Strojniški vestnik - Journal of Mechanical Engineering 64(2018)6, 393-400 © 2018 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2017.5189
Original Scientific Paper
Received for review: 2017-12-30 Received revised form: 2018-02-19 Accepted for publication: 2018-04-16
New Hybrid System of Machine Learning and Statistical Pattern Recognition for a 3D Visibility Network
Matej Babič1* - Karolj Skala2 - Dookhitram Kumar3 - Roman Šturm4
1 Jožef Stefan Institute, Ljubljana, Slovenia 2 Ruder Boškovic Institute, Croatia 3 University of Technology, Mauritius 4 University of Ljubljana, Faculty of Mechanical Engineering, Slovenia
Intelligent systems are an excellent tool to use for solving complex problems in the field of industrial applications. We use the mathematical method of fractal geometry and network theory when laser-hardening techniques are applied. The microstructure of the robot-laser-hardened specimens is very complex; however, we can present it by using a 3D visibility network. We convert the scanning electron microscope (SEM) images of the microstructure to a 3D graph and calculate the density of the visibility network of these 3D networks. We have analyzed the topographical properties of the hardened specimens by using the algorithm for the construction of a visibility network in a 3D space. We develop a new hybrid system of machine learning for predicting carbide content of the hardened specimens by using multiple regression, neural networks, and a genetic algorithm. We find the statistical significance of the relationship between attributes of the hardened specimens, the topological properties of visibility graphs, and carbide content of the hardened specimens._ Keywords: fractal geometry, hybrid system, laser hardened specimens, visibility network, statistical pattern recognition
Highlights
•	We have calculated the statistical properties of the data of the parameters of the hardened specimens.
•	We have described the carbide content of the hardened specimens using the topological properties.
•	We have presented a new intelligent hybrid system model to predict the carbide content of the hardened specimens.
•	Our new method has many applications in pattern recognition, computer graphics, computational geometry, and so on.
0 INTRODUCTION
Robot laser hardening [RLH] [1] is a heat treatment similar to inductive or conventional flame hardening. We can analyze the microstructures of RLH specimens using 3D visibility networks (graphs). A visibility network [2] is a graph of visible areas, which presents a set of nodes and obstacles in the Euclidean plane or space. Fractal geometry [3] was developed by Mandelbrot, who built the Mandelbrot set y=z2 + c with the help of a computer. He provided a new approach in the scientific discipline as he set out and designed a new way of thinking about structures and shapes. The Hurst parameter H [4] is the correlation between random steps X1 and X2, which is followed by the time-to-time difference At. Hurst parameter occurs in many areas of applied mathematics, including fractals and chaos theory, and is used in many fields ranging from biophysics to network computers. The parameter was originally developed in hydrology. However, modern techniques to estimate the Hurst parameter H come from fractal mathematics. The fractal dimension has been used to measure the roughness of sea coasts. The relationship between the fractal dimension D and the Hurst parameter H is given by the equation D = 2 - H for 2D
objects and D=3 - H for 3D objects. We developed a new method to estimate the Hurst parameter H of a 3D object. In this paper, we introduce a new hybrid intelligent system to predict the carbide content of RLH specimens from the topological property of the density of the visibility network and fractal dimension.
1 PREPARATION OF MATERIAL SPECIMENS
The study was done on the standard tool steel labeled as DIN 1.7225 [5]. The tool steel was surface hardened by laser at different speeds and different powers. We use a robot laser cell RV60-40 (Reis Robotics Company). The maximum power of the robot-laser cell is 3000 W. We hardened specimens with an output power of 1500 W. Therefore, we modified the speed parameter v £ [2, 5] mm/s and the temperature parameter T £ [800, 2000] °C. Each sample was prepared by etching and polishing (IMT, Institute of Metals and Technology Ljubljana, Slovenia) for a microscope evaluation (IJS, Jozef Stefan Institute). Fig. 1 was made by field emission scanning electron microscopy, JMS-7600F, JEOL. We wanted to know whether the microstructure of the RLH fractal patterns found a structure from which the Hurst parameter H could be estimated. Fig. 2 presents a 3D graph of the
*Corr. Author's Address: Jožef Stefan Institute, Ljubljana, Slovenia, , babicster@gmail.com
393
microstructure of the RLH specimen. It is converted from Fig. 1 by using Fig. 1 color depth.
Fig. 1. SEM picture of microstructure of the RLH specimen
Fig. 2. 3D graph of microstructure of the RLH specimen
2 DESCRIPTION OF METHOD
We used fractal geometry and a visibility network to determine the complex microstructure of the RLH specimens.
Fig. 3 presents the random vertices of the 3D graph. For better visual presentation, we use 5x5 vertices of the 3D graph. 3D graph presents microstructure of the RLH specimens.
