International Journal of Industrial Engineering, 21(2), 14-21, 2014 INFLUENCE OF DATA QUANTITY ON ACCURACY OF PREDICTIONS IN MODELING TOOL LIFE BY THE USE OF GENETIC ALGORITHMS Pavel Kovac, Vladimir Pucovsky, Marin Gostimirovic, Borislav Savkovic, Dragan Rodic University of Novi Sad, Faculty of Technical Science, Trg Dositeja Obradovica 6, 21000 Novi Sad, Serbia pkovac@uns.ac.rs, pucovski@uns.ac.rs, maring@una.ac.rs, savkovic@una.ac.rs, rodic@una.ac.rs It is widely known that genetic algorithms can be used in search space and modeling problems. In this paper theirs ability to model a function while varying the amount of input data is tested. Function which is used for this research is a tool life function. This concept is chosen because by being able to predict tool life, workshops can optimize their production rate expenses ratio. Also they would gain profit by minimizing number of experiments necessary for acquiring enough input data in process of modeling tool life function. Tool life by its nature is a multiple factor dependent problem. By using four factors, to acquire adequate tool life function, vivid complexity is simulated while acceptable duration of computational time is maintained. As a result almost clear threshold, of data quantity inputted in optimization model to gain acceptable results in means of output function accuracy, is noticed. Keywords: Modeling; Genetic Algorithms; Tool Life; Milling; Heuristic Crossover 1. INTRODUCTION From early days when artificial intelligence was introduced, there is a prevailing trend of discovering capabilities which lies inside this branch of science. As all machine related domain, with this one being no exception, there are limits. These limits and boundaries of usage are often expanded and new purposes are constantly discovered. To be able to achieve this goal one must be a very good student of the best teacher that is known to mankind; mother nature. With an experience of more than five billion years our nature is a number one scientist and we are all proud that we have an opportunity to learn whatever she has to offer. Mastery of creation such a variety of living beings is no easy task and maintaining this delicate balance between species is something that requires time, experience and understanding. No scientist is able to create something graceful, like variety of life on Earth, by share coincidence. There has to be a consistency in process of creating and maintaining this complexity of living beings. Law which lies behind this consistency had prevailed more than we can remember and is a simple postulate which tells us that only those who are most adaptable to their environment will survive. By surviving more than others, less adaptable individuals, every living organism is increasing chance to mate, with equally adaptable member of same specie and creating offspring which posses the same, or higher level of adaptability to their environment. This law of selection is something that enabled creation of this world that we live in. Seeing its effectiveness yet understanding simplicity of this concept, we decided to model it. One way of succeeding in this is through genetic algorithms (GA). Since they have been introduced, in early 1970 s, GA present a very powerful tool in space search and optimization fields. Introduce them to a certain area and, with a proper guidance, they will create a population of their own and eventually yield individuals with highest attributes. Through time many scientist manage to successfully implement GA as a problem solving technique. Sovilj et al. (2009) developed a model for predicting tool life in milling process. Pucovsky et al. (2012) studied dependence between modeling ability of tool life with genetic algorithm and the type of function. Čuš and Balič (2003) used GA to optimize cutting parameters in process of milling. Similar procedure for optimizing parameters in turning processes was employed by Srikanth and Kamala (2008). And optimization of multi-pass turning operations using genetic algorithms for the selection of cutting conditions and cutting tools with tool-wear effect has been successfully reported by Wang and Jahawir (2005). Zhu (2012) managed to implement genetic algorithm with local search in solving the job shop scheduling problem. Since job shop scheduling is major area of interest and progress, Wang et al. (2011) succeeded in constructing the genetic algorithm with a new repair operator for assembly procedure. Ficko et al. (2005) reported