Elektrotehniški vestnik 82(1-2): 31-36, 2015 Original Scientific Paper
Using intelligent-system metods in mechanical engineering to predict the topographical property of materials with the topological property of visibility graphs in a 3D space
Matej Babic1
'Ph.D. Researcher, Slovenia, E-Mail: babicster@gmail.com
Abstract. Intelligent systems are a new wave of the embedded and real-time systems that are highly connected, with a massive processing power and performing complex applications. Their pervasiveness is reshaping the real world and teh way, we interact with our digital life. These intelligent systems are creating new opportunities for industry and business, and new experiences for users and consumers. They can be found in all domains: automotive, rail, aerospace, defence, energy, healthcare, telecoms and consumer electronics. In this paper we use an intelligent system method to predict the roughness of hardened specimens. We use an algorithm for the construction visibility graphs in a 3D space to analyse topographical properties of hardened specimens. Drawing graphs as nodes connected by links in 3D space is visually compelling but computationally difficult. Thus, the construction of the 3D visibility graphs is highly complex and requires in their professional computers or supercomputers. The microstructure of the robot-laser-hardened specimens is very complex; however, we can present it using 3D visibility graphs. For predicting the surface roughness of the hardened specimens we use the neural network, genetic algorithm and multiple regression. Using the intelligent systems we increase production of the laser-hardening process by decreasing the time process and increasing the topographical property of materials.
Keywords: intelligent system, visibility graph, engineering, topography,
Uporaba metod inteligentnih sistemov v inženirstvu za napoved topografske lastnosti materialov
Inteligentni sistemi so nov val vgrajenih sistemov v realnem času, ki so zelo povezani, z veliko procesorske moči in izvajajo zahtevne aplikacije. Njihova vseprisotnost je vplivala tudi na realni svet in na interakcijo na naše digitalno življenje. Ti inteligentni sistemi ustvarjajo nove priložnosti za industrijo in podjetja in nove izkušnje za uporabnike in porabnike. Te je mogoče najti na vseh področjih: avtomobilske, železniške in vesoljske industrije, obrambe, energije, zdravstva, telekomunikacij in zabavne elektronike. V tem članku smo uporabili metode inteligentnih sistemov za napovedovanje hrapavosti kaljenih vzorcev z metodami inteligentnih sistemov. Uporabili smo algoritem za graditev grafov vidljivosti v 3D prostoru za analiziranje topografske lastnosti kaljenih vzorcev. Risanje grafov vidljivosti v 3D prostoru je vizualno privlačno, vendar računsko težko. Tako je graditev grafov vidljivosti v 3D prostoru zelo zapletena in zahteva zmogljive računalnike ali superračunalnike. Mikrostruktura robotskih lasersko kaljenih vzorcev je zelo kompleksna; vendar jo lahko opišemo s pomočjo grafov vidljivosti v 3D prostoru. Za napovedovanje hrapavosti kaljenih vzorcev bomo uporabili nevronske mreže, genetske algoritme in multiplo regresijo. Z inteligentnim sistemom smo povečali proizvodnjo procesa laserskega kaljenja, saj smo pridobili čas procesa in povečali topografske lastnosti materiala.
