137  Advances in Production Engineering & Management ISSN 1854 ‐6250 Volu me 15 | Number 2 | June 2020 | pp 137–1 50 Journal ho me: a p em‐journal.or g https://doi.org /10.14743/apem2020.2.354 Original s cientif i c paper     Comparison of artificial neural network, fuzzy logic and  genetic algorithm for cutting temperature and surface  roughness prediction during the face milling process  Savkovic, B. a,* , Kovac, P. a , Rodic, D. a , Strbac, B. a , Klancnik, S. b   a University of Novi Sad, Faculty of Technical Sciences, Department of Production Engineering, Novi Sad, Serbia  b University of Maribor, Faculty of Mechanical Engineering, Production Engineering Institute, Maribor, Slovenia       A B S T R A C T   A R T I C L E   I N F O This p aper s hows the p os s i bility o f applying a rtificial inte llig e nce m ethods in milli n g, a s one of the m ost common machin i n g operations. The ma in g oal o f the research is t o obtain reliabl e intelligent m odels for selec ted output charac‐ teristics of the m illi ng p rocess , depending o n the i nput p arame ters o f th e process: d epth of c ut, cutt ing s p eed a nd f eed to the t oot h. One o f t h e p r o b l e m s is c ertainly d etermining the v alue o f input parameters o f the p rocessing p ro‐ cess depending on the o bject i v e f unction, i .e. t h e output c har a cteristics o f the milling process. T he s elected ob jective functi o n s in t h i s paper a r e t h e t e m p e r ‐ ature in the c u tting z o n e and arithmetic m e a n roughness of the machine d s u r f a c e . T h e p a p e r e x a m i n e s t h e a c c u r a c y o f t h r e e m o d e l s b a s e d on a rtificial intell igence, ob tained throug h a rtificial neur al n etworks , f uzz y logic, a n d genetic algorith ms. Based on the m ean perce n tage e rror of d evia tion , concl u‐ sions were d r a w n as t o which of the three models i s most a d e qua tely a pplie d and implemented in a ppro p ria t e pr o cess sy st ems, whi ch are based o n a r t i f i ‐ cial intell i gence. © 2020 CPE, Uni versity of M a r ib or. All rights re s erve d.   Keywords: Artificial intell i gence; Artificial neural networks (ANN); Fuzzy log ic ( FL) ; Genetic algori th ms (GA); Face milli ng; Modeling; Surface roughness; Cutting temperature *Corresponding author: sav k o v i c@uns.ac.rs (Savkovic, B.) Article history: Received 14 June 2019 Revised 20 June 2020 Accepted 23 June 2020     1. Introduction   T h e r e i s a nee d t o i m p r o ve t h e ma c h i ni n g p r o c e s s b y a p p l y i ng k n owledge from a dvanced model‐ ing techniques, such a s simulation, which certainl y involves m o deling u sing a rtificial intelligenc e m e t h o d s . T h e d e v e l o p e d m o d e l s a r e u s e d f o r t h e a n a l y s i s , m a n a g e ment a nd s election of o ptimal process parameters, whic h represent a picture o f c omplex r elatio n s h i p s b e t w e e n t h e i n p u t a n d o u t p u t p a r a m e t e r s o f t h e m i l l i n g p r o c e s s . T h e o b t a i n e d m o d e l s c an b e used w ith sufficient accu‐ ra cy in a d a p tive m anag ement and monitorin g o f processes and dec ision makin g i n real time, which is o f great imp o rtance i n the exploitation o f intelligent m an uf acturing s yste ms. It i s also possible to o ptimize the input pr ocess parameters b ased o n the p r o c e s s i n g c o n s t r a i n t s s e t i n o r d e r t o a c h i e v e o ne o r m o r e t a rg e t f un c t i o n s s u c h a s r e d u c i n g cutting f orces and/or m i n imizin g the rough n e ss of t he m achined surface, w hich have the great e st practical value and meanin g f r o m a t e c h n i c a l p o i n t o f v i e w . I n t e r m s o f q u a l i t y o f t h e m a c h ined s urfac e , the e m phasis on the roughness test a s well as the i nfluence o f the cor r esponding pa rameters w as g iven b y a large numb er o f authors [1‐ 4 ]. Applying methods a nd techniques of a rtificial intelligence toge ther w ith mo deling, simulation and optimi z a tion of p ro duction processes lead t o the gen e r a tion o f new and better solutions Savkovic, Kovac, Rodic, Strbac, Klancnik    138  Advances in Production Engineering & Management 15(2) 2020 during m an u f acturin g [ 5‐ 8]. Their app l ication le ads to t h e d ev e lopment of i ntelligent p r o cessing systems that a utomatic ally p er form c omplex p roduction problems, f reeing p eople not o n l y fro m physical but also intellectual wo rk, leaving them to do expert an d creative jo bs. Artificial intelligence can be c onsidered an exp e riment al doctr ine where e x periments ar e per‐ form ed on a computer w i t hin the mod e ls t hat are e x pressed in p ro g r a m s a n d w h o s e t e s t i n g a n d upgradin g a c hieve som e models o f huma n intelligenc e. B y algorith m i t i s u s u a l l y m e a n t a f i n i t e set of p recisely d efined o peratio n s t h a t c a n b e p e r f o r m e d o n a c o m p u t e r . O n e o f t h e a r e a s o f artificial intelligence, togethe r with its