Expert Systems with Applications 40 (2013) 6877–6884

Contents lists available at SciVerse ScienceDirect

Expert Systems with Applications

journal homepage: www.elsevier .com/locate /eswa

An expert system for setting parameters in machining processes

0957-4174/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.eswa.2013.06.051

⇑ Corresponding author. Tel.: +52 01 81 83294020.E-mail addresses: luis.torres.ciidit@gmail.com (L.M. Torres-Treviño), indiraesca

milla@gmail.com (I.G. Escamilla-Salazar), bgzzortiz@gmail.com (B. González-Ortíz),rolando_praga_alejo@uadec.edu.mx (R. Praga-Alejo).

1 Tel.: +52 01 81 83294020.2 Tel.: +52 01 84 41715002.

Luis M. Torres-Treviño a,⇑, Indira G. Escamilla-Salazar b,1, Bernardo González-Ortíz b,1,Rolando Praga-Alejo c,2

a Universidad Autónoma de Nuevo León, UANL, FIME, CIIDIT Av. Universidad S/N Ciudad Universitaria San Nicolás de los Garza Nuevo León, C.P. 66451, Mexicob Universidad Autónoma de Nuevo León, UANL, FIME Av. Universidad S/N Ciudad Universitaria San Nicolás de los Garza Nuevo León, C.P. 66451, Mexicoc Facultad de Sistemas, Universidad Autónoma de Coahuila, Ciudad Universitaria, Carretera a México Km 13, Arteaga, Coahuila, Mexico

a r t i c l e i n f o a b s t r a c t

Keywords:Expert systemsSymbolic regressionProcesses modellingMachining processes

In this paper, an hybrid system is proposed for setting machining parameters from experimental data. A sym-bolic regression alpha–beta is used to build mathematical models. Every model is validated using statisticalanalysis then evolutionary computation is used to minimize or maximize the generated model. Symbolicregressiona–b is used to build mathematical models by estimation of distribution algorithms. A practical caseconsidering measured data of two machining process on three materials are used to illustrate the utility of theexpert system because generates a set of parameters that improve the machining process.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Setting machining parameters is a complex task because a val-idated model of the process is required, then a kind of a search pro-cedure is used on the model to establish a proper set of inputparameters. There are several forms to generate models; however,mathematical models are not black boxes. Neural networks couldbe a very precise model; however, they are black boxes where a ex-plicit formulation about the correlation between variables and theeffects on output response is not evident.

Linear regression could provide a good decision criteria aboutthe impact of the input machining parameters on output response;however, in some cases, could generate poor models for predic-tions. Setting parameters of a process is equivalent to optimize afunction, we establish a criteria about the function to maximizeits response or minimize a cost derived from the function, perexample; then a optimization tools can be applied.

Symbolic regression with genetic programming (GP) are com-monly used for this purpose; however, there are several drawbackslike complexity to manipulate tree data structures, tendency togenerate very large tree structures and consequently high CPUtime consuming; otherwise, GP could generate compact formulaseliminating some variables that could be considered as useless.

In this paper the expert system proposed works with turningand milling processes. With little adaptations can be used in

another processes inclusive not machining ones. Some machiningsystems are a challenge because there are a variety of parametersand materials that define the performance of the process. Turningis one of the most used process in machining and setting parame-ters in this process is made by experience, following tables frombuilders, or by trial and error. More advanced approaches havebeen used like experimental design and robust experiments(Motorcu, 2010), response surface methodology (Bhushan, 2013;Chauhan & Dass, 2012; Villeta, de Agustina, & Manuel Saenz dePipaon, 2012), analysis of variance or ANOVA (Aouici, Yallese, &Fnides, 2011), grey relational theory or grey analysis (Ranganathan& Senthilvelan, 2011) and Taguchi methods (Gaitonde, Karnik, &Davim, 2009; Hanafi, Khamlichi, & Mata Cabrera, 2012; Maniraj,Selladurai, & Sivashanmugam, 2012). Other approaches requires amodel to be used with optimization tools; regression models(Liang, Ye, & Zhang, 2012), neural networks (Senthilkumaar, Selva-rani, & Arunachalam, 2012) are commonly used.

Using these models and by genetic algorithms (Jangra, Jain, &Grover, 2010) and particle swarm optimization (Raja & Baskar,2011) the machining parameters of turning processes can be set.Milling is another machining process more used too like turning.Design of experiments, Taguchi methods (Ji, Liu, & Zhang, 2012;Kadirgama, Noor, & Rahman,2012), analysis of variance (Gopalsam-y, Mondal, & Ghosh, 2009; Mustafa, 2011; Yang, Chuang, & Lin,2009) and response surface methodology (Mangaraj & Singh,2011) are the most used approaches for setting machining param-eters. Optimization approaches like particle swarm optimization(Raja & Baskar, 2012), Kriging interpolation search techniques (Le-baal, Schlegel, & Folea, 2012) have been used for setting the param-eters of milling processes too. Our proposal is based on symbolicregression, However, this approach using genetic programminghas been few used (Raja & Baskar, 2010).