positive experiences in using GA in forming a flexible manufacturing system. Regarding tool life in face milling, statistical approach by the use of response surface method have been covered by Kadirgama et al (2008). Khorasani et al (2011) used both Taguchi s design of experiment and artificial neural networks for tool life prediction in face milling. Pattanaik and Kumar (2011), using a bi-criterion evolution algorithm for identification of Pareto optimal solution, developed a system for product family formation in area of reconfigurable manufacturing. And knapsack problem is now widely considered as a classical example of GA implementation (Ezzaine, 2002). Taking in consideration weight and importance of milling tool life modeling with evolutionary algorithms, very small amount of articles on this subject was noticed. Also no papers discuss on influence of quantity of input data on results of genetic algorithms optimization function. In absence of these two facts this article is presented as a way to, at least partially, fill existing gap. ISSN 1943-670X INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING
Kovac et al. 2. EXPERIMENT Tests were performed on a 14-kW vertical milling machine without cooling lubrication fluid. A single-tooth face, milling cutter of 125 mm diameter, with a carbide P 25 insert SPAN 12 03 ER was used. The working material was a block of 100x120x600 mm of steel AISI 1060 and was fixed on milling machine table (Kovac et al., 2012). Experimenting mode included varying following parameters: cutting speed v [m/s], respectively number of revolution on machine n [ o /min], feed per tooth f t [mm/t], respectively corresponding feed rate f [mm/min], depth of cut a [mm] and width of flank wear VB [mm]. Each variation of mentioned parameters provided value for tool life T [min] which was carefully measured during whole experiment. Results of experiment are shown in Table 1. 3. MODELING FUNCTION Table 1. Results of experiments No v f t a VB T T mod (i) [m/s] [mm/t] [mm] [mm] [min] [min] 1 2.32 0.178 1 0.12 8 8.48 2 3.67 0.178 1 0.12 6 3 3 2.32 0.28 1 0.12 9 5.85 4 3.67 0.28 1 0.12 2 2.07 5 2.32 0.178 2.25 0.12 8 9.1 6 3.67 0.178 2.25 0.12 5.2 3.22 7 2.32 0.28 2.25 0.12 7 6.27 8 3.67 0.28 2.25 0.12 4 2.22 9 2.32 0.178 1 0.28 42 40.72 10 3.67 0.178 1 0.28 16.6 14.4 11 2.32 0.28 1 0.28 30 28.07 12 3.67 0.28 1 0.28 9.2 9.93 13 2.32 0.178 2.25 0.28 43.5 43.68 14 3.67 0.178 2.25 0.28 18.5 15.45 15 2.32 0.28 2.25 0.28 32 30.11 16 3.67 0.28 2.25 0.28 6.5 10.65 17 2.95 0.223 1.5 0.18 13.3 8.97 18 1.83 0.223 1.5 0.18 20 26.48 19 4.65 0.223 1.5 0.18 3.2 3.2 20 2.95 0.142 1.5 0.18 13 13 21 2.95 0.351 1.5 0.18 7 6.18 22 2.95 0.223 0.67 0.18 14 8.37 23 2.95 0.223 3.37 0.18 13 9.62 24 2.95 0.223 1.5 0.08 2 2 25 2.95 0.223 1.5 0.4 28 39.35 To model the function of tool life T, predefined second-order model is used: T = C 1 v x1 f t x2 a x3 VB x4 (1) The objective of GA optimization is to get such solutions for values of the coefficients C 1, x 1, x 2, x 3, and x 4 that the difference between experimental values and values predicted by model are as smaller as possible (Sovilj et al, 2009). This in other words is something to be considered as a fitness function or a measure of success for every 15
Modeling Tool Life by the Use Of Genetic Algorithms individual. Number of individuals that participate in every generation is n. Every individual (chromosome) has five distinctive features (genes) which are before mentioned coefficients C 1, x 1, x 2, x 3 and x 4. General form of fitness function is defined as: j 25 i 1 M 1 P i, j i 100% (2) and it represent a standard function for determining overall average error. It returns a sum of all percentual deviations of experimental values P(i) and values proposed by individual model M(i,j), where i=1 25 marks the number of experiment and j=1 n is specific number of individual model in one generation. 