1 Introduction
Philosophers have been trying for over two thousand years to understand and resolve two big questions of the universe: how does a human mind work, and do non-humans have minds? However, these questions are still unanswered. Some philosophers have picked up the computational approach originated by computer scientists and accepted the idea that machines can do everything that humans can do. Requirements for an intelligent system [1] include security, connectivity, ability to adapt according to the current data and capacity for remote monitoring and management. Essentially, an intelligent system is anything that contains a functional, although not usually generalpurpose, computer with Internet connectivity. An embedded system may be powerful and capable of complex processing and data analysis, but it is usually specialized for tasks relevant to the host machine. Intelligent systems exist all around us in point-of-sale (POS) terminals, digital televisions, traffic lights, smart meters, automobiles, digital signale and airplane controls, and among a great number of other possibilities. As this ongoing trend continues, many
Received 28 November 2014 Accepted 30 January 2015
32
BABIC
foresee a scenario known as the Internet of Things (IoT), in which objects, animals and people can all be provided with unique identifiers and the ability to automatically transfer data over a network without requiring human-to-human or human-to-computer interaction. In this paper we use an intelligent system to predict topography of specimens after heat treatment. 3D visibility graphs can be used in many 3D geometric problems. In this work, the visibility network in a 3D space, which contains more information than the visibility graph, is used to analyse the microstructure of the robot laser-hardened specimens. This algorithm is also useful in many other cases, such as: illumination and rendering, motion planning, pattern recognition, computer graphics, computational geometry and sensor networks. The robot laser surface-hardening [2] heat treatment is complementary to the conventional flame or inductive hardening. Laser hardening is a process of projecting features, such as a non-controlled energy intake, high-performance constancy and an accurate positioning process. A hard martensitic microstructure provides improved surface properties, such as wear resistance and high strength [3]. The aim of the paper is to outline the possibilities of applying the neural network, genetic programming and multyple regression for the prediction of the roughness after robot-laser heat treatment with the topological property density visibility graphs in a 3D space of a microstructure and to assess their perspective use in this field. An application of the algorithm for construction of a 3D visibility graph to analyse the microstructure of the laser technique in hardening a specimen is illustrated in Section 3.
Figure 1. Microstructure of the robot-laser-hardened specimen
3 method
We used a new mathematical method to describe the geometry microstructure the of robot-laser-hardened specimens. In this paper we use the mathematical method graph theory to describe the complexity geometry of the robot-laser-hardened specimens and visibility graphs in a 3D space. Teh algorithms for the 2D visibility graphs already exist [4]. Two arbitrary data values (xa, ya) and (xb, yb) will have visibility, and consequently will become two connected nodes of the associated graph, if any other data (xc, yc) placed between them fulfills (1).
yc < yb + (ya-yb)*(xb-xc)/(xb-xa) .
(1)
2 Materials preparation
The study was undertaken using the tool-steel standard label DIN standard 1.7225. The tool steel was forged with the laser at different speeds and at different powers. So we changed two parameters the speed v £ [2, 5] mm/s with steps of 1 mm/s and the temperature T £ [1000, 1400] °C. Prior to testing, the specimens were subjected first to the mechanical and then to electrolytic polishing in H3Po4+CrO3 at the Institute of Metals and Technology of Ljubljana, Slovenia. After polishing we made images with a scanning electron microscope, JEOL JSM-7600F. Fig. 1 presents the microstructure of the robot-laser-hardened specimens. On these specimens we measured the roughness and hardness before and after the robot-laser-hardening. A profilometer (available from the Jozef Stefan Institute of Ljubljana) was used to measure the surface roughness parameter Ra (arithmetic mean deviation of the roughness profile) and hardness of the robot-laser-hardened specimens.
Firstly, we have a point (vertex) in a 3D space and know how to connect it in a 3D space.
Figure 2. Point in a 3D space microstructure of Fig. 1
The problem of constructing the visibility graph in a 3D space was solved in [5]. Fig. 3 presents a solution of the visibility graph in a 3D space microstructure of Fig. 1. Density p for each visibility graph was calculated with equation (2)
USING INTELLIGENT-SYSTEM METODS IN MECHANICAL ENGINEERING TO PREDICT THE TOPOGRAPHICAL PROPERTY..
33
p=2m/n*(n-1),
(2)
wher m is the number of the edges and n is the number of verteces in the visibility graphs.
Figure 3. Visibility graph in a 3D space microstructure of Fig. 1
To model the results, we used the intelligent system methods, i.e. the neural network, genetic programming method and multiple regression.