6878 L.M. Torres-Treviño et al. / Expert Systems with Applications 40 (2013) 6877–6884

Considering setting of parameters as an optimization problem,different criteria has been considered. Usually surface roughnessis the principal response to determine the efficiency of the machin-ing process turning or milling, however consumption time, cuttingtemperature, tool wear are example of responses that could beconsidered to improve the machining process. In this paper, im-prove the surface roughness will be the criteria for setting theparameters.

This paper is divided in five sections; this section is the intro-duction, Section 2 is a description of an hybrid system used for set-ting parameters. Section 3 is a description of the application wherea comparison with linear regression and genetic programming ismade. Section 4 is the application of the proceed hybrid systemfor setting parameters on the machining process given in the lastsection. Finally, Section 5 includes conclusions and future work.

Fig. 2. Expert system for setting parameters on machining process.

Table 1a Operator parameters and its related mathematicalfunctions.

2. An hybrid system for modelling and optimization ofmachining processes

Setting of parameters is important in machining process be-cause could generate an improvement on quality on machinedpieces (this reflected mainly by surface roughness), material re-moval rate (MRR) reduction of time processing, tool wear ratio(TWR) and cutting temperature, and others which importance de-pends of the process (Fig. 1). Tables of machine fabricants or infor-mation given by the provider of the material to be machined givessome clues about the most suitable set of parameter that must beused; however, all the materials are not included. Another way toestablish the parameters is by the experience of the user, analogieswith related processes or by trial and error.

A new system is proposed using evolutionary computation anda–b operators where a model is build and validated using statisti-cal analysis on residuals, then, the same evolutionary algorithmcan be used to set the optimum set of parameters. An expert sys-tem can be build integrating these approaches as is shown in Fig. 2.

The expert system executes the following steps:

1. Establish a unique machining process and one material.2. Establish input parameters and response under study; other

inputs must be fixed.3. Capture measured data from historical records or an experi-

mental design.4. Develop models by symbolic regression a–b.5. Validate every model using residual analysis.6. Select the model considering low complexity and statistical

metrics.7. Use the model as an objective function.8. Use an evolutionary algorithm to determine optimum values.

These solution will be the ideal set of machining parametersthat would improve the process.

Fig. 1. Setting parameters properly could make improvements on the machiningprocess.

An expert system is an assistant for the user of any machiningprocesses. The requirement is the generation of an experimentaldata and a criteria about the desirable response of the process. Ex-pert system returns a set of machining parameters that satisfy thedesirable response. The measured data could comes from severalsources, historical records, or a experimental design and containsa set of parameters used on the process and the response gener-ated. Several experiments is required; however, when replicationis not possible, a percentage of the measured data can be usedfor building the model and the rest is used for validation. The ex-pert system uses an 80% of measured data for building a mathe-matical model, the rest is used for validation. Every block of theproposed expert system will be described in the followingsubsections.

2.1. Model generation by symbolic regression alpha–beta

In this approach, a mathematical equation is represented by thecombination of a and b operators. An a operators is defined as afunction that requires only one argument and applies only onemathematical operation. Considering a review of several mathe-matical models of real processes, 13 operations are chosen as aoperators (see Table 1). An a operator uses two real numberparameters called k1 and k2 and an integer that describes themathematical operation. The a operator is defined as follows:

Opraðx; k1; k2Þ ¼ aðk1 � xþ k2Þ ð1Þ

where x is an input variable and a is an operation. Depending of thea operator selected, a specific mathematical operation that requires

a Operator Mathematical operation

1 ðk1xþ k2Þ2 ðk1xþ k2Þ2

3 ðk1xþ k2Þ3

4 ðk1xþ k2Þ�1

5 ðk1xþ k2Þ�2

6 ðk1xþ k2Þ�3

7 ðk1xþ k2Þ1=2

8 ðk1xþ k2Þ1=3

9 expðk1xþ k2Þ10 logðk1xþ k2Þ11 sinðk1xþ k2Þ12 cosðk1xþ k2Þ13 tanðk1xþ k2Þ

L.M. Torres-Treviño et al. / Expert Systems with Applications 40 (2013) 6877–6884 6879

only one argument is executed; e.g., if a = 1 then the operationmade is ðk1 � xþ k2Þ, if a = 13 then the operation made istanðk1 � xþ k2Þ. The a operator is an integer number and its valuedeterminate a specific mathematical operation described in Table 1.