Babic et al. [6] present a solution for constructing a visibility network in a 3D space. Fig. 4 presents the results of the problem of constructing a visibility network in a 3D space. We use the statistical topological property of the density of the visibility
Fig. 3. Vertices in a 3D graph
Fig. 4. Visibility network of vertices in a 3D graph
network for pattern recognition from SEM images of the RLH specimens. The density q was calculated for each visibility network by Eq. (1):
q = -
2m
n x
(n -1)
(1)
where m is the number of edges, n is the number of vertices in the visibility network.
We present a method of estimating the Hurst exponent H for 3D objects [7]. First, we use the program Image J to find all the coordinates (x, y, z) of the SEM picture. Secondly, we estimate the Hurst exponent H by using the z-coordinates, which present a long continuous graph (Fig. 5). Also, all points
(xz, y0, zz) present a space component on a 2D graph for all points (xz, zz). All points (xi,j1, zz) present a second space component on a 2D graph for all points (xz, zz). We made a space component for all y, Vz. Then we combined all these space components into one space component. For this long space component, we can estimate the Hurst exponent H. We use the fractal dimension for pattern recognition from SEM images.
Fig. 5. Long continuous graph
We use the method of a visibility network and fractal geometry for statistical pattern recognition. To model the results, we use intelligent system methods, that is, multiple regression, neural network (NN), and genetic programming (GP).
NNs [8] have the ability to solve a variety of problems. The sophistication of NNs is primarily due to their ability to imitate the principle of the functioning of the biological brain, which means that they solve problems similarly to humans. We used the Neuralyst program to create a model with NNs. Neuralyst is a software tool used within Excel. It has the ability to model NNs. We used a multi-tasking neural system with backpropagation and no back
links. We had the option of setting different attributes. Table 1 presents the attributes of the NNS.
Table 1. Attributes of the NN
Learning speed [-]	0.6
Inertial coefficient [-]	0.5
Test mass tolerance [-]	0.02
Tolerance of the learning set [-]	0.03
Number of layers [-]	4
Fig. 6 presents a general multi-layer NN system.
Table 2. Attributes of the GP Size of the population of organisms
500
Maximum number of generations
100
Reproduction probability
0.4
Crossover probability
0.6
Maximum permissible depth in the creation of the population
10
Maximum permissible depth after the operation of crossover of two organisms Smallest permissible depth of organisms in generating new organisms
Tournament size used for selection of organisms
Genetic programming [9] is similar to genetic algorithms and differs only in terms of the presentation method. Individual component in genetic algorithms is presented by a sequence of numbers, and the individual component in genetic programming is presented by a computer program. GP automatic writing of programs according to the nature of natural selection (evolution). At the beginning, we have some randomly written programs, which represent the initial
Fig. 6. General multi-layer NN system
6
2
7
population. Then by crossing and selection, we get the next generation. Table 2 presents the attributes of the genetic programming.
We used the genetic operations of reproduction and crossover. Fig. 7 presents an example of an organism in genetic programming.
(22 -(-^-))*(l7+eos(Y))
Fig. 7. Organism in GP
Multiple regression (MR) [10] is designed to investigate linear causes the relationship between a single dependent variable and one or more independent variables. With it, we determine the statistical feature in the power of connection and we predict the values of the dependent variable. The impact of each of the independent variables is estimated to be independent of the interactions between independent variables.
Hybrid evolutionary computation [11] is a generic, flexible, robust, and versatile method for solving complex global optimization problems and could be used in practical applications. We present a new intelligent hybrid systems model in Fig. 8. Data information is presented in Table 3.