The neural networks [8] have a large appeal to many researchers due to their great closeness to the structure of the brain, a characteristic not shared by more traditional systems. In an analogy to the brain, an entity made up of interconnected neurons, the neural networks are made up of interconnected processing elements called units, which respond in parallel to a set of the input signals given to each. The unit is an equivalent of its brain counterpart, the neuron. Learning is essential to most of these neural network architectures and hence the choice of a learning algorithm [9] is a central issue in the network development. Learning implies that a processing unit is capable of changing its input/output behavior as a result of changes in the environment. Since the activation rule is usually fixed when the network is constructed and since the input/output vector cannot be changed, to change the input/output behavior, the weights corresponding to that input vector need to be adjusted. A method is thus needed with which, at least during the training stage, the weights can be modified in response to the input/output process. Their is a number of such learning rules available for the neural network models. In a neural network, learning can be supervised, in which the network is provided with a correct answer for the output during training, or unsupervised, in which no external teacher is present.
Figure. 4. General multi-layer neural network system
Genetic programming (GP) [9] is an automated method for creating a working computer program from a highlevel problem statement of a problem. GP starts from a high-level statement of "what needs to be done" and automatically creates a computer program to solve the problem. GP starts with a primordial ooze of thousands of randomly created computer programs. This population of programs is progressively evolved over a series of generations. The following evolutionary parameters were selected for the process of simulated evolutions: 500 for the size of the population of organisms, 100 for the maximum number of generations, 0.4 for the reproduction probability, 0.6 for the crossover probability, 6 for the maximum permissible depth in the creation of the population, 10 for the maximum permissible depth after the operation of crossover of two organisms, and 2 for the smallest permissible depth of organisms in generating new organisms. Genetic operations of reproduction and crossover were used. For selection of organisms the tournament method with the tournament size 7 was used.
Figure. 5. Randomly generated mathematical model for the surface roughness of the hardened specimens prediction, represented in the program-tree form
34
BABIC
The multiple regression [6] is a straightforward extension of the simple regression from one to several quantitative explanatory variables. In the multiple regression, we still make the xed-x assumption which indicates that each of the quantitative explanatory variables is measured with a little or no imprecision. All the error model assumptions also apply. They assume teh outcome that for each subject having the same level of the explanatory variables is normally distributed around the true mean (or that the errors are normally distributed with the mean zero), and that the variance, ct2, of the outcome around the true mean (or of the errors) is the same for every other set of the values of the explanatory variables [7]. It is assumed that the errors are independent from each other. The standard ANCOVA model incorporates covariates into an ANOVA model in a straightforward way. If there is one grouping variable, for example, the model for the multiple linear regression, given m observations, is (3)
Y = b + bjXl + b2X2 + ... + bmXm + e,
(3)
where a, is the corrected effect on y given that you are in group i (corrected in the sense that the covariates xj, . . . , xm are taken into account).
prediction with the neural network with the method one live out, and GP prediction with genetic programming. In Table 1, we can see that specimen P20 has the largest density of the visibility graphs in 3D; 0.2960, thus specimen P20 is most complex. Specimen P13 has most roughness after hardening, that is 2350nm. The measured and predicted surface roughness of the laser-hardened robot specimens is shown in the graph in Fig. 8. The genetic programming model is presented in Fig. 7. The genetic programming model presents a 19. 67% deviation from the measured data, which is less than the regression model, which presents a 133. 97% deviation. The best neural network presents a 39. 10% deviation from the measured data.