A b operator is defined as a function that require two argumentsand makes the four basic arithmetic operations b = c so a b operatorequal to 1 imply the plus operator or b(a,b) = a + b, and b(a,b) = a/bif b = 4.

2.1.1. Representation of operatorsBy means of a–b operators several configurations can be estab-

lished. A basic configuration can be defined when an a operator isassigned per input variable then an b operator is used to connecttwo a operators (2). Usually, a simple configuration in majorityof the cases is enough for the regression.

y ¼ bn�1ð. . . b2ðb1ða1ðx1Þ;a2ðx2ÞÞ; ÞÞ; . . . anðxnÞÞ ð2Þ

The representation required is a real vector with n element where nis equal to the number of a operators and k parameters plus b oper-ators. Using one a operator per variable and connect them by boperators, the number of parameters is given by the number of aoperators, the number of b operators and k parameters (two per aoperator). In a basic structure is a + b + 2 ⁄ a, because b = a � 1,and a = number of variables (Nv) then the number of parametersis Nv + (Nv � 1) + 2 ⁄ Nv. A normalized real vector can be used torepresent operators and k parameters, but a and b operators areintegers, so is required the following formulation to get its value:

a ¼ dVðiÞ � 13þ 0:5e ð3Þb ¼ dVðiÞ � 4þ 0:5e ð4Þ

where d.e is the ceiling function. There are 13 a operators defined inTable 1 and 4 b operators (basic algebraic operations) Consider thefollowing example; the vector of parameters is V ¼ ½0:854 0:1240:456 0:232 0:987 0:654 0:0234� for two variables, so two aoperators, one b operator and four k parameters are represented.Decoding is as follows: first a and b operators are decoded usingthe first elements of the vector, then the k parameters are repre-sented on the rest of the elements.

a1 = dV(1) ⁄ 13 + 0.5e = d(0.854 ⁄ 13 + 0.5)e = 12 this representsa cos function,a2 = d(V(2) ⁄ 13 + 0.5)e = d(0.124 ⁄ 13 + 0.5)e = 3 this representsa cubic exponential,b1 = d(V(3) ⁄ 4 + 0.5)e = d(0.456 ⁄ 13 + 0.5)e = 3 this represents amultiplication,k11 = V(4) = 0.232,k21 = V(5) = 0.987,k12 = V(6) = 0.654,k22 = V(7) = 0.0234.

The formulation represented is:

y ¼ cosðk11x1 þ k12Þ � ðk12x2 þ k22Þ3 ð5Þ

In this work, Evonorm is used to solve the problem of selectionthe suitable parameters (k’s) and integers to define a and boperations.

2.2. Evolutionary algorithm Evonorm

Evonorm is an easy way to implement an estimation of distribu-tion algorithm (Torres-T, 2006, Torres-Trevino, 2006). As a evolu-tionary algorithm selection of new individuals and thegeneration of a new population is used; however, the crossoverand mutation mechanism is substituted by an estimation of

parameters of a normal distribution function. The following stepsare used in Evonorm:

1. Evaluation of a population P.2. Deterministic selection of individuals from P to PS.3. Generation of a new population using PS.

A population P is a matrix of size Ip (total of individuals) and Dr

(total of decision variables). A solution is a set of decision variablesand this set is represented as a real vector. Every row of the popu-lation P represents a set of decision variables. The selection mech-anism is deterministic because the most fittest individuals areselected. Usually the number of selected individuals are lower thanthe number of the original population, usually a 20% or 10% of thetotal population. A random variable with normal distribution isestimated per decision variable, so a marginal distribution functionis used. Two parameters are estimated, the mean and the standarddeviation, that is determined using the values of the selected indi-viduals. The population of selected individuals is a matrix Ps of sizeIs (total of individuals selected) and Dr. Eqs. (6) and (7) are used tocalculate the mean and standard deviation considering every vec-tor of the population Ps.

lpr ¼XIs

k¼1

ðPspr;kÞ=Is ð6Þ

rpr ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXIs

k¼1

ðPspr;k � lprÞ2

!,Is

vuut ð7Þ

where pr ¼ 1; . . . ;Dr .A new population is generated using the estimated normal ran-

dom variables. This is a stochastic process, however, an heuristic isused to maintain an equilibrium between exploration and exploi-tation, so new solutions can be found not necessarily near of themean calculated. The best solution found Ix at the moment is in-volved in the generation so in the 50% of the times the mean isused in the calculations and in the other 50% of the time the bestsolution found Ix is used as a mean as is shown in the followingequation:

Pi;pr ¼Nðlpr;rprÞ UðÞ > 0:5NðIxpr ;rprÞ otherwise

�ð8Þ

The random variable U() has a uniform distribution function, N() is arandom variable with a normal distribution function.