4. IMPLEMENTATION OF GENETIC ALGORITHMS GA consists of several steps whose execution leads to the solution (Figure 1). Figure 1. Structure of genetic algorithm For practical realization of the model, software MatLab is used. At the very beginning an initial population of 50 individuals is created. Theirs genes (coefficients) are randomly generated from interval 0 1 using uniform distribution. This indicates that real number coding was used. As fitness scaling function rank method was used. Most fit individual, respectively individual with best raw score is assigned as first on the scaling list, next to fittest is ranked number two and so on. This method is ranking every individual in generation comparing to best individual in that same generation, no matter how good or bad fitness value is. It was selected because it allowed fastest convergence toward the best solution. Selection of individuals for presence in mating pool was executed by roulette wheel method. Size of area on wheel, occupied by a single individual is defined by rank score - better the score, bigger the area. Wheel is then spun and individual with largest area has the most chances to be assigned a slot in mating pool. This action is repeated until all slots in mating pool are assigned. In each generation two of the best individuals are automatically transferred to next generation. This act is called elitism and it guarantees that the best genetic material is passed onto next generation. By setting this parameter high the genetic diversity is quickly reduced which leads to prolonged convergence time. On the other hand setting it low, elite genetic material of every generation may be lost and algorithm stuck in local minimum. Number of individuals created by heuristic crossover is, in this case, 43. Heuristic crossover is carried out by creating children that randomly lie on the line containing the two parents, a small distance away from the parent with the better 16
Kovac et al. fitness value, in the direction away from the parent with the worse fitness value. After transferring two elite individuals from previous generation and creating 43 by crossover, to complete a full population with 50 members, last 5 individuals are created by mutating 5 of their predecessors. With the process of mutation a completely new genetic material is introduced into the population which helps in expanding genetic diversity and search space. It also prevents jamming an algorithm in a local minimum of the function. Uniform mutation is selected with the rate of 0.2. This type of mutation is basically a two-step process. Firstly, the algorithm selects a gene of an individual for mutation, where each gene has the same probability as the mutation rate of being mutated. In the second step, the algorithm replaces each selected entry by a random number selected uniformly from the range for that entry. This whole process of selection, recombination and mutation lasted 500 generations. 5. ANALYSIS OF RESULTS Best results obtained by GA, gave average absolute deviation E of just above 20%. Function with implemented obtained coefficients now looks like: T = 701.407 v -2.2661 f t -0.8211 a 0.0865 VB 1.8512 (3) Using this equation to calculate the tool life, obtained results are shown in last column of Table 1. Figure 2 presents graphical interpretation of comparison experimental and modeled values. Figure 2. Correlation of tool life values with 25 experiments on input In order to investigate influence of data quantity on accuracy of tool life model, whole procedure was repeated, using only first twenty experiments from Table 1. Because there was less information GA showed signs of slower convergence towards optimal solution but in most cases it managed to reach goal in just before 500-th population. Slightly drop in accuracy, have been noticed and calculated average absolute deviation was 20.7%. Difference of 0.63% from previous model is practically unnoticeable. When number of data, used in modeling the tool life function, is reduced to 15, greater changes are noticed. Because algorithm was unable to converge towards optimum solution, number of generation had to be increased to 700. Obtained best solution in this case gave average deviation of 21.93%. Figure 3 is presenting graphical interpretation of results with corresponding coefficients. Fourth case, involving use of 10 parameters, required increase of population number to 1000 in order to successfully converge towards best solution. Calculated average absolute deviation was 23.85% and graphical interpretation, including coefficients, is shown on Figure 4. On final stage of this research, with the use of only 5 experimental combinations of parameters, dramatic increase of deviation was noticed. Even after varying members who are used in fitness function, no better result could be obtained than 37.13% of absolute deviation. Yielded coefficients and graphical comparison of tool life values are shown in Figure 5. For more vivid presentation of modeled results, three dimensional graphs are constructed. On Figure 6 dependency between cutting speed, feed per tooth and tool life is shown. Figure 7 contains cutting speed, flank wear and tool life whereas Figure 8 is showing dependency between feed per tooth, flank wear and tool life. 17