Y=40,2767-
-8,63 95 + 2 XX2-
, 9,70913 9,70913
-8.63695+X2
X3 9,70913
-1.32381+X2
— 1,32381+^2
9,7 0 9 13 9,7 0 9 13 - X2 + ( - 5,0 744 -X2 -5,5 0 744 X X3) X X 3
—8,63 695+X2+X3 —
4,85457 , 9.70913+X2
X2 + X2+X3 ______ , 9.70913+X2
— 1,32381+^2
(5,0 744 X (-X2+X3 + 9,7°913++3X2)
—8,63 695+X2+X3 —
4,85457 9.70913+X2 + X2+X3 , 9.70913+X2 695+ 2XX2
-1,32381+^2
Figure 7. Model of genetic programming Table 1. Parameters of the hardened specimens
Figure 6. Analysis of covariance
4 RESULTS
In Table l, the parameters of the hardened specimens
impacting the roughness are presented. The specimens from Pl to P22 are marked. Parameter Xl presents the temperature in degrees of Celsius [C], X2 presents the
speed of hardening [mm/s], X3 presents the density of the visibility graphs in a 3D space and X4 presents the basic roughness of specimens. The last parameter Y is the measured surface roughness of the laser-hardened
robot specimens. Table 2 presents experimental and prediction data regarding the surface roughness of the
laser hardened robot specimens. In Table 2, symbol S presents the name of the specimens, E experimental data, R prediction with regression, NMl prediction with the neural network with a 50% learn set, NM2
S	Xl	X2	X3	X4	Y
Pl	l000	2	0,l936	24	20l
P2	l000	3	0,2208	24	l7l
P3	l000	4	0,2l44	24	l09
P4	l000	5	0,2256	24	76,3
P5	l400	2	0,2445	24	l320
P6	l400	3	0,222l	24	992
P7	l400	4	0,2036	24	553
P8	l400	5	0,2096	24	652
P9	l000	2	0,2352	20l	337
Pl0	l000	3	0,2288	l7l	307
Pll	l000	4	0,2l44	l09	444
Pl2	l000	5	0,2352	76,3	270
Pl3	l400	2	0,2208	l320	2350
Pl4	l400	3	0,232	992	l900
Pl5	l400	4	0,l984	553	66l
Pl6	l400	5	0,l904	652	759
Pl7	800	0	0,2832	24	l83
Pl8	l400	0	0,2688	24	l330
Pl9	2000	0	0,24l6	24	l740
P20	950	0	0,2l28	24	502
P2l	850	0	0,208	24	l66
P22	0	0	0,296	24	24
USING INTELLIGENT-SYSTEM METODS IN MECHANICAL ENGINEERING TO PREDICT THE TOPOGRAPHICAL PROPERTY..
35
Table 2. Experimental and prediction data
S	ED	R	NM1	NM2	GP
P1	201	305,65	199,6	317,1	214,1
P2	171	407,70 151,2	150,2	205,1
P3	109	305,54 105,3	67,9	137,3
P4	76,3	310,35	101,0	129,8	83,9
P5	1320	1187,6 1314,0	1240,0	1779,3
P6	992	988,25	993,0	987,8	936,6
P7	553	812,56 569,6	706,8	567,1
P8	652	785,76 641,0	562,0	431,3
P9	337	558,47 354,6	419,5	331,7
P10	307	456,31	291,2	215,3	218,0
P11	444	305,54 440,1	404,7	137,3
P12	270	368,69 138,0	19,2	83,4
P13	2350	1043,6 1372,8	2302,5	1367,2
P14	1900	1048,4 953,5	1928,5	1032,7
P15	661	780,95	1465,8	684,4	540,0
P16	759	669,08 673,7	749,4	372,0
P17	183	690,38 465,8	170,9	193,3
P18	1330	1461,8 1990,3	1350,3	731,1
P19	1740	2155,5	2367,7	1759,8	1742,5
P20	502	477,27 621,2	365,0	201,3
P21	166	304,94 266,5	272,9	151,7
P22	24	-377,1	115,2	-64,6	24,3
Figure 8. Measured and predicted surface roughness of the laser-hardened robot specimens
Model Regression
Y=-2176,047851+1,431627245xX1-63,25871916xX2 +6077,409979 xX3
5 Discussion
We use the topological property of the visibility graphs to describe the topographical properties of the hardened specimens. Using an algorithm for constructiong the visibility graphs in a 3D space, we describe the complexity of the hardened specimens. A statistically
significant relationship was found between the roughness, parameters of the robot-laser cell and topological property density of the visibility graphs in 3D. In addition, image analysis of the SEM images of the robot-laser-hardened specimens is an interesting approach. We use three methods of the intelligent system to predict porosity of the robot-laser-hardened specimens. We show that the genetic programming model gives the best prediction results. The neural network model is better than the regression model and as good as the genetic programming model.
6 CONCLUSSION
In the paper we present the use of an intelligent system method, genetic programming and multyple regression to predict the hardness of hardened specimens. We describe a method of the visibility graph in a 3D space to analise complexity of the robot-laser-hardened specimens. The main findings can be summarised as follows:
1.	We describe the topographical properties of the hardened specimens by using the topological properties of the visibility graphs in a 3D space.