2.3. Residual analysis

One effective way to validate a regression model is to collectnew experimental data to determine how well the model performsin practice (Douglas, 2007). The most simple measure is the resid-ual calculated as the difference (e(i)) between new observationsmade by the response of the process y(i) and predicted responsegenerated by the regression model made yðiÞ (Eq. (9)).

eðiÞ ¼ yðiÞ � yðiÞ ð9Þ

The PRESS (prediction error sum of squares) is a measure of howwell a model works to predict new data. Usually a small value ofPRESS is desirable (10). In this case, the PRESS is obtained usingcross validation.

PRESS ¼Xn

i¼1

ðyðiÞ � yðiÞÞ2 ð10Þ

The percentage of variability R2pred is a measurement for indicat-

ing the efficiency of the model to predict new observations. A valuenear of one is desirable on this indicator (11).

6880 L.M. Torres-Treviño et al. / Expert Systems with Applications 40 (2013) 6877–6884

R2pred ¼ 1�

Pni¼1ðyðiÞ � yðiÞÞ

y0y�Pn

i¼1yðiÞ� �2 ð11Þ

2.4. Model selection and optimization

Complexity is determinate adding all the a and b operators usedin the chosen configuration. Cx ¼

Pni¼nða1 þ a2 þ � � � þ an þ b1 þ b2

þ � � � þ bn�1Þ. Percentage of variability R2pred is calculating with 20%

of non used data for model building. A selection with lower com-plexity and with near to one variability percentage is preferred.The objective function uses the chosen model generated to maxi-mize or minimize it. In general, a minimization is more used inmachining, so this is the criteria used.

3. A case of application for setting parameters

As an illustration of the proposal, a setting of parameters of twoprocesses will be made considering two different materials, alu-minium and steel. An experimental design is made consideringone type of aluminium and two types of steel. First, the machiningof the pieces was made using a turning machine model Okuma

Fig. 3. A turning machine of two axis of CNC Okuma LB15.

Fig. 4. Cylinder to be machined made of three materials, Aluminium 6062, Steel1018 and Steel 4140.

LB15 (Fig. 3). A tool type DNMG 432 PG of grade RC8025 was usedfor steel and a tool type DNMG 432 GP of grade CQ23 was used foraluminium. Three kinds of materials were machined made of Alu-minium 6061, Steel 1018 and Steel 4140 of cylindric form as isshown in Fig. 4. Roughness was measured using a roughmeterMitutoyo SJ-301 (Fig. 5) considering the configuration shown inFig. 6. Experimental data is shown in Table 2.

For milling, the machining of the pieces was made using a mill-ing machine model EMCO PC MILL 125 (Fig. 7). A steel tool for fastmilling of 9.6 � 9.6 mm was used for all materials. Pieces of plateform were used for machining considering three kind of materials,Aluminium 6062, Steel 1018 and Steel 4140 (Fig. 8). Roughnesswas measured using the same roughmeter Mitutoyo SJ-301(Fig. 4) considering the configuration shown in Fig. 9. Experimentaldata is shown in Table 3.

3.1. Model generation and comparison using genetic programming andlinear regression

Other paradigms can be used to generate mathematical modelslike linear regression and genetic programming.

Genetic programming uses the following operations fþ;�;�; =; exp; logg for all nodes and is executed ten times considering200 individuals, a simple crossover with a probability of 0.9 and

Fig. 5. A roughmeter Mitutoyo SJ-301.

Fig. 6. Use of the roughmeter on every machined cylinder.

Table 2A sample for experimental data from turning process in Aluminium 6066.

Turning speed (rpm) Feed (mm/min) Roughness (lm)

800 50 3.52800 60 3.15

1000 50 3.071000 60 2.05

Fig. 7. Machining centre EMCO PC MILL 125.

Fig. 8. Plates to be machined made of three materials, Aluminium 6062, Steel 1018and Steel 4140.

Fig. 9. Use of the roughmeter on every machined plate.

Table 3A sample for experimental data from milling process in Aluminium 6066.

Milling speed (rpm) Feed (mm/rev) Roughness (lm)

1900 0.15 2.001900 0.2 2.322500 0.15 2.352500 0.2 2.84

Table 4Statistical metrics results of the best model found of milling with Aluminium 6061 forlinear regression, genetic programming and symbolic regression a–b.

MSE PRESS R2pred

CPU time

Linear regression 0.0030287 0.3028737 0.9901096 0.016Genetic programming 0.0491388 4.9138771 0.8386150 92.55Symbolic regression a–b 0.0005289 0.0528947 0.9980849 40.618

L.M. Torres-Treviño et al. / Expert Systems with Applications 40 (2013) 6877–6884 6881

a simple mutation with a probability of 0.05. There are the samenumber of evaluations in both evolutionary algorithms and statis-tical metrics MSE, PRESS and R2

pred is calculated in every run. An 80%of the experimental data is used for model building and the rest isused for validation. Linear regression is executed under the sameconditions.