sub‐areas, is comput er i nt elligence (soft computing). It is a basic artificial i ntelligenc e to o l t h a t i n v o l v e s s e r i e s o f m e t h o d s and techniques f or t he c oncep‐ tion, d esign and use of a n intelligent s ystem. A s such, the too l is c ertainly a ttractive f or creating various mod e ls that d e scribe cert a in pheno men a i n the produc tio n process. The objective of this paper is to determine the optimal mod e l o btain e d on the basis o f a rtifi‐ c i a l i n t e l l i g e n c e f o r p r e d i c t i n g t h e r o u g h n e s s o f t h e m a c h i n e d surface, i .e. the te mperat ure in t he cutting z on e during o f th e face milling p rocess. T he p roposed m odels ar e realized a s a functio n o f p r o c e s s i n g p a r a m e t e r s : c u t t i n g s p e e d , f e e d p e r t o o t h a n d c u t ting de pth. T h e most com mon artificial i nt elligence met hods are sur e ly: fuzzy logic, a rtifi cial n eural netw orks a nd g enetic a lgo‐ rithms. Accordingly, it is n ece ssary t o determine which of t hes e three types for model creation most closely describes the change in the output characteristics o f th e proces s. 2. Literature review  A r t i f i c i a l n e u r a l n e t w o r k s ( A N N ) a r e n o w a d a y s u s e d i n a l m o s t a l l fields o f science and technolo‐ gy, including m echanic a l engi neerin g. T echnolo g ic al p rocessing p a r a m e t e r s a r e v a l u e s t h a t d e ‐ pend on a large nu mber o f fact ors . T h e r e a r e n o e x a c t f o r m s a n d procedures for determining processing p aram eters, s o in m ost cases, e xperie nce valu es a re used, like v arious b o o k s, tables, g r a p h i c s , e t c. T h e re f o re , n e u r a l n e t wo r k s c a n b e o f g r ea t u se . Instead of a d etailed calc ulation of t h e p r o c e s s i n g p a r a m e t e r s , a n e u r a l n e t w o r k i s c r e a t e d t h a t c a n p redict the u nknown machinin g parameters, after a properly tra ining process [9]. T oday, artif icial neur al n etworks are widely used in th e i n dustrial sector to solv e p roblems [ 1 0‐12 ]. A n e x a m p l e o f t h e i m p l e m e n t a t i o n o f A N N c a n b e s e e n i n t h e p a p e r [ 13]. The applicat ion o f neural n etw o rks for the calculation of c utting f orce, torque a n d monitorin g o f tool w ear during the drilling p rocess is p re sented there. Also, these principles o f neural n etw o rks application can b e s e e n i n o t h e r k i n d s o f c u t t i n g m a t e r i a l p r o c e s s . T h i s p r i m a r ily refers t o the milling p r o cess as one o f th e m o st c om mon cutting p r o cess [14 ]. Th ere ar e pap e rs s howing t he a pplicati o n of the network structure in the m illing p rocess for variables such a s tool g eo metr y and machi n ing re‐ gimes [1 5]. In th e ir r esearch, Lin an d Liu presen t the method ology of creat ing th e n e u r al n etwork s truc‐ ture, emph asizing th e type o f function a s well as the n umber of hidden layers i n the networ k i t s e l f . I t s h o u l d b e p o i n t e d o u t t h a t i t i s v e r y i m p o r t a n t w h i c h type o f n e ural n etwo rk, i.e. the n u m b e r o f n o d e s i n i n d i v i d u a l l a y e r s , i s t h e m o s t a p p r o p r i a t e t o choos e and to o bt ain a suffi‐ ciently reliable m od el. Based on the analysis o f the papers [ 16, 1 7 ] , i t c a n b e c o n c l u d e d t h a t t h e back‐propagation neural n etwork is sufficiently reliable. Also, i t was noticed that the faster c on‐ vergence i s achiev ed u sing a two ‐hid den‐layer network than u sin g a on e‐ hidden‐layer network, with the s am e nu mb er o f nodes. The neur al n etworks app l ication is a l s o present i n t he a dapti v e c ontrol of the s pindle m illing process [18]. ANN are used f or on‐lin e d etermin a t i on of o ptimal m illing p arameters, s p e cifically feed p er to o t h , based on t h e v a lues o f measur ed cu tting f orces. Next, a certainly not less import ant tool o f artificial intellig e n c e i s F u z z y l o g i c . It r epresents the gener a lization of the classical Boolean logic. S ystems b ased o n f u z z y l o g i c a n d f u z z y s e t s c a n be o bserved as a g en erali z ation of e xpert systems based o n r u l es . F u z z y s y s t e m s m a n i f e s t b o t h symbolic and numerical features. I t c a n a l s o b e s a i d t h a t f u z z y l o g i c a n d f u z z y s y s t e m s r e p r e s e n t an e ffective tech n iques to identify a nd c ontrol co mplex non‐li near s yst e ms. F u z z y l o g i c i s a l s o u s e d f o r p r e d i c t i o n . The theory o f fuzzy logic, which h as b een initiated Zad e h [19], is still helpful for th e operati on with Comparison of artificial neural network, fuzzy logic and genetic algorithm for cutting temperature and surface process …   Advances in Production Engineering & Management 15(2) 2020  139 uncertain and inaccurate i nformation. Fuzzy logic is e specially a ttractive b ecause o f its ability to solve