2.	We describe the relationship between roughness and the parameters of the robot-laser cell by using the topological properties of the 3D visibility graphs. This finding is important with regard to certain alloys that are hard to mix because they have different melting temperatures; however, such alloys have better technical characteristics. By varying different parameters (e.g., temperature), the robot-laser cells produce different patterns with different topological properties of the 3D visibility graphs.
3.	To predict the roughness of the hardened specimens, we use a neural network, genetic algorithm and multiple regression.
4.	Using the presented intelligent system we increase production of the laser-hardening process by decreasing time of the process and increase the topographical property of materials.
REFERENCES
[1]	Hutter, M. (2012). "One Decade of Universal Artificial Intelligence". Theoretical Foundations of Artificial General Intelligence. Atlantis Thinking Machines 4. doi:10.2991/978-94-91216-62-6_5. ISBN 978-94-91216-61-9.
[2]	El-Batahgy, A.-M., Ramadan, R.A., Moussa, A.-R. (2013). Laser surface hardening of tool steels - experimental and numerical analysis, Journal of Surface Engineered Materials and Advanced Technology, Vol. 3, No. 2, 146-153,
doi: 10.4236/jsemat.2013.32019.
[3]	Babic, M., Milfelner, M., Belie, I., Kokol, P. (2013). Problems associated with a robot laser cell used for hardening, Materials and Technology, Vol. 47, No. 1, 37-41.
[4]	Lacasa L., Luque B., Ballesteros F., Luque J., and Nuno J.C.(2008). From time series to complex networks: the visibilitygraph. Proceedings of the National Academy of Sciences USA105, 13, 4972-4975.
[5]	Matej Babic. Doctoral dissertation. 2014.
*x
*
r* *
*	n x
•	x
x „ *
* K*
■ A X
i X ■ i
—■ X
£
♦ x
♦ Experimental data
■ Prediction with
Regression a Prediction with NM 50%
x Prediction with NM one live out x Prediction with GP
P1 P3 P5 P7 P9 P11 P13 P15 P17 P19 P21
Specimens
2600
2300
2000
1700
i/l 1400
g 1100
800
500
200
36
BABIC
[6]	Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences, 3rd Ed. Mahwah, NJ: Lawrence Erlbaum Associates.
[7]	Havlicek, L., & Peterson, N., (1977). Effects of the violation of assumptions upon significance levels of the Pearson r. Psychological Bulletin, 84, 373-377. [You can get away with a lot - regression is remarkably robust with respect to violating the assumption of normally distributed residuals. However, extreme outliers can distort your findings very substantially.]
[8]	Graves, Alex; and Schmidhuber, Jürgen; Offline Handwriting Recognition with Multidimensional Recurrent Neural Networks, in Bengio, Yoshua; Schuurmans, Dale; Lafferty, John; Williams, Chris K. I.; and Culotta, Aron (eds.), Advances in Neural Information Processing Systems 22 (NIPS'22), December 7th— 10th, 2009, Vancouver, BC, Neural Information Processing Systems (NIPS) Foundation, 2009, pp. 545-552.
[9]	Dominic, S., Das, R., Whitley, D., Anderson, C. (July 1991). "Genetic reinforcement learning for neural networks". "IJCNN-91-Seattle International Joint Conference on Neural Networks". IJCNN-91-Seattle International Joint Conference on Neural Networks. Seattle, Washington, USA: IEEE. doi:10.1109/IJCNN.1991.155315. ISBN 0-7803-0164-1. Retrieved 29 July 2012.
[10]	J. R. Koza. Course Notes for Genetic Algorithms and Genetic Programming. Spring, (2002).
Matej Babic received his Ph.D. degree in Computer Science from the Faculty of Electrical Engineering and Computer Science of the University of Maribor, Slovenia. He studied Mathematics at the Faculty of Education in Maribor. His research interest is in fractal geometry, graph theory, intelligent systems, hybrid machine learning and topography of materials after hardening.