Operators and parameters are set by Evonorm with a popula-tion of 200 individuals, 50 are selected for generating a new popu-lation and ten runs are made per model, per process (turning andmilling) considering three different materials as was describedabove. Linear regression could give in some cases good models,for description about the impact of every variable; however, ingeneral PRESS and R2

pred makes linear regression useless forprediction.

Genetic programming in general generate best model that lin-ear regression, and in all cases, some variables are vanished in finalexpression generating very compact models, however, their perfor-mance is poor in general. When a model has a better performance,the solution is a very large tree with mathematical model is diffi-cult for extracting. In this cases the population of trees could behuge that the solution is generated after several hours of process-ing. A resume of the performance of the algorithm considering themodelling of two process on three different materials and takingthe best solution found in ten runs is shown in Tables 4–6, for mill-ing and Tables 7–9 for turning. CPU time is an average of ten runsusing a Laptop with Core Duo 2.53 GHz 4 GB RAM.

4. Expert system procedure and results

A mathematical model using symbolic regression are generatedconsidering the same conditions mentioned above, the same size ofthe population, 50 individuals are selected during 200 generations;ten runs are made per run. Considering the solutions shown inTables 10–12 for milling in every run, a criteria of low complexity,low error, high R2

pred and low PRESS can be taken here. The same cri-teria is applied for Tables 13–15 for turning.

For milling, three models are generated considering the ma-chined material. All the equations are normalized. Roughness isy, speed is x1 and feed is x2.

For Aluminium 6061, we have

Table 5Statistical metrics results of the best model found of milling with Steel 1018 for linearregression, genetic programming and symbolic regression a–b.

MSE PRESS R2pred

CPU time

Linear regression 0.0236724 2.3672411 0.9306629 0.021Genetic programming 0.0491388 4.9138771 0.8386150 39.531Symbolic regression a–b 0.0195774 1.9577388 0.9529272 40.934

Table 6Statistical metrics results of the best model found of milling with Steel 4140 for linearregression, genetic programming and symbolic regression a–b.

MSE PRESS R2pred

CPU time

Linear regression 0.0059471 0.5947055 0.9813306 0.0153Genetic programming 0.0491388 4.9138771 0.8386150 42.30Symbolic regression a–b 0.0005041 0.0504113 0.9981101 40.856

Table 7Statistical metrics results of the best model found of turning with Aluminium 6061for linear regression, genetic programming and symbolic regression a–b.

MSE PRESS R2pred

CPU time

Linear regression 0.0523688 5.2368846 0.7925297 0.016Genetic programming 0.0529369 5.2936912 0.7989021 92.790Symbolic regression a–b 0.0004856 0.0485555 0.9979643 40.701

Table 8Statistical metrics results of the best model found of turning with Steel 1018 for linearregression, genetic programming and symbolic regression a–b.

MSE PRESS R2pred

CPU time

Linear regression 0.0457490 4.5748993 0.8525413 0.016Genetic programming 0.0243881 2.438806 0.9252607 579.772Symbolic regression a–b 0.0323083 3.2308277 0.8976131 40.903

Table 9Statistical metrics results of the best model found of turning with Steel 4140 for linearregression, genetic programming and symbolic regression a–b.

MSE PRESS R2pred

CPU time

Linear regression 0.0199622 1.9962207 0.8584523 0.0153Genetic programming 0.0283335 2.8333484 0.8332333 2195.6904Symbolic regression a–

b0.0162632 1.6263237 0.8908043 49.515

Table 10Results of ten runs of symbolic regression alpha–beta for milling Aluminium 6061.

a1 a2 b MSE R2pred

PRESS

11 5 4 0.0011296 0.9967026 0.11296147 5 4 0.0006714 0.9974672 0.0671430

13 2 1 0.0005888 0.9975424 0.05888475 5 4 0.0005289 0.9980849 0.0528947

14 13 1 0.0018420 0.9935738 0.18419674 2 3 0.0006127 0.9980507 0.0612711

12 6 4 0.0011334 0.9962571 0.113336211 6 4 0.0024164 0.9903811 0.2416421

7 5 4 0.0007495 0.9975683 0.074949412 5 4 0.0008007 0.9974256 0.0800666

Table 11Results of ten runs of symbolic regression alpha–beta for milling Steel 1018.

a1 a2 b MSE R2pred

PRESS

4 13 3 0.0209661 0.9390914 2.096614612 6 4 0.0214648 0.9052506 2.146483714 3 1 0.0259359 0.9094338 2.593591212 13 3 0.0195774 0.9529272 1.9577388