problems i n the absence of p recise m athematical mod e ls. This t heory has proved t o be a n effective to ol f or d escribing o bjectiv e s expressed t hrough ling uistic t erms, such a s small , medium and high , wh ich ma y b e d efin ed as t h e fuz z y sets [ 2 0 ]. Application of f uzz y l ogi c t o solve pr oblems i n t h e cutting p r o cess is v ery common and it c a n be s e e n thr o ugh th e o v er view o f follo wing p apers. R ajasek aran et al . [21] i nvestigated th e influ‐ ence o f com b inatio ns o f processing p aram eters i n o rder t o obt a i n a good q uality w h e n finishing machini n g b y t urning. They u sed the fuzz y model i ng t o predic t t he v alue o f surface roughness. Other literature s ources also s how the application of the a d a pt ive appro a ch b ased on the net‐ work o f fuzzy logic system (ANFIS), s e t to s how the correlation o f surface roughness when m a‐ chining by t urning o r mi lling [ 22, 23]. T he i mplement ation of fu z z y l o g i c i n s u r f a c e r o u g h n e s s modelin g w hen finishi n g machi n in g has also b een d iscussed i n pap e r [ 2 4 ] . I t c a n b e s t a t e d t h a t the fuzz y lo gic is a reco g n i zable syste m , sufficientl y dev elope d and widely used [25]. Surface roughness model l ing when f a c e m i l l i n g i s c o n s i d e r e d a c omplex pr o cess. The c oncept of f uzz y r easoning f or f o u r inputs a n d one o u t put fuz z y lo gic u nit (singleton) i s excellently p re‐ s e n t e d i n [ 2 6 ] . C u t t i n g s p e e d , f e e d p e r t o o t h , c u t t i n g d e p t h a n d flank wear w ere set as i nput v ar‐ iables, while the o utput v ariable was t h e rou g hn es s of t he m ac h ined surfac e . Similar issues w ere descr i bed by the a uthors i n paper [27], wher e t h e c u t t i n g s p e e d , f e e d p e r t o o t h , c u t t i n g d e p t h a n d f l a n k w e a r w e r e t a k e n a s i n p u t p a r a m e t ers as w ell, b ut thi s time the output v ariables were to ol lif e and cutting temperature. At the e nd o f this r eview of a rtifici a l intelligence applicatio n , i t i s n e c e s s a r y t o a n a l y z e g e n e t i c a l g o r i t h m s ( G A ) . G e n e t i c a l g o r i t h m s a r e a n e f f e c t i v e w a y t o q u i ckly f ind a s o lution to a c omplex problem. T h e y are c e rtai nly not f ast but they d o a great job o f s earching large areas. T hey are also m ost effective w h en s earching an a rea which is v ery little known or n o t know n at a ll. T er‐ minolo g y an d operators are taken fr om t h e f i e ld o f popul a tio n ge n e t i c s . T h e b a s i c o b j e c t o f g e ‐ netic al gorithms i s the c h romosome, and they r epresent a n insta nt aneou s a pproxi m ation of t he solution for the set goal f unction. E ach chromosome i s encod e d and has a certain qu al ity – fit‐ ness. D uring initialization, the initial population is g ener ated , w h i c h i s a s o l u t i o n o b t a i n e d b y anoth e r opti mizati on method. Then f ollows a r ep etitive pr ocess until the s top c onditio n is m et. T h i s p r o c e s s c o n s i s t s o f t h e e x e c u t i o n o f g e n e t i c o p e r a t o r s o f selection, crossover and mutation. By m ultiple application of t he s el ection operat or , mostly b ad i ndividuals b ecome exti nct, a nd b e t t e r o n e s st a y a l i v e , a n d t h e n e x t s t e p i s c r o s s i n g o v e r b e t w een the go od i ndividuals. The char‐ acteristics of p arents a re transferr ed to children b y crossover o perator. M utation changes th e characteristics of individuals b y rand om c han g e o f g e n es. One s uch procedure en ables the av er‐ age quality o f t he p opulat ion to g row from g enerati on to g en era tion. E ssentially, this i s a heuris‐ tic optimizat i on met h od t hat solves c ertain c ompu ter problems b y simulati ng t he m ech a nism o f natural evolution. A c c o r d i n g l y , i t c a n b e s t a t e d t h a t t h e m e c h a n i s m o n w h i c h G A i s b a s e d , c a n b e u s e d i n o r d e r to o ptimize or t o model the value that o ccur in c er tain p roduct ion processes. T hus, i n addition to the wide d omain of a ppl ication o f t h e g enetic a l g orithm, they a lso fou n d their implem entati on i n designing of CNC c ontrol [28]. When i t comes to a rtificial inte lligence, s pecifically b ased on ge‐ n e t i c a l g o r i t h m s , i t h a s f o u n d i t s a p p l i c a t i o n i n m a c h i n i n g p r o cesses where material i s removed . Thus, ther e i s a n example o f u sin g g e n etic a l g orit hms to p erfo r m opti mization o f p arameters i n the examination of s ur face m orpholo g y [ 29]. Gen e tic algorith ms are also u sed for m o deling t he cutting f orce i n machining proce ss of h ard materials such a s tit a n i u m a l l o y s [ 3 0 ] . T h e y h a v e a l s o found their application in the p roces s ing of a luminium, specific a l l y f o r t h e o p t i m i z a t i o n o f p r o ‐ cessing p arameters [ 31]. There are also p apers in w hich t he a ut hors d eal with m od eling the temper ature during milling w ith the help of GA [32]. 