Table. 3. Attributes of the hardened specimens
S	x1	x2	x3	x4	x5	x6	Y
S1	1000	2	1.91	2.30	0.191	85	39
S2	1000	3	1.96	2.26	0.224	85	45
S3	1000	4	1.95	2.26	0.210	85	43
S4	1000	5	1.94	2.34	0.235	85	41
S5	1400	2	1.92	2.22	0.246	85	36
S6	1400	3	1.98	2.39	0.228	85	49
S7	1400	4	1.95	2.25	0.201	85	45
S8	1400	5	1.98	2.29	0.215	85	48
S9	1000	2	1.97	2.18	0.247	39	46
S10	1000	3	1.86	2.18	0.232	45	32
S11	1000	4	1.98	2.41	0.219	43	45
S12	1000	5	1.94	2.21	0.241	41	42
S13	1400	2	1.98	2.26	0.225	36	28
S14	1400	3	1.58	2.27	0.238	49	19
S15	1400	4	1.97	2.43	0.208	45	41
S16	1400	5	1.81	2.29	0.197	48	38
S17	800	0	1.97	2.23	0.289	85	47
S18	1400	0	1.98	2.24	0.277	85	52
S19	2000	0	1.97	2.26	0.245	85	50
S20	950	0	1.96	2.28	0.217	85	66
S21	850	0	1.95	2.32	0.212	85	80
S22	0	0	1.91	2.30	0.195	85	39
3 RESULTS AND DISCUSSION
The attributes of the hardened specimens influence on the carbide content (Table 3). The specimens are labeled as S1 to S22. Attribute x1 represents the temperature [°C] and x2 represents the speed of RLH [mm/s]. Attributes x3, x4, and x5 represent the keys for pattern recognition. Parameter x3 represents the complexity in 2D, x4 represents the complexity in 3D, x5 represents the density of the visibility networks in a 3D space, and x6 represents the carbides in specimens. The last attribute Y is the measured surface carbide
Genetic Programming	Butiding hybrid system of machine learning
Fig. 8. Intelligent system model and new hybrid intelligent system
content of the RLH specimens. Specimen S22 presents the material before the RLH process. In Table 4, we denote measurement (M) data (D) by MD, prediction data obtained by MR, prediction data obtained by neural network (NN), prediction data obtained by GP, and prediction data obtained by the hybrid system by H. Specimen S14 has a minimal carbide content after hardening, that is, 19 %. Table 4 present the statistical properties of the experimental and predicted patterns. Table 5 present topological properties of 3D visibility network. The measured and predicted carbide content of the RLH specimens is presented in the Fig. 9. The MR model is presented by Eq. (1), GP model is presented by Eq. (2), and hybrid model is presented by Eq. (3). We calculated precision of the GP model, NN and of the MR model by calculating average of absolute difference between measured and predicted data divided by measured data. The GP model has 85.57 % precision, the NN has 90.57 % precision, MR has 80.87 % precision and hybrid system has 62.98 % precision.
Table 5 presents the topological properties of the 3D visibility network. Measured and predicted parts of carbides of the LHR specimens depend on attributes X], X2, X3, X4, X5 and x6 are presented in Fig. 9. We use the statistical topological property of the visibility networks to describe the carbide content in the microstructures. Image analysis of the SEM images of the RLH specimens is an interesting approach. With MR, GP and NN, we predict the carbide content in the microstructures. Finally, we present a new hybrid system of intelligent systems. For measured and predicted parts of carbides of the LHR specimens data, we calculated Kendall correlation coefficient. The best results for prediction give us NN, because the Kendall correlation coefficient (0.021) is most close to experimental data (0.131). Table 3 presents the topological properties of the 3D visibility network and attributes of RLH specimens. In this way, we can see how the attributes of speed and temperature influence the topological structures of visibility graphs in 3D space. Table 6 presents the statistical properties of the topological properties of the extreme number, number of edges, and triadic census type 16 to 300 of the 3D visibility network for RLH specimens. Firstly, we calculated the basic statistical properties of the mean, standard deviation, standard error, median, geometric mean, and harmonic mean of the topological properties of visibility graphs in 3D space of RLH specimens. We found significant positive relationships between the kurtosis, Fisher's G2, the coefficient of variation, the coefficient of dispersion,
Table. 4. Measured and predicted data
S	MD MR	NN	GP	H
S1	39 55.28	38.98	38.7	34.77
S2	45 50.93	44.53	45.0	37.32
S3	43 47.84	42.25	45.0	40.61
S4	41 45.89	42.27	41.4	44.78
S5	36 42.41	36.98	40.8	44.18
S6	49 49.69	48.32	44.3	43.32
S7	45 40.97	44.86	46.7	46.45
S8	48 40.00	48.06	44.6	48.86
S9	46 42.74	45.97	46.2	40.85
S10	32 35.98	32.08	18.8	47.98
S11	45 48.01	44.98	40.0	44.99