5 3 3 0.017311 0.9483113 1.73110439 3 3 0.0162659 0.9432159 1.62659486 6 4 0.0154997 0.9518511 1.54997294 6 4 0.0170191 0.9372961 1.7019099

12 6 4 0.018132 0.9324922 1.81320416 3 3 0.0276132 0.8889107 2.7613215

Table 12Results of ten runs of symbolic regression alpha–beta for milling Steel 4140.

a1 a2 b MSE R2pred

PRESS

8 5 4 0.0021494 0.9908533 0.214943514 2 1 0.0022462 0.991981 0.224615513 10 1 0.0146767 0.9498346 1.467665411 5 4 0.001097 0.9951337 0.109701911 5 4 0.0013498 0.9937916 0.1349795

8 2 3 0.0013676 0.9947859 0.1367617 2 3 0.0028836 0.9891096 0.28835681 5 4 0.0017874 0.9930169 0.17874428 5 4 0.0043414 0.9836714 0.43414319 2 3 0.0012989 0.995129 0.1298891

Table 13Results of ten runs of symbolic regression alpha–beta for milling Aluminium 6061.

a1 a2 b MSE R2pred

PRESS

7 13 3 0.0010347 0.99479 0.103466512 2 3 0.0005041 0.9981101 0.0504113

6 2 3 0.0004064 0.9983851 0.040635614 13 1 0.0018067 0.9910046 0.180673513 5 4 0.0007144 0.9968789 0.071443712 2 3 0.0009399 0.9966245 0.093990412 5 4 0.0006481 0.996913 0.0648124

8 5 4 0.0010296 0.996366 0.10295656 5 4 0.0004856 0.9979643 0.04855558 12 2 0.0020598 0.9921834 0.2059798

Table 14Results of ten runs of symbolic regression alpha–beta for milling Steel 1018.

a1 a2 b MSE R2pred

PRESS

6 8 3 0.0337285 0.892393 3.372851312 8 3 0.0391265 0.8653603 3.912654412 11 3 0.048081 0.8531595 4.8081002

4 10 1 0.0486094 0.8369558 4.86094296 8 3 0.0396538 0.8923186 3.9653846 1 3 0.0532958 0.8306899 5.32958415 8 3 0.0323083 0.8976131 3.23082774 7 3 0.034634 0.8861678 3.46340266 9 4 0.0864425 0.7309233 8.6442534

12 1 3 0.0454872 0.8329595 4.548721

6882 L.M. Torres-Treviño et al. / Expert Systems with Applications 40 (2013) 6877–6884

f ðx1; x2Þ ¼ðk12x2 þ k22Þ2

ðk11x1 þ k21Þð12Þ

where k12 = 0.0498725, k22 = 0.9644290, k11 = 0.8097590, k21 =0.1797934 extracted from the best solution found.

For Steel 1018, we have

f ðx1; x2Þ ¼ðk12x2 þ k22Þ3

ðk11x1 þ k21Þ2ð13Þ

where k12 = 0.1051453, k22 = 0.9538366, k11 = 0.4660222, k21 =0.5070503 extracted from the best solution found.

For Steel 4140, we have

Table 15Results of ten runs of symbolic regression alpha–beta for milling Steel 4140.

a1 a2 b MSE R2pred

PRESS

12 13 3 0.0188565 0.8699418 1.885647612 13 3 0.0179713 0.8559073 1.797129812 6 4 0.0185873 0.8866734 1.858733

4 13 3 0.017213 0.8736789 1.721296912 13 3 0.0190084 0.8848498 1.9008436

6 3 3 0.0183304 0.8846421 1.833041212 1 3 0.024155 0.8804958 2.4154957

4 3 3 0.022798 0.8791102 2.279796712 7 3 0.0223528 0.8630962 2.235276810 10 4 0.0162632 0.8908043 1.6263237

Table 16Optimum machining parameters for milling Aluminium 6061, Steel 1018 and Steel4140.

Material Speed (rpm) Feed (mm/min) Roughness (lm)

Al 6061 2500 0.15 2.7694945St 1018 1464.5425 0.15 1.92St 4140 720 0.15 1.7946024

Table 17Optimum machining parameters for turning Aluminium 6061, Steel 1018 and Steel4140.

Material Speed (rpm) Feed (mm/rev) Roughness (lm)

Al 6061 2500 0.15 1.9814665St 1018 800 50 2.02St 4140 800 50 2.091519

L.M. Torres-Treviño et al. / Expert Systems with Applications 40 (2013) 6877–6884 6883

f ðx1; x2Þ ¼ðk11x1 þ k21Þðk12x2 þ k2

22Þð14Þ

where k12 = 0.0871604, k22 = 0.8812478, k11 = 0.9047789,k21 = 0.1240531 extracted from the best solution found.