3. Materials and methods  Conditions f or p redicting th e a pprop riate machinability values are created b y d e fini ng t he m od‐ el. Those conditions a llow the technologist o r CNC programmer to s e l e c t t h e a p p r o p r i a t e m a ‐ chining regi mes lon g b efore the actu al m achini ng. By knowing th ese valu es o f machi n ab ility, t he Savkovic, Kovac, Rodic, Strbac, Klancnik    140  Advances in Production Engineering & Management 15(2) 2020 conditions are created to achiev e cont rol of machi ning systems . Certainly, assuming that the best production process was previously s elected in r elation t o th e s et criteria [33]. Fig. 1 s hows the scheme o f i n telligent con trol and mon itoring o f th e machi ning p rocess. The f igure shows that the part for modeling c o llected data is loc ated at the c e ntral part of the system. Experimental setup The material u sed for workpiece was aluminum a l l oy. It is an a l loy from 7 000 s e ries w hich c on‐ tains a high p ercentage of z inc ( Z n ) , a s t h e m a i n a l l o y i n g e l e m e n t , a n d m a g n e s i u m ( M g ) a s t h e second a lloying e l e ment. Beside Z n and Mg, the alloy code 7075 also c ont ains c opper (Cu) a s a f o u r t h a l l o y i n g e l e m e n t , i . e . i t i s a m u l t i c o m p o n e n t A l ‐ Z n ‐ M g ‐ C u alloy. T he a lloys 7 075 have high mechanical p roperties, g ood m achinability a nd heat‐treated proc ess, a n d a lso good c orrosion resistance [ 34]. Th ey b elong t o th e group o f hard alloys. T h e y a r e u s u a l l y u s e d i n t h e a v i a t i o n a n d m i l i t a r y i n d u s t r y . T h e f o r m s t h e y a r e u s u a l l y u s e d a r e : s h e ets, plates, w ires, rods, extruded products, structural shap e s, pipes, forgings etc. [35]. F i g . 2 s h o w s t h e t y p i c a l m i c r o s t r u c t u r e o f t h e t e s t e d s a m p l e s o f A l 4 . 4 % C u a l l o y s o b t a i n e d by conventional casting. Table 1 shows the chemical composition o f th e t e sted alloys. The exp e riments was per f ormed on a vertical m illi ng m achine F SS ‐GVK‐3 with a f ac e milling head d iamet e r of  100 mm, w ith removable ins e rts following c har a cteristics: numbe r of t eeth t = 5, e ntranc e angl e  = 7 5 , rake a ngle  = 0 . I n s e r t s a r e m a d e o f t u n g s t e n c a r b i d e q u a l i t y K 2 0 , the following char a cteris tics (l = IC = 12.7 m m; s = 3.18 m m; b s = 1.4 m m ; b  = 1.4 m m ). Measur em en t of c utting t emper a ture w as p erform ed u sing t he m eas uri n g acquisition system shown in Fig 3. The c e ntr a l part of the system is virtual instr u m ent a tion. Fig. 2 Microstructure of tested aluminum alloy Table 1 Chemic a l compositio n of the alloy 707 5 Alloy designati o n Basic element Zn M g Cu C r Fe S i Mn T i 7075 Al 5 .8 2 .52 1.65 0.2 0.18 0.1 0.025 0.025 Fig. 1 Monit ori n g, modeling an d control s i gnal i n machin ing proces s Comparison of artificial neural network, fuzzy logic and genetic algorithm for cutting temperature and surface process …   Advances in Production Engineering & Management 15(2) 2020  141 I n t h e c a s e o f m i l l i n g , u n l i k e t u r n i n g , t h e r e a r e p r o b l e m s o f t r a n s m i t t i n g t h e s i g n a l f r o m t h e t o o l t o t h e m e a s u r i n g i n s t r u m e n t . D u e t o t h e f a c t t h a t t h e m i l l in g tool m oves i n a circular motion d u r i n g t h e p r o c e s s , i t i s n o t p o s s i b l e t o d i r e c t l y m a n a g e t h e t hermocouple wire d irec tly to t h e measuri n g i n strument. Thermoco uple wire connects to copper ring s, which tog e t he r with g ra ph‐ ite brushes provide sliding contact. Contact with c opper rings is p rovided by s prings. T h ermo‐ voltage occu rring w hen measuri n g t e mper ature between 10 t o 50 m V, s o small losses also m ean large measurement errors. The ther mocouple i s made o f Ni a nd CrN i w i r e w i t h d i a m e t e r o f 0 . 1 m m . I n t h e h i g h ‐ t e m p e r a t u r e z o n e , t h e w i r e s w e r e i n s u l a t e d u s i n g a cer a mic tube o f 0. 9 mm i n diamet er, Fi g. 4. The len g th of the tub e was a b o ut 10 mm, a nd t he insulation was P V C. Apart of the m easur e ment a nd a cquisition system, temper ature me a surem ent wa s a lso pe r‐ form ed b y th e Therm o Pr o TP 8S t h e r m al c amer a, w hich s erve d as a n other verificati on of r eli a ble t e m p e r a t u r e m e a s u r e m e n t . F o r t h e p u r p o s e s o f t h i s r e s e a r c h , i . e . measuri n g the r o ughness of t h e m a c h i n e d s u r f a c e , i t w a s u s e d t h e d e v i c e c a l l e d , , M a r S u r f P S 1 ” . T h e m a x i m u m m e a s u r i n g r a n g e i s 3 5 0 μ m ( f r o m ‐ 2 0 0 μ m t o + 1 5 0 μ m ) . T h i s d e v i c e a l s o m e ets the standards of t he I nter‐ nation al Organiz ation for Standardiz a t ion D I N EN I SO 