S12	42 33.04	42.26	42.0	55.08
S13	28 39.91	46.48	27.7	47.05
S14	19 19.88	18.99	22.8	67.35
S15	41 42.15	41.54	45.2	51.32
S16	38 27.23	37.08	38.0	60.50
S17	47 59.78	47.86	47.4	30.50
S18	52 50.58	50.11	49.7	39.58
S19	50 42.10	51.01	50.1	48.54
S20	66 62.98	66.65	47.5	28.93
S21	80 65.82	79.25	46.4	27.35
S22	39 79.59	84.60	84.9	58.25
Table. 5. Topological properties of 3D visibility network				
S	Extreme number	Number of edges	Triadic census type 16 to 300	
S1	120823	3500351		4865624
S2	125787	3308776		4191425
S3	123943	3335861		4267175
S4	124833	3355735		4353872
S5	124626	3314397		4212248
S6	131540	3190001		3796016
S7	126962	3311163		4196282
S8	130799	3173601		3741603
S9	123393	3355056		4256560
S10	126395	3386391		4483986
S11	124296	3315948		4207031
S12	123829	3355735		4353872
S13	128143	3451450		4862060
S14	122500	3685175		5877473
S15	120818	3338595		4199754
S16	116812	3733624		5848517
S17	133031	3178192		3774789
S18	130974	3182544		3819193
S19	131043	3170121		3746658
S20	95090	4151533		7284078
S21	106916	5653616		1764141
S22	86871	5735036		1466536
Model of multiple regression: Y=-99.0509 - 0.0178 x x1 - 3.25717 x x2 + 46.65489 x x3 + 38.06208 x x4 - 63.3748 x x5 + 0.165097 x x6. (2)
Model of genetic programming Y = 0.129654 x (-x6 - x22 -
2 + 2 + X X^ Xr
:(-x 2 + x22)
x3 + x2 J
X2 X X6 X
( O
X + —
X2 Xi + X2 X (X2 + XX2 X X3 ) + X6
(3 X (x2 + X3 ) + X5 )X (3 + 2X X3 X (2 + X3 ) + X6))
(X2 + x3 + X6) X
Y
7.71283 + 2 x x2 - x6 — + -
v	x2 - x3
X
V	3 J
(3)
x
6
X
6
2
X
6
4
V	3 J
X
6
+
X
4
4
x6
Hybrid model
Y2 + Y(A + B) + AB - C — 0,
A — 0.129654
;(-x2 + x2 )
- X3 +1—+-2
x3 + x2
B — 99.0509 + 0.0178x1 + 3.25717x2 - 46.65489x3 + 63.3748x5 -0.165097X6,
CC — X2 X3 X6
, x1 + x2 (x2 + x2 x3 ) + x6	2	+
X6
x2 - x3
(x3 (x2 + x3 ) + x6 )(x3 + 2x3 x (x2 + x3 ) + x6))
f \ X6
X6 + —
X
(x3 x2 + x6
X
7.71283 + 2x2 - x6 + 2 6 +-
X2 X3	X2 X1
X
6
X
2
X
X
6
+
90 80 70 60 50 40 30 20 10 0
& & $ &	rip' rt> £ & & & J?	n$>	A"
o> o> o>	o> o> o> <a> o> o> o> o> o> o> o> o> o>
/¿> ¿V .0S> Ä	.<!?>
♦ Experimental data y = -0.1417X + 45.766 T = 0,131
■ Prediction with MR y = -0.4789X + 51.998 T = - 0,08
A Prediction with NN y = -0.5965X + 53.91 T = 0,021
x Prediction with GP y = -0.4445X + 48.439 T = - 0.008
X Prediction with H y = -0.1457X + 46.61 T = -0,11
Density of the visibility networks in a 3D space of RLH specimens
Fig. 9. Measured and predicted carbide content of the LHR specimens depend on attributes xh x2, x3, x4, x5 and x6
and the topological properties of visibility graphs in 3D space of RLH specimens.
Table. 6. Statistical properties of topological properties of 3D visibility network
SP	Extreme number	Number of edges	Triadic census type 16 to 300
Mean	121792	3599223	4253132
Standard deviation	11531.35	714391.3	1201353
Standard error	2458.49	152308.8	256129.4
Median	124461	3346826	4209640
Geometric mean	121194	3546497	4055020
Harmonic mean	120509	3505535	3790200
Kurtosis	5.90	7.454659	4.719475
Fisher's G2	4.03	5.993685	2.517122
Coefficient of variation	0.094	0.1984849	0.2824632
Coefficient of dispersion	0.05	0.1024648	0.1701942
4 CONCLUSIONS
The paper presents a new method of constructing visibility networks in a 3D space, a new method of describing the complexity of 3D space, and a new hyper-hybrid system of machine learning for the use in mechanical engineering to predict the topographical properties of materials. The paper presents a method of using visibility graphs in 3D
space and fractal geometry to analyze the complexity of RLH specimens. Analyzing the complexity of RLH surfaces is a very hard problem. This new method has many applications in pattern recognition, computer graphics, computational geometry, and so on. The main findings are:
1.	We use the method of network theory and fractal geometry to analyse the microstructure.
2.	For prediction of the carbide content of hardened specimens, we use intelligent system methods, namely a neural network, multiple regression, and a genetic algorithm. The best results for prediction give us neural network.
3.	We present the new hybrid spiral sequences.
4.	The paper introduces a new method of machine learning in metallurgy.
5.	We find the statistical significance of the relationship between attributes of the hardened specimens and the experimental and predicted pattern data.
6.	The paper compares three methods, namely multiple regression, neural network and genetic programming, with a hybrid system of intelligent systems.
5 REFERENCES
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