The best solution considering low complexity and high R2pred is

bolded in every table. For turning three models are generated con-sidering the machined material. All the equations are normalized.Roughness is y, speed is x1 and feed is x2.

For Aluminium 6061, we have

f ðx1; x2Þ ¼ ðk12x1 þ k22Þ�3ðk12x2 þ k22Þ2 ð15Þ

where k12 = 0.0154255, k22 = 0.9998794, k11 = 0.8217534,k21 = 0.1810979 extracted from the best solution found.

For Steel 1018, we have

f ðx1; x2Þ ¼ðk12x2 þ k22Þ1=3

ðk11x1 þ k21Þ2ð16Þ

where k12 = 0.6145229, k22 = 0.9941325, k11 = 0.7644365, k21 =0.0000001 extracted from the best solution found.

for Steel 4140, we have

f ðx1; x2Þ ¼logðk11x1 þ k21Þlogðk12x2 þ k22Þ

ð17Þ

where k12 = 0.0958660, k22 = 0.4830823, k11 = 0.6776486,k21 = 0.0816688 extracted from the best solution found.

4.1. Optimization or setting machining parameters

The following step is to use the same evolutionary algorithmand incorporate the model into the objective function. In all cases,the expert systems apply a criteria of surface roughness minimiza-tion or min f(x1,x2). Evonorm uses a population of 200 individuals,50 individuals are selected and runs on 200 epochs. Only one run isneeded.

The solution is a set of parameters that must be used in order tominimize the roughness. Table 16 shows the ideal set of machiningparameters for turning, and Table 17 shows the ideal set ofmachining parameters for milling.

5. Conclusion

An expert system is proposed to assist machining processesusers in order to generate a set of machining parameters that im-proves the process considering the minimization of surface rough-ness; however, other criteria could be considered and thatincorporation is easy. The expert systems requires of experimentaldata, however, historical records could be considered too con-straining the space of search but under working conditions. A setof models are generated from experimental data. A model is se-lected considering residual analysis and complexity. It is expectedthat always a good model could be generated; however, a low per-formance model could be generated specially when there are fewmeasured data from the process. In examples of turning and mill-ing, a very low number of experimental data information was pro-vided, so models of low performance were generated; however, theresults are superior than linear regression. Parameters givesknowledge about theirs effects on machined pieces. The expertsystem could be used in other industrial process like weldingand chemical process; nevertheless this is part of a future work.

References

Aouici, Hamdi, Yallese, Mohamed Athmane, Fnides, Brahim, et al. (2011). Modelingand optimization of hard turning of X38CrMoV5-1 steel with CBN tool:machining parameters effects on flank wear and surface roughness. Journal ofMechanical Science and Technology, 25(11), 2843–2851. http://dx.doi.org/10.1007/s12206-011-0807-z.

Bhushan, R. K. (2013). Optimization of cutting parameters for minimizing powerconsumption and maximizing tool life during machining of Al alloy SiC particlecomposites. Journal of Cleaner Production, 39, 242–254. http://dx.doi.org/10.1016/j.jclepro.2012.08.008.

Chauhan, S. R., & Dass, Kali (2012). Optimization of machining parameters inturning of titanium (grade-5) alloy using response surface methodology.Materials and Manufacturing Processes, 27(5), 531–537. http://dx.doi.org/10.1080/10426914.2011.593236.

Douglas, C. (2007). Montgomery introduction to linear regression analysis. John Wileyand Sons.

Gaitonde, V. N., Karnik, S. R., & Davim, J. Paulo (2009). Multiperformanceoptimization in turning of free-machining steel using Taguchi method andutility concept. Journal of Materials Engineering and Performance, 18(3), 231–236.http://dx.doi.org/10.1007/s11665-008-9269-6.

Gopalsamy, Bala Murugan, Mondal, Biswanath, & Ghosh, Sukamal (2009). Taguchimethod and ANOVA: an approach for process parameters optimization of hardmachining while machining hardened steel. Journal of Scientific & IndustrialResearch, 68(8), 686–695.

Hanafi, Issam, Khamlichi, Abdellatif, Mata Cabrera, Francisco, et al. (2012).Optimization of cutting conditions for sustainable machining of PEEK-CF30using TiN tools. Journal of Cleaner Production, 33, 1–9. http://dx.doi.org/10.1016/j.jclepro.2012.05.005.

Jangra, Kamal, Jain, Ajai, & Grover, Sandeep (2010). Optimization of multiple-machining characteristics in wire electrical discharge machining of punchingdie using Grey relational analysis. Journal of Scientific & Industrial Research,69(8), 606–612.