3.2 74. The factor v ariation is p erformed a t 5 level values, so t hat ea ch m ean value between adjacent levels of the geometric mean of thes e values. The selected le v e l s of factors are shown i n Table 2. Fig. 3 Scheme of the measurem e nt in face milling process Fig. 4 Prepared cutting i nsert with the rmoc ouple installed in the bod y of the milling head 1 – polygonal inserts, 2 – welded top of the thermocouple, 3 – ceramic tube, 4 – a screw that secures the insert, 5 – tool body, 6 – thermocouple PVC insulated, 7 – glue   Savkovic, Kovac, Rodic, Strbac, Klancnik    142  Advances in Production Engineering & Management 15(2) 2020 Table 2 Levels of the experimental parameters for face milling Levels ( Funct i o n s of affiliation) Cutting speed v (m/min) Cutting speed v (m/s) Feed to the tooth s 1 (mm/t) Depth o f cut a (mm) Spindle spe ed n (min ‐1 ) Highest +1.41 351.86 5.864 0.223 2.6 1120 High +1 282.74 4.712 0.177 1.72 900 Medium 0 223.05 3.717 0.141 1.14 710 Low ‐1 175.93 2.932 0.112 0.75 560 Lowest ‐1.41 141.37 2.356 0.089 0.5 450 4. Modeling using artificial intelligence methods  T h e re a l i za t io n of t h e m od e l u s i ng a rtificial intelligence‐base d t ools was don e b y using programs tha t have a rtif i cia l ne u ra l ne tworks, f u zzy log ic (m a m da n i mode l) a nd g e n e t ic a lg orithm s in the ir structure. E xperimental data w ith a set of 21 experiments s hown i n t h e T a b l e 3 w e r e u s e d t o train th ese s y stems. T a b l e 4 s h o w s t h e e x p e r i m e n t a l d a t a t h a t w e r e u s e d f o r t h e t e s t f o r f u r t h e r a n a l y s i s o f t h e models obtained. Table 3 A pla n of experimental testing with measured values for the pr ocess of training models based on artificial intelligence during face milling No. Factor Measured value s v (m/s) s 1 (mm/t) a (mm) Q ( C) Ra (µm) 1 2.93 0.112 0.75 46 1.074 2 4.71 0.112 0.75 52 1.081 3 2.93 0.177 0.75 53 1.743 4 4.71 0.177 0.75 56 1.645 5 2.93 0.112 1.72 60 1.058 6 4.71 0.112 1.72 67 1.023 7 2.93 0.177 1.72 70 1.898 8 4.71 0.177 1.72 77 1.734 9 3.71 0.141 1.14 60 1.205 10 2.35 0.141 1.14 54 1.133 11 5.86 0.141 1.14 65 1.244 12 3.71 0.089 1.14 55 0.995 13 3.71 0.223 1.14 66 2.522 14 3.71 0.141 0.5 4 7 1 .242 15 3.71 0.141 2.6 76.5 1 .229 16 2.35 0.089 0.5 5 1 0 .915 17 2.35 0.223 2.6 108 1.705 18 3.71 0.223 0.5 6 6 2 .023 19 5.86 0.089 2.6 9 8 0 .969 20 5.86 0.141 0.5 6 6 1 .258 21 5.86 0.223 1.14 94 1.94 Table 4 Experimental data for testing the artif icial intel l igenc e mode l No. Factor Measured value s v (m/s) s 1 (mm/t) a (mm) Q ( C) Ra (µm) 1 3.71 0.141 0.75 51 1.222 2 3.71 0.141 1.72 69 1.28 3 3.71 0.112 1.14 55 1.037 4 3.71 0.177 1.14 62 1.583 5 2.93 0.141 1.14 57 1.263 6 4.71 0.141 1.14 60 1.734 4.1 Neural network‐based model  Traini ng a n d t esting a r e t he m ost i m portan t features o f a neura l netw ork (NN) w hich a t th e same ti m e d e termine the characte ristics of NN. T he t raining wi l l determine whether the neural network c a n provide th e exp e cted r esponse or n ot. If th a t is n o t possible, NN will be trained a g a i n . T h e b a s i c a r c h i t e c t u r e o f t h e a r t i f i c i a l n e u r a l n e t w o r k consists o f an input f u n cti on, w hich can b e in the for m o f bi nary, continuo us or nor mal i zed dat a [ 36 ]. Comparison of artificial neural network, fuzzy logic and genetic algorithm for cutting temperature and surface process …   Advances in Production Engineering & Management 15(2) 2020  143 T h e d i s t r i b u t i o n o f d a t a u s e d f or n etwork training, v alidation o r testing w a s as f ollows: 70 % o f t h e d a t a i s t r a i n i n g , 1 5 % d a t a f o r v a l i d a t i o n , a n d 1 5 % f o r t est data. A two‐layer NN with s ig‐ moid trans fer functio n i n hidden layers a nd linear transfer f unction in o utput layer (fit n et) can arbitrarily i n corporate m u ltidimensio n al m appin g p roble m s, r egarding consistent d ata and suf‐ f i c i e n t n e u r o n s i n i t s h i d d e n l a y e r . T h e u s e d N N h a s o n e h i d d e n l a y e r w i t h 1 0 n e u r o n s . T h e n e t ‐ work is trai ned with L evenberg‐M ar kuard's return p ropagation al gorithm (trainlm). T his algo‐ rithm usuall y requires m ore memory, but less time. Cutting s p e e d v ( m/s), the fe ed p er t ooth s 1 (mm/t) a nd the c utting d epth a ( m m ) are us ed a s input data. These inpu t data a re g rou p ed i nto o n e w h o l e t h a t i s i n d i c a t e d IN = (v, s 1 , a ). O utput data a re Q a n d R a a r e n o t g r o u p e d , b u t a n e w network is created f or e ach one indivi d ually. Due t o that, m ode ls that w e re m ade were t ype 3‐1, three inp u ts and one out put, Fig. 5. F i g . 