up to 15,000
epochs for each network whose accuracy is higher than 0.4
in Table 3.

TABLE V.

LEARNING UP TO 15,000 EPOCHS
Decrease rate of number of units

Number

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1

0.65

0.65

0.64

0.65

0.65

0.64

0.64

0.65

2

0.83

0.87

0.85

0.85

0.87

0.87

0.87

0.84

3

0.83

0.90

0.93

0.95

0.95

0.92

0.93

0.89

4

0.80

0.91

0.94

0.94

0.93

0.91

–

–

5

0.77

0.91

0.95

0.93

0.88

–

–

–

6

0.53

0.91

0.94

0.93

0.85

–

–

–

7

–

0.81

0.95

0.94

–

–

–

–

of layers

C. Augumenting learning data with random noise
Data augmentation improves the performance of deeplearning in pattern recognition [13]. We attempted toaugment the learning data by adding uniformly distributed
random noise to each element of the surface vectors.
The total number of augmented learning data was
54,000: 27,000 original data and 27,000 augmented data inwhich random noise was added to the original data. The total
number of non-augmented learning data for comparing thenumber of matchings. In order to estimate the area of
UAS in real time, we used machine learning for thearea estimation.

augmented learning data was also 54,000: 27,000 original
data repeated.
We compared three noise levels: 0.25 meters, 0.5 meters,
and 1 meter. We used the network with three hidden layerswith a decrease rate of 0.6 and 7 hidden layers with adecrease rate of 0.5 because of high performance.

• Use of deep learning for area estimation
SVMs would require an exponential increase inresources to deal with the enormous 2D surface
vectors from a 3D map. Therefore, we used lesscostly deep learning for the area estimation.

The results show that accuracy for evaluation data
increased to 0.9838 when using the augmented learning dataof the 0.5-meter noise level for learning 7 hidden layers witha decrees rate of 0.5. The learning time for 3,000 epochs was
about 7 hours using an NVIDIA GTX 1080Ti GPGPU.

• Performance evaluation through simulation
We conducted a simulation using a wide range 3D
map from a satellite and determined that our method
could estimate the correct area of the UAS flight withan accuracy of 92.2%.

Because the experiment areas are different, it is difficult
to compare the simulation and the field experiment. The
performance of the field experiment was superior because it
acquired the ground surface shape in more detail than thesimulation and the network configuration was examined
more carefully.
TABLE VI.

• Evaluation in real world
We augmented the learning data with 1% random
noise from a 3D map of a 200 meter square area
made by using LiDAR on the UAS. The MLP withseven hidden layers consisting of 1,500, 750, 375,
187, 93, 46, and 23 units could estimate the flightarea of the UAV when the map was divided into 25
areas with an accuracy of 98.4%, after leaning theaugmented data.

LEARNING UP TO 30,000 EPOCHS
Decrease rate of number of units

Number of layers

0.5

0.6

0.7

3

–

0.97620.9705

40.96150.9607–50.9670––6

0.9756––

7

0.97590.9669–TABLE VII.

We plan to learn an MLP for a huge scale area by using
the satellite data from the Advanced Land Observation
Satellite (ALOS 2) Phased Array type L-band Synthetic
Aperture Radar 2 (PALSAR 2).
ACKNOWLEDGMENTS
This work was supported by the Japan Society for the
Promotion of Science (JSPS KAKENHI Grant Number
17K19972).

AUGUMENTED LEARNING DATA WITH RANDOM NOISE
Noise level

NumberoflayersandOriginal

0.25 m0.50 m[1]
1.00 mdecrease rate
3 layers with a decrease

REFERENCES[2]
0.9762

0.97300.9721

0.9712

0.97590.97820.98380.9813rate of 0.6
7 layers with a decrease
rate of 0.5

[3]
[4]

VI. CONCLUSION[5]

We developed a method to estimate areas by deeplearning of surface vectors acquired by LiDAR. The
following four points are the main contributions of this study.

[6]• Development of an area estimation method using 2D
LiDAR
We proposed a method that can estimate the positionof a UAS by using a lightweight 2D LiDAR mounted
on the UAV. Pattern matching between 2D surface
vectors and 3D maps normally requires a very large

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[11] A. Krizhevsky, I. Sutskever, and G. E. Hinton, Imagenet
classification with deep convolutional neural networks, Advances inneural information processing systems, pp. 1097–1105, 2012.

[Accuracy]
0.977[12] G. E. Hinton, S. Osindero, and Y. W. Teh, “A Fast Learning
Algorithm for Deep Belief Nets,” Journal of Neural Computation,
Vol. 18, Issue 7, pp. 1527–1554, 2006.
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230, Issue C, pp. 184–196, 2017.

0.9762 (3 layers ×0.6, 20,509 epochs)

0.9759 (7 layers ×0.5, 26,779 epochs)

0.975
0.973
0.971
0.969
0.967
0.965

10

5000
5001

10000
10001

15000
15001

20000
20001

25000
25001

30000
[Epochs]

25000
25001

30000
[Epochs][Accuracy]
1
0.9

3 layers ×0.6 acc.=0.9762

0.8

3 layers ×0.7 acc.=0.9705

0.7

4 layers ×0.5 acc.=0.9615

0.6

4 layers ×0.6 acc.=0.9607

0.5

5 layers ×0.5 acc.=0.9670

0.4

6 layers ×0.5 acc.=0.9756

0.3

7 layers ×0.5 acc.=0.9759

0.2

7 layers ×0.6 acc.=0.9669

0.1
0

0
1

5000
5001

10000
10001

15000
15001

20000
20001

Fig. 8. Learning curves of eight networks whose accuracy is higher than 0.94 in Table V.