Ji, Renjie, Liu, Yonghong, Zhang, Yanzhen, et al. (2012). Machining performanceoptimization in end ED milling and mechanical grinding compound process.Materials and Manufacturing Processes, 27(2), 221–228. http://dx.doi.org/10.1080/10426914.2011.568569.

Kadirgama, K., Noor, M. M., & Rahman, M. M. (2012). Optimization of surfaceroughness in end milling using potential support vector machine. ArabianJournal for Science and Engineering, 37(8), 2269–2275. http://dx.doi.org/10.1007/s13369-012-0314-2.

Lebaal, N., Schlegel, D., & Folea, M. (2012). Optimisation of cutting conditions inmachining of cobalt-based refractory material. International Journal of Materials& Product Technology, 44(1–2), 127–143. http://dx.doi.org/10.1504/IJMPT.2012.048187.

6884 L.M. Torres-Treviño et al. / Expert Systems with Applications 40 (2013) 6877–6884

Liang, Ruijun, Ye, Wenhua, Zhang, Haiyan H., et al. (2012). The thermal erroroptimization models for CNC machine tools. International Journal of AdvancesManufacturing Technology, 63(9–12), 1167–1176. http://dx.doi.org/10.1007/s00170-012-3978-6.

Mangaraj, S., & Singh, K. P. (2011). Optimization of machine parameters for millingof pigeon pea using RSM. Food and Bioprocess Technology, 4(5), 762–769. http://dx.doi.org/10.1007/s11947-009-0215-x.

Maniraj, J., Selladurai, V., Sivashanmugam, N., et al. (2012). Hard finish turningparameters optimization for machining of high temperature stainless steel.High Temperature Materials and Processes, 31(6), 679–689. http://dx.doi.org/10.1515/htmp-2012-0142.

Motorcu, Ali Rizzi (2010). The optimization of machining parameters using theTaguchi method for surface roughness of AISI 8660 hardened alloy steel.Strojniski Vestnik – Journal of Mechanical Engineering, 56(6), 391–401.

Mustafa, Ay. (2011). Determination and optimization of the machining parametersof the welded areas in moulds. Scientific Research and Essays, 6(2), 485–492.

Raja, S. Bharathi, & Baskar, N. (2010). Optimization techniques for machiningoperations: a retrospective research based on various mathematical models.International Journal of Advanced Manufacturing Technology, 48, 1075–1090.http://dx.doi.org/10.1007/s00170-009-2351-x.

Raja, S. Bharathi, & Baskar, N. (2011). Particle swarm optimization technique fordetermining optimal machining parameters of different work piece materials inturning operation. International Journal of Advanced Manufacturing Technology,54(5–8), 445–463. http://dx.doi.org/10.1007/s00170-010-2958-y.

Raja, S. Bharathi, & Baskar, N. (2012). Application of particle swarm optimizationtechnique for achieving desired milled surface roughness in minimum

machining time. Expert Systems with Applications, 39(5), 5982–5989. http://dx.doi.org/10.1016/j.eswa.2011.11.110.

Ranganathan, S., & Senthilvelan, T. (2011). Multi-response optimization ofmachining parameters in hot turning using grey analysis. International Journalof Advanced Manufacturing Technology, 56(5–8), 455–462. http://dx.doi.org/10.1007/s00170-011-3198-5.

Senthilkumaar, J. S., Selvarani, P., & Arunachalam, R. M. (2012). Intelligentoptimization and selection of machining parameters in finish turning andfacing of Inconel 718. International Journal of Advanced ManufacturingTechnology, 58(9-12), 885–894. http://dx.doi.org/10.1007/s00170-011-3455-7.

Torres-T, L. (2006). Evonorm, a new evolutionary algorithm to continuousoptimization. In Workshop on optimization by building and using probabilisticmodels (OBUPM) genetic and evolutionary computation conference (GECCO).

Torres-Trevino, L. (2006). Evonorm: easy and effective implementation ofestimation of distribution algorithms. Journal of Research in Computing Science,23, 75–83.

Villeta, Maria, de Agustina, Beatriz, Manuel Saenz de Pipaon, Jose, et al. (2012).Efficient optimisation of machining processes based on technical specificationsfor surface roughness: application to magnesium pieces in the aerospaceindustry. International Journal of Advanced Manufacturing Technology, 69(9–12),1237–1246. http://dx.doi.org/10.1007/s00170-011-3685-8.

Yang, Yung-Kuang, Chuang, Ming-Tsan, & Lin, Show-Shyan (2009). Optimization ofdry machining parameters for high-purity graphite in end milling process viadesign of experiments methods. Journal of Materials Processing Technology,209(9), 4395–4400. http://dx.doi.org/10.1016/j.jmatprotec.2008.11.021.