6 s h o w s a r e g r e s s i o n d i a g r a m i n t h e n e u r a l n e t w o r k t r a i n i n g p r o c e s s , w h e r e t h e g oa l i s t o set the value of the r egression coefficient to b e close to 1, th e r e g r e s s i o n l i n e s h o u l d b e a t a n a n ‐ gle of 4 5  , while most o f the data f rom which the network is trained w ith s h o u l d b e a l o n g t h e line o f regression. W h e n t h e n e t w o r k t r a i n i n g i s c o m p l e t e d , s i m u l a t i o n o f t h e n e u r a l networ k can b e p erformed. It i s necessary to define i nputs (TestIn) , w h i c h a r e c r e a t e d o n t h e b a s e o f T a b l e 4 , a n d b a s e d o n t h o s e i n p u t s t o p e r f o r m s i m u l a t i o n a n d g e t n e w g e n e r a t e d o u t p u t process characteristics (Test_outputs ). Fig. 5 Model of formed neural networks Fig. 6 Diagram of regression in the pro cess of t raining a neural network 4.2 Fuzzy logic‐based model   Implement a t i on of t h e m odel b ased o n fuz z y logic of t he M amdani type consists o f sever a l steps, w h e r e i t i s n e c e s s a r y t o g i v e a c o n t r i b u t i o n i n t e r m s o f e d i t i n g m e m b e r s h i p f u n c t i o n s a n d a p ‐ propriate rules. On t hese b as es, the fuzz y in fere nce syste m c omes t o an e diting, a n d t h e r e i s a graphical representation o f the appropriate solut i ons. Mamd ani type i mpli es that the l a nguage values o f the output v ariable are r e gul a r fuzz y sets, where it is n e ce ssa ry to de f i ne the numbe r of i n p u t s , t h e n a m e s o f t h e i n p u t a n d o u t p u t v a r i a b l e s . As w ith the neur al n et work, there are three input variabl e s (v, s 1 , a ) and the tw o output variabl es (Q, R a ) in face milling. Savkovic, Kovac, Rodic, Strbac, Klancnik    144  Advances in Production Engineering & Management 15(2) 2020 Fig. 7 Editor of fuzzy inference system Editor o f membership f unction enables the display and modificat ion of a ll member ship f unc‐ tions, input and output variables for th e e ntire fuz z y inferenc e s y stem, Fi g 7. For the set problem, the G aussian ( gaussmf) m embership function f or e ach vari abl e i s de‐ fined. G aussi an m embers hip function is t he f uncti on most c o m monl y u s e d i n m o d e l l i n g b y u s i n g t h e f u z z y i n f e r e n c e s y s t e m [ 2 6 , 2 7 ] . T h i s s y m m e t r i c G a u s s i a n f u nction dep e nds on two parame‐ ters σ and C t hat n eed t o be de f ined i n th e proc ess of modelin g, Eq. 1. ;, (1) After accepting the rules compre hensible to the pr ogram pack age, t h a t i s , t h e h i g h e s t v a l u e o f the input parameter is r epresent ed n umerically +1.41 w ritten in a n a t t r ib u t e f o rm w it h Highest, respectively: +1 with High , 0 with Medium , ‐1 with Low a n d ‐ 1 . 4 1 w i t h Lowest definin g a ppropri‐ ate fuz z y set is perform ed . The rules ar e defined so t hat the data t hat define t he c utting t e mper ature are divided into 6 fuzzy subsets labelled (A, B, C , D, E , F) t hat group the approx im ate outp ut v alues arra nged b y the Gaussian d is tribution. For the second o utput proc ess characte ristic, 9 fuzz y sets ( A, B, C , D, E , F, G, H, I) are defin ed accor d ing to the same principle. A c c o r d i n g l y , t h e f i n a l r u l e u n d e r s t a n d a b l e f o r f u z z y l o g i c i s : if speed is l o w e r a n d feed is l ower and depth i s l o w e r , t h e n s u r f a c e r o u g h n e s s i n t h e s e t C , t h i s i s t h e f i r s t o r d e r . T h i s w a y , t h e o t h e r rules, all 21 of them, are defined, T able 5. Table 5 The m odified table with corresponding subsets No. Factor Measured value s v (m/s) s 1 (mm/t) a (mm) Q ( C) Ra (µm) 1 ‐1 ‐ 1 ‐ 1 A C 2 1 ‐1 ‐1 B D 3 ‐1 1 ‐1 B G 4 1 1 ‐ 1 B F 5 ‐1 ‐ 1 1 C C 6 1 ‐1 1 D C 7 ‐1 1 1 D H 8 1 1 1 E G 9 0 0 0 C E 10 ‐1.41 0 0 B D 11 1.41 0 0 D E 12 0 ‐1.41 0 B B 13 0 1.41 0 D I 14 0 0 ‐ 1.41 A E 15 0 0 1.41 E E 16 ‐1.41 ‐1.41 ‐ 1.41 B A 17 ‐1.41 1.41 1.41 F G 18 0 1.41 ‐1.41 D H 19 1.41 ‐1.41 1 .41 F B 20 1.41 0 ‐ 1.41 D E 21 1.41 1.41 0 F H       Comparison of artificial neural network, fuzzy logic and genetic algorithm for cutting temperature and surface process …   Advances in Production Engineering & Management 15(2) 2020  145 4.3 Genetic algorithm‐based model  Predefin ed s econd‐order m odel, obt a i n e d b a s e d o n a p r e v i o u s r e g ression a nalysis based on the design o f th e exp e rime n t , was used t o model th e functio n o f Q ( c u t t i n g t e m p e r a t u r e ) a n d Ra (arithmetic mean rough ness): 2 3 When d eter minin g t he a ppropriate shape o f t he m odel, the geneti c al gorithm method s tarts f r o m t h e i n i t i a l r a n d o m p o p u l a t i o n P (t ). Populatio n P (t) i s c o m p o s e d o f o r g a n i s m s . E a c h o r g a n ‐ ism is one o f the possible solutions t o the problem and consist s of r eal const a nts (gens): C 1 , x 1 , x 2 , x 3 , C 2 , x 4 , x 5 , x 6 . Based on already per f or med examin ations a nd c alculations b ased on regr ession an alysis, as w e l l a s d u e t o f a s t e r d e t e c t i o n o f t h e o p t i m a l s o l u t i o n , t h e l i m i t s i n t h e s e a r c h a r e a h a v e b e e n introduced. Thus, the positioning o f possible solutions, the co efficients