Modeling Tool Life by the Use Of Genetic Algorithms Figure 3. Correlation of tool life values with 15 experiments on input Figure 4. Correlation of tool life values with 10 experiments on input Figure 5. Correlation of tool life values with 5 experiments on input 18
Kovac et al. Figure 6. 3D representation of modeled dependencies of v, f, T Figure 7. 3D representation of modeled dependencies of v, VB, T Figure 8. 3D representation of modeled dependencies of f, VB, T 19
Modeling Tool Life by the Use Of Genetic Algorithms 6. CONCLUSIONS As expected, lowering the number of experiments used for modeling tool life function did have an influence on final accuracy of modeled function. Step of 5 experiments was selected because it was considered an optimal change, not too big which would lead to rapid changes, nor too small to unnecessary increase the computing time. It can be noticed that lowering experimental data to only 10 didn t dramatically change an accuracy of modeled function. On the other hand last case, where only 5 members of experimental data values were used, average deviation was increased by more than half. According to results from this research, in case when 5 variables are yielded by the use of GA, threshold should be set to 10 data values in process of modeling function. As a guideline for further research, functions with different number of variables should be used. Eventually with enough data collected a rule of thumb could be extracted which would spare engineers and researchers of unnecessary experiments. 7. INSIGHT FOR PRACTIOCIONERS Like in most cases, when it comes to artificial intelligence, output of this paper could be widely applied among industrial users. With slight adjustments it could be easily modified to model data during turning and drilling processes. Conclusions which this work presents, as authors are hoping, will be beneficial not only for metal cutting branch but will expand its use to composites, plastics and wood machining. Main thing to consider, if one is planning to use this kind of system more frequently, is to construct and adapt software solution for specific type of surrounding. Higher level of automation will result in efficient system which will contribute to final product cost and profit. 8. REFERENCES [1] Čuš, F. and Balič, J. (2003). Optimization of Cutting Process by GA Approach. Robotics and Computer Integrated manufacturing, 19(1-2):113 121. [2] url: http://www.sciencedirect.com/science/article/pii/s0736584502000686 [3] Ezzaine, Z. (2002). Solving the 0/1 Knapsack Problem Using an Adaptive Genetic Algorithm. Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 16(1): 23 30. [4] url: http://journals.cambridge.org/action/displayabstract?frompage=online&aid=106379 [5] Ficko, M., Brezočnik, M. and Balič, J. (2005). A Model for Forming a Flexible Manufacturing System Using Genetic Algorithms. Strojniški vestnik - Journal of Mechanical Engineering, 51(1): 28 40. [6] url: http://www.sv-jme.eu/archive/sv-jme-volume-2005/ [7] Kadirgama, K., Abou-El-Hossein, K. A., Mohammad, B., Noor, M. M., and Sapuan, S. M. (2008). Prediction of Tool Life by Statistic Method in End-Milling Operation. Scientific Research and Essays, 3(5): 180 186. [8] url: http://www.academicjournals.org/sre/abstracts/abstracts/abstracts2008/may/kadirgama%20e t%20al.htm [9] Khorasani, A. M., Yazdi, M. R. S. and Safizadeh, M. S. (2011). Tool Life Prediction in Face Milling Machining of 7075 Al by Using Artificial Neural Networks (ANN) and Taguchi Design of Experiment (DOE). IACSIT International Journal of Engineering and Technology, 3(1): 30 35. [10] url: http://www.ijetch.org/abstract/196-t308.htm [11] Kovac, P., Rodic, D., Pucovsky, V., Savkovic, B. and Gostimirovic, M. (2012). Application of Fuzzy Logic and Regression Analysis for Modeling Surface Roughness in Face Milling. Journal of Intelligent Manufacturing, doi: 10.1007/s10845-012-0623-z. [12] url: http://link.springer.com/article/10.1007%2fs10845-012-0623-z [13]Pattanaik, L. N. and Kumar, V. (2011). Product Family Formation for Reconfigurable Manufacturing using a Bi-criterion Evolutionary Algorithm. International Journal of Industrial Engineering: Theory, Applications and Practice, 18 (9). [14] url: http://journals.sfu.ca/ijietap/index.php/ijie/article/view/310 20
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