f o r d eterminin g t ool s ta‐ bility, are l o calized to: 60 ≤ C 1 ≤ 8 0 ; 0.1 ≤ x 1 ≤ 0.5; 0 .1 ≤ x 2 ≤ 0.5 ; 0.1 ≤ x 3 ≤ 0.5. A f t e r g e n e r a t i n g t h e i n i t i a l p o p u l a t i o n , t h e i t e r a t i v e p r o c e d u r e of s electi o n , recombin ation (crossover) a nd m utatio n is carried o ut until th e c onver ge nce c riterion is s atisfied, Fig. 8. Fig. 8 Principle o f the genetic algorithm Deter m ining the interactions that occur among differ e nt G A param e t e r s h a s a d i r e c t i m p a c t o n t h e q u a l i t y o f t h e s o l u t i o n a n d k e e p i n g p a r a m e t e r s v a l u e s balanced improves the s o lution of t he GA. For mac hining proc ess modeling, GA w ith the following p aram eters was used: p o pulation size 150, crossover rate 0.8, mu tati on rate 0.03 and number of gen e ratio ns 10 00. The only difference betw een m odelli ng t he f uncti on for cutti n g te mperat u r e and arith m etic mean r oughness is p recisely i n the values o f the search a rea li mits. Thus, the deter m i n ation of the coe fficie n ts t hat ar e represented in t he e quati on for t h e a r ithmetic mean roughness are set to the constr aints in term s of t h e li mit s : 1 0 ≤ C 2 ≤ 2 0 ; ‐ 0 .5 ≤ x 4 ≤ 0.5; 1 ≤ x 5 ≤ 1.5; ‐ 0.5 ≤ x 6 ≤ 0.5. After gener a ting t he o pti m al c onstant s through the genetic algor i t h m s , t h e E q s . 4 a n d 5 h a v e the fi nal for m : Q 72 .551 . . . 4 ɑ 12 . 337 . . . 5 Savkovic, Kovac, Rodic, Strbac, Klancnik    146  Advances in Production Engineering & Management 15(2) 2020 5. Results and discussion  The quantit a tive p redictive potenti a l E, t h e E q . 6 i s e v a l u a t e d d u e t o p e r c e n t a g e o f d e v i a t i o n between th e obtai n ed v alues (usi ng t he c orrespo n ding m odel ) and t h e e x p e c t e d ( e x p e r i m e n t a l ) v a l u e s f o r t h e t e m p e r a t u r e i n t h e c u t t i n g z o n e Q a n d t h e s u r f a c e r o u g h n e s s R ɑ f o r t h e d a t a o n t h e b a s i s o f w h i c h t h e t r a i n i n g o f c o r r e s p o n d i n g m o d e l s o f a r t i f i c i al i ntelligenc e was perfor med. T he results presented ar e gi ven in T able 6 a nd T abl e 7 . Th e v e r i fic ation of t he a ccurac y of thes e m o d e l s w a s p e r f o r me d on t h e b a s i s of 6 a d d i t i o na l e x p e r im en ts p erformed a ccording to the plan given in the second par t of T ables 6 and 7 . Based on t h e aver age per c entage e rror, it can be c oncluded that in both o ut put characteristics o f t h e p r o c e ss f o r t h e d a t a u s e d i n t h e t r a i n i n g of t h e c o r r e s p onding m odel, this p ercentage error d o e s n o t e x c e e d 1 0 % . T h e s i t u a t i o n i s s i m i l a r w i t h t e s t d a t a w h e r e m o d e l s u s e d f o r c u t t i n g t e m ‐ peratures Q a r e a l s o b e l o w 1 0 % , w h i l e i n a r i t h m e t i c m a i n r o u g h n e s s R a o b t a i n s a m a x i m u m deviation of 14 % using an a rtif icial neural n etwor k ‐based m ode l. C omparing a ll three models, it i s c o n c l u d e d t h a t l o o k i n g a t b o t h o u t p u t c h a r a c t e r i s t i c s o f t h e p rocess, the s mallest e rror was made b y th e model b a sed on fu zzy l ogic. Conseq uently, it is rec ommend ed t hat th e knowledge base, b a sed on artificial i ntelli ge nce i s recom men d built into the appropriate process systems.       ∗ 100 %; 1 … ,   ;    6 Table 6 Comparison of NN, FL, a nd GA pr edictive models for cutting tem perature Q Training data No.  Exp. ( C)  N.N. ( C) E (%)  F.L. ( C) E (%)  G.A. (C ) E (%) 1 46 48.80 6.1 48.82 6.13 48.06 4.48 2 52 52.32 0.61 54.17 4.17 55.55 6.82 3 53 54.24 2.35 54.16 2.18 55.06 3.88 4 56 56.67 1.19 54.07 3.44 63.64 13.64 5 60 60.03 0.05 62.29 3.81 62.22 3.69 6 67 67.13 0.19 67.50 0.74 71.91 7.33 7 70 69.94 0.09 67.50 3.58 71.27 1.82 8 77 77.15 0.19 75.98 1.33 82.38 6.98 9 60 60.64 1.06 61.42 2.38 62.99 4.99 10 54 53.87 0.24 53.95 0.09 54.81 1.49 11 65 64.85 0.23 62.03 4.57 72.42 11.41 12 55 55.16 0.29 53.95 1.91 54.95 0.09 13 66 79.13 19.89 67.50 2.27 72.18 9.37 14 47 45.03 4.19 48.94 4.12 48.75 3.73 15 76.5 75.65 1.11 76.00 0.65 81.41 6.42 16 51 51.26 0.51 53.48 4.86 36.99 27.46 17 108 117.68 8.96 101.00 6.48 81.16 24.85 18 66 59.50 9.84 67.50 2.27 55.86 15.36 19 98 97.97 0.03 101.00 3.06 81.63 16.69 20 66 65.99 0.01 67.49 2.26 56.05 15.08 21 94 93.92 0.08 100.96 7.41 82.98 11.72 Average error  2.72 3 .22 9 .39 Testing data 1 51 48.84 4.23 48.058 5.77 55.30 8.44 2 69 65.53 5.03 64.94 5.88 71.59 3.76 3 55 54.98 0.04 55.01 0.02 58.83 6.97 4 62 54.88 11.48 56.81 8.36 67.39 8.71 5 57 55.03 3.45 54.54 4.32 58.62 2.84 6 60 53.96 10.06 56.29 6.18 67.75 12.92 Average error  5 .72 5 .09 7 .27 Comparison of artificial neural network, fuzzy logic and genetic algorithm for cutting temperature and surface process …   Advances in Production Engineering & Management 15(2) 2020  147 Table 7 Comparison of NN, FL, a nd GA pr edictive models for arithmetic mean ro u ghness Ra Training data No. R ɑ Exp. (μ m) R ɑ N.N. (μ m) E (%) R ɑ F.L. (μ m) E (%) R ɑ G.A. (μ m) E (%) 1 1.074 1.071 0.24 1.048 2.38 1.075 0.11 2 1.081 1.075 0.53 1.129 4.53 1.045 3.29 3 1.743 1.418 18.63 1.707 2.04 1.769 1.49 4 1.645 1.643 0.09 1.517 7.8 1 .720 4.56 5 1.058 0.617 41.66 1.066 0.74 1.059 0.11 6 1.023 1.313 28.33 1.057 3.36 1.029 0.68 7 1.898 1.751 7.74 2.002 5.48 1.742 8.18 8 1.734 1.733 0.08 1.722 0.68 1.695 2.27 9 1.205 1.205 0.02 1.244 3.2 1 .352 12.19 10 1.133 1.135 0.21 1.141 0.72 1.389 22.58 11 1.244 1.245 0.1 1 .241 0.26 1.316 5.78 12 0.995 0.999 0.37 1.003 0.84 0.819 17.64 13 2.522 2.488 1.35 2.552 1.19 2.226 11.73 14 1.242 1.237 0.37 1.240 0.14 1.372 10.47 15 1.229 1.218 0.88 1.240 0.9 1 .332 8.38 16 0.915 0.909 0.68 0.940 2.77 0.850 7.10 17 1.705 1.707 0.12 1.725 1.17 2.253 32.15 18 2.023 2.017 0.3 2 .011 0.61 2.259 11.68 19 0.969 1.029 6.21 0.996 2.79 0.786 18.89 20 1.258 1.259 0.08 1.240 1.41 1.336 6.17 21 1.94 1.944 0.19 2.011 3.64 2.167 11.69 Average error  5.15 2 .22 9.39 Testing data 1 1.222 1.253 2.51 1.241 1.50 1.362 11.47 2 1.28 1.022 20.12 1.328 3.73 1.342 4.84 3 1.037 0.911 12.12 1.053 1.59 1.052 1.48 4 1.583 1.763 11.39 1.611 1.79 1.731 9.37 5 1.263 1.124 10.99 1.143 9.54 1.371 8.54 6 1.734 1.240 28.46 1.257 27.51 1.333 8.02 Average error  14.26 7 .61 7 .29 A nother analysis o f the accuracy o f th e correspon ding m odels w as p erfor m ed b ased on sim‐ p l e l i n e a r r e g r e s s i o n . F i g s . 9 a n d 1 0 s h o w d i a g r a m s o f a c t u a l a n d p r e d i c t e d v a l u e s a s w e l l a s t h e calculated c o efficient of d etermi nation for each proposed model . Based on the an aly s is o f the coefficient o f d etermin a ti on in d efini n g the m o st a ccurate m od el f o r p r e d i c t i n g t h e c u t t i n g t e m ‐ perature Q , the following c an b e stated: the fuzzy logic model gave the b est match of a ctual and predicted values (R 2 = 0 . 9 8 2 ) , n e x t t h e n e u r a l n e t w o r k m o d e l (R 2 = 0 .945), and finally t he m ost unfavour abl e p rediction comes fr om a m od el b as ed on GA. In t his c a s e , t h e f i r s t t w o m o d e l s a r e acceptabl e for further implementation in process systems, while the GA model should be avoided. F i g . 1 0 a l s o s h o w s a n a n a l y s i s o f d e v i a t i o n o f t h e v a l u e s o f t h e arithm etic m e a n rou g h n ess, w h e r e i t i s c o n c l u d e d t h a t t h e f u z z y l o g i c m o d e l g i v e s a c o m p l e tely c orrect r epresentation of t he a c t u a l a n d p r e d i c t e d v a l u e s w i t h a v e r y h i g h c o e f f i c i e n t o f d e t ermin a tion. T he v alu e s for the ot h‐ er two m ode l s based o n t he m em bers hip interv al b elon g to the do mai n o f good correlati on. Fig. 9 Diagram of actual and pr e dicted values for cutting t emperature Savkovic, Kovac, Rodic, Strbac, Klancnik Fig. 10 Diagram of the actual and predicted values for the arithmetic mean roughness Based on the overall analysis, taking into account the values based on the quantitative predic- tive potential E as well as the coefficient of determination R 2 , it is concluded that the models based on fuzzy logic are the most suitable for further use. 6. Conclusion By modeling the machinability functions of the milling process, i.e., the machining conditions and the output characteristics of the process, the conditions for a predict control and optimize process parameters have been created. The modeling process was performed using artificial intelligence based methods. Models were realized by artificial neural networks, fuzzy logic and genetic algorithms with the analysis of the accuracy. The obtained models for each machinability function were analyzed and on the basis of least error of deviation, the best model is proposed. An analysis was also performed in terms of the values of the coefficient of determination for each individual model as a function of the corresponding characteristics of the face milling pro- cess. The verification of the accuracy of the model was performed on the basis of additional ex- periments, which were not used in training phase. Based on a comprehensive analysis, it can be concluded that the application of the Fuzzy logic is the most adequate in the examined process. A further recommendation would be in the application of artificial neural networks in the first place, and then genetic algorithms in the second place. The successful theoretical and experimental research has demonstrated the applicability of new modeling methods to milling processes. Also, models developed using artificial intelligence tools have a potential application in the industry. Consequently, the results of this research have their significance in that view, i.e., they can be integrated into manufacturing systems within which the tools of the integrated memory for the knowledge base are represented. References [1] Klancnik, S., Begic-Hajdarevic, D., Paulic, M., Ficko, M., Cekic, A., Husic, M.C. (2015). 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